Finite Group Databasebeta

← #11864637

Subgroups — #11864637

Order 1152.

1629 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×#63809C211yesmaximal, characteristic, complemented
4#10594528C211yesmaximal, characteristic, complemented
5C3⋊D3×#102C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4776C211yesmaximal, characteristic, complemented
8#10591461C211yesmaximal, characteristic, complemented
9#10591447C211yesmaximal, characteristic, complemented
10#10590958C211yesmaximal, characteristic, complemented
11#10590942C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590616C211yesmaximal, characteristic, complemented
14#10590612C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#80149—31nomaximal
17#80087—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3811—21no—
22C2×D3×#67—21no—
23C22×#626—21no—
24C2×#3804—21no—
25#64314—24no—
26#64314—24no—
27C2×D3×D12C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3798C2211yescharacteristic
30C2×#3796C2211yescharacteristic
31C2×#3796C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic, complemented
33C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40#63937—24no—
41#63916—21no—
42#63912—21no—
43#63908C2211yescharacteristic, complemented
44#63899—21no—
45#63885—21no—
46#63856C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63809—24no—
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×#916—31no—
68C2×#916—31no—
69C2×#914—31no—
70C2×#911—31no—
71#5629—31no—
72#5608—31no—
73C3×#450—31no—
74C3×#449—31no—
75#5239—31no—
76#5217—31no—
77#5173—31no—
78#5172—31no—
79#5169—31no—
80#5156—31no—
81#5047—31no—
82#5036—31no—
83#4808—31no—
84#4803—31no—
85#4781D311yescharacteristic, complemented
86#4776D311yescharacteristic, complemented
87#4773—31no—
88#4771—31no—
89D3×#102—31no—
90D3×#102—31no—
91D3×#102—61no—
92#4734—31no—
93#4731—31no—
94#4727—31no—
95#4727—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C22×D32—21no—
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3D414yescomplemented
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—22no—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120#3811—28no—
121D3×#67—28no—
122C2×#627D411yescharacteristic
123C2×#626—28no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626D411yescharacteristic
129C2×#626D411yescharacteristic
130C2×#625—21no—
131C2×#625D411yescharacteristic
132C2×#624—21no—
133#3804—28no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136D3×D12—22no—
137D3×D12—22no—
138#3799—22no—
139#3799—22no—
140#3798—22no—
141#3798—22no—
142#3796—22no—
143#3796—22no—
144#3796—22no—
145#3796D414yescomplemented
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C8×C3⋊D3—22no—
152C3×#214—22no—
153C3×#213—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×#204—22no—
161#3724—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3718—22no—
165#3717—22no—
166#3714—22no—
167#3713—22no—
168#3712—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179#1004—64no—
180#1004—64no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237C2×D311yescharacteristic
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C22×D12—31no—
198C22×D12—61no—
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×D8—31no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#215—31no—
209#939—61no—
210#938—31no—
211#938—61no—
212C2×#214C2×D311yescharacteristic, complemented
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213C2×D311yescharacteristic, complemented
217#930—31no—
218#924—31no—
219#916—64no—
220#916—64no—
221#914—64no—
222#911—64no—
223C2×D24—31no—
224C2×#204—31no—
225C2×#204C2×D311yescharacteristic, complemented
226C2×#204C2×D311yescharacteristic, complemented
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×D3×C8—31no—
230C2×D3×C8—31no—
231C2×D3×C8—61no—
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—31no—
244C3×#102—21no—
245C3×#102—31no—
246C3×#102C2×D311yescharacteristic, complemented
247C3×#102C2×D311yescharacteristic, complemented
