Finite Group Databasebeta

← #11864642

Subgroups — #11864642

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1039 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594528C211yesmaximal, characteristic, complemented
5#10592502C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591586C211yesmaximal, characteristic, complemented
10#10590959C211yesmaximal, characteristic, complemented
11#10590944C211yesmaximal, characteristic, complemented
12#10590942C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15#10590593C211yesmaximal, characteristic, complemented
16#80231—31nomaximal
17#80087—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64320—24no—
22#64320—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×D3×D12—21no—
26C2×D3×D12—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3798—21no—
30C2×#3798C2211yescharacteristic
31C2×#3796C2211yescharacteristic, complemented
32C2×#3743C2211yescharacteristic, complemented
33C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
34C2×C3×#216C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40#63950—24no—
41#63916—21no—
42#63912—21no—
43#63908C2211yescharacteristic, complemented
44#63899—21no—
45#63885—21no—
46#63856C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52#63798—24no—
53C32×#103C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67C2×#919—31no—
68C2×#916—31no—
69C2×#914—31no—
70C2×#911—31no—
71#5629—31no—
72#5608—31no—
73C3×#452—31no—
74C3×#449—31no—
75#5239—31no—
76#5238—31no—
77#5187—31no—
78#5172—31no—
79#5169—31no—
80#5156—31no—
81#5046—31no—
82#5036—31no—
83#4810D311yescharacteristic, complemented
84#4808D311yescharacteristic, complemented
85#4803—31no—
86#4803—31no—
87#4803—61no—
88#4776—31no—
89#4773—31no—
90D3×#102—31no—
91D3×#102—31no—
92#4732—31no—
93#4731—31no—
94#4727—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832D414yescomplemented
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627D411yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626D411yescharacteristic
127C2×#626D411yescharacteristic
128C2×#625—21no—
129C2×#625—21no—
130C2×#625D411yescharacteristic
131C2×D3×Dic3—21no—
132#3802—28no—
133#3802—22no—
134#3802D414yescomplemented
135D3×D12—28no—
136D3×D12—28no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—22no—
141#3798—28no—
142#3798—22no—
143#3798—22no—
144#3796—22no—
145#3796—22no—
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3743—22no—
152C3×#216—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×D24—22no—
160C3×#204—22no—
161#3724—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3717—22no—
165#3715—22no—
166#3714—22no—
167#3713—22no—
168#3710—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172#1009—64no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239C2×D311yescharacteristic
181C2×#239C2×D311yescharacteristic
182C2×#237—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×D8—31no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205#946—31no—
206C2×#216C2×D311yescharacteristic, complemented
207C2×#215—31no—
208C2×#215—31no—
209C2×#215C2×D311yescharacteristic, complemented
210#939—61no—
211#938—31no—
212#938—61no—
213C2×#214—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930—31no—
218#924—31no—
219#919—64no—
220#916—64no—
221#914—64no—
222#911—64no—
223C2×D24—31no—
