Finite Group Databasebeta

← #25064142

Subgroups — #25064142

Order 11008.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148632C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19137230C211yesmaximal, characteristic, complemented
4#19133169C211yesmaximal, characteristic, complemented
5#19133166C211yesmaximal, characteristic, complemented
6#19133157C211yesmaximal, characteristic, complemented
7#19133151C211yesmaximal, characteristic, complemented
8#19133144C211yesmaximal, characteristic, complemented
9#19133130C211yesmaximal, characteristic, complemented
10#19133129C211yesmaximal, characteristic, complemented
11#19133113C211yesmaximal, characteristic, complemented
12#19133096C211yesmaximal, characteristic, complemented
13#19133083C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C43×#1513C211yesmaximal, 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#14582975—21no—
39#14582968—21no—
40#14582967—21no—
41(C22⋊D43)⋊C8—21no—
42#14582953C2211yescharacteristic
43#14582949C2211yescharacteristic
44#14582861C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊C8×D43C2211yescharacteristic
47#14582793—21no—
48#14582780—21no—
49#14582775—21no—
50#14582770—21no—
51#14582766C2211yescharacteristic
52#14582763C2211yescharacteristic
53#14582762C2211yescharacteristic
54#14582746C2211yescharacteristic
55#95×D43C2211yescharacteristic
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
69C43×#407C2211yescharacteristic
70C43×#380C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621900—21no—
76C2×#10621900C2×C411yescharacteristic
77C22×Dic86C2×C411yescharacteristic, complemented
78C2×Q8×D43C2×C411yescharacteristic
79C22×C22⋊D43D411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82C2×#10621872—21no—
83C22×C43⋊C8—21no—
84C2×C8×D43—21no—
85#13063324—21no—
86#13063324C2×C411yescharacteristic, complemented
87#13063323C2×C411yescharacteristic, complemented
88#13063320—21no—
89#13063319—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063317—21no—
94#13063316—21no—
95#13063316C2×C411yescharacteristic, complemented
96#13063315—21no—
97#13063312—21no—
98#13063312C2×C411yescharacteristic, complemented
99#13063311—21no—
100#13063311—21no—
101#13063309—21no—
102#13063308—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063306—21no—
107#13063306—21no—
108#13063306—21no—
109#13063305C2×C411yescharacteristic
110#13063305C2×C411yescharacteristic
111#13063304—21no—
112#13063304—21no—
113#13063304—21no—
114#13063304C2×C411yescharacteristic, complemented
115#13063304C2×C411yescharacteristic, complemented
116#13063304C2311yescharacteristic
117#13063304C2311yescharacteristic
118#13063303—21no—
119#13063303—21no—
120#13063302—21no—
121#13063302—21no—
122#13063302—21no—
123#13063302—21no—
124#13063302—21no—
125#13063301C2×C411yescharacteristic
126#13063297—21no—
127#13063297—21no—
128#13063296—21no—
129#13063296C2×C411yescharacteristic
130#13063293—21no—
131Q8×Dic43C2×C411yescharacteristic, complemented
132C4×Dic86—21no—
133#13063290—21no—
134#13063290C2×C411yescharacteristic, complemented
135#13063290C2×C411yescharacteristic, complemented
136D4×Dic43—21no—
137D4×Dic43—21no—
138D4×Dic43—21no—
139D4×Dic43C2×C411yescharacteristic, complemented
140C4×C22⋊D43—21no—
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063283C2×C411yescharacteristic
152#13063282—21no—
153#13063281—21no—
154#13063281—21no—
155#13063281—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic, complemented
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43—21no—
162C4⋊C4×D43C2×C411yescharacteristic
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43D411yescharacteristic
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063235—21no—
179C8×Dic43—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic, complemented
188C23×C4×C43C2311yescharacteristic
189C2×M16×C43—21no—
