Finite Group Databasebeta

← #11864091

Subgroups — #11864091

Order 1152.

1591 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594632C211yesmaximal, characteristic, complemented
5#10592501C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591586C211yesmaximal, characteristic, complemented
10#10590962C211yesmaximal, characteristic, complemented
11#10590960C211yesmaximal, characteristic, complemented
12#10590937C211yesmaximal, characteristic, complemented
13#10590614C211yesmaximal, characteristic, complemented
14#10590613C211yesmaximal, characteristic, complemented
15#10590594C211yesmaximal, characteristic, complemented
16#80227—31nomaximal
17#80083—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64319—24no—
22#64319—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3796C2211yescharacteristic
28C2×#3795—21no—
29C2×#3795—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C2×#3743C2211yescharacteristic
33#64101C2211yescharacteristic
34C2×C3×#216C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40#63951—24no—
41#63922—21no—
42#63908C2211yescharacteristic, complemented
43#63902—21no—
44#63898—21no—
45#63856C2211yescharacteristic, complemented
46#63854—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic
52#63798—24no—
53C32×#103C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, 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×D3×#41—31no—
66C2×D3×#41—31no—
67C2×#918—31no—
68C2×#915—31no—
69C2×#914—31no—
70C2×#911—31no—
71#5627—31no—
72#5606—31no—
73C3×#452—31no—
74C3×#449—31no—
75#5239—31no—
76#5238—31no—
77#5187—31no—
78#5173—31no—
79#5172—31no—
80#5158—31no—
81#5047—31no—
82#5037—31no—
83#4810D311yescharacteristic, complemented
84#4808D311yescharacteristic, complemented
85#4802—31no—
86#4802—31no—
87#4802—61no—
88#4783—31no—
89#4781—31no—
90#4770—31no—
91#4770—31no—
92#4734—31no—
93#4733—31no—
94#4726—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3D414yescomplemented
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634—21no—
104C2×#634C2311yescharacteristic
105C3×#239—22no—
106C3×#239—22no—
107C3×#239—22no—
108C3×#239—22no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#625—21no—
122C2×#625—21no—
123C2×#625—21no—
124C2×#625—21no—
125C2×#624D411yescharacteristic
126C2×D3×Dic3—21no—
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3D411yescharacteristic
130C2×D3×Dic3D411yescharacteristic
131#3802—28no—
132#3802—22no—
133#3802D414yescomplemented
134C4×D32—28no—
135C4×D32—22no—
136C4×D32—22no—
137#3796—22no—
138#3796—22no—
139#3795—28no—
140#3795—28no—
141#3795—22no—
142#3795—22no—
143#3795—22no—
144#3795—22no—
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4×C3⋊Dic3—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#3719—22no—
165#3716—22no—
166#3715—22no—
167#3713—22no—
168#3712—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172D3×#41—64no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239C2×D311yescharacteristic
178C2×#239C2×D311yescharacteristic
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—61no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—31no—
185C2×#237—61no—
186C2×#237—61no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—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×#216—31no—
207C2×#216C2×D311yescharacteristic, complemented
208C2×#215—31no—
209C2×#215C2×D311yescharacteristic, complemented
210#938—31no—
211#937—61no—
212D4×Dic3—61no—
213C2×#214—31no—
214C2×#214—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930—31no—
218#924—31no—
219#918—64no—
220#915—64no—
221#914—64no—
222#911—64no—
223C2×Dic12—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)—31no—
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—61no—
232#897C2×D311yescharacteristic, complemented
233#895C2×D311yescharacteristic, complemented
