Finite Group Databasebeta

← #25064261

Subgroups — #25064261

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148335C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19137458C211yesmaximal, characteristic, complemented
4#19133172C211yesmaximal, characteristic, complemented
5#19133157C211yesmaximal, characteristic, complemented
6#19133148C211yesmaximal, characteristic
7#19133147C211yesmaximal, characteristic, complemented
8#19133130C211yesmaximal, characteristic, complemented
9#19133126C211yesmaximal, characteristic, complemented
10#19133105C211yesmaximal, characteristic, complemented
11#19133096C211yesmaximal, characteristic
12#19133093C211yesmaximal, characteristic, complemented
13#19133078C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C43×#1509C211yesmaximal, characteristic, complemented
16#14583616—21no—
17#14583608—21no—
18#14583588—21no—
19#14583586—21no—
20#14583585—21no—
21#14583582—21no—
22#14583578—21no—
23#14583572—21no—
24#14583529C411yescharacteristic, complemented
25#14583518C411yescharacteristic, complemented
26#14583514C411yescharacteristic, complemented
27#14583512C411yescharacteristic, complemented
28#14583507C411yescharacteristic, complemented
29#14583469C411yescharacteristic, complemented
30#14583456C2211yescharacteristic
31#14583451C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583409C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#14583378C411yescharacteristic, complemented
36#14583375C411yescharacteristic, complemented
37C2×#13063282C2211yescharacteristic
38#14582961—21no—
39#14582959—21no—
40#14582953C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582949C2211yescharacteristic
43#14582924—21no—
44#14582861C2211yescharacteristic
45C22⋊C8×D43C2211yescharacteristic
46#14582856—21no—
47#14582783—21no—
48#14582780—21no—
49#14582770—21no—
50#14582767C2211yescharacteristic
51#14582763C2211yescharacteristic
52#14582761C2211yescharacteristic
53C4×(C2×D43)⋊C4—21no—
54#14582744C2211yescharacteristic
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×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C4×C4⋊C4×C43C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621900C2×C411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×#10621872—21no—
80C2×C8×D43—21no—
81#13063325C2×C411yescharacteristic, complemented
82#13063325C2×C411yescharacteristic, complemented
83#13063324—21no—
84#13063324C2×C411yescharacteristic, complemented
85#13063323C2×C411yescharacteristic, complemented
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063317—21no—
94#13063317—21no—
95#13063316—21no—
96#13063316—21no—
97#13063316C2×C411yescharacteristic, complemented
98#13063315—21no—
99#13063315—21no—
100#13063315—21no—
101#13063312C2×C411yescharacteristic, complemented
102#13063311—21no—
103#13063311—21no—
104#13063309—21no—
105#13063308—21no—
106#13063307—21no—
107#13063307—21no—
108#13063307—21no—
109#13063306—21no—
110#13063305—21no—
111#13063305C2×C411yescharacteristic
112#13063305C2×C411yescharacteristic
113#13063304—21no—
114#13063304—21no—
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#13063296C2×C411yescharacteristic
126#13063293—21no—
127Q8×Dic43C2×C411yescharacteristic, complemented
128C4×Dic86—21no—
129C4×Dic86—21no—
130C4×Dic86C2×C411yescharacteristic, complemented
131C4×Dic86C2×C411yescharacteristic, complemented
132#13063290—21no—
133#13063290—21no—
134#13063290C2×C411yescharacteristic, complemented
135#13063290C2×C411yescharacteristic, complemented
136D4×Dic43—21no—
137D4×Dic43—21no—
138D4×Dic43C2×C411yescharacteristic, complemented
139C4×C22⋊D43—21no—
140(C22⋊D43)⋊C4—21no—
141(C22⋊D43)⋊C4—21no—
142#13063284—21no—
143#13063283—21no—
144#13063283C2×C411yescharacteristic
145#13063282—21no—
146#13063282C2×C411yescharacteristic
147#13063282C2×C411yescharacteristic
148#13063282C2×C411yescharacteristic
149#13063282C2×C411yescharacteristic
150#13063282D411yescharacteristic
151#13063282D411yescharacteristic
152#13063282D411yescharacteristic
153#13063282D411yescharacteristic
154#13063281—21no—
155#13063281—21no—
156#13063281—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43—21no—
162C4⋊C4×D43C2×C411yescharacteristic
