Finite Group Databasebeta

← #11884425

Subgroups — #11884425

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2#10595078C211yesmaximal, characteristic, complemented
3#10594919C211yesmaximal, characteristic, complemented
4C2×#63795C211yesmaximal, characteristic, complemented
5C3×#5115C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591182C211yesmaximal, characteristic, complemented
8#10591182C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590861C211yesmaximal, characteristic, complemented
13#10590838C211yesmaximal, characteristic, complemented
14#10590773C211yesmaximal, characteristic, complemented
15#10590765C211yesmaximal, characteristic, complemented
16#80728—31nomaximal
17#79497—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C2×#3746C2211yescharacteristic, complemented
24#64113—24no—
25C2×#3745C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27C2×#3744C2211yescharacteristic, complemented
28C3×#930C2211yescharacteristic
29C3×#930C2211yescharacteristic, complemented
30C3×C4×#67C2211yescharacteristic
31C2×C3×D24C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63983—21no—
34#63979—21no—
35#63971—21no—
36#63958—21no—
37#63921—21no—
38#63912—21no—
39#63911C2211yescharacteristic, complemented
40#63909C2211yescharacteristic
41#63894C2211yescharacteristic
42#63881—21no—
43#63860C2211yescharacteristic
44#63857C2211yescharacteristic
45#63853—21no—
46#63844C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63795—24no—
52C3×#830C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic
54C3×#821C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×#818C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63564C2211yescharacteristic, complemented
63C2×#911—31no—
64C2×#908—31no—
65C2×#904—31no—
66C2×#904—31no—
67C2×#904—61no—
68#5612—31no—
69#5599—31no—
70#5553—31no—
71#5550—31no—
72C3×#466—31no—
73C3×#435—31no—
74#5154—31no—
75#5134—31no—
76#5115D311yescharacteristic, complemented
77#5111D311yescharacteristic, complemented
78#5037—31no—
79#5037—31no—
80#4889—31no—
81#4886—31no—
82#4845—31no—
83#4843—31no—
84#4786—31no—
85#4783—31no—
86#4773—31no—
87#4767—31no—
88#4734—31no—
89#4734—31no—
90#4733—31no—
91#4732—31no—
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—22no—
100#3828—41no—
101#3828—41no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#624—21no—
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3795—22no—
124#3795—41no—
125C2×C32×C8—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3746—22no—
129#3745—22no—
130#3744—22no—
131#3744D414yescomplemented
132C3×#217D411yescharacteristic
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×ΓL(1,𝔽25)—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3716—22no—
153#3716—41no—
154#3714—22no—
155#3714—41no—
156#3268—91noSylow
157C2×#237—31no—
158C2×D3×D4—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—61no—
165C2×#235—61no—
166C22×D12—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C22×C3×C8—21no—
170C22×C3×C8C2×D311yescharacteristic, complemented
171C22×C3×C8C2×D311yescharacteristic, complemented
172C3×#121—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#940—31no—
176#940—61no—
177#940—61no—
178#939—61no—
179#938—61no—
180#937—61no—
181#937—61no—
182#936—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#213—31no—
186C2×#213—31no—
187#930—31no—
188#930C2×D311yescharacteristic
189#930C2×D311yescharacteristic, complemented
190C4×#67C2×D311yescharacteristic
191#924—31no—
192#911—64no—
193#908—64no—
194C2×Dic12—31no—
195C2×Dic12—31no—
196C2×Dic12—61no—
197#904—64no—
198#904—64no—
199#904—68no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—61no—
205C2×D24C2×D311yescharacteristic
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—61no—
213C2×#204—61no—
214C2×ΓL(1,𝔽25)C2×D311yescharacteristic
215#897—31no—
216#895—31no—
217#894—61no—
218#893—31no—
219#893—61no—
220#887—31no—
221#884—61no—
222#884—61no—
223#884—61no—
224#884—61no—
225#883—61no—
226#67⋊C4—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229#875—31no—
230#874—31no—
231C4×D12—31no—
232C4×Dic6—31no—
233C3×#107—31no—
234C3×C4⋊C8—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#830C2×D311yescharacteristic, complemented
241#821—31no—
242#821—31no—
243#821C2×D311yescharacteristic
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8C2×D311yescharacteristic
246#818C2×D311yescharacteristic, complemented
247#816—31no—
248#816—31no—
249#815C2×D311yescharacteristic, complemented
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#810—31no—
252#810—31no—
