Finite Group Databasebeta

← #25064159

Subgroups — #25064159

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148632C211yesmaximal, characteristic
2#19143626C211yesmaximal, characteristic, complemented
3#19137235C211yesmaximal, characteristic, complemented
4#19133168C211yesmaximal, characteristic, complemented
5#19133165C211yesmaximal, characteristic, complemented
6#19133148C211yesmaximal, characteristic, complemented
7#19133138C211yesmaximal, characteristic, complemented
8#19133135C211yesmaximal, characteristic, complemented
9#19133127C211yesmaximal, characteristic, complemented
10#19133126C211yesmaximal, characteristic, complemented
11#19133117C211yesmaximal, characteristic, complemented
12#19133105C211yesmaximal, characteristic, complemented
13#19133092C211yesmaximal, characteristic, complemented
14#19133078C211yesmaximal, characteristic, complemented
15C43×#1516C211yesmaximal, characteristic, complemented
16#14583617C411yescharacteristic, complemented
17#14583608—21no—
18#14583591C411yescharacteristic, complemented
19#14583588C411yescharacteristic, complemented
20#14583580—21no—
21#14583578—21no—
22#14583562C411yescharacteristic, complemented
23#14583556C411yescharacteristic, complemented
24#14583555C411yescharacteristic, complemented
25#14583549C411yescharacteristic, complemented
26#14583548C411yescharacteristic, complemented
27#14583536—21no—
28#14583517—21no—
29#14583492—21no—
30#14583491—21no—
31#14583451C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583409C2211yescharacteristic
34C2×#13063304C2211yescharacteristic
35C22⋊Q8×D43C2211yescharacteristic
36#14583378—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41C8×C22⋊D43—21no—
42#14582953C2211yescharacteristic
43#14582949C2211yescharacteristic
44#14582863C2211yescharacteristic
45#14582861C2211yescharacteristic
46C22⋊C8×D43C2211yescharacteristic
47#14582799—21no—
48#14582796—21no—
49#14582793—21no—
50#14582791—21no—
51#14582761C2211yescharacteristic
52#14582759C2211yescharacteristic
53#14582758C2211yescharacteristic
54#14582750C2211yescharacteristic
55#14582744C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582637C2211yescharacteristic
59#14582637C2211yescharacteristic
60#14582636C2211yescharacteristic
61#14582636C2211yescharacteristic
62#14582635C2211yescharacteristic
63#14582635C2211yescharacteristic
64#14582635C2211yescharacteristic
65#14582635C2211yescharacteristic
66#14582633C2211yescharacteristic
67#14582633C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic
70C43×#381C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621900—21no—
76C2×#10621900C2×C411yescharacteristic
77C22×Dic86C2×C411yescharacteristic
78C2×Q8×D43C2×C411yescharacteristic
79C22×C22⋊D43D411yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×C8×D43—21no—
84#13063324—21no—
85#13063324C2×C411yescharacteristic
86#13063323C2×C411yescharacteristic
87#13063320—21no—
88#13063319—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063317—21no—
93#13063316—21no—
94#13063316C2×C411yescharacteristic
95#13063315—21no—
96#13063312—21no—
97#13063312C2×C411yescharacteristic
98#13063311—21no—
99#13063311—21no—
100#13063309—21no—
101#13063308—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063306—21no—
106#13063306—21no—
107#13063306—21no—
108#13063305C2×C411yescharacteristic
109#13063305C2×C411yescharacteristic
110#13063304—21no—
111#13063304—21no—
112#13063304—21no—
113#13063304C2×C411yescharacteristic
114#13063304C2×C411yescharacteristic
115#13063304C2311yescharacteristic
116#13063304C2311yescharacteristic
117#13063303—21no—
118#13063303—21no—
119#13063302—21no—
120#13063302—21no—
121#13063302—21no—
122#13063302—21no—
123#13063302—21no—
124#13063301C2×C411yescharacteristic
125#13063297—21no—
126#13063297—21no—
127#13063296—21no—
128#13063296C2×C411yescharacteristic
129#13063293—21no—
130Q8×Dic43C2×C411yescharacteristic
131C4×Dic86—21no—
132#13063290—21no—
133#13063290C2×C411yescharacteristic
134#13063290C2×C411yescharacteristic
135D4×Dic43—21no—
136D4×Dic43—21no—
137D4×Dic43—21no—
138D4×Dic43C2×C411yescharacteristic
139C4×C22⋊D43—21no—
140C4×C22⋊D43C2×C411yescharacteristic
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43D411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063283C2×C411yescharacteristic
151#13063282—21no—
152#13063281—21no—
