Finite Group Databasebeta

← #36312849

Subgroups — #36312849

Order 21248.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921550C212yesmaximal, complemented
2#24921499C216yesmaximal, complemented
3#24921471C212yesmaximal, complemented
4#24921428C216yesmaximal, complemented
5#24921372C213yesmaximal, complemented
6#24921348C213yesmaximal, complemented
7#24921276C211yesmaximal, characteristic, complemented
8#24921244C211yesmaximal, characteristic, complemented
9#24921217C213yesmaximal, complemented
10#24921209C213yesmaximal, complemented
11#24921143C211yesmaximal, characteristic, complemented
12#24921079C212yesmaximal, complemented
13#24921075C216yesmaximal, complemented
14Q8×#13050589C212yesmaximal, complemented
15#24921014C216yesmaximal, complemented
16#24920891C213yesmaximal, complemented
17#24920887C213yesmaximal, complemented
18#24920755C213yesmaximal, complemented
19C2×#19128253C213yesmaximal, complemented
202−1+4×Dic83C211yesmaximal, characteristic, complemented
21#24920674C211yesmaximal, characteristic, complemented
22C2×#41×Dic83C211yesmaximal, characteristic, complemented
23C83×#3489C211yesmaximal, characteristic, complemented
24C2×#14581839C2211yescharacteristic
25Q8×Dic166C2212yescomplemented
26#19128427C2212yescomplemented
27#19128426C2216yescomplemented
28#19128426C2216yescomplemented
29#19128422C2216yescomplemented
30#19128422C2216yescomplemented
31#19128421C2216yescomplemented
32#19128420C2216yescomplemented
33#19128420C2216yescomplemented
34#19128415C2216yescomplemented
35#19128410C2216yescomplemented
36#19128409C2216yes—
37#19128409C2216yescomplemented
38#19128408C2216yes—
39#19128394C22112yescomplemented
40#19128393C2216yes—
41#19128391C2216yes—
42#19128391C2216yescomplemented
43#19128388C22112yescomplemented
44#19128388C22112yescomplemented
45#19128388C22112yescomplemented
46#19128386C22112yescomplemented
47#19128385C2216yescomplemented
48#19128382C22112yes—
49#19128377C22112yes—
50D4×Dic166C2216yescomplemented
51Q8×C22⋊D83C2212yes—
52Q8×C22⋊D83C2212yescomplemented
53Q8×C22⋊D83C2212yescomplemented
54#19128358C2212yes—
55#19128357C22112yescomplemented
56#19128351C2216yescomplemented
57#19128350C2216yes—
58#19128350C2216yescomplemented
59#19128350C2216yescomplemented
60#19128345C2216yes—
61#19128332C2213yescomplemented
62#19128329C2213yescomplemented
63#19128324C2216yescomplemented
64#19128320C2216yescomplemented
65#19128318C2216yescomplemented
66#19128318C2216yescomplemented
67#19128312C2216yescomplemented
68#19128311C2216yescomplemented
69#19128311C2216yescomplemented
70#19128311C2216yescomplemented
71#19128296C22112yescomplemented
72#19128295C22112yescomplemented
73#19128279C2213yes—
74#19128275C2213yescomplemented
75#19128272C2213yes—
76#19128272C2213yescomplemented
77#19128256C2216yescomplemented
78#19128254C2213yescomplemented
79#19128253C2216yes—
80#19128253C2216yes—
81#19128253C2213yes—
82#19128253C2216yes—
83#19128253C2213yescomplemented
84#19128253C2216yescomplemented
85#19128253C2216yescomplemented
86#19128253C2216yescomplemented
87#19128253C2216yescomplemented
88#19128253C2216yescomplemented
89#19128247C2213yescomplemented
90#19128246C2211yescharacteristic
91#19128246C2213yescomplemented
92C2×#14581791C2213yescomplemented
93C2×#14581790C2213yescomplemented
94#19128237C2213yes—
95#19128237C2213yescomplemented
96#19128232C2213yes—
97#19128232C2213yescomplemented
98#19128232C22112yescomplemented
99#19128232C2216yescomplemented
100#19128231C2216yes—
101#19128231C2216yescomplemented
102#19128230C2216yescomplemented
103#19128228C22112yescomplemented
104#19128228C2216yescomplemented
105#19128228C2216yescomplemented
106C2×#14581782C2216yescomplemented
107#19128212C2213yes—
108#19128207C2216yes—
109#19128207C2216yes—
110C2×#14581771C2213yes—
111C2×#14581769C2216yes—
112#19128184C2211yescharacteristic
113#19128184C2213yescomplemented
114#19128184C2216yescomplemented
115#19128182C2213yescomplemented
116#19128180C2216yescomplemented
117#19128179C2213yescomplemented
118#19128179C2212yescomplemented
119#19128178C2213yescomplemented