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic, complemented
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2×C411yescharacteristic, complemented
194#121×C43C2311yescharacteristic
195#120×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43—21no—
198#117×C43C2×C411yescharacteristic, complemented
199C2×C4⋊C4×C43—21no—
200C2×C22⋊C4×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
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—42no—
246C2×C4×D43—81no—
247C2×C4×D43—81no—
248C2×C4×D43—81no—
249C2×C4×D43C22×C411yescharacteristic
250C2×C4×D43C22×C411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86—21no—
256C2×Dic86—81no—
257C2×Dic86C22×C411yescharacteristic
258C2×Dic86C22×C411yescharacteristic
259M16×C43—81no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—81no—
265C4⋊C4×C43C22×C411yescharacteristic
266C4⋊C4×C43C22×C411yescharacteristic
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—81no—
273C42×C43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—81no—
283C22⋊Dic43C22⋊C411yescharacteristic
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
286C22⋊Dic43C22⋊C411yescharacteristic
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—42no—
292(C2×D43)⋊C4C22⋊C411yescharacteristic
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43C22×C411yescharacteristic
302C4⋊Dic43C22×C411yescharacteristic
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—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—81no—
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318Dic43⋊C4C22⋊C411yescharacteristic
319Dic43⋊C4C22⋊C411yescharacteristic
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—81no—
325C4×Dic43C22×C411yescharacteristic
326C4×Dic43C22×C411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—81no—
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—22no—
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—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—41no—
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—
410C4×D43—84no—
411Dic86—42no—
412Dic86—41no—
413Dic86—41no—
414Dic86—81no—
415Dic86—81no—
416C8×C43—41no—
417C8×C43—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17598—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—21no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—81no—
433C22×C43—81no—
434C22×C43C22×C22⋊C411yescharacteristic
435C22×C43#57711yescharacteristic
436C22×C43#57811yescharacteristic
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43#42112yes—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—41no—
450C4×C43—41no—
451C4×C43—41no—
452C4×C43—81no—
453C4×C43—81no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—41no—
461Dic43—41no—
462Dic43—41no—
463Dic43—41no—
464Dic43—81no—
465Dic43—81no—
466#3520—431no—
467#2974—431no—
468#2318—431no—
469#1521—431no—
470#1520—431no—
471#1518—431no—
472#1516—431no—
473#1515—431no—
474#1513D4311yescharacteristic, complemented
475#1512—431no—
476#1511—431no—
477#1508—431no—
478#1504—431no—
479#1501—431no—
480C2×#328—431no—
481C2×C43—21no—
482C2×C43—21no—
483C2×C43—41no—
484C2×C43—41no—
485C2×C43—81no—
486C2×C43#288311yescharacteristic
487C2×C43#289811yescharacteristic
488C2×C43C2×#42111yescharacteristic
489D43—22no—
490D43—41no—
491#556—431no—
492#554—861no—
493#552—431no—
494#552—431no—
495#551—861no—
496#551—861no—
497D4×Q8—431no—
498#548—431no—
499#548—431no—
500#547—431no—
501#547—431no—
502#546—861no—
503#542—861no—
504#539—861no—
505#539—861no—
506#533—431no—
507#529—431no—
508#525—431no—
509#525C2×D4311yescharacteristic
510C2×C22⋊Q8—431no—
511C2×C22⋊Q8—431no—
512#520—861no—
513C2×C4×D4—431no—
514#436—861no—
515#435—861no—
516#435—861no—
517C8×D4—861no—
518#432—431no—
519#431—431no—
520#407—431no—
521#407C2×D4311yescharacteristic
522C2×C22⋊C8—431no—
523C2×C22⋊C8—431no—
524#388—861no—
525#387—861no—
526#386—861no—
527#385—861no—
528#383—431no—
