Finite Group Databasebeta

← #11867149

Subgroups — #11867149

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#121C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3#10594922C211yesmaximal, characteristic, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C3×#5041C211yesmaximal, characteristic, complemented
6C3×#5038C211yesmaximal, characteristic, complemented
7#10591464C211yesmaximal, characteristic, complemented
8#10591454C211yesmaximal, characteristic, complemented
9#10591426C211yesmaximal, characteristic, complemented
10#10591177C211yesmaximal, characteristic, complemented
11#10591164C211yesmaximal, characteristic, complemented
12#10590612C211yesmaximal, characteristic, complemented
13#10590583C211yesmaximal, characteristic, complemented
14#10590522C211yesmaximal, characteristic, complemented
15#10590508C211yesmaximal, characteristic, complemented
16#80715—31nomaximal
17#80657—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C32×#121C2211yescharacteristic
23#64148—21no—
24#64147C2211yescharacteristic
25#64139C2211yescharacteristic
26#64104C2211yescharacteristic
27C4⋊C4×C3⋊D3C2211yescharacteristic
28#64093—21no—
29C22⋊C4×C3⋊D3—21no—
30C2×C3×#214C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic, complemented
33C3×#924C2211yescharacteristic, complemented
34C22×C3×C3⋊C8C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36#63981—21no—
37#67⋊Dic3—21no—
38#63937—24no—
39#63916C2211yescharacteristic, complemented
40#63881—21no—
41#63871C2211yescharacteristic, complemented
42#63853—21no—
43#63849C2211yescharacteristic
44C2×#3717C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46C2×#3712—24no—
47C2×#3712C2211yescharacteristic
48C2×#3712C2211yescharacteristic
49C2×#3712C2211yescharacteristic, complemented
50C2×#3712C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#808C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C22×ΓL(1,𝔽25)—31no—
66C22×ΓL(1,𝔽25)—31no—
67#5627—31no—
68#5606—31no—
69D3×#121—31no—
70D3×#121—31no—
71D3×#121—61no—
72C3×#466—31no—
73C3×#465—31no—
74#5174—31no—
75#5159—31no—
76#5115—31no—
77#5114—31no—
78#5048—31no—
79#5041D311yescharacteristic, complemented
80#5038—31no—
81#5038D311yescharacteristic, complemented
82#4886—31no—
83#4881—31no—
84#4865—31no—
85#4861—31no—
86#4812—31no—
87#4803—31no—
88#4782—31no—
89#4782—31no—
90#4780—31no—
91#4771—31no—
92#4770—31no—
93#4770—31no—
94C23×C3⋊D3—21no—
95C23×C3⋊D3D411yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101C2×#638—21no—
102C22×C3⋊Dic3D411yescharacteristic
103D4×C3⋊D3—22no—
104D4×C3⋊D3—22no—
105D4×C3⋊D3—44no—
106C2×C4⋊(C3⋊D3)—21no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—21no—
111C2×C4×C3⋊D3D411yescharacteristic
112C2×C4×C3⋊D3D411yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C3×#67—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×D3×Dic3—21no—
121#3796—22no—
122#3796—22no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3757—21no—
126#3752—21no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C3×#217—21no—
131C3×#214—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8—22no—
138C2×C3×C3⋊C8—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143Dic3⋊Dic3—21no—
144#3722—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148#3717—22no—
149#3714—22no—
150#3712—22no—
151#3712—22no—
152#3712—22no—
153#3712D414yescomplemented
154#3055—91noSylow
155C2×#239—31no—
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C2×D3×D4—62no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—61no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C22×C3×C8—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×#121—21no—
172C3×#121—31no—
173C3×#121C2×D311yescharacteristic
174C3×#121C2×D311yescharacteristic
175#946—31no—
176C2×#215—31no—
177#939—61no—
178#939—61no—
179#939—62no—
180#938—31no—
181#938—31no—
182#938—31no—
183#938—61no—
184#937—61no—
185D4×Dic3—61no—
