Finite Group Databasebeta

← #11889088

Subgroups — #11889088

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#626C211yesmaximal, characteristic
2#10594584C211yesmaximal, characteristic, complemented
3#10592475C211yesmaximal, characteristic, complemented
4C3×#4770C211yesmaximal, characteristic, complemented
5C3×#4766C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591416C211yesmaximal, characteristic, complemented
8#10591405C211yesmaximal, characteristic, complemented
9#10590879C211yesmaximal, characteristic, complemented
10#10590838C211yesmaximal, characteristic, complemented
11#10590738C211yesmaximal, characteristic, complemented
12#10590650C211yesmaximal, characteristic, complemented
13#10590550C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#81189—31nomaximal
17#78934—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#626—21no—
21C2×#3754C2211yescharacteristic
22C2×#3744C2211yescharacteristic, complemented
23#64106C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C3×#892C2211yescharacteristic, complemented
27C3×#890C2211yescharacteristic, complemented
28#63981—21no—
29#63978—21no—
30#63977—21no—
31#63916C2211yescharacteristic
32#63911C2211yescharacteristic
33#63909C2211yescharacteristic
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic, complemented
36#63869—21no—
37#63861—21no—
38#63857C2211yescharacteristic, complemented
39#63854—21no—
40#63844C2211yescharacteristic, complemented
41#63836—21no—
42C2×#3716C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61D4×#67—31no—
62#5694—31no—
63D4×D12—31no—
64#5529—31no—
65C3×#478—31no—
66C3×#418—31no—
67#5218—31no—
68#5134—31no—
69#5127—31no—
70#5067—31no—
71#5018—31no—
72#5003—31no—
73#4886—31no—
74#4882—31no—
75#4866—31no—
76#4864—31no—
77#4848—31no—
78#4836—31no—
79#4778—31no—
80#4776—31no—
81#4776—31no—
82#4776—31no—
83#4776—61no—
84#4774—31no—
85#4770D311yescharacteristic, complemented
86D3×#102—31no—
87D3×#102—31no—
88#4766D311yescharacteristic, complemented
89#4764—31no—
90#4762—31no—
91#4757—31no—
92C23×C3⋊D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—44no—
112C2×#626D411yescharacteristic
113C2×#624—21no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3754—22no—
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3744—41no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716—41no—
144#3710—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C22×D12—61no—
153C2×C3×M16—31no—
154C3×#125—31no—
155C3×C4×D4—31no—
156C3×#117—31no—
157#953—61no—
158#940—31no—
159#939—61no—
160#938—31no—
161#937—61no—
162D4×Dic3C2×D311yescharacteristic
163C2×#214—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—61no—
167#930—31no—
168#930—61no—
169C4×#67—31no—
170#924—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—61no—
175C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#898—61no—
179#897—31no—
180#897—31no—
181#897—31no—
182#897—61no—
183#895—31no—
184#895—31no—
185#894—61no—
186#892—61no—
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190#890—61no—
191#890C2×D311yescharacteristic, complemented
192#887—31no—
193#883—61no—
194#882—61no—
195#882—61no—
196#879—61no—
197#874—31no—
198C4×D12—31no—
199#872—61no—
200#870—61no—
201C4×Dic6—31no—
202C3×#107—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic
211C3×#102C2×D311yescharacteristic
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic, complemented
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223#818C2×D311yescharacteristic, complemented
224#816—31no—
225#815—31no—
226Dic3⋊C8C2×D311yescharacteristic, complemented
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic, complemented
235#808C2×D311yescharacteristic, complemented
236#807—31no—
237#807—31no—
238#803—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275#626—22no—
276#626—42no—
277#626—42no—
278#626—42no—
279#626—81no—
280#624—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—31no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—31no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—121no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323C2×#67—124no—
324C22×Dic3—21no—
325D3×D4—22no—
326D3×D4—41no—
327D3×D4—62no—
328D3×D4—62no—
329D3×D4—122no—
330D3×D4—121no—
331D3×D4—121no—
332D3×D4—122no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—124no—
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—61no—
352C3×M16—121no—
353C2×C3×C8—21no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369C3×C42—61no—
370#217—21no—
371#217—31no—
372#217—61no—
373#217—61no—
374#214—62no—
375#214—62no—
376#214—122no—
377#214—121no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—121no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—31no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405C4×Dic3—21no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3C22×D311yescharacteristic
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—121no—
415#204—121no—
416#204—122no—
417#204—121no—
418ΓL(1,𝔽25)—41no—
419D3×C8—121no—
420D3×C8—121no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—84no—
431C2×C3⋊D3AGL(1,ℤ/8)12yes—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—84no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—31no—
457C22×C8—91no—
458#127—91no—
459#126—181no—
460#125—31no—
461#125—181no—
462#123—181no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465#121—91no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—31no—
472C4×D4—91no—
473#117—31no—
474#117—181no—
475C2×C4⋊C4—91no—
476#107—31no—
477#107—91no—
478#106—31no—
479C4⋊C8—31no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102D3211yescharacteristic
490C22⋊C8—91no—
491C22⋊C8—91no—
492#97—91no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—41no—
497C23×C3—61no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—241no—
501C22×D3—21no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—81no—
510C22×D3—121no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—124no—
516C22×D3—242no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—242no—
