Finite Group Databasebeta

← #11864088

Subgroups — #11864088

Order 1152.

1597 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×C3×#915C211yesmaximal, characteristic, complemented
3#10595301C211yesmaximal, characteristic, complemented
4C2×#63925C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591602C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591557C211yesmaximal, characteristic, complemented
10#10591521C211yesmaximal, characteristic, complemented
11#10591520C211yesmaximal, characteristic, complemented
12#10590966C211yesmaximal, characteristic, complemented
13#10590965C211yesmaximal, characteristic, complemented
14#10590939C211yesmaximal, characteristic, complemented
15#10590936C211yesmaximal, characteristic, complemented
16#83980—31nomaximal
17#80083—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic
22D3×#239—24no—
23D3×#239—24no—
24C2×D3×D12—21no—
25C2×D3×D12C2211yescharacteristic
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799—21no—
29C2×#3799C2211yescharacteristic
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64147C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C3×#938C2211yescharacteristic, complemented
37C2×C3×#214C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#915—24no—
40C2×C3×Dic12C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
42#63983—21no—
43Dic3×#67—21no—
44#63969—21no—
45#63952—21no—
46#63925—24no—
47#63871C2211yescharacteristic, complemented
48#63856C2211yescharacteristic, complemented
49#63841C2211yescharacteristic
50C2×#3717C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×C3×#137—31no—
68#5828—31no—
69C2×#949—31no—
70C2×#915D311yescharacteristic, complemented
71C2×#911—31no—
72#5606—31no—
73C3×#449—31no—
74#5239—31no—
75#5225—31no—
76#5187—31no—
77#5187—31no—
78#5187—31no—
79#5187—31no—
80#5172—31no—
81#5172—31no—
82#5172—31no—
83#5172—31no—
84#5172—61no—
85#5172D311yescharacteristic, complemented
86#5158—31no—
87#5131—31no—
88#5126—31no—
89#5037—31no—
90#4808—31no—
91#4802—31no—
92#4783—31no—
93#4770—31no—
94#4733—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101#3832—22no—
102#3832—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C3×#239—22no—
111C3×#239—22no—
112C3×D3×Q8—22no—
113C3×D3×Q8D414yescomplemented
114C3×#237—22no—
115C3×#237—22no—
116C2×C3×D12—21no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#624—21no—
129C2×#624D411yescharacteristic
130C2×D3×Dic3—21no—
131C2×D3×Dic3D411yescharacteristic
132C2×D3×Dic3D411yescharacteristic
133D3×D12—28no—
134D3×D12—22no—
135D3×D12D414yescomplemented
136C4×D32—28no—
137C4×D32—22no—
138C4×D32—22no—
139#3799—28no—
140#3799—22no—
141#3799—22no—
142#3796—28no—
143#3796—22no—
144#3796—22no—
145C32×SD16—22no—
146C2×C32×C8C2311yescharacteristic
147#3757—21no—
148#3753—22no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#217—21no—
152C3×#216—22no—
153C3×#214—22no—
154C3×#213—22no—
155C3×C4⋊Dic3C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C3×Dic12—22no—
159C3×ΓL(1,𝔽25)—22no—
160#3724—21no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165Dic32—21no—
166#3717—22no—
167#3715—22no—
168#3711—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173D3×#41—64no—
174D3×#41—64no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic
185C2×D3×Q8C2×D311yescharacteristic
186C2×#237—31no—
187C2×#237—61no—
188C2×#237C2×D311yescharacteristic
189C2×D3×D4—31no—
190C2×D3×D4—61no—
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—
199C3×#137—64no—
200C2×C3×Q16—31no—
201C2×C3×Q16—31no—
202C2×C3×SD16—21no—
203C2×C3×SD16—31no—
204C2×C3×SD16C2×D311yescharacteristic, complemented
205C2×C3×SD16C2×D311yescharacteristic, complemented
206C2×C3×D8—31no—
207C2×C3×M16—31no—
208C3×#121—31no—
209#949—64no—
210#946—31no—
211#946—31no—
212C2×#216C2×D311yescharacteristic, complemented
213C2×#215—31no—
214C2×#215—31no—
215#938—31no—
216#938—31no—
217#938—61no—
218#938C2×D311yescharacteristic, complemented
219#937—61no—
220#937—61no—
221#935—61no—
222D4×Dic3—61no—
223C2×#214—31no—
224C2×#214C2×D311yescharacteristic, complemented
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—61no—
228C2×#213C2×D311yescharacteristic, complemented
229C4×#67—61no—
230C4×#67—61no—
