Finite Group Databasebeta

← #11864092

Subgroups — #11864092

Order 1152.

1592 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594626C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4802C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10590970C211yesmaximal, characteristic, complemented
11#10590963C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590615C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80083—31nomaximal
17#78959—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239—24no—
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799—21no—
28C2×#3799C2211yescharacteristic
29C2×#3796—21no—
30C2×#3796C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C2×#3756C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C3×#895C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic
40#63946—24no—
41#63922—21no—
42#63916C2211yescharacteristic, complemented
43Dic3×D12—21no—
44#63891—21no—
45#63880—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic
52#63795—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#942—31no—
68C2×#915—31no—
69C2×#911—31no—
70C2×#908—31no—
71#5606—31no—
72#5524—31no—
73C3×#449—31no—
74C3×#419—31no—
75#5239—31no—
76#5172—31no—
77#5158—31no—
78#5126—31no—
79#5037—31no—
80#5001—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810D311yescharacteristic, complemented
85#4808—31no—
86#4808—31no—
87#4808—31no—
88#4808—31no—
89#4808—31no—
90#4808—61no—
91#4802D311yescharacteristic, complemented
92#4783—31no—
93#4770—31no—
94#4733—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99#3832—22no—
100#3832—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C3×#239—22no—
107C3×#239—22no—
108C3×D3×Q8—22no—
109C3×D3×Q8D414yescomplemented
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×#624D411yescharacteristic
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3D411yescharacteristic
130C2×D3×Dic3D411yescharacteristic
131D3×D12—28no—
132D3×D12—22no—
133D3×D12D414yescomplemented
134C4×D32—28no—
135C4×D32—22no—
136C4×D32—22no—
137#3799—28no—
138#3799—22no—
139#3799—22no—
140#3796—28no—
141#3796—22no—
142#3796—22no—
143#3795—22no—
144#3795—22no—
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3756—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3744—22no—
152C3×#215—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4×Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×D24—22no—
160C3×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3716—22no—
166#3715—22no—
167#3714—22no—
168#3711—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172D3×#41—64no—
173D3×#41—64no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—64no—
182C2×#239—64no—
183C2×#239C2×D311yescharacteristic
184C2×D3×Q8C2×D311yescharacteristic
185C2×#237—31no—
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—61no—
193C22×D12—31no—
194C22×D12—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C2×C3×M16—31no—
202C3×#121—31no—
203C3×#117—31no—
204C2×#216—31no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—61no—
208#942—64no—
209C2×#215—31no—
210C2×#215C2×D311yescharacteristic, complemented
211#938—31no—
212#937—61no—
213D4×Dic3—61no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#213—31no—
217#924—31no—
218C2×#208—31no—
219#915—64no—
220#911—64no—
221#908—64no—
222C2×Dic12—31no—
223C2×D24—31no—
224C2×D24C2×D311yescharacteristic, complemented
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—61no—
229C2×ΓL(1,𝔽25)—31no—
230C2×ΓL(1,𝔽25)C2×D311yescharacteristic
231#897—31no—
232#897—31no—
233#897—31no—
234#897—61no—
235#895—31no—
236#895C2×D311yescharacteristic, complemented
237#892C2×D311yescharacteristic
238#886—61no—
239#883—61no—
240#882—61no—
241#67⋊C4—61no—
242C4×D12—61no—
243C4×D12—61no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103C2×D311yescharacteristic, complemented
249C3×#103C2×D311yescharacteristic, complemented
250C3×#102—31no—
251C3×C22⋊C8—31no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#830—31no—