529#382—431no—
530#381—431no—
531#380C2×D4311yescharacteristic
532C4×C22⋊C4—431no—
533C2×#95—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#328—431no—
544#328C2×D4311yescharacteristic
545#328C2×D4311yescharacteristic
546#327—431no—
547#327—431no—
548#327C2×D4311yescharacteristic
549#327C2×D4311yescharacteristic
550C43#1759811yescharacteristic, complemented, Sylow
551C2×#41—431no—
552C2×#41—861no—
553C2×#41C4×D4311yescharacteristic, complemented
554C22×Q8—431no—
555C22×Q8—431no—
556C22×D4—431no—
557C23×C4—431no—
558C23×C4—861no—
559C23×C4C22×D4311yescharacteristic
560C2×M16—21no—
561C2×M16—861no—
562C22×C8—861no—
563C22×C8—861no—
564C4⋊Q8—431no—
565C4⋊Q8—431no—
566C4⋊Q8—861no—
567#126—861no—
568#126—861no—
569#126—861no—
570#126—861no—
571#126—861no—
572#125—431no—
573#125—861no—
574#125—861no—
575#125—861no—
576#124—431no—
577#124—861no—
578#124—861no—
579#124—861no—
580#123—21no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#123—861no—
587#123—861no—
588#123—861no—
589C22⋊Q8—431no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592C22⋊Q8—431no—
593C22⋊Q8—431no—
594C22⋊Q8—431no—
595C22⋊Q8—431no—
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⋊Q8—861no—
605C22⋊Q8—861no—
606C22⋊Q8C4×D4311yescharacteristic, complemented
607C22⋊Q8C22×D4311yescharacteristic
608#121—431no—
609#121—861no—
610#121—861no—
611#121—861no—
612#121C4×D4311yescharacteristic, complemented
613#121C22×D4311yescharacteristic
614#120—21no—
615#120—861no—
616C4×Q8—431no—
617C4×Q8—431no—
618C4×Q8—431no—
619C4×Q8—861no—
620C4×Q8—861no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—431no—
624C4×D4—431no—
625C4×D4—431no—
626C4×D4—431no—
627C4×D4—431no—
628C4×D4—431no—
629C4×D4—431no—
630C4×D4—431no—
631C4×D4—431no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636C4×D4—861no—
637C4×D4—861no—
638#117—431no—
639#117—861no—
640#117—861no—
641#117—861no—
642#117—861no—
643#117C4×D4311yescharacteristic, complemented
644C2×C4⋊C4—21no—
645C2×C4⋊C4—431no—
646C2×C4⋊C4—431no—
647C2×C4⋊C4—431no—
648C2×C4⋊C4—861no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4—861no—
651C2×C4⋊C4—861no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—431no—
654C2×C22⋊C4—431no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—861no—
659C2×C42—431no—
660C2×C42—861no—
661C4⋊C8—861no—
662C4⋊C8—861no—
663C22⋊C8—21no—
664C22⋊C8—431no—
665C22⋊C8—431no—
666C22⋊C8—861no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669C22⋊C8C22×D4311yescharacteristic
670C22⋊C8C22×D4311yescharacteristic
671#97—861no—
672C4×C8—861no—
673#95—431no—
674#95—431no—
675#95—861no—
676#95—861no—
677#95—861no—
678#95—861no—
679#95—861no—
680#95C22×D4311yescharacteristic
681#95C22×D4311yescharacteristic
682C24—431no—
683C24D4×D4311yescharacteristic
684#41—81no—
685#41—3441no—
686#41—1724no—
687C2×Q8—431no—
688C2×Q8—431no—
689C2×Q8—861no—
690C2×Q8—861no—
691C2×Q8—861no—
692C2×Q8—3441no—
693C2×Q8—3441no—
694C2×Q8C2×C4×D4311yescharacteristic
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—431no—
699C2×D4—431no—
700C2×D4—431no—
701C2×D4—431no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—1722no—
705C2×D4C2×C4×D4311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—81no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—3441no—
726C22×C4—3441no—
727C22×C4—3441no—
728C22×C4—1722no—
729C22×C4C2×C4×D4311yescharacteristic
730C22×C4C2×C4×D4311yescharacteristic
731C22×C4D4×D4311yescharacteristic
732C22×C4D4×D4311yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—81no—
736M16—3441no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—3441no—
742C2×C8—3441no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—81no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
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—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—3441no—
770C4⋊C4C2×C4×D4311yescharacteristic