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C2×(C2×D43)⋊C4D411yescharacteristic
166C22⋊C4×D43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43C2311yescharacteristic
169C4⋊(C43⋊C8)—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172C22⋊(C43⋊C8)C2311yescharacteristic
173C22⋊(C43⋊C8)C2311yescharacteristic
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176#13063235—21no—
177C4×C43⋊C8—21no—
178C8×Dic43—21no—
179C43⋊#95—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic, complemented
189#124×C43C2×C411yescharacteristic, complemented
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic, complemented
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic, complemented
196#117×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C42×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#97×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43C2×D411yescharacteristic
207C2×Q8×C43C22×C411yescharacteristic
208C2×D4×C43—21no—
209C2×D4×C43C22×C411yescharacteristic
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225Q8×D43—42no—
226#10621900—42no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—81no—
233C2×C4×D43C22×C411yescharacteristic
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C2×D411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86C22×C411yescharacteristic
241C2×Dic86C22×C411yescharacteristic
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—42no—
249C4⋊C4×C43C22×C411yescharacteristic
250C4⋊C4×C43C22×C411yescharacteristic
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C42×C43—21no—
257C42×C43—81no—
258C42×C43C22×C411yescharacteristic
259C42×C43C22×C411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267C22⋊Dic43—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—42no—
273(C2×D43)⋊C4C22⋊C411yescharacteristic
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275(C2×D43)⋊C4C22⋊C411yescharacteristic
276(C2×D43)⋊C4C22⋊C411yescharacteristic
277(C2×D43)⋊C4C22⋊C411yescharacteristic
278(C2×D43)⋊C4C22⋊C411yescharacteristic
279(C2×D43)⋊C4C22⋊C411yescharacteristic
280(C2×D43)⋊C4C22⋊C411yescharacteristic
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43C22×C411yescharacteristic
289C4⋊Dic43C22×C411yescharacteristic
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—81no—
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—42no—
318C4×Dic43C22×C411yescharacteristic
319C4×Dic43C22×C411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324#10621872—42no—
325C8×D43—42no—
326C23×C43—21no—
327C23×C43C22×D411yescharacteristic
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—22no—
331C22×D43—41no—
332C22×D43C2×C22⋊C411yescharacteristic
333C22×D43C2×C22⋊C411yescharacteristic
334Q8×C43—41no—
335D4×C43—41no—
336D4×C43—41no—
337D4×C43—41no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—81no—
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C23×C411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C22⋊D43—42no—
359C22⋊D43—81no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—42no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—81no—
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—41no—
385C4×D43—41no—
386C4×D43—42no—
387C4×D43—81no—
388C4×D43—84no—
389Dic86—42no—
390Dic86—41no—
391Dic86—41no—
392Dic86—81no—
393Dic86—81no—
394C8×C43—41no—
395C8×C43—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398#17609—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43C22×C22⋊C411yescharacteristic
405C22×C43#57711yescharacteristic
406C22×C43#57811yescharacteristic
407C2×D43—21no—
408C2×D43—21no—
409C2×D43—21no—
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43#41012yes—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—42no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—41no—
425C4×C43—81no—
426Dic43—21no—
427Dic43—21no—
428Dic43—21no—
429Dic43—21no—
430Dic43—21no—
431Dic43—21no—
432Dic43—41no—
433Dic43—41no—
434Dic43—41no—
435Dic43—41no—
436Dic43—81no—
437Dic43—81no—
438#3495—431no—
439#2924—431no—
440#2343—431no—
441#1521—431no—
442#1518—431no—
443#1516—431no—
444#1515—431no—
445#1512—431no—
446#1511—431no—
447#1509D4311yescharacteristic, complemented
448#1506—431no—
