Finite Group Databasebeta

← #25064265

Subgroups — #25064265

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#19148342C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19137452C211yesmaximal, characteristic, complemented
4#19133170C211yesmaximal, characteristic, complemented
5#19133157C211yesmaximal, characteristic, complemented
6#19133150C211yesmaximal, characteristic
7#19133132C211yesmaximal, characteristic, complemented
8#19133126C211yesmaximal, characteristic, complemented
9#19133121C211yesmaximal, characteristic, complemented
10#19133105C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic
12#19133094C211yesmaximal, characteristic, complemented
13#19133080C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C43×#1515C211yesmaximal, characteristic, complemented
16#14583621—21no—
17#14583603—21no—
18#14583590—21no—
19#14583582—21no—
20#14583581—21no—
21#14583581—21no—
22#14583576—21no—
23#14583573—21no—
24#14583526C411yescharacteristic, complemented
25#14583523C411yescharacteristic, complemented
26#14583521C411yescharacteristic, complemented
27#14583510C411yescharacteristic, complemented
28#14583507C411yescharacteristic, complemented
29#14583474C411yescharacteristic, complemented
30#14583451C2211yescharacteristic
31#14583435C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583412C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#14583381C411yescharacteristic, 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#14582786—21no—
48#14582781—21no—
49#14582773—21no—
50#14582763C2211yescharacteristic
51#14582761C2211yescharacteristic
52C4×C4⋊Dic43C2211yescharacteristic
53#14582746—21no—
54#14582744C2211yescharacteristic
55#95×D43C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582636C2211yescharacteristic
59#14582636C2211yescharacteristic
60#14582636C2211yescharacteristic
61#14582636C2211yescharacteristic
62#14582635C2211yescharacteristic
63#14582635C2211yescharacteristic
64#14582634C2211yescharacteristic
65#14582634C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#533C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#383C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#328C2211yescharacteristic
74C43×#328C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×#10621872—21no—
80C2×C8×D43—21no—
81#13063324C2×C411yescharacteristic, complemented
82#13063323—21no—
83#13063323C2×C411yescharacteristic, complemented
84#13063320—21no—
85#13063320—21no—
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063319—21no—
91#13063319—21no—
92#13063317—21no—
93#13063317C2×C411yescharacteristic, complemented
94#13063316C2×C411yescharacteristic, complemented
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063314—21no—
101#13063314C2×C411yescharacteristic, complemented
102#13063313—21no—
103#13063313C2×C411yescharacteristic, complemented
104#13063310—21no—
105#13063310—21no—
106#13063310—21no—
107#13063310—21no—
108#13063310—21no—
109#13063309—21no—
110#13063308—21no—
111#13063305C2×C411yescharacteristic
112#13063304C2311yescharacteristic
113#13063303—21no—
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063303—21no—
118#13063302—21no—
119#13063302—21no—
120#13063301—21no—
121#13063301—21no—
122#13063301C2×C411yescharacteristic
123#13063301C2×C411yescharacteristic
124#13063300C2×C411yescharacteristic
125#13063299C2311yescharacteristic
126#13063295—21no—
127Q8×Dic43C2×C411yescharacteristic, complemented
128Q8×Dic43C2×C411yescharacteristic, complemented
129C4×Dic86—21no—
130C4×Dic86C2×C411yescharacteristic, complemented
131#13063290—21no—
132#13063290—21no—
133#13063290C2×C411yescharacteristic, complemented
134C4×D172—21no—
135C4×D172C2×C411yescharacteristic, complemented
136#13063287—21no—
137#13063287—21no—
138#13063287C2×C411yescharacteristic, complemented
139C4×C22⋊D43—21no—
140(C22⋊D43)⋊C4—21no—
141(C22⋊D43)⋊C4—21no—
142#13063283—21no—
143#13063283—21no—
144#13063283C2×C411yescharacteristic
145#13063282—21no—
146#13063282—21no—
147#13063282—21no—
148#13063282C2×C411yescharacteristic
149#13063282C2×C411yescharacteristic
150#13063282C2×C411yescharacteristic
151#13063282C2×C411yescharacteristic
152#13063282D411yescharacteristic
153#13063282D411yescharacteristic
154#13063282D411yescharacteristic
155#13063282D411yescharacteristic
156#13063281—21no—
157C2×C4⋊Dic43—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43—21no—
162C4⋊C4×D43—21no—
163C4⋊C4×D43C2×C411yescharacteristic
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4D411yescharacteristic
166C2×(C2×D43)⋊C4D411yescharacteristic
167C22⋊C4×D43—21no—
168C2×C4×Dic43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171C4⋊(C43⋊C8)—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063235—21no—
179C4×C43⋊C8—21no—
180C8×Dic43—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C4⋊Q8×C43C2×C411yescharacteristic, complemented