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816C2×D311yescharacteristic, complemented
264#810C2×D311yescharacteristic, complemented
265#809—31no—
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—22no—
279C2×D32—41no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—24no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)C2×D412yes—
293C4×C3⋊D3—24no—
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—21no—
297#634—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C2×D411yescharacteristic
301C2×C3×Dic3C2×D411yescharacteristic
302C3×D12—24no—
303C3×D12—21no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—42no—
307C3×D12C2×D412yes—
308C3×C4×D3—24no—
309C3×C4×D3—24no—
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3C2×D412yes—
313C3×C4×D3C2×D412yes—
314C3×Dic6—21no—
315C3×Dic6—24no—
316C3×Dic6C2×D412yes—
317#626—24no—
318#626—24no—
319#626—24no—
320#626—42no—
321#625—42no—
322#624—24no—
323#624—22no—
324D3×Dic3—24no—
325D3×Dic3—22no—
326D3×Dic3—22no—
327D3×Dic3—42no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—91no—
334C2×AGL(1,ℤ/8)—91no—
335#525—91no—
336#452—91no—
337#452—91no—
338#452—91no—
339#452—91no—
340#449—31no—
341#449—91no—
342#449—91no—
343#449—91no—
344#419—31no—
345#418—91no—
346#407—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—21no—
354C2×C3×Q8—34no—
355C2×C3×Q8—31no—
356C2×C3×Q8—61no—
357C2×C3×Q8—62no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—31no—
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378#239—22no—
379#239—22no—
380#239—62no—
381#239—62no—
382#239—68no—
383#239—62no—
384#239—68no—
385#239—62no—
386#239—62no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—122no—
391#239—122no—
392D3×Q8—22no—
393D3×Q8D1214yescomplemented
394#237—62no—
395#237—68no—
396#237—62no—
397#237—62no—
398#237—62no—
399D3×D4—34no—
400D3×D4—68no—
401D3×D4—62no—
402#235—62no—
403#235—68no—
404#235—62no—
405#235—62no—
406#235—62no—
407C2×D12—21no—
408C2×D12—21no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—34no—
412C2×D12—61no—
413C2×D12—62no—
414C2×D12—68no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—121no—
422C2×D12C22×D311yescharacteristic
423C2×D12C22×D311yescharacteristic
424C2×C4×D3—21no—
425C2×C4×D3—21no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—68no—
436C2×C4×D3—68no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—61no—
445C2×C4×D3—121no—
446C2×C4×D3C22×D311yescharacteristic
447C2×C4×D3C22×D311yescharacteristic
448C2×Dic6—21no—
449C2×Dic6—31no—
450C2×Dic6—31no—
451C2×Dic6—61no—
452C2×Dic6C22×D311yescharacteristic
453C3×SD16—62no—
454C3×D8—62no—
455C3×M16—62no—
456C2×C3×C8—21no—
457C2×C3×C8—31no—
458C2×C3×C8—31no—
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C3×C4⋊C4—21no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—61no—
466C3×C22⋊C4—61no—
467C3×C42—61no—
468#217—61no—
469#217—61no—
470#216—62no—
471#216—62no—
472#216—62no—
473#216—122no—
474#215—22no—
475#215—62no—
476#214—62no—
477#214—62no—
478#213—62no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—121no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3—61no—
489C4⋊Dic3—121no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—61no—
492C4×Dic3—21no—
493#208—62no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8C22×D311yescharacteristic
498C2×C3⋊C8C22×D311yescharacteristic
499Dic12—62no—
500D24—22no—
501D24—62no—
502#204—62no—
503#204—62no—
504#204—62no—
505#204—122no—
506ΓL(1,𝔽25)—22no—
507ΓL(1,𝔽25)—62no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—44no—
528D32—48no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—21no—
534C3⋊Dic3—41no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—91no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—31no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#137—184no—
554AGL(1,ℤ/8)—184no—
555C2×Q16—91no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—31no—
562C2×D8—91no—
563C2×M16—31no—