449#1504—431no—
450#1503—431no—
451#1500—431no—
452C2×#328—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—81no—
456C2×C43C2×#41011yescharacteristic
457C2×C43#289811yescharacteristic
458C2×C43#290111yescharacteristic
459D43—22no—
460D43—41no—
461#556—861no—
462#554—861no—
463#552—861no—
464#552—861no—
465#552—861no—
466#552—861no—
467#551—861no—
468#551—861no—
469#544—431no—
470#542—431no—
471#542—431no—
472#541—431no—
473#541—431no—
474#536—431no—
475#533—431no—
476#533—431no—
477#529—431no—
478#529C2×D4311yescharacteristic
479#525—431no—
480C2×C22⋊Q8—431no—
481#520—431no—
482#519—431no—
483C2×#117—431no—
484#433—861no—
485#433—861no—
486#432—431no—
487#432C2×D4311yescharacteristic
488#431—431no—
489#431—431no—
490#424—861no—
491#407—431no—
492C2×C22⋊C8—431no—
493#405—861no—
494#387—861no—
495#387—861no—
496#385—861no—
497#383—431no—
498#382—431no—
499#381—431no—
500C4×C4⋊C4C2×D4311yescharacteristic
501C4×C22⋊C4—861no—
502#376—431no—
503C2×#95—431no—
504#328—431no—
505#328—431no—
506#328—431no—
507#328—431no—
508#328—431no—
509#328—431no—
510#328—431no—
511#328—431no—
512#328—431no—
513#328—431no—
514#328C2×D4311yescharacteristic
515#328C2×D4311yescharacteristic
516#327—431no—
517#327—431no—
518#327C2×D4311yescharacteristic
519#327C2×D4311yescharacteristic
520C43#1760911yescharacteristic, complemented, Sylow
521C2×#41—431no—
522C22×Q8—431no—
523C23×C4—431no—
524C23×C4—861no—
525C2×M16—861no—
526C22×C8—861no—
527C4⋊Q8—431no—
528C4⋊Q8—431no—
529C4⋊Q8—431no—
530C4⋊Q8—431no—
531C4⋊Q8—861no—
532#126—21no—
533#126—861no—
534#126—861no—
535#126—861no—
536#126—861no—
537#126—861no—
538#126—861no—
539#126—861no—
540#125—431no—
541#125—861no—
542#125—861no—
543#125—861no—
544#125—861no—
545#125—861no—
546#125—861no—
547#125—861no—
548#125C4×D4311yescharacteristic, complemented
549#124—431no—
550#124—861no—
551#124—861no—
552#124C4×D4311yescharacteristic, complemented
553#123—21no—
554#123—861no—
555#123—861no—
556#123—861no—
557#123—861no—
558#123—861no—
559#123—861no—
560C22⋊Q8—431no—
561C22⋊Q8—431no—
562C22⋊Q8—431no—
563C22⋊Q8—431no—
564C22⋊Q8—431no—
565C22⋊Q8—861no—
566C22⋊Q8—861no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8—861no—
570C22⋊Q8—861no—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573C22⋊Q8—861no—
574C22⋊Q8—861no—
575C22⋊Q8C22×D4311yescharacteristic
576#121—431no—
577#121C22×D4311yescharacteristic
578#120—861no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—431no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×Q8—861no—
587C4×Q8—861no—
588C4×Q8C4×D4311yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—431no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4C4×D4311yescharacteristic, complemented
597#117—21no—
598#117—431no—
599#117—431no—
600#117—431no—
601#117—431no—
602#117—431no—
603#117—431no—
604#117—431no—
605#117—431no—
606#117—431no—
607#117—861no—
608#117—861no—
609#117—861no—
610#117—861no—
611#117—861no—
612#117—861no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—431no—
615C2×C4⋊C4—431no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4—861no—
620C2×C22⋊C4—431no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C42—21no—
625C2×C42—431no—
626C2×C42—861no—
627C2×C42C22×D4311yescharacteristic
628C4⋊C8—21no—
629C4⋊C8—861no—
630C4⋊C8—861no—
631C4⋊C8—861no—
632C22⋊C8—431no—
633C22⋊C8—431no—
634C22⋊C8—861no—
635C22⋊C8—861no—
636C22⋊C8C22×D4311yescharacteristic
637C22⋊C8C22×D4311yescharacteristic
638#97—21no—
639#97—861no—
640C4×C8—861no—
641C4×C8—861no—
642#95—431no—
643#95—431no—
644#95—861no—
645#95—861no—
646#95—861no—
647#95—861no—
648#95—861no—
649#95—861no—
650#95C22×D4311yescharacteristic
651#95C22×D4311yescharacteristic
652C24—431no—
653#41—1722no—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—861no—
657C2×Q8—861no—
658C2×Q8—861no—
659C2×Q8—1722no—
660C2×Q8C2×C4×D4311yescharacteristic
661C2×D4—21no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4C2×C4×D4311yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—3441no—
682C22×C4—1722no—
683C22×C4—1722no—
684C22×C4—1722no—
685C22×C4D4×D4311yescharacteristic
686C22×C4D4×D4311yescharacteristic
687C22×C4C23×D4311yescharacteristic