188C4⋊Q8×C43C2×C411yescharacteristic, complemented
189#125×C43—21no—
190C22⋊Q8×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192C22⋊Q8×C43C2311yescharacteristic
193C4×Q8×C43—21no—
194C4×Q8×C43C2×C411yescharacteristic, complemented
195C4×Q8×C43C2×C411yescharacteristic, complemented
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201#97×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43C2×D411yescharacteristic
207C2×Q8×C43—21no—
208C2×Q8×C43C22×C411yescharacteristic
209C2×Q8×C43C22×C411yescharacteristic
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221#10621902—42no—
222Q8×D43—42no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172C22×C411yescharacteristic
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—81no—
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C22×C411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×C4×D43C2×D411yescharacteristic
239C2×Dic86—21no—
240C2×Dic86—21no—
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—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C22×C411yescharacteristic
252C4⋊C4×C43C22×C411yescharacteristic
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C42×C43—21no—
256C42×C43—21no—
257C42×C43C22×C411yescharacteristic
258C42×C43C22×C411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C22⋊Dic43—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—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—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—42no—
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
281(C2×D43)⋊C4C22⋊C411yescharacteristic
282(C2×D43)⋊C4C22⋊C411yescharacteristic
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—42no—
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—42no—
317C4×Dic43—81no—
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×C43C22×D411yescharacteristic
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—22no—
330C22×D43—21no—
331C22×D43—41no—
332C22×D43C2×C22⋊C411yescharacteristic
333C22×D43C2×C22⋊C411yescharacteristic
334Q8×C43—41no—
335Q8×C43—41no—
336Q8×C43—81no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—41no—
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×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C23×C411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C22⋊D43—41no—
358C22⋊D43—41no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—22no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378D172—41no—
379D172—42no—
380D172—81no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—41no—
384C4×D43—41no—
385C4×D43—42no—
386C4×D43—42no—
387C4×D43—81no—
388C4×D43—81no—
389C4×D43—81no—
390C4×D43—84no—
391Dic86—42no—
392Dic86—41no—
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×C43C22×C22⋊C411yescharacteristic
402C22×C43#57711yescharacteristic
403C22×C43#57811yescharacteristic
404C2×D43—21no—
405C2×D43—21no—
406C2×D43—21no—
407C2×D43—21no—
408C2×D43—21no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—41no—
414C2×D43#41012yes—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—41no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—41no—
425C4×C43—81no—
426C4×C43—81no—
427Dic43—21no—
428Dic43—21no—
429Dic43—21no—
430Dic43—21no—
431Dic43—21no—
432Dic43—21no—
433Dic43—42no—
434Dic43—41no—
435Dic43—41no—
436Dic43—41no—
437Dic43—81no—
438#3495—431no—
439#2924—431no—
440#2343—431no—
441#1521—431no—
442#1518—431no—
443#1516—431no—
444#1515D4311yescharacteristic, complemented
445#1512—431no—
446#1511—431no—
447#1509—431no—
448#1506—431no—
449#1504—431no—
450#1503—431no—
451#1500—431no—
452C2×#328—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43C2×#41011yescharacteristic
456C2×C43#289811yescharacteristic
457C2×C43#290111yescharacteristic
458D43—22no—
459D43—41no—
460D43—81no—
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#533C2×D4311yescharacteristic
477#529—431no—
478#529—431no—
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#383C2×D4311yescharacteristic
498#382—431no—
499#381—431no—
500C4×C4⋊C4—431no—
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#328C2×D4311yescharacteristic
513#328C2×D4311yescharacteristic
514#328C2×D4311yescharacteristic
515#328C2×D4311yescharacteristic
516#327—431no—
517#327—431no—
518#327—431no—
519#327—431no—
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—861no—
530C4⋊Q8C4×D4311yescharacteristic, complemented
531C4⋊Q8C4×D4311yescharacteristic, complemented
532#126—861no—
533#126—861no—
534#126—861no—
535#126—861no—
536#126—861no—
537#126—861no—
538#126—861no—
539#126—861no—
540#125—21no—
541#125—431no—
542#125—431no—
543#125—861no—
544#125—861no—
545#125—861no—
546#125—861no—
547#125—861no—
548#125—861no—
549#124—431no—
550#124—431no—
551#124—861no—
552#124—861no—
553#123—861no—
554#123—861no—
555#123—861no—
556#123—861no—
557#123—861no—
558#123—861no—
559#123—861no—
