Finite Group Databasebeta

← #25064132

Subgroups — #25064132

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#19148646C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic, complemented
3#19137231C211yesmaximal, characteristic, complemented
4#19133172C211yesmaximal, characteristic, complemented
5#19133165C211yesmaximal, characteristic, complemented
6#19133158C211yesmaximal, characteristic, complemented
7#19133148C211yesmaximal, characteristic, complemented
8#19133147C211yesmaximal, characteristic, complemented
9#19133135C211yesmaximal, characteristic, complemented
10#19133126C211yesmaximal, characteristic, complemented
11#19133113C211yesmaximal, characteristic, complemented
12#19133096C211yesmaximal, characteristic, complemented
13#19133083C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C43×#1512C211yesmaximal, characteristic, complemented
16#14583622C411yescharacteristic, complemented
17#14583606—21no—
18#14583587C411yescharacteristic, complemented
19#14583587C411yescharacteristic, complemented
20#14583572—21no—
21#14583572—21no—
22Q8×D172C411yescharacteristic, complemented
23#14583557C411yescharacteristic, complemented
24#14583557C411yescharacteristic, complemented
25#14583554C411yescharacteristic, complemented
26#14583553C411yescharacteristic, complemented
27#14583545—21no—
28#14583520—21no—
29#14583490—21no—
30#14583490—21no—
31#14583456C2211yescharacteristic
32#14583409C2211yescharacteristic
33#14583409C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35C22⋊Q8×D43C2211yescharacteristic
36#14583379—21no—
37C2×C4×D172C2211yescharacteristic
38#14582976—21no—
39#14582972—21no—
40#14582972—21no—
41#14582964—21no—
42#14582952C2211yescharacteristic
43#14582861C2211yescharacteristic
44#14582861C2211yescharacteristic
45C22⋊C8×D43C2211yescharacteristic
46C22⋊C8×D43C2211yescharacteristic
47#14582789—21no—
48#14582784—21no—
49#14582777—21no—
50#14582770—21no—
51#14582767C2211yescharacteristic
52#14582761C2211yescharacteristic
53#14582758C2211yescharacteristic
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×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#382C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621900C2×C411yescharacteristic
77C2×#10621900C2×C411yescharacteristic, complemented
78C2×Q8×D43C2×C411yescharacteristic
79C2×Q8×D43C2×C411yescharacteristic, complemented
80C22×D172D411yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063325—21no—
89#13063325C2×C411yescharacteristic, complemented
90#13063325C2×C411yescharacteristic, complemented
91#13063320—21no—
92#13063320—21no—
93#13063320—21no—
94#13063320—21no—
95#13063317—21no—
96#13063316—21no—
97#13063316—21no—
98#13063313—21no—
99#13063311—21no—
100#13063311—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063309—21no—
105#13063307—21no—
106#13063307—21no—
107#13063307—21no—
108#13063307—21no—
109#13063305—21no—
110#13063305—21no—
111#13063305C2×C411yescharacteristic
112#13063305C2×C411yescharacteristic
113#13063305C2×C411yescharacteristic, complemented
114#13063305C2×C411yescharacteristic, complemented
115#13063304—21no—
116#13063304—21no—
117#13063304C2311yescharacteristic
118#13063304C2311yescharacteristic
119#13063303—21no—
120#13063303—21no—
121#13063302—21no—
122#13063302—21no—
123#13063302—21no—
124#13063302—21no—
125#13063301C2×C411yescharacteristic
126#13063301C2×C411yescharacteristic, complemented
127#13063299—21no—
128#13063298—21no—
129#13063298—21no—
130#13063296C2×C411yescharacteristic
131#13063296C2×C411yescharacteristic, complemented
132#13063293—21no—
133#13063293—21no—
134C4×Dic86—21no—
135C4×Dic86—21no—
136C4×Dic86C2×C411yescharacteristic, complemented
137C4×Dic86C2×C411yescharacteristic, complemented
138C4×D172—21no—