120#19128177C2212yescomplemented
121#41×Dic83C2213yes—
122#41×Dic83C2213yes—
123#41×Dic83C2213yes—
124#41×Dic83C2211yescharacteristic
125#41×Dic83C2211yescharacteristic
126#41×Dic83C2211yescharacteristic
127#41×Dic83C2213yes—
128#41×Dic83C2211yescharacteristic
129#41×Dic83C2213yescomplemented
130#41×Dic83C2216yescomplemented
131#19128169C2213yescomplemented
132C4×#13050589C2216yes—
133C4×#13050589C2216yescomplemented
134C4×#13050589C2216yescomplemented
135C2×Q8×Dic83C2211yescharacteristic
136C2×Q8×Dic83C2211yescharacteristic
137C2×Q8×Dic83C2213yescomplemented
138C2×Q8×Dic83C2212yescomplemented
139C2×#14581757C2213yescomplemented
140C2×#14581757C2216yescomplemented
141C4×Q8×D83C2212yescomplemented
142C2×D4×Dic83C2213yes—
143C2×D4×Dic83C2213yes—
144C2×#14581751C2213yes—
145C2×#14581748C2216yes—
146C22×C4×Dic83C2213yes—
147C2×2−1+4×C83C2211yescharacteristic
148C22×#41×C83C2211yescharacteristic
149D4×Q8×C83C2212yes—
150#548×C83C2212yes—
151#547×C83C2216yes—
152#546×C83C2216yes—
153#537×C83C2213yes—
154#536×C83C2213yes—
155#525×C83C2213yes—
156C2×C22⋊Q8×C83C2213yes—
157#520×C83C2211yescharacteristic
158#14581839—28no—
159C2×#13050590C2313yes—
160C2×#13050589C2316yes—
161C2×#13050589C2312yes—
162C2×#13050589C2316yes—
163C22×Dic166C2313yes—
164C22×Dic166C2316yes—
165C2×Q8×D83C2312yes—
166C23×Dic83C2313yes—
167C23×Dic83C2313yes—
168#14581792C2316yes—
169#14581791C2316yes—
170#14581791C2316yes—
171#14581791C2316yes—
172#14581791C2316yes—
173#14581791C2313yes—
174#14581791C2311yescharacteristic
175#14581790C2316yes—
176#14581790C2316yes—
177#14581790C2316yes—
178#14581790C2313yes—
179#14581790C2316yes—
180#14581788C2311yescharacteristic
181#14581787C23112yes—
182#14581787C2316yes—
183#14581787C2316yes—
184#14581785C23112yes—
185#14581785C23112yes—
186#14581785C23112yes—
187#14581785C23112yes—
188#14581785C2316yes—
189#14581785C23112yes—
190#14581785C2316yes—
191#14581784C2316yes—
192#14581783C2313yes—
193#14581783C2313yes—
194#14581783C2316yes—
195#14581783C23112yes—
196#14581783C23112yes—
197#14581782C23112yes—
198#14581782C23112yes—
199#14581782C23112yes—
200#14581782C2316yes—
201#14581782C23112yes—
202#14581782C2316yes—
203#14581782C23112yes—
204#14581781C2313yes—
205#14581779C2316yes—
206#14581779C23112yes—
207#14581779C2313yes—
208#14581778C23112yes—
209#14581778C2316yes—
210#14581778C2312yes—
211#14581776C2316yes—
212#14581776C2316yes—
213#14581775C2316yes—
214#14581775C23112yes—
215#14581774C23112yes—
216#14581773C23112yes—
217#14581773C23112yes—
218#14581773C23112yes—
219#14581773C2316yes—
220#14581773C2316yes—
221#14581772C23112yes—
222#14581771C23112yes—
223#14581771C2316yes—
224#14581771C2316yes—
225#14581771C2316yes—
226#14581771C2316yes—
227#14581771C2313yes—
228#14581771C2316yes—
229#14581771C2313yes—
230#14581769C23112yes—
231#14581769C23112yes—
232#14581769C23112yes—
233#14581769C23112yes—
234#14581769C2316yes—
235#14581769C23112yes—
236#14581769C2316yes—
237#14581769C2316yes—
238#14581769C2316yes—
239#14581768C2316yes—
240#14581768C2316yes—
241#14581768C2316yes—
242#14581766C2313yes—
243#14581766C2311yescharacteristic
244#14581764C23112yes—
245#14581764C2316yes—
246#14581764C2316yes—
247#14581764C2316yes—
248#14581764C2312yes—
249#14581763C2316yes—
250#14581761C2316yes—
251Q8×Dic83C2316yes—
252Q8×Dic83C2316yes—
253Q8×Dic83C2312yes—
254Q8×Dic83C2311yescharacteristic
255Q8×Dic83C2311yescharacteristic
256Q8×Dic83C2316yes—
257Q8×Dic83C2316yes—
258Q8×Dic83C2313yes—
259Q8×Dic83C2311yescharacteristic
260Q8×Dic83C2313yes—
261Q8×Dic83C2311yescharacteristic
262Q8×Dic83C2313yes—
263Q8×Dic83C2313yes—
264Q8×Dic83C2316yes—
265Q8×Dic83C2313yes—
266Q8×Dic83C2313yes—
267C4×Dic166C2316yes—
268C4×Dic166C2316yes—
269C4×Dic166C2316yes—
270C4×Dic166C2316yes—
271#14581757C23112yes—
272#14581757C23112yes—
273#14581757C2316yes—
274#14581757C2316yes—
275#14581757C2316yes—
276#14581757C2313yes—
277#14581757C2316yes—
278#14581757C2316yes—
279#14581757C23112yes—
280#14581757C2313yes—
281D4×Dic83C2313yes—
282D4×Dic83C2316yes—
283D4×Dic83C2313yes—