231#926—31no—
232#924—31no—
233C2×#208—31no—
234#915—24no—
235#911—64no—
236C2×Dic12C2×D311yescharacteristic, complemented
237C2×#204—31no—
238C2×ΓL(1,𝔽25)—31no—
239C2×ΓL(1,𝔽25)C2×D311yescharacteristic
240#897—31no—
241#892—31no—
242#883—61no—
243#67⋊C4—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—61no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#830—31no—
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260#821C2×D311yescharacteristic, complemented
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—61no—
267(C2×D3)⋊C8C2×D311yescharacteristic, complemented
268#816—31no—
269#810—31no—
270#809—31no—
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
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—
285C32×D4—21no—
286C32×D4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C2411yescharacteristic
289#638—42no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3C2×D411yescharacteristic
292C4⋊(C3⋊D3)—24no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)C2×D412yes—
295C4×C3⋊D3—24no—
296C4×C3⋊D3—21no—
297C4×C3⋊D3—21no—
298C3×#67—42no—
299C3×#67—42no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—42no—
304C2×C3×Dic3C2×D411yescharacteristic
305C2×C3×Dic3C2×D411yescharacteristic
306C3×D12—24no—
307C3×D12—21no—
308C3×D12C2×D412yes—
309C3×C4×D3—24no—
310C3×C4×D3—24no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—24no—
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6C2×D412yes—
320#626—24no—
321#626—24no—
322#626—24no—
323#624—24no—
324#624—22no—
325D3×Dic3—24no—
326D3×Dic3—22no—
327D3×Dic3—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—31no—
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—91no—
345#418—91no—
346#407—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—34no—
357C2×C3×Q8—31no—
358C2×C3×Q8—31no—
359C2×C3×Q8—61no—
360C2×C3×Q8—62no—
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×D4—21no—
364C2×C3×D4—31no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C22×C3×C4—61no—
375C2×#67—21no—
376C2×#67—21no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—121no—
383C22×Dic3—21no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—61no—
387#239—22no—
388#239—22no—
389#239—62no—
390#239—62no—
391#239—68no—
392#239—62no—
393#239—68no—
394#239—62no—
395#239—62no—
396#239—62no—
397#239—62no—
398#239—62no—
399#239—122no—
400#239—122no—
401D3×Q8—22no—
402D3×Q8#6714yescomplemented
403#237—22no—
404#237—22no—
405#237—62no—
406#237—68no—
407#237—62no—
408D3×D4—34no—
409D3×D4—68no—
410D3×D4—62no—
411#235—62no—
412#235—68no—
413#235—62no—
414C2×D12—21no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—34no—
418C2×D12—61no—
419C2×D12—62no—
420C2×D12—68no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—61no—
426C2×D12—121no—
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—21no—
429C2×C4×D3—21no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—61no—
437C2×C4×D3—62no—
438C2×C4×D3—62no—
439C2×C4×D3—68no—
440C2×C4×D3—68no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—62no—
447C2×C4×D3—62no—
448C2×C4×D3—121no—
449C2×C4×D3C22×D311yescharacteristic
450C2×C4×D3C22×D311yescharacteristic
451C2×Dic6—21no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×Q16—62no—
456C3×SD16—22no—
457C3×SD16—22no—
458C3×SD16—42no—
459C3×SD16—62no—
460C3×D8—62no—
461C3×M16—62no—
462C2×C3×C8—21no—
463C2×C3×C8—31no—
464C2×C3×C8—31no—
465C2×C3×C8C22×D311yescharacteristic
466C2×C3×C8C22×D311yescharacteristic
467C3×C4⋊C4—31no—
468C3×C22⋊C4—61no—
469#217—21no—
470#217—61no—
471#217—61no—
472#217—61no—
473#217—61no—
474#217—121no—
475#216—22no—
476#215—62no—
477#215—62no—
478#214—22no—
479#214—62no—
480#213—22no—
481#213—62no—
482#213—62no—
483#213—122no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3—61no—
492C4⋊Dic3C22×D311yescharacteristic
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496C4×Dic3—61no—
497C4×Dic3—61no—
498#208—62no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504Dic12—22no—
505#204—62no—
506ΓL(1,𝔽25)—22no—
507ΓL(1,𝔽25)—62no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—44no—
528D32—48no—
529C32×C4—22no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—21no—
533C3⋊Dic3—41no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