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141C4×D172C2×C411yescharacteristic
142C4×D172C2×C411yescharacteristic
143C4×D172D411yescharacteristic
144C4×D172D411yescharacteristic
145C4×D172D411yescharacteristic
146C4×D172D411yescharacteristic
147D4×Dic43—21no—
148D4×Dic43—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063284—21no—
154#13063283—21no—
155#13063283—21no—
156#13063283C2×C411yescharacteristic
157#13063283C2×C411yescharacteristic, complemented
158C2×C4⋊Dic43—21no—
159C2×C4⋊Dic43D411yescharacteristic
160C2×Dic43⋊C4—21no—
161C4⋊C4×D43—21no—
162C4⋊C4×D43—21no—
163C4⋊C4×D43C2×C411yescharacteristic
164C4⋊C4×D43C2×C411yescharacteristic, complemented
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4D411yescharacteristic
169C2×(C2×D43)⋊C4D411yescharacteristic
170C22⋊C4×D43—21no—
171C22⋊C4×D43—21no—
172C2×C4×Dic43—21no—
173C4⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180C4×C43⋊C8—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×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#97×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43C2×D411yescharacteristic
207C23×D43C2×D411yescharacteristic
208C2×Q8×C43C22×C411yescharacteristic
209C2×D4×C43—21no—
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227Q8×D43—81no—
228Q8×D43—81no—
229#10621900—81no—
230#10621900—81no—
231#10621898—44no—
232C2×D172—42no—
233C2×D172C22⋊C411yescharacteristic
234C2×D172C22⋊C411yescharacteristic
235C2×D172C22⋊C411yescharacteristic
236C2×D172C22⋊C411yescharacteristic
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—42no—
242C2×C4×D43—81no—
243C2×C4×D43—81no—
244C2×C4×D43—81no—
245C2×C4×D43—81no—
246C2×C4×D43C22×C411yescharacteristic
247C2×C4×D43C22×C411yescharacteristic
248C2×C4×D43C22×C411yescharacteristic
249C2×C4×D43C22×C411yescharacteristic
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×C4×D43C2×D411yescharacteristic
254C2×Dic86—21no—
255C2×Dic86—21no—
256C2×Dic86—21no—
257C2×Dic86C22×C411yescharacteristic
258C2×Dic86C22×C411yescharacteristic
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—81no—
266C4⋊C4×C43C22×C411yescharacteristic
267C4⋊C4×C43C22×C411yescharacteristic
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C42×C43—21no—
274C42×C43C22×C411yescharacteristic
275C42×C43C22×C411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—42no—
291(C2×D43)⋊C4—81no—
292(C2×D43)⋊C4—81no—
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43C22⋊C411yescharacteristic
309C4⋊Dic43C22⋊C411yescharacteristic
310C4⋊Dic43C22⋊C411yescharacteristic
311C4⋊Dic43C22⋊C411yescharacteristic
312C4⋊Dic43C22×C411yescharacteristic
313C4⋊Dic43C22×C411yescharacteristic
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—81no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—81no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330#10621872—81no—
331#10621872—81no—
332C8×D43—81no—
333C8×D43—81no—
334C23×C43—21no—
335C23×C43C22×D411yescharacteristic
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—22no—
341C22×D43—41no—
342C22×D43—41no—
343C22×D43—41no—
344C22×D43C2×C22⋊C411yescharacteristic
345C22×D43C2×C22⋊C411yescharacteristic
346C22×D43C2×C22⋊C411yescharacteristic
347C22×D43C2×C22⋊C411yescharacteristic
348Q8×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—41no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—42no—
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×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C23×C411yescharacteristic
371C2×C4×C43C22×D411yescharacteristic
372C22⋊D43—42no—
373C22⋊D43—42no—
374C22⋊D43—81no—
375C22⋊D43—81no—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—81no—
389C2×Dic43—81no—
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394D172—22no—
395D172—22no—
396D172—41no—
397D172—41no—