224C2×D24C2×D311yescharacteristic, complemented
225C2×#204—31no—
226C2×#204C2×D311yescharacteristic, complemented
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×ΓL(1,𝔽25)—61no—
230C2×D3×C8—31no—
231C2×D3×C8—31no—
232#897C2×D311yescharacteristic, complemented
233#896—61no—
234#895—61no—
235#895C2×D311yescharacteristic, complemented
236D3×C4⋊C4—31no—
237D3×C4⋊C4—31no—
238D3×C4⋊C4—61no—
239#884—61no—
240#884—61no—
241#884—61no—
242#878—61no—
243C3×#103—21no—
244C3×#103C2×D311yescharacteristic, complemented
245C3×#103C2×D311yescharacteristic, complemented
246C3×#102—31no—
247C3×#102—31no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250#835—31no—
251#835—31no—
252#835—61no—
253#832—31no—
254#832—31no—
255#830—31no—
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—31no—
261#821—61no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#809—31no—
267#809—31no—
268#809—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3C2×D411yescharacteristic
277C22×C3×D3C2×D411yescharacteristic
278C2×D32—24no—
279C2×D32—24no—
280C2×D32—24no—
281C2×D32—81no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8C2×D412yes—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4C2411yescharacteristic
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—24no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)C2×D412yes—
297C4×C3⋊D3—24no—
298C4×C3⋊D3—81no—
299C4×C3⋊D3C2×D412yes—
300C4×C3⋊D3C2×D412yes—
301C2×C3×Dic3—21no—
302C2×C3×Dic3C2×D411yescharacteristic
303C2×C3×Dic3C2×D411yescharacteristic
304C3×D12—24no—
305C3×D12—24no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—81no—
311C3×D12C2×D412yes—
312C3×D12C2×D412yes—
313C3×C4×D3—24no—
314C3×C4×D3—24no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×Dic6—21no—
320C3×Dic6—21no—
321#627—22no—
322#626—24no—
323#626—24no—
324#626—22no—
325#626—22no—
326#626—42no—
327#625—22no—
328#625—24no—
329#625—81no—
330D3×Dic3—42no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—31no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—31no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C2×C3×Q8—21no—
361C2×C3×Q8—31no—
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C22×Dic3—61no—
386#239—22no—
387#239—22no—
388#239—22no—
389#239—22no—
390#239—34no—
391#239—34no—
392#239—64no—
393#239—62no—
394#239—62no—
395#239—62no—
396#239—62no—
397#239—122no—
398#237—62no—
399#237—62no—
400D3×D4—34no—
401D3×D4—34no—
402D3×D4—62no—
403D3×D4—62no—
404D3×D4—62no—
405D3×D4—62no—
406D3×D4—68no—
407D3×D4—68no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—68no—
411D3×D4—68no—
412#235—62no—
413#235—62no—
414#235—62no—
415#235—62no—
416#235—68no—
417#235—68no—
418C2×D12—21no—
419C2×D12—21no—
420C2×D12—21no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—31no—
425C2×D12—61no—
426C2×D12—62no—
427C2×D12—62no—
428C2×D12—68no—
429C2×D12—68no—
430C2×D12—61no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—62no—
436C2×D12—61no—
437C2×D12—121no—
438C2×D12C22×D311yescharacteristic
439C2×D12C22×D311yescharacteristic
440C2×D12C22×D311yescharacteristic
441C2×C4×D3—21no—
442C2×C4×D3—21no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—121no—
452C2×C4×D3—121no—
453C2×C4×D3C22×D311yescharacteristic
454C2×C4×D3C22×D311yescharacteristic
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6C22×D311yescharacteristic
