Finite Group Databasebeta

← #11884317

Subgroups — #11884317

Order 1152.

1062 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
1C2×#63810C211yesmaximal, characteristic, complemented
2C2×#63798C211yesmaximal, characteristic, complemented
3#10594005C211yesmaximal, characteristic, complemented
4#10593896C211yesmaximal, characteristic, complemented
5#10592405C211yesmaximal, characteristic, complemented
6C3×#4715C211yesmaximal, characteristic, complemented
7C3×#4711C211yesmaximal, characteristic, complemented
8#10590965C211yesmaximal, characteristic, complemented
9#10590965C211yesmaximal, characteristic, complemented
10#10590964C211yesmaximal, characteristic, complemented
11#10590943C211yesmaximal, characteristic, complemented
12#10590858C211yesmaximal, characteristic, complemented
13#10590843C211yesmaximal, characteristic, complemented
14#10590363C211yesmaximal, characteristic, complemented
15#10590348C211yesmaximal, characteristic, complemented
16#81882—31nomaximal
17#79879—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×#3743C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×Dic12C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C3×#875C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×#869C2211yescharacteristic, complemented
34#63923—21no—
35D3×(C2×D3)⋊C4—21no—
36#63916C2211yescharacteristic
37#63909—21no—
38#63906—21no—
39#63891—21no—
40#63890—21no—
41#63890—21no—
42D3×C4⋊Dic3—21no—
43#63871C2211yescharacteristic
44#63871C2211yescharacteristic
45#63871C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50#63810—24no—
51#63798—24no—
52C32×#97C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×#817C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63C2×#919—31no—
64C2×#914—31no—
65C2×#912—31no—
66C2×#911—31no—
67#5726—31no—
68#5676—31no—
69#5555—31no—
70#5554—31no—
71C3×#497—31no—
72C3×#442—31no—
73#5189—31no—
74#5187—31no—
75#5187—31no—
76#5172—31no—
77#5171—31no—
78#5169—31no—
79#5083—31no—
80#5057—31no—
81#5019—31no—
82#5016—31no—
83#4867—31no—
84#4864—31no—
85#4783—31no—
86#4783—31no—
87#4781—31no—
88#4776—31no—
89#4715D311yescharacteristic, complemented
90#4711D311yescharacteristic, complemented
91#4706—31no—
92#4706—31no—
93#4706—61no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116#3796—22no—
117#3796—22no—
118#3796—22no—
119#3796—41no—
120#3796—41no—
121#3796—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124C32×C42C2311yescharacteristic
125#3752D411yescharacteristic
126#3752D411yescharacteristic
127C4⋊(C3⋊Dic3)D411yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3743—22no—
131C8×C3⋊D3—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic12—22no—
141C3×Dic12—41no—
142C3×D24D414yescomplemented
143C3×#204—22no—
144C3×#204—41no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149#3722—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3715—22no—
153#3715—22no—
154#3715—22no—
155#3713—22no—
156#3267—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C3×C4⋊Q8—31no—
171C3×#124—31no—
172C3×C4×D4—31no—
173C3×C4×D4—31no—
174#946—31no—
175#946—31no—
176#946—31no—
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180#938—31no—
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#213—31no—
185C2×#213—31no—
186#930—61no—
187#930—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×C4⋊Dic3—61no—
190#919—64no—
191#914—64no—
192#912—64no—
193#911—64no—
194C2×Dic12C2×D311yescharacteristic, complemented
195C2×Dic12C2×D311yescharacteristic, complemented
196C2×D24C2×D311yescharacteristic
197C2×#204C2×D311yescharacteristic
198C2×#204C2×D311yescharacteristic
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—61no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204C2×D3×C8—61no—
205#897—31no—
206#897—31no—
207#897—31no—
208#895—31no—
209#895—61no—
210#894—61no—
211#894—61no—
212D3×C4⋊C4—61no—
213#886—61no—
214#886—61no—
215#886—61no—
216#884—61no—
217#883—61no—
218#882—61no—
219#882—61no—
220D3×C22⋊C4—61no—
221#875C2×D311yescharacteristic
222C4×D12—31no—
223C4×D12—31no—
224C4×D12—61no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic, complemented
227#869C2×D311yescharacteristic, complemented
228C3×#106—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#97—21no—
232C3×#97C2×D311yescharacteristic, complemented
233C3×#97C2×D311yescharacteristic, complemented
234#835—31no—
235#835—31no—
236#835—31no—
237#832—31no—
238#821C2×D311yescharacteristic
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—61no—
245(C2×D3)⋊C8—61no—
246#817C2×D311yescharacteristic, complemented
247#810—31no—
248#810—31no—
249#810—31no—
250#809—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—31no—
253C4⋊(C3⋊C8)—61no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—41no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12C2×D412yes—
282C3×D12C2×D412yes—
283C3×C4×D3—42no—
284C3×C4×D3—81no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#626—81no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3⋊(C3⋊C8)—21no—
302C3⋊(C3⋊C8)—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—31no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—31no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337#239—62no—
338#239—62no—
339#239—62no—
340#239—121no—
341#239—121no—
342#239—121no—
343#237—62no—
344#237—62no—
345#237—62no—
346#237—121no—
347#237—121no—
348#237—121no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—121no—
352D3×D4—121no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×Dic6C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×Q16—62no—
378C3×Q16—121no—
379C3×SD16—62no—
380C3×SD16—121no—
381C3×D8—34no—
382C2×C3×C8—21no—