284D4×Dic83C2313yes—
285D4×Dic83C2313yes—
286D4×Dic83C2316yes—
287D4×Dic83C23112yes—
288D4×Dic83C2316yes—
289D4×Dic83C2316yes—
290D4×Dic83C2313yes—
291D4×Dic83C2313yes—
292D4×Dic83C2313yes—
293D4×Dic83C2316yes—
294D4×Dic83C2313yes—
295D4×Dic83C2316yes—
296D4×Dic83C2316yes—
297D4×Dic83C2316yes—
298D4×Dic83C2311yescharacteristic
299D4×Dic83C2316yes—
300D4×Dic83C2313yes—
301#14581754C2313yes—
302#14581754C2311yescharacteristic
303C4×C22⋊D83C2316yes—
304C4×C22⋊D83C2316yes—
305C4×C22⋊D83C2316yes—
306C4×C22⋊D83C2316yes—
307C4×C22⋊D83C23112yes—
308(C22⋊D83)⋊C4C2316yes—
309(C22⋊D83)⋊C4C2316yes—
310(C22⋊D83)⋊C4C2312yes—
311(C22⋊D83)⋊C4C2316yes—
312(C22⋊D83)⋊C4C2316yes—
313(C22⋊D83)⋊C4C2316yes—
314#14581751C2316yes—
315#14581751C2313yes—
316#14581751C2313yes—
317#14581751C23112yes—
318#14581751C2313yes—
319#14581751C2316yes—
320#14581751C2316yes—
321#14581751C2313yes—
322#14581751C2313yes—
323#14581751C2316yes—
324#14581750C2316yes—
325#14581750C2316yes—
326#14581750C2316yes—
327#14581749C2316yes—
328#14581748C23112yes—
329#14581748C23112yes—
330#14581748C2316yes—
331#14581748C2316yes—
332#14581748C23112yes—
333#14581748C2316yes—
334#14581748C23112yes—
335#14581748C2316yes—
336C2×C4⋊Dic83C2313yes—
337C2×C4⋊Dic83C2316yes—
338C2×C4⋊Dic83C2313yes—
339C2×C4⋊Dic83C2313yes—
340C2×C4⋊Dic83C2316yes—
341C2×Dic83⋊C4C2316yes—
342C2×Dic83⋊C4C2316yes—
343C2×Dic83⋊C4C2316yes—
344C2×Dic83⋊C4C2316yes—
345C2×Dic83⋊C4C2316yes—
346C4⋊C4×D83C2316yes—
347C2×C22⋊Dic83C2316yes—
348C2×C22⋊Dic83C2316yes—
349C2×C4×Dic83C2311yescharacteristic
350C2×C4×Dic83C2313yes—
351C2×C4×Dic83C2313yes—
352C2×C4×Dic83C2313yes—
353C2×C4×Dic83C2313yes—
354C2×C4×Dic83C2313yes—
355C2×C4×Dic83C2313yes—
356C2×C4×Dic83C2313yes—
357C2×C4×Dic83C2313yes—
358C2×C4×Dic83C2313yes—
359C2×C4×Dic83C2313yes—
360C2×C4×Dic83C2313yes—
361C2×C4×Dic83C2316yes—
362C2×C4×Dic83C2316yes—
363C2×C4×Dic83C2316yes—
364C42×D83C2316yes—
3652−1+4×C83—28no—
366C2×#41×C83—28no—
367C2×#41×C83C2313yes—
368C2×#41×C83C2316yes—
369C2×#41×C83C2311yescharacteristic
370C2×#41×C83C2313yes—
371C2×#41×C83C2313yes—
372C2×#41×C83C2311yescharacteristic
373C22×Q8×C83C2311yescharacteristic
374C22×Q8×C83C2312yes—
375C22×Q8×C83C2313yes—
376C22×D4×C83C2313yes—
377C23×C4×C83C2313yes—
378C4⋊Q8×C83C2316yes—
379#124×C83C2316yes—
380#123×C83C2316yes—
381#123×C83C23112yes—
382C22⋊Q8×C83C2316yes—
383C22⋊Q8×C83C2313yes—
384C22⋊Q8×C83C2316yes—
385C22⋊Q8×C83C2316yes—
386C22⋊Q8×C83C2313yes—
387C22⋊Q8×C83C2316yes—
388#121×C83C2316yes—
389#121×C83C23112yes—
390#121×C83C2311yescharacteristic
391#121×C83C2313yes—
392#120×C83C2316yes—
393C4×Q8×C83C2312yes—
394C4×D4×C83C2316yes—
395C4×D4×C83C2316yes—
396C4×D4×C83C2316yes—
397#117×C83C2313yes—
398C2×C4⋊C4×C83C2313yes—
399C2×C4⋊C4×C83C2316yes—
400C2×C22⋊C4×C83C2316yes—
401#13050590—212no—
402#13050589—224no—
403#13050589—28no—
404#13050589—412no—
405C2×Dic166—212no—
406C2×Dic166—412no—
407C2×Dic166C2412yes—
408C2×Dic166C2416yes—
409C2×Dic166C2416yes—
410C2×Dic166C2413yes—
411C2×Dic166C24112yes—
412Q8×D83—28no—
413C2×D332C2411yescharacteristic
414C2×C22⋊D83C2412yes—
415C2×C22⋊D83C2416yes—
416C2×C22⋊D83C2412yes—
417C2×C22⋊D83C2412yes—
418C2×C22⋊D83C2416yes—
419C22×Dic83—212no—
420C22×Dic83—46no—
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2413yes—
423C22×Dic83C2413yes—
424C22×Dic83C2413yes—
425C22×Dic83C2413yes—
426C22×Dic83C2416yes—
427C22×Dic83C2413yes—
428C22×Dic83C2413yes—
429C22×Dic83C2413yes—
430C22×Dic83C2412yes—
431C22×Dic83C2416yes—
432C22×Dic83C2413yes—
433C22×Dic83C2413yes—
434C22×Dic83C2416yes—
435C22×Dic83C2413yes—
436C22×Dic83C2411yescharacteristic
437C2×C4×D83C2416yes—
438C2×C4×D83C2412yes—
439C2×C4×D83C2416yes—
440C4⋊Dic83C2416yes—
441C4⋊Dic83C2411yescharacteristic
442C4⋊Dic83C2413yes—
443C4⋊Dic83C2413yes—
444C4⋊Dic83C2413yes—
445C4⋊Dic83C2416yes—
446C4⋊Dic83C2416yes—
447C4⋊Dic83C2416yes—
448C4⋊Dic83C24112yes—
449C4⋊Dic83C2416yes—
450C4⋊Dic83C2416yes—
451C4⋊Dic83C2416yes—
452C4⋊Dic83C2413yes—
453C4⋊Dic83C2413yes—
454Dic83⋊C4C24112yes—
455Dic83⋊C4C2412yes—
456Dic83⋊C4C2416yes—