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—64no—
554AGL(1,ℤ/8)—184no—
555C2×Q16—31no—
556C2×Q16—31no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16D3211yescharacteristic, complemented
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—91no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
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—21no—
587C23×C3—21no—
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—41no—
591C23×C3—61no—
592C22×D3—21no—
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—61no—
596C22×D3—64no—
597C22×D3—62no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—64no—
601C22×D3—62no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3D3×D411yescharacteristic
612C22×D3D3×D411yescharacteristic
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—22no—
616C3×Q8—32no—
617C3×Q8—41no—
618C3×Q8—64no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8D3×D412yes—
623C3×Q8C2×#6712yes—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—32no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—64no—
632C3×D4—61no—
633C3×D4—122no—
634C3×D4—122no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—31no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—31no—
642C2×C3×C4—41no—
643C2×C3×C4—64no—
644C2×C3×C4—64no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—122no—
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653#67—42no—
654#67—42no—
655#67—64no—
656#67—64no—
657#67—64no—
658#67—122no—
659#67—122no—
660#67—242no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—42no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3—64no—
670C2×Dic3—62no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—121no—
674C2×Dic3D3×D411yescharacteristic
675C2×Dic3D3×D411yescharacteristic
676D12—24no—
677D12—21no—
678D12—32no—
679D12—32no—
680D12—62no—
681D12—64no—
682D12—64no—
683D12—64no—
684D12—64no—
685D12—64no—
686D12—61no—
687D12—61no—
688D12—121no—
689D12—124no—
690D12D3×D412yes—
691C4×D3—24no—
692C4×D3—24no—
693C4×D3—21no—
694C4×D3—21no—
695C4×D3—62no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—62no—
701C4×D3—64no—
702C4×D3—62no—
703C4×D3—61no—
704C4×D3—61no—
705C4×D3—61no—
706C4×D3—61no—
707C4×D3—62no—
708C4×D3—121no—
709C4×D3—121no—
710C4×D3—124no—
711C4×D3D3×D412yes—
712C4×D3C2×#6712yes—
713Dic6—21no—
714Dic6—24no—
715Dic6—21no—
716Dic6—21no—
717Dic6C2×#6712yes—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—41no—
721C3×C8—61no—
722C3×C8—61no—
723C3⋊C8—21no—
724C3⋊C8—21no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—121no—
728C2×C32—81no—
729C2×C32C2×#12011yescharacteristic
730C2×C32#57511yescharacteristic
731C2×C32#57511yescharacteristic
732C3⋊D3—41no—
733C3⋊D3—42no—
734C3×D3—22no—
735C3×D3—41no—
736C3×D3—42no—
737C24—91no—
738C24—181no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—62no—
743#41—182no—
744#41—182no—
745#41—188no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—182no—
750#41—182no—
751C2×Q8—34no—
752C2×Q8—31no—
753C2×Q8—31no—
754C2×Q8—61no—
755C2×Q8—62no—
756C2×Q8C2×D3211yescharacteristic
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—94no—
762C2×D4—91no—
763C2×D4—181no—
764C2×D4—182no—
765C2×D4—181no—
766C2×D4—188no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C2×D4C2×D3211yescharacteristic
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—91no—
780C22×C4—181no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—181no—
784C22×C4—188no—
785C22×C4—181no—
786Q16—62no—
787Q16—62no—
788SD16—22no—
789SD16—62no—
790SD16—182no—
791SD16—182no—
792D8—62no—
793D8—182no—
794M16—62no—
795M16—182no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—91no—
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—91no—
802C4⋊C4—181no—
803C4⋊C4—181no—
804C22⋊C4—61no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—181no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—62no—
823C22×C3—61no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3C2×D3×D411yescharacteristic
830C22×C3C2×D3×D411yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—22no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—61no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—62no—