234#894—61no—
235#893—61no—
236#892—31no—
237#892—31no—
238#892—61no—
239#883—61no—
240#882—61no—
241#67⋊C4—61no—
242#67⋊C4—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(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#816—31no—
265#816—61no—
266#810—31no—
267#810—31no—
268#810—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3C2×D411yescharacteristic
272C22×C3×D3—21no—
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⋊Dic3—21no—
290C2×C3⋊Dic3C2×D411yescharacteristic
291C4×C3⋊D3—24no—
292C4×C3⋊D3C2×D412yes—
293C4×C3⋊D3C2×D412yes—
294#634—21no—
295#634—24no—
296#634C2×D412yes—
297C2×C3×Dic3—21no—
298C2×C3×Dic3C2×D411yescharacteristic
299C2×C3×Dic3C2×D411yescharacteristic
300C3×D12—24no—
301C3×D12—24no—
302C3×D12—21no—
303C3×D12—21no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—42no—
307C3×D12C2×D412yes—
308C3×D12C2×D412yes—
309C3×C4×D3—24no—
310C3×C4×D3—24no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×Dic6—21no—
316C3×Dic6—21no—
317#626—42no—
318#625—24no—
319#625—24no—
320#625—24no—
321#625—42no—
322#624—22no—
323D3×Dic3—24no—
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—31no—
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—31no—
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383#239—22no—
384#239—22no—
385#239—22no—
386#239—22no—
387#239—62no—
388#239—62no—
389D3×Q8—34no—
390D3×Q8—34no—
391D3×Q8—64no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—122no—
395#237—62no—
396#237—62no—
397#237—62no—
398#237—62no—
399#237—62no—
400#237—62no—
401#237—68no—
402#237—68no—
403D3×D4—34no—
404D3×D4—34no—
405D3×D4—62no—
406D3×D4—62no—
407D3×D4—68no—
408D3×D4—68no—
409#235—62no—
410#235—62no—
411#235—68no—
412#235—68no—
413#235—62no—
414#235—62no—
415C2×D12—21no—
416C2×D12—21no—
417C2×D12—21no—
418C2×D12—61no—
419C2×D12C22×D311yescharacteristic
420C2×D12C22×D311yescharacteristic
421C2×D12C22×D311yescharacteristic
422C2×C4×D3—21no—
423C2×C4×D3—21no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—61no—
431C2×C4×D3—62no—
432C2×C4×D3—62no—
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—121no—
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—31no—
446C2×Dic6—31no—
447C2×Dic6—61no—
448C2×Dic6—61no—
449C2×Dic6—61no—
450C2×Dic6—121no—
451C2×Dic6C22×D311yescharacteristic
452C3×Q16—62no—
453C3×SD16—62no—
454C3×SD16—62no—
455C3×D8—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—61no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—61no—
466C3×C22⋊C4—61no—
467#217—61no—
468#217—61no—
469#216—22no—
470#216—62no—
471#215—22no—
472#215—62no—
473#214—62no—
474#214—62no—
475#213—62no—
476#213—62no—
477(C2×D3)⋊C4—21no—
478(C2×D3)⋊C4—21no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—121no—
484C4⋊Dic3—21no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C4×Dic3—121no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—61no—
496C2×C3⋊C8C22×D311yescharacteristic
497C2×C3⋊C8C22×D311yescharacteristic
498Dic12—62no—
499D24—22no—
500#204—22no—
501#204—62no—
502ΓL(1,𝔽25)—62no—
503ΓL(1,𝔽25)—62no—
504ΓL(1,𝔽25)—62no—
505ΓL(1,𝔽25)—62no—
506ΓL(1,𝔽25)—122no—
507C22×C32C22×D411yescharacteristic
508C2×C3⋊D3—21no—
509C2×C3⋊D3—21no—
510C2×C3⋊D3#12012yes—
511C2×C3×D3—21no—
512C2×C3×D3—21no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526D32—44no—
527D32—48no—
528C32×C4—22no—
529C32×C4—41no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—22no—
533C3⋊Dic3—41no—
534C3⋊Dic3#12012yes—
535C3×Dic3—21no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C2×#41—31no—
539C2×#41—31no—
540C2×#41—91no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—181no—
544C2×#41—181no—
545C2×#41—184no—
546C2×#41—184no—
547C22×Q8—91no—
548C22×D4—91no—
549C22×D4—181no—
550C23×C4—91no—
551C23×C4—181no—
552#137—184no—
553AGL(1,ℤ/8)—184no—
554C2×Q16—31no—