457Dic83⋊C4C2416yes—
458Dic83⋊C4C2416yes—
459Dic83⋊C4C24112yes—
460Dic83⋊C4C24112yes—
461Dic83⋊C4C24112yes—
462Dic83⋊C4C2416yes—
463Dic83⋊C4C2416yes—
464Dic83⋊C4C2416yes—
465Dic83⋊C4C24112yes—
466Dic83⋊C4C2416yes—
467Dic83⋊C4C2416yes—
468Dic83⋊C4C2416yes—
469C22⋊Dic83C2416yes—
470C22⋊Dic83C2416yes—
471C22⋊Dic83C2416yes—
472C22⋊Dic83C24112yes—
473C22⋊Dic83C2416yes—
474C22⋊Dic83C2416yes—
475C22⋊Dic83C2412yes—
476C22⋊Dic83C2416yes—
477C22⋊Dic83C2416yes—
478C22⋊Dic83C2416yes—
479C22⋊Dic83C2416yes—
480C22⋊Dic83C2416yes—
481(C2×D83)⋊C4C2416yes—
482(C2×D83)⋊C4C2416yes—
483(C2×D83)⋊C4C2416yes—
484(C2×D83)⋊C4C2412yes—
485(C2×D83)⋊C4C2416yes—
486(C2×D83)⋊C4C2412yes—
487C4×Dic83C2411yescharacteristic
488C4×Dic83C2413yes—
489C4×Dic83C24112yes—
490C4×Dic83C2413yes—
491C4×Dic83C24112yes—
492C4×Dic83C2416yes—
493C4×Dic83C2413yes—
494C4×Dic83C2413yes—
495C4×Dic83C2413yes—
496C4×Dic83C2416yes—
497C4×Dic83C2416yes—
498C4×Dic83C2413yes—
499C4×Dic83C2411yescharacteristic
500C4×Dic83C2413yes—
501C4×Dic83C2413yes—
502C4×Dic83C2413yes—
503C4×Dic83C2416yes—
504C4×Dic83C2411yescharacteristic
505C4×Dic83C2411yescharacteristic
506C4×Dic83C2416yes—
507C4×Dic83C2413yes—
508C4×Dic83C2413yes—
509C4×Dic83C2413yes—
510C24×C83C2413yes—
511#41×C83—24no—
512#41×C83—212no—
513#41×C83—224no—
514#41×C83—212no—
515#41×C83—212no—
516#41×C83#4118yescomplemented
517C2×Q8×C83—24no—
518C2×Q8×C83—28no—
519C2×Q8×C83—212no—
520C2×Q8×C83C2416yes—
521C2×Q8×C83C2413yes—
522C2×Q8×C83C2413yes—
523C2×Q8×C83C2411yescharacteristic
524C2×D4×C83—212no—
525C2×D4×C83C2413yes—
526C2×D4×C83C2416yes—
527C2×D4×C83C2416yes—
528C2×D4×C83C2412yes—
529C2×D4×C83C2411yescharacteristic
530C2×D4×C83C2416yes—
531C2×D4×C83C2413yes—
532C22×C4×C83—212no—
533C22×C4×C83C2411yescharacteristic
534C22×C4×C83C2413yes—
535C22×C4×C83C2416yes—
536C22×C4×C83C2413yes—
537C22×C4×C83C2413yes—
538C22×C4×C83C2416yes—
539C22×C4×C83C2413yes—
540C22×C4×C83C2416yes—
541C22×C4×C83C2413yes—
542C4⋊C4×C83C24112yes—
543C4⋊C4×C83C2416yes—
544C4⋊C4×C83C2416yes—
545C4⋊C4×C83C2411yescharacteristic
546C4⋊C4×C83C2413yes—
547C4⋊C4×C83C2416yes—
548C22⋊C4×C83C2416yes—
549C22⋊C4×C83C2416yes—
550C22⋊C4×C83C24112yes—
551C22⋊C4×C83C2416yes—
552C22⋊C4×C83C2416yes—
553C22⋊C4×C83C2412yes—
554C42×C83C2416yes—
555C23×C83—26no—
556C23×C83—26no—
557C23×C83—43no—
558C23×C83C2513yes—
559C23×C83C2512yes—
560C23×C83C2513yes—
561C23×C83C2511yescharacteristic
562C22×D83C2512yes—
563Q8×C83—26no—
564Q8×C83—212no—
565Q8×C83—26no—
566Q8×C83C2×#4114yes—
567D4×C83—212no—
568D4×C83—212no—
569D4×C83—24no—
570D4×C83—26no—
571D4×C83—22no—
572D4×C83—46no—
573D4×C83C2×#41112yes—
574C2×C4×C83—26no—
575C2×C4×C83—212no—
576C2×C4×C83—22no—
577C2×C4×C83—26no—
578C2×C4×C83—26no—
579C2×C4×C83—26no—
580C2×C4×C83—212no—
581C2×C4×C83—46no—
582C2×C4×C83C2×#41112yes—
583C2×C4×C83C2512yes—
584C2×C4×C83C2516yes—
585C2×C4×C83C2516yes—
586C2×C4×C83C2511yescharacteristic
587C2×C4×C83C2513yes—
588C2×C4×C83C2513yes—
589C2×C4×C83C2511yescharacteristic
590C22⋊D83—212no—
591C22⋊D83—24no—
592C22⋊D83—24no—
593C22⋊D83—24no—
594C22⋊D83—46no—
595C2×Dic83—212no—
596C2×Dic83—26no—
597C2×Dic83—26no—
598C2×Dic83—26no—
599C2×Dic83—26no—
600C2×Dic83—26no—
601C2×Dic83—24no—
602C2×Dic83—22no—
603C2×Dic83—26no—
604C2×Dic83—26no—
605C2×Dic83—43no—
606C2×Dic83—43no—
607C2×Dic83—43no—
608C2×Dic83—46no—
609C2×Dic83—46no—
610C2×Dic832−1+414yescomplemented
611C2×Dic83C2513yes—
612C2×Dic83C2511yescharacteristic
613C2×Dic83C2513yes—
614C2×Dic83C2512yes—
615C2×Dic83C2513yes—
616C2×Dic83C2513yes—
617C2×Dic83C2516yes—
618C2×Dic83C2516yes—
619C2×Dic83C2511yescharacteristic
620C2×Dic83C2511yescharacteristic
621C2×Dic83C2511yescharacteristic
622D332—22no—
623C4×D83—212no—
624C4×D83—24no—
625C4×D83—46no—
626Dic166—212no—
627Dic166—26no—
628Dic166—24no—
629Dic166—212no—
630Dic166—412no—
631C22×C83—21no—
632C22×C83—23no—
633C22×C83—23no—
634C22×C83—21no—
635C22×C83—22no—
636C22×C83—23no—
637C22×C83—23no—
638C22×C83—22no—
639C22×C83—23no—
640C22×C83—22no—
641C22×C83—412no—
642C22×C83C22×#4116yes—
643C22×C83C2×2−1+412yes—