253#809—31no—
254#809—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—81no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—42no—
277C4×C3⋊D3—42no—
278#634—21no—
279#634—21no—
280#634—21no—
281#634C2×D412yes—
282C3×#67—41no—
283C3×#67—81no—
284C3×#67—81no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296#626—42no—
297#626—42no—
298#626—81no—
299#626—81no—
300#625—42no—
301#624—81no—
302D3×Dic3—42no—
303C32×C8—21no—
304C32×C8C2×D412yes—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C2×AGL(1,ℤ/8)—91no—
308C2×#135—91no—
309#550—91no—
310#546—91no—
311#496—91no—
312#468—91no—
313#466—31no—
314#464—91no—
315#459—91no—
316#452—91no—
317#449—91no—
318#449—91no—
319#447—91no—
320#440—91no—
321#435—31no—
322C23×D3—61no—
323C23×D3—61no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—121no—
346C2×#67—121no—
347C2×#67D1211yescharacteristic
348C22×Dic3—61no—
349#237—62no—
350#237—121no—
351D3×D4—62no—
352D3×D4—121no—
353#235—62no—
354#235—62no—
355#235—62no—
356#235—62no—
357#235—62no—
358#235—64no—
359#235—64no—
360#235—121no—
361#235—121no—
362#235—121no—
363#235—121no—
364#235—121no—
365#235—122no—
366#235—122no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—121no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—31no—
392C2×Dic6—31no—
393C2×Dic6—31no—
394C2×Dic6—31no—
395C2×Dic6—61no—
396C2×Dic6—61no—
397C3×D8—62no—
398C3×M16—62no—
399C2×C3×C8—24no—
400C2×C3×C8—22no—
401C2×C3×C8—22no—
402C2×C3×C8—21no—
403C2×C3×C8—21no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C22×D311yescharacteristic
410C3×C4⋊C4—31no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—31no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C42—31no—
418#217—61no—
419#217—61no—
420#217—61no—
421#217D1211yescharacteristic
422#214—62no—
423#214—121no—
424#213—62no—
425#213—121no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4D1211yescharacteristic
436C4⋊Dic3—61no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4D1211yescharacteristic
443C4×Dic3—61no—
444C4×Dic3—61no—
445C4×Dic3C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448Dic12—62no—
449Dic12—62no—
450Dic12—64no—
451D24—22no—
452D24—62no—
453D24—62no—
454D24—64no—
455D24—62no—
456D24—121no—
457#204—34no—
458#204—34no—
459#204—64no—
460#204—64no—
461#204—62no—
462#204—62no—
463#204—62no—
464#204—121no—
465ΓL(1,𝔽25)—22no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485D32—84no—
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—22no—
490C3⋊Dic3—41no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C2×#41—91no—
498C2×#41—91no—
499C22×D4—91no—
500AGL(1,ℤ/8)—184no—
501#135—184no—
502C2×Q16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×M16—31no—
512C22×C8D3211yescharacteristic, complemented
513#127—91no—
514#127—181no—
515#124—91no—
516#123—181no—
517C22⋊Q8—91no—
518#121—31no—
519#121—31no—
520#121—91no—
521#121—181no—
522#121—181no—
523#121—181no—
524#120—181no—
525C4×Q8—91no—
526C4×D4—31no—
527C4×D4—91no—
528C4×D4—181no—
529C2×C22⋊C4—181no—
530#107—31no—
531C4⋊C8—31no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8—31no—
540#97—31no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3C2×D1211yescharacteristic
546C23×C3D3×D411yescharacteristic
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3C2×D1211yescharacteristic
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—121no—
567C3×D4—241no—
568C3×D4—241no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4C2×D1211yescharacteristic
585C2×C3×C4D3×D411yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588#67—41no—
589#67—81no—
590#67—81no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—124no—
600#67—124no—
601#67—241no—
602#67—241no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—122no—
612C2×Dic3C2×D1211yescharacteristic
613C2×Dic3C2×D1211yescharacteristic
614C2×Dic3C2×D1211yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—32no—
620D12—32no—
621D12—62no—
622D12—62no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—121no—
630D12—121no—
631D12—122no—
632D12—122no—
633D12—241no—
634D12—241no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—241no—
645C4×D3—241no—
646Dic6—32no—
647Dic6—32no—
648Dic6—62no—
649Dic6—61no—
650Dic6—61no—
651Dic6—62no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—61no—
656Dic6—121no—
657Dic6—121no—
658C3×C8—22no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—22no—
662C3×C8—61no—
663C3×C8—61no—
664C3×C8D3×D412yes—
665C3×C8D3×D412yes—
666C3⋊C8—21no—
667C3⋊C8—21no—
668C2×C32—41no—
669C2×C32D4211yescharacteristic
670C2×C32#57511yescharacteristic