555C2×Q16—91no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×D8—31no—
561C2×D8—91no—
562C2×M16—91no—
563C2×M16—91no—
564#123—181no—
565C22⋊Q8—31no—
566C22⋊Q8—91no—
567#121—31no—
568#121—91no—
569#120—181no—
570C4×D4—181no—
571C4×D4—181no—
572#117—91no—
573#103—91no—
574#103—91no—
575#103—91no—
576#103D3211yescharacteristic, complemented
577#102—31no—
578#102—31no—
579#102—91no—
580#102—91no—
581C22⋊C8—31no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—61no—
596C22×D3—64no—
597C22×D3—64no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—121no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3D3×D411yescharacteristic
609C22×D3D3×D411yescharacteristic
610C3×Q8—21no—
611C3×Q8—21no—
612C3×Q8—22no—
613C3×Q8—41no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8D3×D412yes—
617C3×Q8D3×D412yes—
618C3×D4—32no—
619C3×D4—32no—
620C3×D4—64no—
621C3×D4—64no—
622C3×D4—61no—
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—31no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—64no—
637C2×C3×C4—64no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645#67—64no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—122no—
652#67—122no—
653#67—122no—
654C2×Dic3—21no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—64no—
661C2×Dic3—64no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—122no—
669C2×Dic3D3×D411yescharacteristic
670C2×Dic3D3×D411yescharacteristic
671D12—24no—
672D12—24no—
673D12—21no—
674D12—21no—
675D12—21no—
676D12—21no—
677D12—42no—
678D12—122no—
679D12D3×D412yes—
680D12D3×D412yes—
681C4×D3—24no—
682C4×D3—24no—
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—32no—
688C4×D3—32no—
689C4×D3—32no—
690C4×D3—32no—
691C4×D3—62no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—62no—
695C4×D3—62no—
696C4×D3—62no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—124no—
702C4×D3—122no—
703Dic6—21no—
704Dic6—21no—
705Dic6—32no—
706Dic6—32no—
707Dic6—62no—
708Dic6—64no—
709Dic6—64no—
710Dic6—61no—
711Dic6—61no—
712Dic6—124no—
713Dic6—121no—
714C3×C8—21no—
715C3×C8—21no—
716C3×C8—41no—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—121no—
724C2×C32C2×#12011yescharacteristic
725C2×C32#57511yescharacteristic
726C2×C32#57511yescharacteristic
727C3⋊D3—22no—
728C3×D3—41no—
729C3×D3—41no—
730C3×D3—42no—
731C3×D3—42no—
732C3×D3—81no—
733C24—91no—
734C24—181no—
735#41—62no—
736#41—62no—
737#41—62no—
738#41—62no—
739#41—182no—
740#41—182no—
741#41—182no—
742#41—182no—
743#41—188no—
744#41—188no—
745#41—182no—
746#41—182no—
747C2×Q8—31no—
748C2×Q8—94no—
749C2×Q8—91no—
750C2×Q8—181no—
751C2×Q8—182no—
752C2×Q8C2×D3211yescharacteristic
753C2×D4—31no—
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—94no—
760C2×D4—181no—
761C2×D4—182no—
762C2×D4—181no—
763C2×D4—188no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4—181no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—188no—
781C22×C4—181no—
782Q16—62no—
783Q16—182no—
784SD16—62no—
785SD16—62no—
786SD16—182no—
787SD16—182no—
788D8—62no—
789D8—182no—
790M16—182no—
791M16—182no—
792C2×C8—31no—
793C2×C8—31no—
794C2×C8—91no—
795C2×C8C2×D3211yescharacteristic
796C4⋊C4—61no—
797C4⋊C4—91no—
798C4⋊C4—181no—
799C4⋊C4C2×D3211yescharacteristic
800C22⋊C4—61no—
801C22⋊C4—61no—
802C22⋊C4—181no—
803C22⋊C4—181no—
804C22⋊C4—181no—
805C42—181no—
806C22×C3—21no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—121no—
816C22×C3—121no—
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—21no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—32no—
833C2×D3—32no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—62no—
842C2×D3—61no—
843C2×D3—61no—
844C2×D3—61no—
845C2×D3—61no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—124no—
849C2×D3—128no—
850C2×D3—124no—
851C2×D3—128no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—42no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—61no—