644C22×C83C2611yescharacteristic
645C2×D83—22no—
646C2×D83—22no—
647C2×D83—22no—
648C4×C83—21no—
649C4×C83—23no—
650C4×C83—26no—
651C4×C83—22no—
652C4×C83—26no—
653C4×C83C22×#4112yes—
654C4×C83C22×#4116yes—
655Dic83—26no—
656Dic83—22no—
657Dic83—23no—
658Dic83—23no—
659Dic83—26no—
660Dic83—23no—
661Dic83—23no—
662Dic83—21no—
663Dic83C2×2−1+412yes—
664Dic83C2×2−1+412yes—
665Dic83#58512yes—
666#62805—831nomaximal, Sylow
667C2×C83—22no—
668C2×C83—26no—
669C2×C83—42no—
670C2×C83—43no—
671C2×C83C23×#4111yescharacteristic
672C2×C83C22×2−1+411yescharacteristic
673C2×C83C2×#58511yescharacteristic
674D83—42no—
675#3523—832no—
676#3520—836no—
677#3518—832no—
678#3515—836no—
679#3511—833no—
680#3509—833no—
681#3503—831no—
682#3499—831no—
683#3495—833no—
684#3495—833no—
685#3489—831no—
686#3489D8311yescharacteristic, complemented
687#3482—832no—
688#3482—836no—
689Q8×#41—832no—
690#3475—836no—
691#3461—833no—
692#3461—833no—
693#3444—833no—
694C2×#533—833no—
695C4×2−1+4—831no—
696C4×2−1+4—831no—
697C2×C4×#41—831no—
698C83#6280511yescharacteristic, complemented, Sylow
699C2×2−1+4—831no—
700C2×2−1+4C2×D8311yescharacteristic
701C22×#41C2×D8311yescharacteristic
702Q82—832no—
703#557—836no—
704#557—836no—
705#557—832no—
706#556—836no—
707#556—836no—
708#556—836no—
709#556—836no—
710#556—836no—
711#555—836no—
712#554—836no—
713#554—836no—
714#554—836no—
715#554—836no—
716#553—8312no—
717#552—8312no—
718#552—8312no—
719#552—8312no—
720#552—836no—
721#552—836no—
722#552—836no—
723#552—836no—
724#552—8312no—
725#551—8312no—
726#551—8312no—
727D4×Q8—832no—
728D4×Q8—832no—
729D4×Q8—832no—
730D4×Q8—836no—
731D4×Q8C2×D8312yes—
732#548—832no—
733#548—8312no—
734#548C2×D8312yes—
735#547—836no—
736#547—836no—
737#547—836no—
738#547—836no—
739#547C2×D8316yes—
740#546—836no—
741#546C2×D8316yes—
742#544—833no—
743#544—833no—
744#542—836no—
745#542—836no—
746#542—836no—
747#542—836no—
748#541—836no—
749#541—836no—
750#541—836no—
751#541—836no—
752#539—8312no—
753#539—8312no—
754#537—833no—
755#537C2×D8313yes—
756#536—833no—
757#536—833no—
758#536—833no—
759#536C2×D8313yes—
760#533—836no—
761#533—833no—
762#533—836no—
763#533—836no—
764#533—836no—
765#533—836no—
766#533—836no—
767#533—836no—
768#533—836no—
769#533—833no—
770#533—836no—
771#533—833no—
772#532—833no—
773#532—831no—
774#532—833no—
775C2×C4⋊Q8—833no—
776C2×C4⋊Q8—833no—
777#529—836no—
778#529—836no—
779#529—836no—
780#529—8312no—
781#529—833no—
782#529—833no—
783#529—833no—
784#529—833no—
785#529—8312no—
786#529—836no—
787#529—836no—
788#529—836no—
789C2×#125—836no—
790#525—833no—
791#525—836no—
792#525—836no—
793#525C2×D8313yes—
794C2×C22⋊Q8—833no—
795C2×C22⋊Q8—836no—
796C2×C22⋊Q8C2×D8313yes—
797#520—831no—
798#520—833no—
799#520—836no—
800#520—836no—
801#520—833no—
802#520C2×D8311yescharacteristic
803#519—833no—
804#519—832no—
805#519—832no—
806#519—833no—
807C4×#41—831no—
808C4×#41—833no—
809C4×#41—833no—
810C4×#41—831no—
811C4×#41—831no—
812C4×#41—833no—
813C4×#41—833no—
814C4×#41—831no—
815C4×#41—833no—
816C4×#41—836no—
817C4×#41—836no—
818C4×#41—836no—
819C4×#41—836no—
820C4×#41—833no—
821C2×C4×Q8—831no—
822C2×C4×Q8—831no—
823C2×C4×Q8—833no—
824C2×C4×Q8—832no—
825C2×C4×Q8—832no—
826C2×C4×Q8—833no—
827C2×C4×Q8—836no—
828C2×C4×D4—833no—
829C2×C4×D4—833no—
830C2×#117—833no—
831C2×#117—836no—
832C22×C42—833no—
8332−1+4—28no—
8342−1+4—1668no—
835C2×#41—28no—
836C2×#41—836no—
837C2×#41—832no—
838C2×#41—836no—
839C2×#41—833no—
840C2×#41C22×D8313yes—
841C2×#41C22×D8313yes—
842C2×#41C22×D8311yescharacteristic
843C2×#41C22×D8313yes—
844C2×#41C22×D8316yes—
845C2×#41C22×D8311yescharacteristic
846C22×Q8—832no—
847C22×Q8—836no—
848C22×Q8—833no—
849C22×Q8C22×D8311yescharacteristic
850C22×Q8C22×D8313yes—
851C22×Q8C22×D8312yes—
852C22×D4C22×D8313yes—
853C23×C4—833no—
854C23×C4—833no—
855C23×C4C22×D8313yes—
856C4⋊Q8—833no—
857C4⋊Q8—836no—
858C4⋊Q8—836no—
859C4⋊Q8—836no—
860C4⋊Q8—836no—
861C4⋊Q8—833no—
862C4⋊Q8—836no—
863C4⋊Q8—836no—
864C4⋊Q8—836no—
865C4⋊Q8—831no—
866C4⋊Q8—836no—
867C4⋊Q8—836no—
868C4⋊Q8C22×D8316yes—
869#127—831no—