520C22×D3D3×D411yescharacteristic
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—22no—
524C3×D4—41no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—122no—
528C3×D4#23512yes—
529C3×D4#23912yes—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—42no—
546#67—62no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—124no—
553#67—241no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—42no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567D12—21no—
568D12—21no—
569D12—62no—
570D12—62no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—121no—
576D12—122no—
577D12—122no—
578D12—122no—
579D12—241no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—121no—
587C4×D3—121no—
588C4×D3—122no—
589C4×D3—122no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—121no—
595Dic6—121no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—41no—
599C3×C8—61no—
600C3×C8—61no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C3⋊C8—61no—
604C3⋊C8—61no—
605C3⋊C8—121no—
606C2×C32—42no—
607C2×C32#54611yescharacteristic
608C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
609C2×C32#57711yescharacteristic
610C3⋊D3—22no—
611C3⋊D3—81no—
612C3×D3—41no—
613C3×D3—81no—
614C24—61no—
615C24—181no—
616C2×Q8—91no—
617C2×D4—31no—
618C2×D4—61no—
619C2×D4—62no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—121no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4—182no—
629C2×D4—364no—
630C2×D4—361no—
631C2×D4C2×D3211yescharacteristic
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—91no—
635C22×C4—181no—
636SD16—182no—
637SD16—361no—
638SD16—361no—
639M16—121no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—361no—
644C2×C8C2×D3211yescharacteristic
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—61no—
666C42—181no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—21no—
670C22×C3—42no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3C2×D3×D411yescharacteristic
685C22×C3C2×D3×D411yescharacteristic
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—32no—
690C2×D3—32no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—62no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—84no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—122no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—241no—
710C2×D3—241no—
711C2×D3—244no—
712C2×D3—244no—
713C2×D3—248no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—81no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4C2×#23511yescharacteristic
726C3×C4#100411yescharacteristic
727C3×C4C2×#23911yescharacteristic
728C3×C4#100911yescharacteristic
729Dic3—21no—
730Dic3—21no—
731Dic3—21no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—61no—
736Dic3—61no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741C32#331011yescharacteristic, complemented, Sylow
742C23—21no—
743C23—31no—
744C23—61no—
745C23—91no—
746C23—122no—
747C23—122no—
748C23—181no—
749C23—241no—
750C23—362no—
751C23—362no—
752C23—721no—
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—61no—
757D4—61no—
758D4—122no—
759D4—182no—
760D4—181no—
761D4—181no—
762D4—362no—
763D4—362no—
764D4—362no—
765D4—362no—
766D4—721no—
767D4#379912yes—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—91no—
778C2×C4—122no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—362no—
783C2×C4C22×D3211yescharacteristic
784C8—21no—
785C8—61no—
786C8—61no—
787C8—181no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—42no—
793C2×C3—82no—
794C2×C3—121no—
795C2×C3—241no—
796C2×C3#549011yescharacteristic
797C2×C3#563011yescharacteristic
798C2×C3#577011yescharacteristic
799C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
800C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
801C2×C3#577511yescharacteristic
802D3—41no—
803D3—62no—
804D3—62no—
805D3—81no—
806D3—122no—
807D3—242no—
808D3—241no—
809D3—241no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—92no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—181no—
821C22—181no—
822C22—244no—
823C22—361no—
824C22—361no—
825C22—361no—
826C22—724no—
827C22D32×D411yescharacteristic
828C4—41no—
829C4—61no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—181no—
836C4—361no—
837C4C2×#379911yescharacteristic
838C4#6431411yescharacteristic
839C3—21no—
840C3#7893411yescharacteristic, complemented
841C3#8118911yescharacteristic, complemented
842C2—42no—
843C2—121no—
844C2—182no—
845C2—241no—
846C2—721no—
847C2#1059418711yescharacteristic
848C2#1059473611yescharacteristic
849C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD4×#626C2
hypercenter#102D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594584C2semidirect
3. #10592475C2semidirect
4. C3×#4770C2semidirect
5. C3×#4766C2semidirect
6. #10591459C2semidirect
7. #10591416C2semidirect
8. #10591405C2semidirect
9. #10590879C2semidirect
10. #10590838C2semidirect
11. #10590738C2semidirect
12. #10590650C2semidirect
13. #10590550C2semidirect
14. #10590507C2semidirect
15. #10590425C2semidirect
22. C2×#3744C22semidirect
23. #64106C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C3×#892C22semidirect
27. C3×#890C22semidirect
35. #63900C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
42. C2×#3716C22semidirect
43. C2×#3710C22semidirect
45. #63647C22semidirect
46. #63636C22semidirect
49. C3×#821C22semidirect
50. C3×#818C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#808C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
85. #4770D3semidirect
88. #4766D3semidirect
175. C2×ΓL(1,𝔽25)C2×D3semidirect
187. #892C2×D3semidirect
191. #890C2×D3semidirect
218. #821C2×D3semidirect
223. #818C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
234. #809C2×D3semidirect
235. #808C2×D3semidirect
741. C32#3310semidirect
840. C3#78934semidirect
841. C3#81189semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
#105945842
#105924752
C3×#47702
C3×#47662
#105914592
#105914162
#105914052
#105908792
#105908382
#105907382
#105906502
#105905502
#105905072
#105904252
#811893
#789343