688M16—1722no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—1722no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—42no—
699C4⋊C4—431no—
700C4⋊C4—431no—
701C4⋊C4—431no—
702C4⋊C4—431no—
703C4⋊C4—431no—
704C4⋊C4—431no—
705C4⋊C4—431no—
706C4⋊C4—431no—
707C4⋊C4—431no—
708C4⋊C4—431no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—3441no—
729C4⋊C4C2×C4×D4311yescharacteristic
730C4⋊C4C2×C4×D4311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—431no—
737C22⋊C4—431no—
738C22⋊C4—431no—
739C22⋊C4—431no—
740C22⋊C4—431no—
741C22⋊C4—431no—
742C22⋊C4—431no—
743C22⋊C4—431no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—1722no—
755C42—21no—
756C42—81no—
757C42—431no—
758C42—431no—
759C42—431no—
760C42—431no—
761C42—861no—
762C42—861no—
763C42—861no—
764C42—861no—
765C42—861no—
766C42—861no—
767C42—1722no—
768C42C2×C4×D4311yescharacteristic
769C42C2×C4×D4311yescharacteristic
770C42D4×D4311yescharacteristic
771C42D4×D4311yescharacteristic
772C23—21no—
773C23—431no—
774C23—431no—
775C23—862no—
776C23—861no—
777C23—861no—
778C23—1721no—
779C23C2×D4×D4311yescharacteristic
780Q8—41no—
781Q8—3441no—
782Q8—3441no—
783Q8—1721no—
784Q8—1721no—
785Q8—1722no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—3441no—
790D4—1722no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4—431no—
806C2×C4—431no—
807C2×C4—431no—
808C2×C4—431no—
809C2×C4—431no—
810C2×C4—431no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—3444no—
820C2×C4—3441no—
821C2×C4—3441no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1722no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1722no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1721no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4C22⋊C4×D4311yescharacteristic
835C2×C4C22⋊C4×D4311yescharacteristic
836C2×C4C22⋊C4×D4311yescharacteristic
837C2×C4C22⋊C4×D4311yescharacteristic
838C2×C4C22×C4×D4311yescharacteristic
839C2×C4C2×D4×D4311yescharacteristic
840C8—41no—
841C8—41no—
842C8—1721no—
843C8—1721no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—432no—
850C22—861no—
851C22—861no—
852C22—861no—
853C22—861no—
854C22—861no—
855C22—1722no—
856C22—1722no—
857C22C2×C22⋊C4×D4311yescharacteristic
858C22#1458370911yescharacteristic
859C22#1458371511yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—42no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—81no—
871C4—861no—
872C4—861no—
873C4—861no—
874C4—861no—
875C4—861no—
876C4—861no—
877C4—3441no—
878C4—3441no—
879C4—1721no—
880C4—1721no—
881C4—1721no—
882C4—1721no—
883C2—21no—
884C2—21no—
885C2—81no—
886C2—862no—
887C2—1721no—
888C2#410×D4311yescharacteristic
889C2#1914312611yescharacteristic
890C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#14583409C22
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17609
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19137458C2semidirect
4. #19133172C2semidirect
5. #19133157C2semidirect
7. #19133147C2semidirect
8. #19133130C2semidirect
9. #19133126C2semidirect
10. #19133105C2semidirect
12. #19133093C2semidirect
13. #19133078C2semidirect
14. #328×D43C2semidirect
15. C43×#1509C2semidirect
24. #14583529C4semidirect
25. #14583518C4semidirect
26. #14583514C4semidirect
27. #14583512C4semidirect
28. #14583507C4semidirect
29. #14583469C4semidirect
35. #14583378C4semidirect
36. #14583375C4semidirect
81. #13063325C2×C4semidirect
82. #13063325C2×C4semidirect
84. #13063324C2×C4semidirect
85. #13063323C2×C4semidirect
97. #13063316C2×C4semidirect
101. #13063312C2×C4semidirect
127. Q8×Dic43C2×C4semidirect
130. C4×Dic86C2×C4semidirect
131. C4×Dic86C2×C4semidirect
134. #13063290C2×C4semidirect
135. #13063290C2×C4semidirect
138. D4×Dic43C2×C4semidirect
188. #125×C43C2×C4semidirect
189. #124×C43C2×C4semidirect
193. C4×Q8×C43C2×C4semidirect
195. C4×D4×C43C2×C4semidirect
447. #1509D43semidirect
520. C43#17609semidirect
548. #125C4×D43semidirect
552. #124C4×D43semidirect
588. C4×Q8C4×D43semidirect
596. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191483352
#191432542
#191374582
#191331722
#191331572
#191331482
#191331472
#191331302
#191331262
#191331052
#191330962
#191330932
#191330782
#328×D432
C43×#15092
#1760943