458C3×Q16—62no—
459C3×SD16—62no—
460C3×SD16—62no—
461C3×D8—62no—
462C2×C3×C8—21no—
463C2×C3×C8—31no—
464C2×C3×C8—31no—
465C2×C3×C8C22×D311yescharacteristic
466C2×C3×C8C22×D311yescharacteristic
467C3×C4⋊C4—21no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D311yescharacteristic
471C3×C22⋊C4—61no—
472C3×C22⋊C4—61no—
473#217—61no—
474#217—61no—
475#216—22no—
476#215—22no—
477#215—62no—
478#215—62no—
479#214—62no—
480#213—62no—
481#213—62no—
482#213—62no—
483(C2×D3)⋊C4—21no—
484(C2×D3)⋊C4—21no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487C4⋊Dic3—21no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—121no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8C22×D311yescharacteristic
500C2×C3⋊C8C22×D311yescharacteristic
501D24—22no—
502D24—62no—
503#204—22no—
504#204—62no—
505ΓL(1,𝔽25)—62no—
506ΓL(1,𝔽25)—62no—
507ΓL(1,𝔽25)—122no—
508D3×C8—62no—
509D3×C8—62no—
510C22×C32C22×D411yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—41no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3#12012yes—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532D32—84no—
533D32—84no—
534D32—84no—
535C32×C4—22no—
536C32×C4—41no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—41no—
540C3⋊Dic3#12012yes—
541C3×Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544H(5,𝔽2)—184no—
545H(5,𝔽2)—184no—
546C2×#41—31no—
547C2×#41—31no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—181no—
552C22×D4—91no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—181no—
556C22×D4—181no—
557C22×D4—181no—
558AGL(1,ℤ/8)—184no—
559#135—184no—
560C2×Q16—31no—
561C2×SD16—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×D8—31no—
566C2×D8—91no—
567C2×D8—91no—
568C2×M16—91no—
569C22×C8—91no—
570C22⋊Q8—31no—
571C22⋊Q8—91no—
572C22⋊Q8—181no—
573#121—31no—
574#121—91no—
575#121—181no—
576#121—181no—
577#121—181no—
578C2×C4⋊C4—91no—
579#103—91no—
580#103D3211yescharacteristic, complemented
581#102—31no—
582#102—31no—
583#102—91no—
584#102—91no—
585#102—91no—
586#102—91no—
587C22⋊C8—31no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—61no—
602C22×D3—64no—
603C22×D3—64no—
604C22×D3—64no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—121no—
611C22×D3—241no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3D3×D411yescharacteristic
624C22×D3D3×D411yescharacteristic
625C3×Q8—21no—
626C3×Q8—21no—
627C3×Q8—22no—
628C3×Q8—41no—
629C3×Q8—61no—
630C3×Q8—61no—
631C3×Q8D3×D412yes—
632C3×Q8D3×D412yes—
633C3×D4—32no—
634C3×D4—32no—
635C3×D4—64no—
636C3×D4—64no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—241no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—64no—
652C2×C3×C4—64no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660#67—62no—
661#67—62no—
662#67—64no—
663#67—64no—
664#67—64no—
665#67—64no—
666#67—62no—
667#67—62no—
668#67—122no—
669#67—241no—
670#67—241no—
671C2×Dic3—21no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—121no—
678C2×Dic3—122no—
679C2×Dic3D3×D411yescharacteristic
680C2×Dic3D3×D411yescharacteristic
681D12—24no—
682D12—24no—
683D12—21no—
684D12—21no—
685D12—21no—
686D12—21no—
687D12—32no—
688D12—32no—
689D12—62no—
690D12—64no—
691D12—64no—
692D12—62no—
693D12—62no—
694D12—64no—
695D12—64no—
696D12—61no—
697D12—61no—
698D12—81no—
699D12—121no—
700D12—124no—
701D12—122no—
702D12D3×D412yes—
703D12D3×D412yes—