186C2×#214C2×D311yescharacteristic, complemented
187C2×#213—31no—
188C2×#213C2×D311yescharacteristic, complemented
189#930—31no—
190#930—31no—
191#930—61no—
192#930C2×D311yescharacteristic, complemented
193#924C2×D311yescharacteristic, complemented
194C22×C3⋊C8C2×D311yescharacteristic, complemented
195C22×C3⋊C8C2×D311yescharacteristic, complemented
196#914—64no—
197#911—64no—
198C2×D24—31no—
199C2×#204—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—64no—
209C2×ΓL(1,𝔽25)—64no—
210#897—31no—
211#895—31no—
212#895—31no—
213#895—31no—
214#895—61no—
215#894—61no—
216#893—61no—
217#892—31no—
218#892—31no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—31no—
221D3×C4⋊C4—61no—
222#884—61no—
223#884—61no—
224#884—62no—
225#883—61no—
226#882—61no—
227#67⋊C4—61no—
228#67⋊C4—61no—
229D3×C22⋊C4—61no—
230D3×C22⋊C4—61no—
231D3×C22⋊C4—62no—
232C3×#107—31no—
233C3×#106—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238#835—31no—
239#832—31no—
240#832C2×D311yescharacteristic, complemented
241#832C2×D311yescharacteristic, complemented
242#821—31no—
243#821—31no—
244#821—31no—
245#818—31no—
246#817—31no—
247#816—31no—
248#810C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251#809C2×D311yescharacteristic, complemented
252#808—31no—
253#808C2×D311yescharacteristic, complemented
254#807—31no—
255#807C2×D311yescharacteristic, complemented
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3⋊D3—22no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—22no—
261C22×C3⋊D3—41no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3C2×D411yescharacteristic
266C22×C3⋊D3C2×D411yescharacteristic
267C22×C3×D3—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—42no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276#638—42no—
277#638—42no—
278#638—42no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3C2×D411yescharacteristic
282C2×C3⋊Dic3C2×D411yescharacteristic
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—42no—
286C4×C3⋊D3—22no—
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C4×C3⋊D3—22no—
290C4×C3⋊D3—42no—
291C4×C3⋊D3C2×D412yes—
292C4×C3⋊D3#4112yes—
293C3×#67—42no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×Dic6—21no—
300C3×Dic6—21no—
301#626—42no—
302#626—42no—
303D3×Dic3—42no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8C2×D412yescomplemented
307C3×C3⋊C8C2×D412yescomplemented
308C2×AGL(1,ℤ/8)—91no—
309C22×M16—91no—
310#525—91no—
311C2×#121—91no—
312#469—91no—
313#469—91no—
314#468—91no—
315#468—91no—
316#466—31no—
317#466—91no—
318#465—31no—
319#465—91no—
320#428—91no—
321#418—91no—
322#417—91no—
323C23×D3—31no—
324C23×D3—31no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—62no—
329C2×C3×Q8—31no—
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—21no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—21no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—61no—
352C2×#67—61no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357#239—62no—
358#239—62no—
359#237—62no—
360#237—62no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—62no—
364D3×D4—62no—
365D3×D4—122no—
366D3×D4—122no—
367D3×D4—128no—
368D3×D4—124no—
369D3×D4—124no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—62no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—61no—
396C2×C4×D3—61no—
397C2×C4×D3—61no—
398C2×C4×D3—62no—
399C2×C4×D3—122no—
400C2×C4×D3—122no—
401C2×Dic6C22×D311yescharacteristic
402C3×SD16—62no—
403C3×D8—62no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—31no—
408C2×C3×C8—62no—
409C2×C3×C8—62no—
410C3×C4⋊C4—21no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—31no—
413C3×C4⋊C4—61no—
414C3×C4⋊C4C22×D311yescharacteristic
415C3×C4⋊C4C22×D311yescharacteristic
416C3×C22⋊C4—22no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421#217—21no—
422#217—61no—
423#217—61no—
424#217—61no—
425#217—62no—
426#215—62no—
427#214—22no—