870#126—836no—
871#126—836no—
872#126—8312no—
873#126—836no—
874#126—836no—
875#126—8312no—
876#126—8312no—
877#126—8312no—
878#126—8312no—
879#126—8312no—
880#125—836no—
881#125—8312no—
882#125—8312no—
883#125—8312no—
884#125—836no—
885#125—833no—
886#125—833no—
887#125—8312no—
888#125—8312no—
889#125—836no—
890#125—8312no—
891#125—8312no—
892#125—836no—
893#124—833no—
894#124—833no—
895#124—836no—
896#124—8312no—
897#124—832no—
898#124—836no—
899#124—8312no—
900#124C22×D8316yes—
901#123—836no—
902#123—836no—
903#123—8312no—
904#123—8312no—
905#123—8312no—
906#123—836no—
907#123—8312no—
908#123—836no—
909#123—836no—
910#123—8312no—
911#123C22×D8316yes—
912#123C22×D83112yes—
913C22⋊Q8—836no—
914C22⋊Q8—836no—
915C22⋊Q8—836no—
916C22⋊Q8—833no—
917C22⋊Q8—836no—
918C22⋊Q8—836no—
919C22⋊Q8—836no—
920C22⋊Q8—833no—
921C22⋊Q8—836no—
922C22⋊Q8—8312no—
923C22⋊Q8—836no—
924C22⋊Q8—8312no—
925C22⋊Q8—836no—
926C22⋊Q8—8312no—
927C22⋊Q8—8312no—
928C22⋊Q8—8312no—
929C22⋊Q8—836no—
930C22⋊Q8—836no—
931C22⋊Q8—836no—
932C22⋊Q8—8312no—
933C22⋊Q8—8312no—
934C22⋊Q8C22×D8313yes—
935C22⋊Q8C22×D8316yes—
936C22⋊Q8C22×D8316yes—
937C22⋊Q8C22×D8316yes—
938C22⋊Q8C22×D8313yes—
939C22⋊Q8C22×D8316yes—
940#121—836no—
941#121—832no—
942#121—836no—
943#121—836no—
944#121—836no—
945#121—8312no—
946#121—831no—
947#121—833no—
948#121C22×D8311yescharacteristic
949#121C22×D8313yes—
950#121C22×D83112yes—
951#121C22×D8316yes—
952#120—836no—
953#120C22×D8316yes—
954C4×Q8—831no—
955C4×Q8—836no—
956C4×Q8—833no—
957C4×Q8—831no—
958C4×Q8—833no—
959C4×Q8—833no—
960C4×Q8—831no—
961C4×Q8—831no—
962C4×Q8—833no—
963C4×Q8—833no—
964C4×Q8—836no—
965C4×Q8—836no—
966C4×Q8—832no—
967C4×Q8—836no—
968C4×Q8—833no—
969C4×Q8—836no—
970C4×Q8—836no—
971C4×Q8—836no—
972C4×Q8—833no—
973C4×Q8—836no—
974C4×Q8—836no—
975C4×Q8—8312no—
976C4×Q8—8312no—
977C4×Q8—8312no—
978C4×Q8—833no—
979C4×Q8—836no—
980C4×Q8—836no—
981C4×Q8—836no—
982C4×Q8—836no—
983C4×Q8—836no—
984C4×Q8C22×D8312yes—
985C4×D4—833no—
986C4×D4—833no—
987C4×D4—833no—
988C4×D4—836no—
989C4×D4—836no—
990C4×D4—833no—
991C4×D4—833no—
992C4×D4—833no—
993C4×D4—833no—
994C4×D4—836no—
995C4×D4—836no—
996C4×D4—833no—
997C4×D4—836no—
998C4×D4—831no—
999C4×D4—836no—
1000C4×D4—833no—
1001C4×D4—836no—
1002C4×D4—8312no—
1003C4×D4—836no—
1004C4×D4—836no—
1005C4×D4—8312no—
1006C4×D4—836no—
1007C4×D4—836no—
1008C4×D4—836no—
1009C4×D4—836no—
1010C4×D4—831no—
1011C4×D4—833no—
1012C4×D4—836no—
1013C4×D4—832no—
1014C4×D4—836no—
1015C4×D4—836no—
1016C4×D4—836no—
1017C4×D4—836no—
1018C4×D4C22×D8316yes—
1019C4×D4C22×D8316yes—
1020C4×D4C22×D8316yes—
1021#117—833no—
1022#117—833no—
1023#117—836no—
1024#117—833no—
1025#117—836no—
1026#117—833no—
1027#117—833no—
1028#117—836no—
1029#117—8312no—
1030#117—836no—
1031#117—836no—
1032#117—836no—
1033#117—836no—
1034#117—836no—
1035#117—8312no—
1036#117—8312no—
1037#117—8312no—
1038#117—8312no—
1039#117—836no—
1040#117—836no—
1041#117—836no—
1042#117—836no—
1043#117C22×D8313yes—
1044C2×C4⋊C4—833no—
1045C2×C4⋊C4—833no—
1046C2×C4⋊C4—836no—
1047C2×C4⋊C4—836no—
1048C2×C4⋊C4—836no—
1049C2×C4⋊C4—836no—
1050C2×C4⋊C4—833no—
1051C2×C4⋊C4—836no—
1052C2×C4⋊C4—836no—
1053C2×C4⋊C4—836no—
1054C2×C4⋊C4—836no—
1055C2×C4⋊C4C22×D8313yes—
1056C2×C4⋊C4C22×D8316yes—
1057C2×C22⋊C4—836no—
1058C2×C22⋊C4—836no—
1059C2×C22⋊C4C22×D8316yes—
1060C2×C42—833no—
1061C2×C42—836no—
1062C2×C42—836no—
1063C2×C42—833no—
1064C2×C42—833no—
1065C2×C42—833no—
1066C2×C42—833no—
1067C2×C42—836no—
1068C2×C42—833no—
1069C2×C42—833no—
1070C2×C42—833no—
1071C2×C42—833no—
1072C2×C42—833no—
1073C2×C42—833no—
1074C2×C42—831no—
1075C2×C42—836no—
1076C24C23×D8313yes—
1077#41—24no—
1078#41—212no—
1079#41—224no—
1080#41—212no—
1081#41—212no—
1082#41—33212no—
1083#41—1668no—
1084#41—16624no—
1085#41—16612no—
1086#41#1305058918yescomplemented
1087C2×Q8—24no—
1088C2×Q8—28no—
1089C2×Q8—212no—
1090C2×Q8—33212no—
1091C2×Q8—8312no—
1092C2×Q8—832no—
1093C2×Q8—836no—
1094C2×Q8—833no—
1095C2×Q8—836no—
1096C2×Q8—1668no—
1097C2×Q8—16612no—
1098C2×Q8C23×D8316yes—
1099C2×Q8C23×D8313yes—