564C2×M16—91no—
565#123—181no—
566C22⋊Q8—91no—
567C22⋊Q8—91no—
568#121—31no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—31no—
574#103—31no—
575#103—31no—
576#103—31no—
577#103D3211yescharacteristic, complemented
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C23×C3—61no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—31no—
593C22×D3—31no—
594C22×D3—61no—
595C22×D3—64no—
596C22×D3—62no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—64no—
600C22×D3—62no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3D3×D411yescharacteristic
611C22×D3D3×D411yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—22no—
615C3×Q8—32no—
616C3×Q8—41no—
617C3×Q8—64no—
618C3×Q8—61no—
619C3×Q8C2×D1212yes—
620C3×Q8D3×D412yes—
621C3×D4—32no—
622C3×D4—64no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—122no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—31no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—31no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646#67—64no—
647#67—64no—
648#67—64no—
649#67—122no—
650#67—122no—
651#67—122no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—31no—
655C2×Dic3—31no—
656C2×Dic3—61no—
657C2×Dic3—62no—
658C2×Dic3—64no—
659C2×Dic3—62no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—121no—
663C2×Dic3—122no—
664C2×Dic3D3×D411yescharacteristic
665C2×Dic3D3×D411yescharacteristic
666D12—24no—
667D12—21no—
668D12—21no—
669D12—21no—
670D12—32no—
671D12—32no—
672D12—42no—
673D12—62no—
674D12—64no—
675D12—64no—
676D12—64no—
677D12—64no—
678D12—64no—
679D12—61no—
680D12—61no—
681D12—121no—
682D12—124no—
683D12—122no—
684D12D3×D412yes—
685C4×D3—24no—
686C4×D3—24no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—62no—
690C4×D3—64no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—62no—
695C4×D3—64no—
696C4×D3—62no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—62no—
702C4×D3—121no—
703C4×D3—121no—
704C4×D3—124no—
705C4×D3—122no—
706C4×D3C2×D1212yes—
707C4×D3D3×D412yes—
708Dic6—21no—
709Dic6—24no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—121no—
715Dic6—121no—
716Dic6C2×D1212yes—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—41no—
720C3×C8—61no—
721C3×C8—61no—
722C3⋊C8—21no—
723C3⋊C8—21no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C2×C32C2×#12011yescharacteristic
728C2×C32#57511yescharacteristic
729C2×C32#57511yescharacteristic
730C3⋊D3—41no—
731C3⋊D3—42no—
732C3×D3—22no—
733C3×D3—41no—
734C3×D3—42no—
735C3×D3—81no—
736C24—91no—
737C24—181no—
738#41—62no—
739#41—62no—
740#41—182no—
741#41—182no—
742#41—182no—
743#41—182no—
744#41—188no—
745#41—182no—
746#41—182no—
747#41—188no—
748#41—182no—
749#41—182no—
750C2×Q8—34no—
751C2×Q8—31no—
752C2×Q8—61no—
753C2×Q8—62no—
754C2×Q8—91no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—94no—
761C2×D4—91no—
762C2×D4—181no—
763C2×D4—182no—
764C2×D4—181no—
765C2×D4—188no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—181no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—181no—
782C22×C4—181no—
783C22×C4—188no—
784C22×C4—181no—
785Q16—182no—
786Q16—182no—
787SD16—62no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791D8—62no—
792D8—182no—
793M16—62no—
794M16—182no—
795C2×C8—31no—
796C2×C8—31no—
797C2×C8—91no—
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—31no—
800C4⋊C4—181no—
801C4⋊C4—181no—
802C4⋊C4C2×D3211yescharacteristic
803C22⋊C4—61no—
804C22⋊C4—61no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—61no—
809C22×C3—21no—
810C22×C3—32no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—62no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3C2×D3×D411yescharacteristic
823C22×C3C2×D3×D411yescharacteristic
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—22no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—62no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—61no—
841C2×D3—62no—
842C2×D3—61no—
843C2×D3—122no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—124no—