771C4⋊C4C2×C4×D4311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—81no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—431no—
784C22⋊C4—431no—
785C22⋊C4—431no—
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—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—3441no—
799C22⋊C4—1722no—
800C42—21no—
801C42—431no—
802C42—431no—
803C42—431no—
804C42—431no—
805C42—861no—
806C42—861no—
807C42—861no—
808C42—861no—
809C42—3441no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—41no—
815C23—431no—
816C23—431no—
817C23—862no—
818C23—861no—
819C23—861no—
820C23—1721no—
821C23C22⋊C4×D4311yescharacteristic
822C23C22⋊C4×D4311yescharacteristic
823C23C2×D4×D4311yescharacteristic
824Q8—41no—
825Q8—3441no—
826Q8—3441no—
827Q8—1721no—
828Q8—1721no—
829Q8—1722no—
830D4—41no—
831D4—42no—
832D4—41no—
833D4—41no—
834D4—81no—
835D4—862no—
836D4—862no—
837D4—3441no—
838D4—1721no—
839D4—1721no—
840D4—1722no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
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—41no—
856C2×C4—81no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—431no—
862C2×C4—431no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—861no—
869C2×C4—3441no—
870C2×C4—3444no—
871C2×C4—3441no—
872C2×C4—3441no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1722no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1722no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1722no—
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22⋊C4×D4311yescharacteristic
890C2×C4C22×C4×D4311yescharacteristic
891C2×C4C2×D4×D4311yescharacteristic
892C8—41no—
893C8—41no—
894C8—1721no—
895C8—1721no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—81no—
908C22—81no—
909C22—432no—
910C22—861no—
911C22—861no—
912C22—861no—
913C22—861no—
914C22—861no—
915C22—1722no—
916C22—1722no—
917C22C2×C22⋊C4×D4311yescharacteristic
918C22#1458370911yescharacteristic
919C22#1458371511yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4—81no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—861no—
934C4—861no—
935C4—3441no—
936C4—3441no—
937C4—1721no—
938C4—1721no—
939C4—1721no—
940C4—1721no—
941C2—21no—
942C2—21no—
943C2—41no—
944C2—41no—
945C2—81no—
946C2—862no—
947C2—1721no—
948C2#1914305311yescharacteristic
949C2#1914312611yescharacteristic
950C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19148632C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17598
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19137230C2semidirect
4. #19133169C2semidirect
5. #19133166C2semidirect
6. #19133157C2semidirect
7. #19133151C2semidirect
8. #19133144C2semidirect
9. #19133130C2semidirect
10. #19133129C2semidirect
11. #19133113C2semidirect
12. #19133096C2semidirect
13. #19133083C2semidirect
14. #328×D43C2semidirect
15. C43×#1513C2semidirect
16. #14583617C4semidirect
18. #14583591C4semidirect
19. #14583588C4semidirect
22. #14583562C4semidirect
23. #14583556C4semidirect
24. #14583555C4semidirect
25. #14583549C4semidirect
26. #14583548C4semidirect
77. C22×Dic86C2×C4semidirect
86. #13063324C2×C4semidirect
87. #13063323C2×C4semidirect
95. #13063316C2×C4semidirect
98. #13063312C2×C4semidirect
114. #13063304C2×C4semidirect
115. #13063304C2×C4semidirect
131. Q8×Dic43C2×C4semidirect
134. #13063290C2×C4semidirect
135. #13063290C2×C4semidirect
139. D4×Dic43C2×C4semidirect
156. C2×C4⋊Dic43C2×C4semidirect
187. C2×#41×C43C2×C4semidirect
191. C22⋊Q8×C43C2×C4semidirect
193. #121×C43C2×C4semidirect
198. #117×C43C2×C4semidirect
474. #1513D43semidirect
550. C43#17598semidirect
553. C2×#41C4×D43semidirect
606. C22⋊Q8C4×D43semidirect
612. #121C4×D43semidirect
643. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486322
#191436312
#191372302
#191331692
#191331662
#191331572
#191331512
#191331442
#191331302
#191331292
#191331132
#191330962
#191330832
#328×D432
C43×#15132
#1759843