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250#835—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#830—31no—
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#810C2×D311yescharacteristic, complemented
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—81no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—24no—
279C22×C3×D3—21no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3C2×D411yescharacteristic
283C22×C3×D3C2×D411yescharacteristic
284C2×D32—24no—
285C2×D32—81no—
286C2×D32—81no—
287C32×D4—21no—
288C32×D4C2×D412yes—
289C2×C32×C4—21no—
290C2×C32×C4C2411yescharacteristic
291#638—24no—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)C2×D412yes—
296C4×C3⋊D3—81no—
297C4×C3⋊D3C2×D412yes—
298C4×C3⋊D3C2×D412yes—
299C3×#67—24no—
300C3×#67—24no—
301C2×C3×Dic3—24no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3C2×D411yescharacteristic
305C2×C3×Dic3C2×D411yescharacteristic
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—81no—
310C3×D12C2×D412yes—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6C2×D412yes—
319#627—22no—
320#626—24no—
321#626—24no—
322#626—24no—
323#626—22no—
324#626—22no—
325#626—42no—
326#625—22no—
327#625—81no—
328#624—24no—
329D3×Dic3—24no—
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—91no—
340#452—91no—
341#450—31no—
342#450—91no—
343#449—31no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—121no—
357C3×#41—62no—
358C3×#41—62no—
359C2×C3×Q8—31no—
360C2×C3×Q8—31no—
361C2×C3×D4—21no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C2×C3×D4—62no—
367C2×C3×D4—61no—
368C2×C3×D4—62no—
369C2×C3×D4C22×D311yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—61no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—68no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—68no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—121no—
391C22×Dic3—21no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394#239—34no—
395#239—62no—
396#239—62no—
397#239—62no—
398#239—62no—
399#239—62no—
400#237—22no—
401#237—22no—
402#237—34no—
403#237—62no—
404#237—62no—
405#237—62no—
406#237—68no—
407D3×D4—22no—
408D3×D4—22no—
409D3×D4—34no—
410D3×D4—34no—
411D3×D4—64no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—62no—
415D3×D4—62no—
416D3×D4—68no—
417D3×D4—68no—
418D3×D4—68no—
419D3×D4—122no—
420#235—62no—
421#235—62no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—68no—
426#235—62no—
427C2×D12—21no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—61no—
433C2×D12—62no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—68no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—61no—
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×D3C22×D311yescharacteristic
453C2×C4×D3C22×D311yescharacteristic
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6C22×D311yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C3×SD16—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—62no—
476#216—62no—
477#215—62no—
478#214—22no—
479#213—22no—
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—62no—
502#204—22no—
503#204—22no—
504#204—62no—
505ΓL(1,𝔽25)—62no—
506ΓL(1,𝔽25)—62no—
507D3×C8—62no—
508D3×C8—62no—
509D3×C8—122no—
510C22×C32—22no—
511C22×C32—41no—
512C22×C32—41no—
513C22×C32C22×D411yescharacteristic
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—84no—
520C2×C3⋊D3#12012yes—
521C2×C3×D3—22no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534D32—84no—
535C32×C4—41no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3⋊Dic3—41no—
539C3⋊Dic3#12012yes—
540C3×Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544H(5,𝔽2)—184no—
545H(5,𝔽2)—184no—
546C2×#41—31no—
547C2×#41—91no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—181no—
552C22×D4—31no—
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—91no—
561C2×SD16—31no—
562C2×SD16—31no—
563C2×SD16—31no—
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—31no—
580#103—91no—
581#102—31no—
582#102—91no—
583#102—91no—
584#102—91no—
585#102—91no—
586#102D3211yescharacteristic, complemented
