Finite Group Databasebeta

← #11884312

Subgroups — #11884312

Order 1152.

1066 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic, complemented
2C2×#63794C211yesmaximal, characteristic, complemented
3#10594633C211yesmaximal, characteristic, complemented
4#10594530C211yesmaximal, characteristic, complemented
5#10592568C211yesmaximal, characteristic, complemented
6C3×#4867C211yesmaximal, characteristic, complemented
7C3×#4864C211yesmaximal, characteristic, complemented
8#10590870C211yesmaximal, characteristic, complemented
9#10590722C211yesmaximal, characteristic, complemented
10#10590616C211yesmaximal, characteristic, complemented
11#10590616C211yesmaximal, characteristic, complemented
12#10590615C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590565C211yesmaximal, characteristic, complemented
15#10590540C211yesmaximal, characteristic, complemented
16#80921—31nomaximal
17#80675—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×#3745C2211yescharacteristic
23#64102C2211yescharacteristic
24#64102C2211yescharacteristic, complemented
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33#63922—21no—
34#63921—21no—
35#63916—21no—
36#63912—21no—
37C4×#625C2211yescharacteristic
38#63900—21no—
39#63873C2211yescharacteristic, complemented
40#63863C2211yescharacteristic
41#63854—21no—
42#63854—21no—
43#63854—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63808—24no—
51#63794—24no—
52C32×#106C2211yescharacteristic, complemented
53#63642C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55#63636C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic
60#63572C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×#919—31no—
64C2×#914—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5631—31no—
68#5631—31no—
69#5630—31no—
70#5612—31no—
71C3×#470—31no—
72C3×#465—31no—
73#5190—31no—
74#5167—31no—
75#5127—31no—
76#5111—31no—
77#5047—31no—
78#5047—31no—
79#5046—31no—
80#5037—31no—
81#4869—31no—
82#4869—31no—
83#4869—61no—
84#4867D311yescharacteristic, complemented
85#4864D311yescharacteristic, complemented
86#4819—31no—
87#4818—31no—
88#4818—31no—
89#4810—31no—
90#4808—31no—
91#4808—31no—
92#4787—31no—
93#4776—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625D411yescharacteristic
111C2×#624—21no—
112C2×#624—21no—
113C2×#624—21no—
114D3×D12—22no—
115D3×D12—41no—
116#3799—22no—
117#3799—22no—
118#3799—22no—
119#3799—41no—
120#3799—41no—
121#3799—41no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3752—21no—
126#3752—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3745D414yescomplemented
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×#204—22no—
141C3×ΓL(1,𝔽25)—22no—
142C3×D3×C8—22no—
143#3724—21no—
144#3724—21no—
145#3724D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150#3718—41no—
151#3717—22no—
152#3717—22no—
153#3717—22no—
154#3715—41no—
155#3714—22no—
156#3267—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173#947—31no—
174#944—31no—
175#944—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182#938—61no—
183#937—61no—
184#936—31no—
185C2×#214—31no—
186C2×#213—31no—
187C4×#67—31no—
188C4×#67—31no—
189#919—64no—
190#914—64no—
191#908—64no—
192C2×Dic12C2×D311yescharacteristic, complemented
193#904—64no—
194C2×D24—31no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—61no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic
203C2×D3×C8C2×D311yescharacteristic, complemented
204#897C2×D311yescharacteristic
205#897C2×D311yescharacteristic
206#897C2×D311yescharacteristic, complemented
207#895—61no—
208#895C2×D311yescharacteristic
209#894—61no—
210#894—61no—
211#894—61no—
212#893—31no—
213#893—31no—
214#893—31no—
215#893—31no—
216#893—61no—
217#893—61no—
218D3×C4⋊C4—61no—
219D3×C4⋊C4—61no—
220#884—61no—
221#884—61no—
222#883—61no—
223#883—61no—
224#883—61no—
225#882—61no—
226D3×C22⋊C4—61no—
227D3×C22⋊C4—61no—
228C3×#106—21no—
229C3×#106C2×D311yescharacteristic, complemented
230C3×#106C2×D311yescharacteristic, complemented
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—31no—