153#13063281—21no—
154#13063281—21no—
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C4⋊C4×D43—21no—
163C4⋊C4×D43C2×C411yescharacteristic
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43—21no—
166C2×C22⋊Dic43D411yescharacteristic
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4D411yescharacteristic
170C22⋊C4×D43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C22×C8×C43—21no—
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2×C411yescharacteristic
194#121×C43C2311yescharacteristic
195#120×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43—21no—
198#117×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C23×D43C2×D411yescharacteristic
208#41×C43—81no—
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43C22×C411yescharacteristic
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—81no—
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—42no—
227C2×C22⋊D43C22⋊C411yescharacteristic
228C2×C22⋊D43C22⋊C411yescharacteristic
229C2×C22⋊D43C22⋊C411yescharacteristic
230C2×C22⋊D43C22⋊C411yescharacteristic
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240Q8×D43—81no—
241#10621900—44no—
242#10621900—81no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—81no—
246C2×C4×D43C22×C411yescharacteristic
247C2×C4×D43C22×C411yescharacteristic
248C2×C4×D43C2×D411yescharacteristic
249C2×C4×D43C2×D411yescharacteristic
250C2×Dic86—21no—
251C2×Dic86—21no—
252C2×Dic86—21no—
253C2×Dic86—81no—
254C2×Dic86C22×C411yescharacteristic
255C2×Dic86C22×C411yescharacteristic
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—81no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C22×C411yescharacteristic
262C4⋊C4×C43C22×C411yescharacteristic
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—81no—
269C42×C43—21no—
270C22⋊Dic43—21no—
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43—81no—
279C22⋊Dic43C22⋊C411yescharacteristic
280C22⋊Dic43C22⋊C411yescharacteristic
281C22⋊Dic43C22⋊C411yescharacteristic
282C22⋊Dic43C22⋊C411yescharacteristic
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—81no—
288(C2×D43)⋊C4—81no—
289(C2×D43)⋊C4C22⋊C411yescharacteristic
290(C2×D43)⋊C4C22⋊C411yescharacteristic
291(C2×D43)⋊C4C22⋊C411yescharacteristic
292(C2×D43)⋊C4C22⋊C411yescharacteristic
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—81no—
299C4⋊Dic43C22×C411yescharacteristic
300C4⋊Dic43C22×C411yescharacteristic
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—42no—
314Dic43⋊C4—81no—
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318Dic43⋊C4C22⋊C411yescharacteristic
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—42no—
324C4×Dic43—81no—
325C4×Dic43C22×C411yescharacteristic
326C4×Dic43C22×C411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329#10621877—81no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332#10621872—81no—
333C8×D43—81no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43C2×C22⋊C411yescharacteristic
340C23×C43C2×C22⋊C411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—41no—
345C22×D43—41no—
346C22×D43C2×C22⋊C411yescharacteristic
347C22×D43C2×C22⋊C411yescharacteristic
348Q8×C43—41no—
349D4×C43—41no—
350D4×C43—42no—
351D4×C43—41no—
352D4×C43—41no—
353D4×C43—81no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—81no—
370C2×C4×C43C2×C22⋊C411yescharacteristic
371C2×C4×C43C2×C22⋊C411yescharacteristic
372C2×C4×C43C23×C411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C22⋊D43—22no—
375C22⋊D43—22no—
376C22⋊D43—41no—
377C22⋊D43—41no—
378C22⋊D43—42no—
379C22⋊D43—81no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—22no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—41no—
388C2×Dic43—42no—
389C2×Dic43—42no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—81no—
397C2×Dic43—81no—
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400C2×Dic43C2×C22⋊C411yescharacteristic
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403C2×Dic43C2×C22⋊C411yescharacteristic
404C4×D43—41no—
405C4×D43—41no—
406C4×D43—41no—
407C4×D43—41no—
408C4×D43—42no—
409C4×D43—81no—
410Dic86—42no—
411Dic86—41no—
412Dic86—41no—
413Dic86—81no—
414Dic86—81no—
415C8×C43—41no—
416C8×C43—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419#17600—431nomaximal, Sylow
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—81no—
432C22×C43—81no—
433C22×C43C22×C22⋊C411yescharacteristic