398C4×D43—41no—
399C4×D43—41no—
400C4×D43—41no—
401C4×D43—41no—
402C4×D43—41no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—41no—
406C4×D43—42no—
407C4×D43—42no—
408C4×D43—81no—
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—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43C22×C22⋊C411yescharacteristic
427C22×C43#57711yescharacteristic
428C22×C43#57811yescharacteristic
429C2×D43—21no—
430C2×D43—21no—
431C2×D43—21no—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—21no—
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—81no—
443C2×D43—81no—
444C2×D43#42112yes—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—41no—
452C4×C43—41no—
453C4×C43—41no—
454C4×C43—81no—
455C4×C43—81no—
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#1513—431no—
475#1512D4311yescharacteristic, complemented
476#1511—431no—
477#1508—431no—
478#1504—431no—
479#1501—431no—
480C2×#328—431no—
481C2×C43—21no—
482C2×C43—21no—
483C2×C43—81no—
484C2×C43#288311yescharacteristic
485C2×C43#289811yescharacteristic
486C2×C43C2×#42111yescharacteristic
487D43—22no—
488D43—41no—
489D43—41no—
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#529C2×D4311yescharacteristic
508#525—431no—
509#525—431no—
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#432C2×D4311yescharacteristic
519#431—431no—
520#407—431no—
521#407—431no—
522C2×C22⋊C8—431no—
523C2×C22⋊C8—431no—
524#388—861no—
525#387—861no—
526#386—861no—
527#385—861no—
528#383—431no—
529#382C2×D4311yescharacteristic
530#381—431no—
531#380—431no—
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—431no—
553C2×#41—861no—
554C22×Q8—431no—
555C22×Q8—431no—
556C22×D4—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—861no—
560C2×M16—861no—
561C2×M16—861no—
562C22×C8—861no—
563C22×C8—861no—
564C4⋊Q8—431no—
565C4⋊Q8—431no—
566C4⋊Q8—861no—
567#126—21no—
568#126—861no—
569#126—861no—
570#126—861no—
571#126—861no—
572#125—861no—
573#125—861no—
574#125—861no—
575#125C4×D4311yescharacteristic, complemented
576#124—861no—
577#124—861no—
578#124—861no—
579#124C4×D4311yescharacteristic, complemented
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—431no—
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⋊Q8—861no—
607C22⋊Q8C22×D4311yescharacteristic
608#121—431no—
609#121—431no—
610#121—861no—
611#121—861no—
612#121—861no—
613#121C22×D4311yescharacteristic
614#120—861no—
615#120—861no—
616C4×Q8—431no—
617C4×Q8—431no—
618C4×Q8—861no—
619C4×Q8—861no—
620C4×Q8C4×D4311yescharacteristic, complemented
621C4×D4—21no—
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—
636C4×D4—861no—
637C4×D4C4×D4311yescharacteristic, complemented
638#117—21no—
639#117—431no—
640#117—431no—
641#117—861no—
642#117—861no—
643#117—861no—
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—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—861no—
660C2×C42C22×D4311yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—861no—
663C22⋊C8—431no—
664C22⋊C8—431no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669C22⋊C8C22×D4311yescharacteristic
670C22⋊C8C22×D4311yescharacteristic
671#97—21no—
672C4×C8—861no—
673#95—21no—
674#95—431no—
675#95—431no—
676#95—861no—
677#95—861no—
678#95—861no—
679#95—861no—
680#95C22×D4311yescharacteristic
681#95C22×D4311yescharacteristic
682C24—431no—
683C24—431no—
684#41—3441no—
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—431no—
697C2×D4—431no—
698C2×D4—431no—
699C2×D4—431no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—1722no—
705C2×D4C2×C4×D4311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—3441no—
728C22×C4—3441no—
729C22×C4—3441no—
730C22×C4—3441no—
731C22×C4—1722no—
732C22×C4D4×D4311yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—3441no—