848C2×D3—128no—
849C2×D3—124no—
850C2×D3—128no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3#88212yes—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—32no—
863C3×C4—42no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—61no—
867C3×C4—62no—
868C3×C4—81no—
869C3×C4—121no—
870C3×C4C22×D1211yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874Dic3—22no—
875Dic3—21no—
876Dic3—41no—
877Dic3—61no—
878Dic3—61no—
879Dic3—121no—
880Dic3—121no—
881Dic3—121no—
882Dic3—241no—
883Dic3#88212yes—
884C32#300511yescharacteristic, complemented, Sylow
885C23—31no—
886C23—31no—
887C23—61no—
888C23—61no—
889C23—91no—
890C23—184no—
891C23—182no—
892C23—181no—
893C23—361no—
894C23—361no—
895C23—362no—
896C23—362no—
897Q8—21no—
898Q8—32no—
899Q8—64no—
900Q8—61no—
901Q8—181no—
902Q8—181no—
903Q8D3×D1212yes—
904D4—32no—
905D4—64no—
906D4—61no—
907D4—61no—
908D4—61no—
909D4—92no—
910D4—122no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—362no—
917D4—362no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—31no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—31no—
924C2×C4—64no—
925C2×C4—64no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—91no—
931C2×C4—184no—
932C2×C4—182no—
933C2×C4—182no—
934C2×C4—184no—
935C2×C4—182no—
936C2×C4—184no—
937C2×C4—181no—
938C2×C4—181no—
939C2×C4—181no—
940C2×C4—362no—
941C2×C4C22×D3211yescharacteristic
942C8—21no—
943C8—61no—
944C8—61no—
945C8—181no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—62no—
950C2×C3—121no—
951C2×C3—122no—
952C2×C3—241no—
953C2×C3C2×#88211yescharacteristic
954C2×C3D3×#12011yescharacteristic
955C2×C3#576811yescharacteristic
956C2×C3#577311yescharacteristic
957C2×C3#577711yescharacteristic
958C2×C3#577711yescharacteristic
959D3—22no—
960D3—41no—
961D3—42no—
962D3—81no—
963D3—121no—
964D3—122no—
965D3—121no—
966D3—122no—
967D3—241no—
968D3—242no—
969C22—32no—
970C22—61no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—62no—
975C22—61no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—181no—
982C22—181no—
983C22—182no—
984C22—181no—
985C22—364no—
986C22—368no—
987C22—361no—
988C22—361no—
989C22D32×D411yescharacteristic
990C4—22no—
991C4—32no—
992C4—41no—
993C4—61no—
994C4—62no—
995C4—121no—
996C4—181no—
997C4—361no—
998C4C2×D3×D1211yescharacteristic
999C4D32×D411yescharacteristic
1000C3—21no—
1001C3#7895911yescharacteristic, complemented
1002C3#8008311yescharacteristic, complemented
1003C2—62no—
1004C2—121no—
1005C2—122no—
1006C2—241no—
1007C2—361no—
1008C2—362no—
1009C2D3×#88211yescharacteristic
1010C2#1059474411yescharacteristic
1011C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3005
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×D3×#239C2semidirect
2. C2×#63946C2semidirect
3. C2×#63795C2semidirect
4. #10594626C2semidirect
5. #10592507C2semidirect
6. C3×#4810C2semidirect
7. C3×#4802C2semidirect
8. #10591599C2semidirect
9. #10591593C2semidirect
10. #10590970C2semidirect
11. #10590963C2semidirect
12. #10590936C2semidirect
13. #10590618C2semidirect
14. #10590615C2semidirect
15. #10590592C2semidirect
32. C2×#3756C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×D24C22semidirect
38. C3×#895C22semidirect
42. #63916C22semidirect
46. #63857C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4810D3semidirect
91. #4802D3semidirect
109. C3×D3×Q8D4semidirect
133. D3×D12D4semidirect
210. C2×#215C2×D3semidirect
224. C2×D24C2×D3semidirect
236. #895C2×D3semidirect
248. C3×#103C2×D3semidirect
249. C3×#103C2×D3semidirect
252. #835C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. #816C2×D3semidirect
264. #810C2×D3semidirect
270. #809C2×D3semidirect
393. D3×Q8D12semidirect
577. #103D32semidirect
884. C32#3005semidirect
1001. C3#78959semidirect
1002. C3#80083semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639462
C2×#637952
#105946262
#105925072
C3×#48102
C3×#48022
#105915992
#105915932
#105909702
#105909632
#105909362
#105906182
#105906152
#105905922
#800833
#789593