1100C2×Q8C23×D8313yes—
1101C2×Q8C23×D8311yescharacteristic
1102C2×D4—212no—
1103C2×D4—836no—
1104C2×D4—832no—
1105C2×D4—832no—
1106C2×D4—836no—
1107C2×D4—832no—
1108C2×D4—831no—
1109C2×D4C23×D8316yes—
1110C2×D4C23×D8316yes—
1111C2×D4C23×D8313yes—
1112C2×D4C23×D8311yescharacteristic
1113C2×D4C23×D8312yes—
1114C2×D4C23×D8316yes—
1115C2×D4C23×D8313yes—
1116C22×C4—212no—
1117C22×C4—3326no—
1118C22×C4—833no—
1119C22×C4—833no—
1120C22×C4—833no—
1121C22×C4—836no—
1122C22×C4—836no—
1123C22×C4—836no—
1124C22×C4—831no—
1125C22×C4—833no—
1126C22×C4—831no—
1127C22×C4—832no—
1128C22×C4—833no—
1129C22×C4—833no—
1130C22×C4—833no—
1131C22×C4—833no—
1132C22×C4—833no—
1133C22×C4—833no—
1134C22×C4—836no—
1135C22×C4—832no—
1136C22×C4—836no—
1137C22×C4—16612no—
1138C22×C4C23×D8311yescharacteristic
1139C22×C4C23×D8313yes—
1140C22×C4C23×D8313yes—
1141C22×C4C23×D8313yes—
1142C22×C4C23×D8313yes—
1143C22×C4C23×D8316yes—
1144C22×C4C23×D8316yes—
1145C22×C4C23×D8316yes—
1146C22×C4C23×D8313yes—
1147C4⋊C4—833no—
1148C4⋊C4—836no—
1149C4⋊C4—836no—
1150C4⋊C4—836no—
1151C4⋊C4—833no—
1152C4⋊C4—836no—
1153C4⋊C4—836no—
1154C4⋊C4—8312no—
1155C4⋊C4—836no—
1156C4⋊C4—836no—
1157C4⋊C4—8312no—
1158C4⋊C4—833no—
1159C4⋊C4—836no—
1160C4⋊C4—833no—
1161C4⋊C4—833no—
1162C4⋊C4—836no—
1163C4⋊C4—8312no—
1164C4⋊C4—8312no—
1165C4⋊C4—8312no—
1166C4⋊C4—8312no—
1167C4⋊C4—832no—
1168C4⋊C4—831no—
1169C4⋊C4—836no—
1170C4⋊C4—836no—
1171C4⋊C4—836no—
1172C4⋊C4—836no—
1173C4⋊C4—836no—
1174C4⋊C4—836no—
1175C4⋊C4—836no—
1176C4⋊C4C23×D8316yes—
1177C4⋊C4C23×D8316yes—
1178C4⋊C4C23×D8313yes—
1179C4⋊C4C23×D83112yes—
1180C4⋊C4C23×D8316yes—
1181C4⋊C4C23×D8311yescharacteristic
1182C22⋊C4—836no—
1183C22⋊C4—836no—
1184C22⋊C4—836no—
1185C22⋊C4—836no—
1186C22⋊C4—836no—
1187C22⋊C4—8312no—
1188C22⋊C4—836no—
1189C22⋊C4—832no—
1190C22⋊C4—836no—
1191C22⋊C4—836no—
1192C22⋊C4—836no—
1193C22⋊C4—836no—
1194C22⋊C4—832no—
1195C22⋊C4—832no—
1196C22⋊C4—836no—
1197C22⋊C4—836no—
1198C22⋊C4—836no—
1199C22⋊C4—836no—
1200C22⋊C4C23×D8316yes—
1201C22⋊C4C23×D83112yes—
1202C22⋊C4C23×D8312yes—
1203C22⋊C4C23×D8316yes—
1204C22⋊C4C23×D8316yes—
1205C22⋊C4C23×D8316yes—
1206C42—831no—
1207C42—831no—
1208C42—833no—
1209C42—831no—
1210C42—831no—
1211C42—833no—
1212C42—833no—
1213C42—836no—
1214C42—836no—
1215C42—833no—
1216C42—833no—
1217C42—833no—
1218C42—833no—
1219C42—833no—
1220C42—833no—
1221C42—833no—
1222C42—833no—
1223C42—833no—
1224C42—836no—
1225C42—836no—
1226C42—8312no—
1227C42—8312no—
1228C42—836no—
1229C42C23×D8316yes—
1230C23—26no—
1231C23—26no—
1232C23—43no—
1233C23—832no—
1234C23C24×D8313yes—
1235C23C24×D8312yes—
1236C23C24×D8313yes—
1237C23C24×D8311yescharacteristic
1238Q8—212no—
1239Q8—26no—
1240Q8—26no—
1241Q8—33212no—
1242Q8—16612no—
1243Q8—1664no—
1244Q8—16612no—
1245Q8—1666no—
1246Q8C2×#1305058914yes—
1247D4—212no—
1248D4—212no—
1249D4—24no—
1250D4—26no—
1251D4—22no—
1252D4—46no—
1253D4—3326no—
1254D4—1664no—
1255D4—1664no—
1256D4—16612no—
1257D4—1664no—
1258D4—1662no—
1259D4C2×#13050589112yes—
1260C2×C4—26no—
1261C2×C4—212no—
1262C2×C4—22no—
1263C2×C4—26no—
1264C2×C4—26no—
1265C2×C4—26no—
1266C2×C4—212no—
1267C2×C4—46no—
1268C2×C4—3326no—
1269C2×C4—3323no—
1270C2×C4—3323no—
1271C2×C4—3323no—
1272C2×C4—3326no—
1273C2×C4—3326no—
1274C2×C4—834no—
1275C2×C4—831no—
1276C2×C4—831no—
1277C2×C4—831no—
1278C2×C4—833no—
1279C2×C4—831no—
1280C2×C4—833no—
1281C2×C4—832no—
1282C2×C4—833no—
1283C2×C4—833no—
1284C2×C4—836no—
1285C2×C4—836no—
1286C2×C4—1664no—
1287C2×C4—1662no—
1288C2×C4—1666no—
1289C2×C4—1666no—
1290C2×C4—1666no—
1291C2×C4—1666no—
1292C2×C4—1666no—
1293C2×C4—1666no—
1294C2×C4—1664no—
1295C2×C4—16612no—
1296C2×C4—1666no—
1297C2×C4—16612no—
1298C2×C4C2×#13050589112yes—
1299C2×C4C24×D8311yescharacteristic
1300C2×C4C24×D8316yes—
1301C2×C4C24×D8313yes—
1302C2×C4C24×D8312yes—
1303C2×C4C24×D8316yes—
1304C2×C4C24×D8311yescharacteristic
1305C2×C4C24×D8313yes—
1306C22—21no—
1307C22—23no—
1308C22—23no—
1309C22—21no—
1310C22—22no—
1311C22—23no—
1312C22—23no—
1313C22—22no—
1314C22—22no—
1315C22—23no—
1316C22—412no—
1317C22—1662no—
1318C22—1662no—