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—21no—
746C4⋊C4—21no—
747C4⋊C4—81no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—431no—
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—431no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—431no—
784C22⋊C4—431no—
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—861no—
796C22⋊C4—861no—
797C22⋊C4—3441no—
798C22⋊C4—3441no—
799C22⋊C4—1722no—
800C42—21no—
801C42—861no—
802C42—861no—
803C42—861no—
804C42—861no—
805C42—3441no—
806C42C2×C4×D4311yescharacteristic
807C42C2×C4×D4311yescharacteristic
808C42D4×D4311yescharacteristic
809C42D4×D4311yescharacteristic
810C23—21no—
811C23—431no—
812C23—431no—
813C23—431no—
814C23—431no—
815C23—862no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
820C23—1721no—
821C23—1721no—
822C23—1721no—
823C23C2×D4×D4311yescharacteristic
824Q8—41no—
825Q8—3441no—
826Q8—3441no—
827Q8—1721no—
828Q8—1721no—
829Q8—1722no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—862no—
834D4—862no—
835D4—3441no—
836D4—3441no—
837D4—1721no—
838D4—1721no—
839D4—1722no—
840D4—1722no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—431no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—3441no—
864C2×C4—3441no—
865C2×C4—3444no—
866C2×C4—3441no—
867C2×C4—3441no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
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—1721no—
886C2×C4C22⋊C4×D4311yescharacteristic
887C2×C4C22⋊C4×D4311yescharacteristic
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—41no—
899C22—41no—
900C22—41no—
901C22—432no—
902C22—861no—
903C22—861no—
904C22—861no—
905C22—861no—
906C22—861no—
907C22—861no—
908C22—861no—
909C22—861no—
910C22—861no—
911C22—861no—
912C22—861no—
913C22—3441no—
914C22—3441no—
915C22—1722no—
916C22—1722no—
917C22C2×C22⋊C4×D4311yescharacteristic
918C22#1458370911yescharacteristic
919C22#1458371511yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—81no—
930C4—81no—
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—81no—
944C2—862no—
945C2—1721no—
946C2—1721no—
947C2—1721no—
948C2#1914305411yescharacteristic
949C2#1914312611yescharacteristic
950C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1512C2
socleC22×C43C22×C22⋊C4
prime radical#19148646C2
cosocleC22×C4×C43C24
hypercenter#1512D43
hypocenterC43#17598
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #19143632C2semidirect
3. #19137231C2semidirect
4. #19133172C2semidirect
5. #19133165C2semidirect
6. #19133158C2semidirect
7. #19133148C2semidirect
8. #19133147C2semidirect
9. #19133135C2semidirect
10. #19133126C2semidirect
11. #19133113C2semidirect
12. #19133096C2semidirect
13. #19133083C2semidirect
14. #328×D43C2semidirect
15. C43×#1512C2semidirect
16. #14583622C4semidirect
18. #14583587C4semidirect
19. #14583587C4semidirect
22. Q8×D172C4semidirect
23. #14583557C4semidirect
24. #14583557C4semidirect
25. #14583554C4semidirect
26. #14583553C4semidirect
77. C2×#10621900C2×C4semidirect
79. C2×Q8×D43C2×C4semidirect
89. #13063325C2×C4semidirect
90. #13063325C2×C4semidirect
113. #13063305C2×C4semidirect
114. #13063305C2×C4semidirect
126. #13063301C2×C4semidirect
131. #13063296C2×C4semidirect
136. C4×Dic86C2×C4semidirect
137. C4×Dic86C2×C4semidirect
157. #13063283C2×C4semidirect
164. C4⋊C4×D43C2×C4semidirect
188. #125×C43C2×C4semidirect
189. #124×C43C2×C4semidirect
193. C4×Q8×C43C2×C4semidirect
195. C4×D4×C43C2×C4semidirect
475. #1512D43semidirect
550. C43#17598semidirect
575. #125C4×D43semidirect
579. #124C4×D43semidirect
620. C4×Q8C4×D43semidirect
637. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486462
#191436322
#191372312
#191331722
#191331652
#191331582
#191331482
#191331472
#191331352
#191331262
#191331132
#191330962
#191330832
#328×D432
C43×#15122
#1759843