704C4×D3—24no—
705C4×D3—24no—
706C4×D3—21no—
707C4×D3—21no—
708C4×D3—21no—
709C4×D3—21no—
710C4×D3—32no—
711C4×D3—32no—
712C4×D3—32no—
713C4×D3—32no—
714C4×D3—62no—
715C4×D3—62no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—124no—
719C4×D3—122no—
720C4×D3—241no—
721C4×D3—241no—
722C4×D3—242no—
723Dic6—21no—
724Dic6—21no—
725Dic6—62no—
726Dic6—62no—
727C3×C8—21no—
728C3×C8—21no—
729C3×C8—41no—
730C3×C8—61no—
731C3×C8—61no—
732C3⋊C8—21no—
733C3⋊C8—21no—
734C3⋊C8—61no—
735C3⋊C8—61no—
736C3⋊C8—121no—
737C2×C32C2×#12011yescharacteristic
738C2×C32#57611yescharacteristic
739C2×C32#57711yescharacteristic
740C3⋊D3—22no—
741C3⋊D3—42no—
742C3×D3—41no—
743C3×D3—41no—
744C3×D3—42no—
745C3×D3—42no—
746C3×D3—81no—
747C24—181no—
748C24—181no—
749C24—181no—
750#41—62no—
751#41—62no—
752#41—62no—
753#41—62no—
754#41—94no—
755#41—182no—
756#41—182no—
757#41—188no—
758#41—182no—
759#41—182no—
760#41—182no—
761C2×Q8—31no—
762C2×Q8—91no—
763C2×Q8C2×D3211yescharacteristic
764C2×D4—31no—
765C2×D4—31no—
766C2×D4—31no—
767C2×D4—61no—
768C2×D4—61no—
769C2×D4—61no—
770C2×D4—91no—
771C2×D4—91no—
772C2×D4—94no—
773C2×D4—91no—
774C2×D4—91no—
775C2×D4—181no—
776C2×D4—181no—
777C2×D4—181no—
778C2×D4—182no—
779C2×D4—182no—
780C2×D4—182no—
781C2×D4—182no—
782C2×D4—188no—
783C2×D4—188no—
784C2×D4—181no—
785C2×D4—182no—
786C2×D4—181no—
787C2×D4—188no—
788C2×D4—181no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—91no—
794C22×C4—181no—
795C22×C4—181no—
796C22×C4—181no—
797Q16—62no—
798SD16—62no—
799SD16—62no—
800SD16—182no—
801SD16—182no—
802D8—62no—
803D8—182no—
804D8—182no—
805M16—182no—
806C2×C8—31no—
807C2×C8—31no—
808C2×C8—91no—
809C2×C8—182no—
810C2×C8C2×D3211yescharacteristic
811C4⋊C4—61no—
812C4⋊C4—91no—
813C4⋊C4—181no—
814C4⋊C4—181no—
815C4⋊C4C2×D3211yescharacteristic
816C22⋊C4—61no—
817C22⋊C4—61no—
818C22⋊C4—181no—
819C22⋊C4—181no—
820C22×C3—21no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—61no—
828C22×C3—61no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3C2×D3×D411yescharacteristic
837C22×C3C2×D3×D411yescharacteristic
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—21no—
841C2×D3—21no—
842C2×D3—21no—
843C2×D3—21no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—32no—
847C2×D3—32no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—62no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—121no—
863C2×D3—121no—
864C2×D3—122no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—241no—
870C2×D3—241no—
871C2×D3—244no—
872C2×D3—244no—
873C2×D3—244no—
874C2×D3—244no—
875C2×D3—244no—
876C2×D3—244no—
877C3×C4—22no—
878C3×C4—22no—
879C3×C4—21no—
880C3×C4—21no—
881C3×C4—42no—
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—61no—
885C3×C4—61no—
886C3×C4—81no—
887C3×C4—121no—
888C3×C4C2×D3×D411yescharacteristic
889C3×C4C2×D3×D411yescharacteristic
890C3×C4C2×D3×D411yescharacteristic
891C3×C4C2×D3×D411yescharacteristic
892Dic3—21no—
893Dic3—21no—
894Dic3—32no—
895Dic3—32no—
896Dic3—41no—
897Dic3—62no—
898Dic3—121no—
899Dic3—121no—
900Dic3—241no—
901C32#301211yescharacteristic, complemented, Sylow
902C23—31no—
903C23—31no—
904C23—61no—
905C23—61no—
906C23—61no—
907C23—91no—
908C23—184no—
909C23—184no—
910C23—184no—
911C23—181no—
912C23—721no—
913C23—721no—
914C23—721no—
915C23—721no—
916C23—721no—
917C23—721no—
918Q8—21no—
919Q8—61no—