1319C22—1662no—
1320C22C22×#1305058916yes—
1321C222−1+4×D8312yes—
1322C22C25×D8311yescharacteristic
1323C4—21no—
1324C4—23no—
1325C4—26no—
1326C4—22no—
1327C4—26no—
1328C4—832no—
1329C4—832no—
1330C4—832no—
1331C4—1666no—
1332C4—1663no—
1333C4—1663no—
1334C4—1662no—
1335C4—1663no—
1336C4—1661no—
1337C4—1666no—
1338C4—1663no—
1339C4C22×#1305058916yes—
1340C4C22×#1305058912yes—
1341C2—22no—
1342C2—26no—
1343C2—43no—
1344C2—42no—
1345C2—3322no—
1346C2C23×#1305058911yescharacteristic
1347C2C2×2−1+4×D8311yescharacteristic
1348C2#585×D8311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3489C2
hypercenter#3489D83
hypocenterC83#62805
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3489

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24921550C2semidirect
2. #24921499C2semidirect
3. #24921471C2semidirect
4. #24921428C2semidirect
5. #24921372C2semidirect
6. #24921348C2semidirect
7. #24921276C2semidirect
8. #24921244C2semidirect
9. #24921217C2semidirect
10. #24921209C2semidirect
11. #24921143C2semidirect
12. #24921079C2semidirect
13. #24921075C2semidirect
14. Q8×#13050589C2semidirect
15. #24921014C2semidirect
16. #24920891C2semidirect
17. #24920887C2semidirect
18. #24920755C2semidirect
19. C2×#19128253C2semidirect
20. 2−1+4×Dic83C2semidirect
21. #24920674C2semidirect
22. C2×#41×Dic83C2semidirect
23. C83×#3489C2semidirect
25. Q8×Dic166C22semidirect
26. #19128427C22semidirect
27. #19128426C22semidirect
28. #19128426C22semidirect
29. #19128422C22semidirect
30. #19128422C22semidirect
31. #19128421C22semidirect
32. #19128420C22semidirect
33. #19128420C22semidirect
34. #19128415C22semidirect
35. #19128410C22semidirect
37. #19128409C22semidirect
39. #19128394C22semidirect
42. #19128391C22semidirect
43. #19128388C22semidirect
44. #19128388C22semidirect
45. #19128388C22semidirect
46. #19128386C22semidirect
47. #19128385C22semidirect
50. D4×Dic166C22semidirect
52. Q8×C22⋊D83C22semidirect
53. Q8×C22⋊D83C22semidirect
55. #19128357C22semidirect
56. #19128351C22semidirect
58. #19128350C22semidirect
59. #19128350C22semidirect
61. #19128332C22semidirect
62. #19128329C22semidirect
63. #19128324C22semidirect
64. #19128320C22semidirect
65. #19128318C22semidirect
66. #19128318C22semidirect
67. #19128312C22semidirect
68. #19128311C22semidirect
69. #19128311C22semidirect
70. #19128311C22semidirect
71. #19128296C22semidirect
72. #19128295C22semidirect
74. #19128275C22semidirect
76. #19128272C22semidirect
77. #19128256C22semidirect
78. #19128254C22semidirect
83. #19128253C22semidirect
84. #19128253C22semidirect
85. #19128253C22semidirect
86. #19128253C22semidirect
87. #19128253C22semidirect
88. #19128253C22semidirect
89. #19128247C22semidirect
91. #19128246C22semidirect
92. C2×#14581791C22semidirect
93. C2×#14581790C22semidirect
95. #19128237C22semidirect
97. #19128232C22semidirect
98. #19128232C22semidirect
99. #19128232C22semidirect
101. #19128231C22semidirect
102. #19128230C22semidirect
103. #19128228C22semidirect
104. #19128228C22semidirect
105. #19128228C22semidirect
106. C2×#14581782C22semidirect
113. #19128184C22semidirect
114. #19128184C22semidirect
115. #19128182C22semidirect
116. #19128180C22semidirect
117. #19128179C22semidirect
118. #19128179C22semidirect
119. #19128178C22semidirect
120. #19128177C22semidirect
129. #41×Dic83C22semidirect
130. #41×Dic83C22semidirect
131. #19128169C22semidirect
133. C4×#13050589C22semidirect
134. C4×#13050589C22semidirect
137. C2×Q8×Dic83C22semidirect
138. C2×Q8×Dic83C22semidirect
139. C2×#14581757C22semidirect
140. C2×#14581757C22semidirect
141. C4×Q8×D83C22semidirect
516. #41×C83#41semidirect
610. C2×Dic832−1+4semidirect
686. #3489D83semidirect
698. C83#62805semidirect
1086. #41#13050589semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249215502
#249214992
#249214712
#249214282
#249213722
#249213482
#249212762
#249212442
#249212172
#249212092
#249211432
#249210792
#249210752
Q8×#130505892
#249210142
#249208912
#249208872
#249207552
C2×#191282532
2−1+4×Dic832
#249206742
C2×#41×Dic832
C83×#34892
#6280583