560C22⋊Q8—21no—
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⋊Q8C22×D4311yescharacteristic
575C22⋊Q8C22×D4311yescharacteristic
576#121—431no—
577#121—431no—
578#120—861no—
579C4×Q8—21no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—431no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×Q8—861no—
587C4×Q8C4×D4311yescharacteristic, complemented
588C4×Q8C4×D4311yescharacteristic, complemented
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
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—431no—
614C2×C4⋊C4—431no—
615C2×C4⋊C4—431no—
616C2×C4⋊C4—861no—
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—431no—
625C2×C42—861no—
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—21no—
643#95—21no—
644#95—431no—
645#95—431no—
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—21no—
655C2×Q8—431no—
656C2×Q8—861no—
657C2×Q8—861no—
658C2×Q8—1722no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×Q8C2×C4×D4311yescharacteristic
661C2×D4—431no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—861no—
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—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
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—431no—
710C4⋊C4—431no—
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—3441no—
728C4⋊C4—1722no—
729C4⋊C4C2×C4×D4311yescharacteristic
730C4⋊C4C2×C4×D4311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—431no—
734C22⋊C4—431no—
735C22⋊C4—431no—
736C22⋊C4—431no—
737C22⋊C4—431no—
738C22⋊C4—431no—
739C22⋊C4—431no—
740C22⋊C4—431no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
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—21no—
757C42—431no—
758C42—431no—
759C42—431no—
760C42—431no—
761C42—861no—
762C42—861no—
763C42—861no—
764C42—861no—
765C42—861no—
766C42—3441no—
767C42—1722no—
768C42C2×C4×D4311yescharacteristic
769C42C2×C4×D4311yescharacteristic
770C42D4×D4311yescharacteristic
771C42D4×D4311yescharacteristic
772C23—431no—
773C23—431no—
774C23—862no—
775C23—861no—
776C23—861no—
777C23—861no—
778C23—1721no—
779C23C2×D4×D4311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—81no—
783Q8—3441no—
784Q8—1721no—
785Q8—1722no—
786D4—3441no—
787D4—1721no—
788D4—1722no—
789D4—1721no—
790D4—1721no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
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—41no—
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—862no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—3441no—
820C2×C4—3441no—
821C2×C4—3441no—
822C2×C4—3444no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1722no—
826C2×C4—1722no—
827C2×C4—1721no—
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—432no—
847C22—861no—
848C22—861no—
849C22—861no—
850C22—861no—
851C22—861no—
852C22—1722no—
853C22—1722no—
854C22—1721no—
855C22—1721no—
856C22—1721no—
857C22C2×C22⋊C4×D4311yescharacteristic
858C22#1458370811yescharacteristic
859C22#1458371511yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—81no—
871C4—81no—
872C4—861no—
873C4—861no—
874C4—861no—
875C4—861no—
876C4—861no—
877C4—861no—
878C4—3441no—
879C4—1722no—
880C4—1721no—
881C4—1721no—
882C4—1721no—
883C2—21no—
884C2—21no—
885C2—862no—
886C2—3441no—
887C2—1721no—
888C2#410×D4311yescharacteristic
889C2#1914312711yescharacteristic
890C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1515C2
socleC22×C43C22×C22⋊C4
prime radical#14583412C22
cosocleC22×C4×C43C24
hypercenter#1515D43
hypocenterC43#17609
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19137452C2semidirect
4. #19133170C2semidirect
5. #19133157C2semidirect
7. #19133132C2semidirect
8. #19133126C2semidirect
9. #19133121C2semidirect
10. #19133105C2semidirect
12. #19133094C2semidirect
13. #19133080C2semidirect
14. #328×D43C2semidirect
15. C43×#1515C2semidirect
24. #14583526C4semidirect
25. #14583523C4semidirect
26. #14583521C4semidirect
27. #14583510C4semidirect
28. #14583507C4semidirect
29. #14583474C4semidirect
35. #14583381C4semidirect
36. #14583375C4semidirect
81. #13063324C2×C4semidirect
83. #13063323C2×C4semidirect
93. #13063317C2×C4semidirect
94. #13063316C2×C4semidirect
101. #13063314C2×C4semidirect
103. #13063313C2×C4semidirect
127. Q8×Dic43C2×C4semidirect
128. Q8×Dic43C2×C4semidirect
130. C4×Dic86C2×C4semidirect
133. #13063290C2×C4semidirect
135. C4×D172C2×C4semidirect
138. #13063287C2×C4semidirect
187. C4⋊Q8×C43C2×C4semidirect
188. C4⋊Q8×C43C2×C4semidirect
194. C4×Q8×C43C2×C4semidirect
195. C4×Q8×C43C2×C4semidirect
444. #1515D43semidirect
520. C43#17609semidirect
530. C4⋊Q8C4×D43semidirect
531. C4⋊Q8C4×D43semidirect
587. C4×Q8C4×D43semidirect
588. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191483422
#191432542
#191374522
#191331702
#191331572
#191331502
#191331322
#191331262
#191331212
#191331052
#191330982
#191330942
#191330802
#328×D432
C43×#15152
#1760943