671C2×C32#57611yescharacteristic
672C3⋊D3—42no—
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—81no—
676C3×D3—81no—
677C24—181no—
678#41—182no—
679#41—182no—
680#41—182no—
681#41—361no—
682#41—361no—
683#41—361no—
684C2×Q8—91no—
685C2×Q8—91no—
686C2×D4—31no—
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—361no—
702C22×C4—31no—
703C22×C4—181no—
704C22×C4—181no—
705C22×C4—181no—
706C22×C4—181no—
707C22×C4C2×D3211yescharacteristic
708Q16—182no—
709SD16—94no—
710SD16—182no—
711SD16—182no—
712SD16—361no—
713D8—62no—
714D8—182no—
715D8—182no—
716D8—361no—
717M16—62no—
718C2×C8—22no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8C2×D3211yescharacteristic
722C2×C8C2×D3211yescharacteristic
723C4⋊C4—31no—
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—181no—
727C4⋊C4—181no—
728C22⋊C4—31no—
729C22⋊C4—31no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C42—31no—
738C42—181no—
739C22×C3—22no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3C22×D1211yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—122no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—244no—
788C2×D3—244no—
789C3×C4—22no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—121no—
798C3×C4—121no—
799C3×C4C2×D3×D411yescharacteristic
800C3×C4C2×D3×D411yescharacteristic
801C3×C4#100911yescharacteristic
802C3×C4#100911yescharacteristic
803Dic3—21no—
804Dic3—21no—
805Dic3—21no—
806Dic3—41no—
807Dic3—41no—
808Dic3—62no—
809Dic3—62no—
810Dic3—122no—
811Dic3—122no—
812Dic3—121no—
813Dic3—121no—
814C32#326811yescharacteristic, complemented, Sylow
815C23—31no—
816C23—61no—
817C23—61no—
818C23—181no—
819C23—181no—
820C23—362no—
821C23—362no—
822C23—721no—
823C23D3×D1211yescharacteristic
824Q8—92no—
825Q8—181no—
826Q8—181no—
827Q8—181no—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—92no—
833D4—121no—
834D4—181no—
835D4—181no—
836D4—181no—
837D4—241no—
838D4—241no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845D4—721no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4—721no—
861C2×C4D3×D1211yescharacteristic
862C2×C4C22×D3211yescharacteristic
863C8—21no—
864C8—61no—
865C8—61no—
866C8#381112yes—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—42no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—121no—
874C2×C3—241no—
875C2×C3—241no—
876C2×C3D4×D1211yescharacteristic
877C2×C3#560911yescharacteristic
878C2×C3#574811yescharacteristic
879C2×C3#575211yescharacteristic
880C2×C3#575711yescharacteristic
881C2×C3#576811yescharacteristic
882D3—41no—
883D3—81no—
884D3—81no—
885D3—122no—
886D3—122no—
887D3—242no—
888D3—242no—
889D3—241no—
890D3—241no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—182no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—724no—
910C22C2×D3×D1211yescharacteristic
911C4—21no—
912C4—61no—
913C4—61no—
914C4—61no—
915C4—121no—
916C4—121no—
917C4—182no—
918C4—361no—
919C4#6430811yescharacteristic
920C4C2×#381111yescharacteristic
921C3—21no—
922C3#7949711yescharacteristic, complemented
923C3#8072811yescharacteristic, complemented
924C2—41no—
925C2—121no—
926C2—241no—
927C2—241no—
928C2—362no—
929C2—721no—
930C2#1059467611yescharacteristic
931C2#1059467811yescharacteristic
932C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. #10595078C2semidirect
3. #10594919C2semidirect
4. C2×#63795C2semidirect
5. C3×#5115C2semidirect
6. C3×#5111C2semidirect
7. #10591182C2semidirect
8. #10591182C2semidirect
9. #10590969C2semidirect
10. #10590947C2semidirect
11. #10590883C2semidirect
12. #10590861C2semidirect
13. #10590838C2semidirect
14. #10590773C2semidirect
15. #10590765C2semidirect
19. C2×#3828C22semidirect
22. C22×C32×C8C22semidirect
23. C2×#3746C22semidirect
27. C2×#3744C22semidirect
29. C3×#930C22semidirect
39. #63911C22semidirect
46. #63844C22semidirect
48. C2×#3716C22semidirect
52. C3×#830C22semidirect
54. C3×#821C22semidirect
56. C3×#818C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
62. #63564C22semidirect
76. #5115D3semidirect
77. #5111D3semidirect
131. #3744D4semidirect
170. C22×C3×C8C2×D3semidirect
171. C22×C3×C8C2×D3semidirect
189. #930C2×D3semidirect
240. #830C2×D3semidirect
244. #821C2×D3semidirect
246. #818C2×D3semidirect
249. #815C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
512. C22×C8D32semidirect
814. C32#3268semidirect
922. C3#79497semidirect
923. C3#80728semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
#105950782
#105949192
C2×#637952
C3×#51152
C3×#51112
#105911822
#105909692
#105909472
#105908832
#105908612
#105908382
#105907732
#105907652
#807283
#794973