434C22×C43#57711yescharacteristic
435C22×C43#57811yescharacteristic
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—81no—
443C2×D43—81no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—41no—
449C4×C43—41no—
450C4×C43—41no—
451C4×C43—81no—
452C4×C43—81no—
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—41no—
459Dic43—41no—
460Dic43—41no—
461Dic43—41no—
462Dic43—81no—
463Dic43—81no—
464Dic43#42112yes—
465#3520—431no—
466#2974—431no—
467#2319—431no—
468#1520—431no—
469#1520—431no—
470#1516—431no—
471#1516D4311yescharacteristic, complemented
472#1513—431no—
473#1513—431no—
474#1511—431no—
475#1511—431no—
476#1509—431no—
477#1506—431no—
478#1503—431no—
479#1500—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—41no—
483C2×C43—41no—
484C2×C43—81no—
485C2×C43#288311yescharacteristic
486C2×C43#289811yescharacteristic
487C2×C43C2×#42111yescharacteristic
488D43—41no—
489D43—41no—
490#556—431no—
491#554—861no—
492#552—431no—
493#552—431no—
494#551—861no—
495#551—861no—
496D4×Q8—431no—
497#548—431no—
498#548—431no—
499#547—431no—
500#547—431no—
501#546—861no—
502#542—861no—
503#539—861no—
504#539—861no—
505#533—431no—
506#529—431no—
507#525—431no—
508#525C2×D4311yescharacteristic
509C2×C22⋊Q8—431no—
510C2×C22⋊Q8—431no—
511#520—861no—
512C2×C4×D4—431no—
513#436—861no—
514#435—861no—
515#435—861no—
516C8×D4—861no—
517#432—431no—
518#431—431no—
519#407—431no—
520#407—431no—
521C2×C22⋊C8—431no—
522C2×C22⋊C8C2×D4311yescharacteristic
523#390—861no—
524#389—861no—
525#388—861no—
526#388—861no—
527#381—431no—
528#381C2×D4311yescharacteristic
529#380—431no—
530#380—431no—
531C4×C4⋊C4—431no—
532#376—431no—
533#328—431no—
534#328—431no—
535#328—431no—
536#328—431no—
537#328—431no—
538#328—431no—
539#328—431no—
540#328—431no—
541#328—431no—
542#328—431no—
543#328C2×D4311yescharacteristic
544#328C2×D4311yescharacteristic
545#327—431no—
546#327—431no—
547#327C2×D4311yescharacteristic
548#327C2×D4311yescharacteristic
549C43#1760011yescharacteristic, complemented, Sylow
550C2×#41—431no—
551C2×#41—861no—
552C2×#41C4×D4311yescharacteristic
553C22×Q8—431no—
554C22×Q8—431no—
555C22×D4—431no—
556C23×C4—431no—
557C23×C4C22×D4311yescharacteristic
558C2×M16—861no—
559C2×M16—861no—
560C22×C8—21no—
561C22×C8—861no—
562C4⋊Q8—431no—
563C4⋊Q8—431no—
564C4⋊Q8—861no—
565#126—861no—
566#126—861no—
567#126—861no—
568#126—861no—
569#126—861no—
570#125—431no—
571#125—861no—
572#125—861no—
573#125—861no—
574#124—431no—
575#124—861no—
576#124—861no—
577#124—861no—
578#123—21no—
579#123—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#123—861no—
587C22⋊Q8—431no—
588C22⋊Q8—431no—
589C22⋊Q8—431no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592C22⋊Q8—431no—
593C22⋊Q8—431no—
594C22⋊Q8—861no—
595C22⋊Q8—861no—
596C22⋊Q8—861no—
597C22⋊Q8—861no—
598C22⋊Q8—861no—
599C22⋊Q8—861no—
600C22⋊Q8—861no—
601C22⋊Q8—861no—
602C22⋊Q8—861no—
603C22⋊Q8—861no—
604C22⋊Q8C4×D4311yescharacteristic
605C22⋊Q8C22×D4311yescharacteristic
606#121—431no—
607#121—861no—
608#121—861no—
609#121—861no—
610#121C4×D4311yescharacteristic
611#121C22×D4311yescharacteristic
612#120—21no—
613#120—861no—
614C4×Q8—431no—
615C4×Q8—431no—
616C4×Q8—431no—
617C4×Q8—861no—
618C4×Q8—861no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—431no—
622C4×D4—431no—
623C4×D4—431no—
624C4×D4—431no—
625C4×D4—431no—
626C4×D4—431no—
627C4×D4—431no—
628C4×D4—431no—
629C4×D4—431no—
630C4×D4—861no—
631C4×D4—861no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636#117—431no—
637#117—861no—
638#117—861no—
639#117—861no—
640#117—861no—
641#117C4×D4311yescharacteristic
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—861no—
646C2×C4⋊C4—861no—
647C2×C4⋊C4—861no—
648C2×C4⋊C4—861no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4—861no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—431no—
653C2×C22⋊C4—431no—
654C2×C22⋊C4—861no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—861no—
659C2×C42—431no—
660C2×C42—861no—
661C2×C42—861no—
662C4⋊C8—861no—
663C4⋊C8—861no—
664C22⋊C8—21no—
665C22⋊C8—431no—
666C22⋊C8—431no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669C22⋊C8—861no—
670C22⋊C8C22×D4311yescharacteristic
671C22⋊C8C22×D4311yescharacteristic
672#97—861no—
673C4×C8—861no—
674#95—21no—
675#95—431no—
676#95—431no—
677#95—861no—
678#95—861no—