844C2×D3—61no—
845C2×D3—62no—
846C2×D3—61no—
847C2×D3—122no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—124no—
852C2×D3—128no—
853C2×D3—124no—
854C2×D3—128no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—241no—
860C2×D3—241no—
861C2×D3#93712yes—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—32no—
867C3×C4—42no—
868C3×C4—61no—
869C3×C4—62no—
870C3×C4—121no—
871C3×C4—121no—
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C22×#6711yescharacteristic
876Dic3—22no—
877Dic3—21no—
878Dic3—41no—
879Dic3—41no—
880Dic3—61no—
881Dic3—61no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—241no—
886Dic3#93712yes—
887C32#300511yescharacteristic, complemented, Sylow
888C23—21no—
889C23—31no—
890C23—31no—
891C23—61no—
892C23—91no—
893C23—184no—
894C23—182no—
895C23—181no—
896C23—361no—
897C23—361no—
898C23—362no—
899C23—362no—
900Q8—21no—
901Q8—32no—
902Q8—64no—
903Q8—61no—
904Q8—61no—
905Q8—61no—
906Q8D3×#6712yes—
907D4—21no—
908D4—21no—
909D4—32no—
910D4—64no—
911D4—61no—
912D4—92no—
913D4—122no—
914D4—122no—
915D4—184no—
916D4—184no—
917D4—184no—
918D4—184no—
919D4—181no—
920D4—362no—
921C2×C4—21no—
922C2×C4—31no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—31no—
926C2×C4—64no—
927C2×C4—64no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—91no—
934C2×C4—122no—
935C2×C4—184no—
936C2×C4—182no—
937C2×C4—182no—
938C2×C4—184no—
939C2×C4—182no—
940C2×C4—184no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—61no—
947C8—61no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—62no—
953C2×C3—81no—
954C2×C3—81no—
955C2×C3—121no—
956C2×C3—122no—
957C2×C3—161no—
958C2×C3D3×#12011yescharacteristic
959C2×C3#576811yescharacteristic
960C2×C3#577311yescharacteristic
961C2×C3#577711yescharacteristic
962C2×C3#577711yescharacteristic
963C2×C3C2×#93711yescharacteristic
964D3—22no—
965D3—41no—
966D3—42no—
967D3—121no—
968D3—122no—
969D3—121no—
970D3—122no—
971D3—241no—
972D3—242no—
973C22—32no—
974C22—41no—
975C22—41no—
976C22—41no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—61no—
981C22—62no—
982C22—61no—
983C22—121no—
984C22—121no—
985C22—181no—
986C22—181no—
987C22—182no—
988C22—181no—
989C22—364no—
990C22—368no—
991C22—361no—
992C22—361no—
993C22D32×D411yescharacteristic
994C4—22no—
995C4—32no—
996C4—61no—
997C4—62no—
998C4—121no—
999C4—121no—
1000C4—181no—
1001C4—361no—
1002C4D32×D411yescharacteristic
1003C4C2×D3×#6711yescharacteristic
1004C3—21no—
1005C3#8008311yescharacteristic, complemented
1006C3#8398011yescharacteristic, complemented
1007C2—62no—
1008C2—81no—
1009C2—121no—
1010C2—122no—
1011C2—361no—
1012C2—362no—
1013C2#1059474411yescharacteristic
1014C2#1059474611yescharacteristic
1015C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×C3×#915C2semidirect
3. #10595301C2semidirect
4. C2×#63925C2semidirect
5. #10592871C2semidirect
6. C3×#5172C2semidirect
7. #10591602C2semidirect
8. #10591597C2semidirect
9. #10591557C2semidirect
10. #10591521C2semidirect
11. #10591520C2semidirect
12. #10590966C2semidirect
13. #10590965C2semidirect
14. #10590939C2semidirect
15. #10590936C2semidirect
32. C2×C32×SD16C22semidirect
33. #64147C22semidirect
34. C2×#3753C22semidirect
35. C2×C3×#216C22semidirect
36. C3×#938C22semidirect
37. C2×C3×#214C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×Dic12C22semidirect
47. #63871C22semidirect
48. #63856C22semidirect
50. C2×#3717C22semidirect
51. C2×#3715C22semidirect
53. #63662C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#915D3semidirect
85. #5172D3semidirect
113. C3×D3×Q8D4semidirect
135. D3×D12D4semidirect
204. C2×C3×SD16C2×D3semidirect
205. C2×C3×SD16C2×D3semidirect
212. C2×#216C2×D3semidirect
218. #938C2×D3semidirect
224. C2×#214C2×D3semidirect
228. C2×#213C2×D3semidirect
236. C2×Dic12C2×D3semidirect
252. #835C2×D3semidirect
260. #821C2×D3semidirect
267. (C2×D3)⋊C8C2×D3semidirect
402. D3×Q8#67semidirect
560. C2×SD16D32semidirect
887. C32#3005semidirect
1005. C3#80083semidirect
1006. C3#83980semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×C3×#9152
#105953012
C2×#639252
#105928712
C3×#51722
#105916022
#105915972
#105915572
#105915212
#105915202
#105909662
#105909652
#105909392
#105909362
#839803
#800833