235#830—31no—
236#830—31no—
237(C2×D3)⋊C8—31no—
238(C2×D3)⋊C8—31no—
239#815—31no—
240#815—31no—
241#815—61no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244#810C2×D311yescharacteristic, complemented
245#810C2×D311yescharacteristic, complemented
246#810C2×D311yescharacteristic, complemented
247#809—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809—61no—
253#809C2×D311yescharacteristic
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)C2×D412yes—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—42no—
272C4×C3⋊D3—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—81no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#626—42no—
295#625—41no—
296#624—42no—
297#624—42no—
298#624—42no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—31no—
309#465—31no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—61no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333#239—62no—
334#239—62no—
335#239—62no—
336#239—121no—
337#239—121no—
338#239—121no—
339D3×D4—62no—
340D3×D4—121no—
341#235—62no—
342#235—62no—
343#235—62no—
344#235—121no—
345#235—121no—
346#235—121no—
347C2×D12—21no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—121no—
372C2×C4×D3—121no—
373C2×C4×D3C22×D311yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×SD16—62no—
380C3×M16—62no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—62no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400#217—31no—
401#217—31no—
402#217—61no—
403#217—61no—
404#216—121no—
405#216—121no—
406#215—62no—
407#215—62no—
408#215—62no—
409#215—121no—
410#214—121no—
411#213—62no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426C4⋊Dic3—21no—
427C4⋊Dic3—21no—
428C4⋊Dic3—21no—
429Dic3⋊C4—31no—
430Dic3⋊C4—31no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—61no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—22no—
444D24—34no—
445D24—34no—
446D24—64no—
447D24—62no—
448#204—22no—
449#204—62no—
450#204—62no—
451#204—62no—
452ΓL(1,𝔽25)—22no—
453D3×C8—22no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470D32—84no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C2×#41—91no—
484C2×#41—91no—
485C22×D4—91no—
486AGL(1,ℤ/8)—184no—
487#135—184no—
488C2×Q16—31no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×D8—91no—
496C2×D8—91no—
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—91no—
500#124—91no—
501#123—181no—
502#123—181no—
503#123—181no—
504C22⋊Q8—31no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507#121—31no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—91no—
512C4×D4—91no—
513C4×D4—91no—
514C2×C4⋊C4—181no—
515C2×C22⋊C4—181no—
516#106D3211yescharacteristic, complemented
517C4⋊C8—91no—
518#103—31no—
519#103—31no—
520#103—31no—
521#102—31no—
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3D3×D411yescharacteristic
544C22×D3D3×D411yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—241no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—121no—
577#67—121no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3D3×D411yescharacteristic
588C2×Dic3D3×D411yescharacteristic
589D12—21no—
590D12—21no—
591D12—32no—
592D12—32no—
593D12—32no—
594D12—32no—
595D12—62no—
596D12—62no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—81no—
602D12—121no—
603D12—121no—
604D12—122no—
605D12—122no—
606D12—122no—
607D12—122no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—242no—
621C4×D3—241no—
622C4×D3—241no—
623C4×D3—242no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—22no—
631C3×C8—61no—
632C3×C8—61no—
633C3×C8D3×D412yes—
634C3×C8D3×D412yes—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C2×C32D4211yescharacteristic
641C2×C32#57511yescharacteristic
642C2×C32#57711yescharacteristic
643C3⋊D3—42no—
644C3⋊D3—42no—
645C3×D3—41no—
646C3×D3—41no—
647C3×D3—81no—
648C24—181no—
649#41—182no—
650#41—182no—
651#41—182no—
652#41—361no—
653#41—361no—
654#41—361no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—91no—