383C2×C3×C8—21no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—21no—
397C3×C42C22×D311yescharacteristic
398C3×C42C22×D311yescharacteristic
399#217—61no—
400#215—62no—
401#215—62no—
402#215—62no—
403#214—62no—
404#214—62no—
405#214—62no—
406#213—62no—
407#213—62no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3C22×D311yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—61no—
444Dic12—22no—
445Dic12—41no—
446D24D1214yescomplemented
447#204—22no—
448#204—41no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—62no—
451ΓL(1,𝔽25)—122no—
452D3×C8—62no—
453D3×C8—62no—
454D3×C8—122no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—91no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—31no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—31no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97D3211yescharacteristic, complemented
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—241no—
545C22×D3—241no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×D4—32no—
553C3×D4—32no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—122no—
567C2×C3×C4—241no—
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579#67—241no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—122no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—121no—
599D12—121no—
600D12—122no—
601D12—122no—
602D12—122no—
603D12—122no—
604D12—241no—
605D12C2×D1212yes—
606D12C2×D1212yes—
607C4×D3—42no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—81no—
617C4×D3—121no—
618C4×D3—121no—
619C4×D3—121no—
620C4×D3—121no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—22no—
633C3×C8—41no—
634C3×C8C2×D1212yes—
635C3×C8D3×D412yes—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8—121no—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—41no—
646C3⋊D3—41no—
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—182no—
652#41—182no—
653#41—182no—
654#41—361no—
655#41—361no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—182no—
670C2×D4—361no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—62no—
679Q16—121no—
680SD16—62no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685D8—34no—
686D8—182no—
687M16—182no—
688C2×C8—91no—
689C2×C8—91no—
690C2×C8—182no—
691C2×C8C2×D3211yescharacteristic
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—91no—
706C22⋊C4—91no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42C2×D3211yescharacteristic
712C22×C3—21no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—62no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4C22×D1211yescharacteristic
767C3×C4C2×D3×D411yescharacteristic
768C3×C4#100411yescharacteristic
769C3×C4#100911yescharacteristic
770Dic3—41no—
771Dic3—41no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—61no—
783C23—61no—
784C23—61no—
785C23—91no—
786C23—91no—
787C23—362no—
788C23—362no—
789C23—721no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—32no—
797D4—32no—
798D4—61no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—361no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—122no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—241no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4#380211yescharacteristic
825C2×C4#380211yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—21no—
828C8—181no—
829C8—181no—
830C8D3×D1212yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—122no—
835C2×C3—122no—
836C2×C3—241no—
837C2×C3D4×D1211yescharacteristic
838C2×C3#571711yescharacteristic
839C2×C3#577311yescharacteristic
840C2×C3#577511yescharacteristic
841C2×C3#577711yescharacteristic
842C2×C3#577811yescharacteristic
843D3—42no—
844D3—42no—
845D3—81no—
846D3—122no—
847D3—121no—
848D3—121no—
849D3—121no—
850D3—121no—
851D3—241no—
852C22—62no—
853C22—62no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—724no—
868C22C2×#380211yescharacteristic
869C4—21no—
870C4—21no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—181no—
878C4C2×D3×D1211yescharacteristic
879C4#6430711yescharacteristic
880C3—21no—
881C3#7987911yescharacteristic, complemented
882C3#8188211yescharacteristic, complemented
883C2—122no—
884C2—122no—
885C2—241no—
886C2—361no—
887C2—361no—
888C2#1059400411yescharacteristic
889C2#1059471811yescharacteristic
890C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63810C2semidirect
2. C2×#63798C2semidirect
3. #10594005C2semidirect
4. #10593896C2semidirect
5. #10592405C2semidirect
6. C3×#4715C2semidirect
7. C3×#4711C2semidirect
8. #10590965C2semidirect
9. #10590965C2semidirect
10. #10590964C2semidirect
11. #10590943C2semidirect
12. #10590858C2semidirect
13. #10590843C2semidirect
14. #10590363C2semidirect
15. #10590348C2semidirect
21. C2×#3796C22semidirect
23. C2×C8×C3⋊D3C22semidirect
25. C2×C3×Dic12C22semidirect
26. C2×C3×Dic12C22semidirect
32. C3×C4×D12C22semidirect
33. C3×#869C22semidirect
45. #63871C22semidirect
48. C2×#3715C22semidirect
52. C32×#97C22semidirect
54. #63647C22semidirect
55. C4⋊(C3⋊(C3⋊C8))C22semidirect
57. C3×#821C22semidirect
58. C3×#817C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
61. #63565C22semidirect
89. #4715D3semidirect
90. #4711D3semidirect
142. C3×D24D4semidirect
194. C2×Dic12C2×D3semidirect
195. C2×Dic12C2×D3semidirect
226. C4×D12C2×D3semidirect
227. #869C2×D3semidirect
232. C3×#97C2×D3semidirect
233. C3×#97C2×D3semidirect
239. #821C2×D3semidirect
246. #817C2×D3semidirect
446. D24D12semidirect
527. #97D32semidirect
781. C32#3267semidirect
881. C3#79879semidirect
882. C3#81882semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
C2×#637982
#105940052
#105938962
#105924052
C3×#47152
C3×#47112
#105909652
#105909642
#105909432
#105908582
#105908432
#105903632
#105903482
#818823
#798793