679#95C22×D4311yescharacteristic
680#95C22×D4311yescharacteristic
681C24—431no—
682C24D4×D4311yescharacteristic
683#41—81no—
684#41—3441no—
685#41—1724no—
686C2×Q8—431no—
687C2×Q8—431no—
688C2×Q8—861no—
689C2×Q8—861no—
690C2×Q8—861no—
691C2×Q8—3441no—
692C2×Q8—3441no—
693C2×Q8C2×C4×D4311yescharacteristic
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—431no—
698C2×D4—431no—
699C2×D4—431no—
700C2×D4—431no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—1722no—
704C2×D4C2×C4×D4311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—81no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—3441no—
725C22×C4C2×C4×D4311yescharacteristic
726C22×C4C2×C4×D4311yescharacteristic
727C22×C4D4×D4311yescharacteristic
728C22×C4D4×D4311yescharacteristic
729C22×C4D4×D4311yescharacteristic
730C22×C4C23×D4311yescharacteristic
731M16—3441no—
732M16—3441no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—81no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—3441no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—431no—
742C4⋊C4—431no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—3441no—
765C4⋊C4—3441no—
766C4⋊C4—1722no—
767C4⋊C4C2×C4×D4311yescharacteristic
768C4⋊C4C2×C4×D4311yescharacteristic
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—81no—
775C22⋊C4—431no—
776C22⋊C4—431no—
777C22⋊C4—431no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—3441no—
796C22⋊C4—3441no—
797C22⋊C4—3441no—
798C42—21no—
799C42—431no—
800C42—431no—
801C42—431no—
802C42—431no—
803C42—861no—
804C42—861no—
805C42—861no—
806C42—861no—
807C42—3441no—
808C42—1722no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—41no—
813C23—41no—
814C23—431no—
815C23—431no—
816C23—861no—
817C23—861no—
818C23—1721no—
819C23—1721no—
820C23C22⋊C4×D4311yescharacteristic
821C23C22⋊C4×D4311yescharacteristic
822C23C2×D4×D4311yescharacteristic
823Q8—41no—
824Q8—3441no—
825Q8—3441no—
826Q8—1721no—
827Q8—1721no—
828Q8—1722no—
829D4—41no—
830D4—42no—
831D4—41no—
832D4—41no—
833D4—81no—
834D4—862no—
835D4—862no—
836D4—3441no—
837D4—1721no—
838D4—1721no—
839D4—1722no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—431no—
862C2×C4—862no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—861no—
869C2×C4—3441no—
870C2×C4—3441no—
871C2×C4—3441no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1722no—
877C2×C4—1722no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1722no—
886C2×C4C22⋊C4×D4311yescharacteristic
887C2×C4C22⋊C4×D4311yescharacteristic
888C2×C4C22×C4×D4311yescharacteristic
889C2×C4C2×D4×D4311yescharacteristic
890C8—41no—
891C8—41no—
892C8—1721no—
893C8—1721no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—81no—
906C22—81no—
907C22—861no—
908C22—861no—
909C22—861no—
910C22—861no—
911C22—861no—
912C22—861no—
913C22—3441no—
914C22—3441no—
915C22C2×C22⋊C4×D4311yescharacteristic
916C22#1458370611yescharacteristic
917C22#1458371311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—81no—
926C4—81no—
927C4—432no—
928C4—861no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—3441no—
934C4—3441no—
935C4—1721no—
936C4—1721no—
937C4—1721no—
938C4—1721no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—1721no—
945C2—1721no—
946C2#1914305311yescharacteristic
947C2#1914312411yescharacteristic
948C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19148632C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17600
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #19143626C2semidirect
3. #19137235C2semidirect
4. #19133168C2semidirect
5. #19133165C2semidirect
6. #19133148C2semidirect
7. #19133138C2semidirect
8. #19133135C2semidirect
9. #19133127C2semidirect
10. #19133126C2semidirect
11. #19133117C2semidirect
12. #19133105C2semidirect
13. #19133092C2semidirect
14. #19133078C2semidirect
15. C43×#1516C2semidirect
16. #14583617C4semidirect
18. #14583591C4semidirect
19. #14583588C4semidirect
22. #14583562C4semidirect
23. #14583556C4semidirect
24. #14583555C4semidirect
25. #14583549C4semidirect
26. #14583548C4semidirect
471. #1516D43semidirect
549. C43#17600semidirect

Maximal subgroups

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

subgroupindex
#191486322
#191436262
#191372352
#191331682
#191331652
#191331482
#191331382
#191331352
#191331272
#191331262
#191331172
#191331052
#191330922
#191330782
C43×#15162
#1760043