662C2×D4—91no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—361no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676Q16—62no—
677Q16—361no—
678SD16—62no—
679SD16—182no—
680SD16—182no—
681SD16—182no—
682SD16—361no—
683D8—94no—
684D8—182no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8—91no—
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—91no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4C2×D3211yescharacteristic
698C4⋊C4C2×D3211yescharacteristic
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—91no—
710C22×C3—21no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3C2×D3×D411yescharacteristic
721C22×C3C2×D3×D411yescharacteristic
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—244no—
750C2×D3—244no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—81no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4#100911yescharacteristic
767C3×C4#100911yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—41no—
771Dic3—41no—
772Dic3—41no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—121no—
778Dic3—121no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—31no—
781C23—31no—
782C23—61no—
783C23—181no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—721no—
788Q8—61no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794D4—61no—
795D4—61no—
796D4—92no—
797D4—92no—
798D4—181no—
799D4—181no—
800D4—241no—
801D4—362no—
802D4—362no—
803D4—362no—
804D4—362no—
805D4—361no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—91no—
818C2×C4—91no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—721no—
824C2×C4C22×D3211yescharacteristic
825C8—61no—
826C8—61no—
827C8—181no—
828C8#380212yes—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—121no—
833C2×C3—121no—
834C2×C3—241no—
835C2×C3#560911yescharacteristic
836C2×C3#560911yescharacteristic
837C2×C3#576211yescharacteristic
838C2×C3#576811yescharacteristic
839C2×C3#577711yescharacteristic
840C2×C3#577811yescharacteristic
841D3—41no—
842D3—41no—
843D3—81no—
844D3—122no—
845D3—122no—
846D3—122no—
847D3—122no—
848D3—242no—
849D3—242no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—182no—
860C22—182no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—724no—
866C22D32×D411yescharacteristic
867C4—41no—
868C4—41no—
869C4—61no—
870C4—61no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4—181no—
875C4—181no—
876C4C2×#380211yescharacteristic
877C4#6432011yescharacteristic
878C3—21no—
879C3#8067511yescharacteristic, complemented
880C3#8092111yescharacteristic, complemented
881C2—121no—
882C2—121no—
883C2—241no—
884C2—362no—
885C2—362no—
886C2#1059461811yescharacteristic
887C2#1059474611yescharacteristic
888C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#63808C2semidirect
2. C2×#63794C2semidirect
3. #10594633C2semidirect
4. #10594530C2semidirect
5. #10592568C2semidirect
6. C3×#4867C2semidirect
7. C3×#4864C2semidirect
8. #10590870C2semidirect
9. #10590722C2semidirect
10. #10590616C2semidirect
11. #10590616C2semidirect
12. #10590615C2semidirect
13. #10590596C2semidirect
14. #10590565C2semidirect
15. #10590540C2semidirect
21. C2×#3799C22semidirect
24. #64102C22semidirect
25. C2×C3×Dic12C22semidirect
28. C2×C3×D3×C8C22semidirect
31. C3×#897C22semidirect
39. #63873C22semidirect
44. C2×#3718C22semidirect
47. C2×#3717C22semidirect
52. C32×#106C22semidirect
53. #63642C22semidirect
55. #63636C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
60. #63572C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4867D3semidirect
85. #4864D3semidirect
129. #3745D4semidirect
192. C2×Dic12C2×D3semidirect
203. C2×D3×C8C2×D3semidirect
206. #897C2×D3semidirect
229. C3×#106C2×D3semidirect
230. C3×#106C2×D3semidirect
244. #810C2×D3semidirect
245. #810C2×D3semidirect
246. #810C2×D3semidirect
516. #106D32semidirect
779. C32#3267semidirect
879. C3#80675semidirect
880. C3#80921semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C2×#637942
#105946332
#105945302
#105925682
C3×#48672
C3×#48642
#105908702
#105907222
#105906162
#105906152
#105905962
#105905652
#105905402
#809213
#806753