920Q8—61no—
921Q8—182no—
922Q8#380212yes—
923D4—32no—
924D4—32no—
925D4—64no—
926D4—64no—
927D4—61no—
928D4—61no—
929D4—61no—
930D4—61no—
931D4—92no—
932D4—184no—
933D4—182no—
934D4—182no—
935D4—184no—
936D4—184no—
937D4—184no—
938D4—182no—
939D4—181no—
940D4—241no—
941D4—362no—
942D4—721no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—31no—
946C2×C4—31no—
947C2×C4—64no—
948C2×C4—64no—
949C2×C4—61no—
950C2×C4—61no—
951C2×C4—61no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—91no—
955C2×C4—92no—
956C2×C4—92no—
957C2×C4—184no—
958C2×C4—181no—
959C2×C4—362no—
960C2×C4—721no—
961C2×C4C22×D3211yescharacteristic
962C8—21no—
963C8—61no—
964C8—61no—
965C8—181no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—121no—
970C2×C3—122no—
971C2×C3—121no—
972C2×C3—122no—
973C2×C3—241no—
974C2×C3D3×#12011yescharacteristic
975C2×C3D3×#12011yescharacteristic
976C2×C3#576911yescharacteristic
977C2×C3#577011yescharacteristic
978C2×C3#577411yescharacteristic
979C2×C3#577811yescharacteristic
980D3—41no—
981D3—42no—
982D3—41no—
983D3—42no—
984D3—62no—
985D3—62no—
986D3—81no—
987D3—122no—
988D3—122no—
989D3—122no—
990D3—242no—
991C22—61no—
992C22—61no—
993C22—62no—
994C22—62no—
995C22—61no—
996C22—61no—
997C22—61no—
998C22—61no—
999C22—92no—
1000C22—121no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—181no—
1008C22—181no—
1009C22—182no—
1010C22—361no—
1011C22—361no—
1012C22—724no—
1013C22—724no—
1014C22—724no—
1015C22D32×D411yescharacteristic
1016C4—22no—
1017C4—41no—
1018C4—61no—
1019C4—61no—
1020C4—92no—
1021C4—121no—
1022C4—361no—
1023C4C2×#380211yescharacteristic
1024C4D32×D411yescharacteristic
1025C3—21no—
1026C3#8008711yescharacteristic, complemented
1027C3#8023111yescharacteristic, complemented
1028C2—121no—
1029C2—121no—
1030C2—122no—
1031C2—122no—
1032C2—182no—
1033C2—241no—
1034C2—362no—
1035C2#1059425811yescharacteristic
1036C2#1059475511yescharacteristic
1037C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×#63950C2semidirect
3. C2×#63798C2semidirect
4. #10594528C2semidirect
5. #10592502C2semidirect
6. C3×#4810C2semidirect
7. C3×#4808C2semidirect
8. #10591597C2semidirect
9. #10591586C2semidirect
10. #10590959C2semidirect
11. #10590944C2semidirect
12. #10590942C2semidirect
13. #10590596C2semidirect
14. #10590595C2semidirect
15. #10590593C2semidirect
31. C2×#3796C22semidirect
32. C2×#3743C22semidirect
33. C4⋊C4×C3⋊D3C22semidirect
34. C2×C3×#216C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
43. #63908C22semidirect
46. #63856C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3710C22semidirect
53. C32×#103C22semidirect
54. #63662C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4810D3semidirect
84. #4808D3semidirect
101. #3832D4semidirect
134. #3802D4semidirect
206. C2×#216C2×D3semidirect
209. C2×#215C2×D3semidirect
224. C2×D24C2×D3semidirect
226. C2×#204C2×D3semidirect
232. #897C2×D3semidirect
235. #895C2×D3semidirect
244. C3×#103C2×D3semidirect
245. C3×#103C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
580. #103D32semidirect
901. C32#3012semidirect
1026. C3#80087semidirect
1027. C3#80231semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#639502
C2×#637982
#105945282
#105925022
C3×#48102
C3×#48082
#105915972
#105915862
#105909592
#105909442
#105909422
#105905962
#105905952
#105905932
#802313
#800873