587C22⋊C8—31no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—41no—
596C23×C3—64no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—241no—
600C23×C3—241no—
601C22×D3—21no—
602C22×D3—24no—
603C22×D3—21no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—61no—
607C22×D3—64no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—64no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—81no—
614C22×D3—81no—
615C22×D3—124no—
616C22×D3—121no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—242no—
626C22×D3—242no—
627C22×D3D3×D411yescharacteristic
628C22×D3D3×D411yescharacteristic
629C3×Q8—32no—
630C3×Q8—61no—
631C3×Q8—61no—
632C3×Q8—61no—
633C3×D4—21no—
634C3×D4—21no—
635C3×D4—22no—
636C3×D4—32no—
637C3×D4—41no—
638C3×D4—64no—
639C3×D4—64no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—241no—
644C3×D4D3×D412yes—
645C3×D4D3×D412yes—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—41no—
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×C4—61no—
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661#67—24no—
662#67—24no—
663#67—62no—
664#67—62no—
665#67—64no—
666#67—64no—
667#67—64no—
668#67—62no—
669#67—62no—
670#67—64no—
671#67—64no—
672#67—124no—
673#67—122no—
674#67—241no—
675#67—241no—
676C2×Dic3—24no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—61no—
682C2×Dic3—64no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—121no—
686C2×Dic3—122no—
687C2×Dic3D3×D411yescharacteristic
688C2×Dic3D3×D411yescharacteristic
689D12—21no—
690D12—21no—
691D12—21no—
692D12—32no—
693D12—32no—
694D12—62no—
695D12—62no—
696D12—62no—
697D12—64no—
698D12—64no—
699D12—64no—
700D12—61no—
701D12—61no—
702D12—81no—
703D12—121no—
704D12—122no—
705D12D3×D412yes—
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—64no—
719C4×D3—122no—
720C4×D3—241no—
721C4×D3—241no—
722C4×D3—242no—
723Dic6—21no—
724Dic6—21no—
725Dic6—21no—
726Dic6—62no—
727Dic6—62no—
728Dic6D3×D412yes—
729C3×C8—21no—
730C3×C8—21no—
731C3×C8—41no—
732C3×C8—61no—
733C3×C8—61no—
734C3⋊C8—21no—
735C3⋊C8—21no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—121no—
739C2×C32—42no—
740C2×C32C2×#12011yescharacteristic
741C2×C32#57611yescharacteristic
742C2×C32#57711yescharacteristic
743C3⋊D3—22no—
744C3⋊D3—42no—
745C3×D3—41no—
746C3×D3—42no—
747C3×D3—41no—
748C3×D3—81no—
749C24—61no—
750C24—181no—
751C24—181no—
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—
761#41—182no—
762#41—182no—
763C2×Q8—31no—
764C2×Q8—31no—
765C2×Q8—91no—
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—61no—
769C2×D4—61no—
770C2×D4—62no—
771C2×D4—61no—
772C2×D4—62no—
773C2×D4—91no—
774C2×D4—91no—
775C2×D4—94no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—181no—
779C2×D4—182no—
780C2×D4—182no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—188no—
784C2×D4—181no—
785C2×D4—182no—
786C2×D4—181no—
787C2×D4—188no—
788C2×D4—188no—
789C2×D4—181no—
790C2×D4C2×D3211yescharacteristic
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—61no—
794C22×C4—91no—
795C22×C4—181no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799Q16—182no—
800SD16—62no—
801SD16—62no—
802SD16—62no—
803SD16—182no—
804D8—62no—
805D8—182no—
806D8—182no—
807M16—182no—
808C2×C8—31no—
809C2×C8—31no—
810C2×C8—91no—
811C2×C8—182no—
812C2×C8C2×D3211yescharacteristic
813C4⋊C4—61no—
814C4⋊C4—91no—
815C4⋊C4—181no—
816C4⋊C4—181no—
817C4⋊C4C2×D3211yescharacteristic
818C22⋊C4—61no—
819C22⋊C4—61no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—21no—
825C22×C3—42no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—61no—
831C22×C3—61no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—62no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—244no—
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×D3×D411yescharacteristic
847C2×D3—21no—
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—32no—
855C2×D3—32no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—84no—
871C2×D3—122no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—241no—
877C2×D3—241no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—248no—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—61no—