860C3×C4—61no—
861C3×C4—81no—
862C3×C4—121no—
863C3×C4C2×D3×D411yescharacteristic
864C3×C4C2×D3×D411yescharacteristic
865C3×C4C2×D3×D411yescharacteristic
866C3×C4C2×D3×D411yescharacteristic
867Dic3—21no—
868Dic3—21no—
869Dic3—32no—
870Dic3—32no—
871Dic3—41no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—122no—
876Dic3—121no—
877Dic3—121no—
878Dic3—241no—
879C32#300511yescharacteristic, complemented, Sylow
880C23—31no—
881C23—31no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23—91no—
886C23—184no—
887C23—182no—
888C23—361no—
889C23—361no—
890C23—362no—
891C23—362no—
892Q8—21no—
893Q8—61no—
894Q8—61no—
895Q8—92no—
896Q8—184no—
897Q8—181no—
898Q8#380212yes—
899D4—32no—
900D4—32no—
901D4—64no—
902D4—64no—
903D4—61no—
904D4—61no—
905D4—61no—
906D4—61no—
907D4—122no—
908D4—184no—
909D4—184no—
910D4—184no—
911D4—362no—
912D4—362no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—31no—
916C2×C4—31no—
917C2×C4—64no—
918C2×C4—64no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—91no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—184no—
928C2×C4—182no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4—184no—
932C2×C4—184no—
933C2×C4—181no—
934C2×C4—181no—
935C2×C4—362no—
936C2×C4C22×D3211yescharacteristic
937C8—21no—
938C8—61no—
939C8—61no—
940C8—181no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—121no—
945C2×C3—122no—
946C2×C3—121no—
947C2×C3—122no—
948C2×C3—241no—
949C2×C3D3×#12011yescharacteristic
950C2×C3D3×#12011yescharacteristic
951C2×C3#576811yescharacteristic
952C2×C3#576811yescharacteristic
953C2×C3#577311yescharacteristic
954C2×C3#577711yescharacteristic
955D3—41no—
956D3—42no—
957D3—41no—
958D3—42no—
959D3—62no—
960D3—62no—
961D3—81no—
962D3—122no—
963C22—61no—
964C22—61no—
965C22—61no—
966C22—61no—
967C22—62no—
968C22—62no—
969C22—61no—
970C22—61no—
971C22—92no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—181no—
980C22—181no—
981C22—364no—
982C22—368no—
983C22D32×D411yescharacteristic
984C4—22no—
985C4—41no—
986C4—61no—
987C4—61no—
988C4—92no—
989C4—121no—
990C4—182no—
991C4—361no—
992C4C2×#380211yescharacteristic
993C4D32×D411yescharacteristic
994C3—21no—
995C3#8008311yescharacteristic, complemented
996C3#8022711yescharacteristic, complemented
997C2—121no—
998C2—121no—
999C2—122no—
1000C2—122no—
1001C2—182no—
1002C2—241no—
1003C2#1059425811yescharacteristic
1004C2#1059474511yescharacteristic
1005C2#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×#64319C2semidirect
2. C2×#63951C2semidirect
3. C2×#63798C2semidirect
4. #10594632C2semidirect
5. #10592501C2semidirect
6. C3×#4810C2semidirect
7. C3×#4808C2semidirect
8. #10591597C2semidirect
9. #10591586C2semidirect
10. #10590962C2semidirect
11. #10590960C2semidirect
12. #10590937C2semidirect
13. #10590614C2semidirect
14. #10590613C2semidirect
15. #10590594C2semidirect
34. C2×C3×#216C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
42. #63908C22semidirect
45. #63856C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
53. C32×#103C22semidirect
54. #63662C22semidirect
55. #63643C22semidirect
56. #63637C22semidirect
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
100. Q8×C3⋊D3D4semidirect
133. #3802D4semidirect
207. C2×#216C2×D3semidirect
209. C2×#215C2×D3semidirect
224. C2×D24C2×D3semidirect
226. C2×#204C2×D3semidirect
232. #897C2×D3semidirect
233. #895C2×D3semidirect
244. C3×#103C2×D3semidirect
245. C3×#103C2×D3semidirect
261. (C2×D3)⋊C8C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
576. #103D32semidirect
879. C32#3005semidirect
995. C3#80083semidirect
996. C3#80227semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×#639512
C2×#637982
#105946322
#105925012
C3×#48102
C3×#48082
#105915972
#105915862
#105909622
#105909602
#105909372
#105906142
#105906132
#105905942
#802273
#800833