888C3×C4—61no—
889C3×C4—62no—
890C3×C4—81no—
891C3×C4—121no—
892C3×C4C2×D3×D411yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896Dic3—22no—
897Dic3—21no—
898Dic3—21no—
899Dic3—32no—
900Dic3—32no—
901Dic3—41no—
902Dic3—62no—
903Dic3—121no—
904Dic3—121no—
905Dic3—241no—
906C32#301211yescharacteristic, complemented, Sylow
907C23—21no—
908C23—31no—
909C23—31no—
910C23—64no—
911C23—61no—
912C23—61no—
913C23—91no—
914C23—184no—
915C23—184no—
916C23—181no—
917C23—241no—
918C23—241no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23—721no—
923Q8—32no—
924Q8—61no—
925Q8—61no—
926Q8—61no—
927Q8—182no—
928D4—21no—
929D4—32no—
930D4—64no—
931D4—64no—
932D4—61no—
933D4—61no—
934D4—61no—
935D4—92no—
936D4—182no—
937D4—182no—
938D4—184no—
939D4—184no—
940D4—184no—
941D4—184no—
942D4—182no—
943D4—181no—
944D4—241no—
945D4—362no—
946D4—721no—
947D4#380212yes—
948C2×C4—21no—
949C2×C4—31no—
950C2×C4—31no—
951C2×C4—64no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—91no—
959C2×C4—92no—
960C2×C4—92no—
961C2×C4—184no—
962C2×C4—184no—
963C2×C4—181no—
964C2×C4—362no—
965C2×C4—721no—
966C2×C4C22×D3211yescharacteristic
967C8—21no—
968C8—61no—
969C8—61no—
970C8—181no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—42no—
975C2×C3—42no—
976C2×C3—82no—
977C2×C3—121no—
978C2×C3—122no—
979C2×C3—121no—
980C2×C3—241no—
981C2×C3D3×#12011yescharacteristic
982C2×C3D3×#12011yescharacteristic
983C2×C3#576211yescharacteristic
984C2×C3#577011yescharacteristic
985C2×C3#577411yescharacteristic
986C2×C3#577411yescharacteristic
987D3—41no—
988D3—42no—
989D3—41no—
990D3—64no—
991D3—62no—
992D3—62no—
993D3—81no—
994D3—122no—
995D3—122no—
996D3—242no—
997C22—22no—
998C22—41no—
999C22—41no—
1000C22—61no—
1001C22—61no—
1002C22—61no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—62no—
1007C22—92no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—181no—
1014C22—181no—
1015C22—182no—
1016C22—244no—
1017C22—361no—
1018C22—361no—
1019C22—724no—
1020C22—724no—
1021C22D32×D411yescharacteristic
1022C4—41no—
1023C4—61no—
1024C4—61no—
1025C4—62no—
1026C4—92no—
1027C4—121no—
1028C4—361no—
1029C4C2×#380211yescharacteristic
1030C4D32×D411yescharacteristic
1031C3—21no—
1032C3#8008711yescharacteristic, complemented
1033C3#8014911yescharacteristic, complemented
1034C2—42no—
1035C2—121no—
1036C2—121no—
1037C2—122no—
1038C2—182no—
1039C2—241no—
1040C2—362no—
1041C2#1059425811yescharacteristic
1042C2#1059473511yescharacteristic
1043C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3012
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
1. C2×#64314C2semidirect
2. C2×#63937C2semidirect
3. C2×#63809C2semidirect
4. #10594528C2semidirect
5. C3⋊D3×#102C2semidirect
6. C3×#4781C2semidirect
7. C3×#4776C2semidirect
8. #10591461C2semidirect
9. #10591447C2semidirect
10. #10590958C2semidirect
11. #10590942C2semidirect
12. #10590823C2semidirect
13. #10590616C2semidirect
14. #10590612C2semidirect
15. #10590595C2semidirect
31. C2×#3796C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. C4⋊C4×C3⋊D3C22semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
43. #63908C22semidirect
46. #63856C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3712C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
85. #4781D3semidirect
86. #4776D3semidirect
102. D4×C3⋊D3D4semidirect
145. #3796D4semidirect
212. C2×#214C2×D3semidirect
216. C2×#213C2×D3semidirect
225. C2×#204C2×D3semidirect
226. C2×#204C2×D3semidirect
232. #897C2×D3semidirect
235. #895C2×D3semidirect
246. C3×#102C2×D3semidirect
247. C3×#102C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
266. #810C2×D3semidirect
270. #809C2×D3semidirect
586. #102D32semidirect
906. C32#3012semidirect
1032. C3#80087semidirect
1033. C3#80149semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#639372
C2×#638092
#105945282
C3⋊D3×#1022
C3×#47812
C3×#47762
#105914612
#105914472
#105909582
#105909422
#105908232
#105906162
#105906122
#105905952
#801493
#800873