428#213—22no—
429#213—62no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442C4⋊Dic3—31no—
443C4⋊Dic3—31no—
444C4⋊Dic3—61no—
445C4⋊Dic3—61no—
446C4⋊Dic3C22×D311yescharacteristic
447C4⋊Dic3C22×D311yescharacteristic
448Dic3⋊C4—21no—
449Dic3⋊C4—61no—
450Dic3⋊C4—61no—
451Dic3⋊C4—61no—
452Dic3⋊C4—62no—
453C4×Dic3—61no—
454C4×Dic3—61no—
455C2×C3⋊C8—22no—
456C2×C3⋊C8—22no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D311yescharacteristic
461D24—62no—
462#204—62no—
463ΓL(1,𝔽25)—34no—
464ΓL(1,𝔽25)—34no—
465ΓL(1,𝔽25)—62no—
466ΓL(1,𝔽25)—62no—
467ΓL(1,𝔽25)—62no—
468ΓL(1,𝔽25)—62no—
469ΓL(1,𝔽25)—62no—
470ΓL(1,𝔽25)—62no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32AGL(1,ℤ/8)12yescomplemented
477C22×C32C22×D411yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—44no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—84no—
488C2×C3⋊D3#12112yes—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C32×C4—21no—
493C32×C4—41no—
494C32×C4C22×D411yescharacteristic
495C32×C4C2×#4111yescharacteristic
496C3⋊Dic3—21no—
497C3⋊Dic3—41no—
498C3⋊Dic3#12112yes—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41—91no—
503C22×D4—91no—
504C22×D4—181no—
505C23×C4—91no—
506AGL(1,ℤ/8)—184no—
507C2×SD16—31no—
508C2×SD16—91no—
509C2×D8—31no—
510C2×D8—91no—
511C2×M16—91no—
512C2×M16—91no—
513C2×M16—91no—
514C2×M16—91no—
515C2×M16—184no—
516C22×C8—31no—
517C22×C8—31no—
518#123—181no—
519C22⋊Q8—31no—
520C22⋊Q8—91no—
521#121—31no—
522#121—91no—
523#121—91no—
524#121—91no—
525#121—91no—
526#121—181no—
527#121—181no—
528#121D3211yescharacteristic
529#120—181no—
530C4×D4—181no—
531C4×D4—181no—
532#117—91no—
533C2×C4⋊C4—91no—
534C2×C22⋊C4—181no—
535#107—31no—
536#107—91no—
537#106—31no—
538#106—91no—
539#103—31no—
540#103—91no—
541#102—31no—
542#102—31no—
543#102—31no—
544#102—91no—
545#102—91no—
546#102—91no—
547C23×C3—22no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—61no—
552C23×C3D3×D411yescharacteristic
553C23×C3D3×D411yescharacteristic
554C22×D3—21no—
555C22×D3—31no—
556C22×D3—31no—
557C22×D3—31no—
558C22×D3—31no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—64no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—122no—
575C22×D3—124no—
576C22×D3—124no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—124no—
580C22×D3—122no—
581C22×D3—122no—
582C3×Q8—61no—
583C3×Q8—61no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—41no—
589C3×D4—41no—
590C3×D4—44no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—61no—
594C3×D4—61no—
595C3×D4—122no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—22no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4D3×D411yescharacteristic
611C2×C3×C4D3×D411yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614#67—42no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—124no—
620#67—124no—
621#67—122no—
622#67—122no—
623#67—124no—
624#67—122no—
625#67—122no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—31no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—62no—
636C2×Dic3—62no—
637C2×Dic3—62no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—122no—
641C2×Dic3—122no—
642D12—21no—
643D12—21no—
644D12—61no—
645D12—61no—
646D12—61no—
647D12—61no—
648D12—121no—
649D12—121no—
650D12—124no—
651D12—122no—
652D12—122no—
653D12—122no—
654D12—122no—
655C4×D3—32no—
656C4×D3—32no—
657C4×D3—32no—
658C4×D3—32no—
659C4×D3—62no—
660C4×D3—62no—
661C4×D3—62no—
662C4×D3—62no—
663C4×D3—62no—
664C4×D3—62no—
665C4×D3—61no—
666C4×D3—61no—
667C4×D3—61no—
668C4×D3—61no—
669C4×D3—122no—
670C4×D3—121no—
671C4×D3—121no—
672C4×D3—122no—
673C4×D3—122no—
674C4×D3—124no—
675C4×D3—122no—
676C4×D3—122no—
677Dic6—21no—
678Dic6—21no—
679C3×C8—32no—
680C3×C8—32no—
681C3×C8—61no—
682C3×C8—61no—
683C3⋊C8—21no—
684C3⋊C8—21no—
685C3⋊C8D3×D412yescomplemented
686C3⋊C8D3×D412yescomplemented
687C2×C32—22no—
688C2×C32—81no—
689C2×C32C2×#12111yescharacteristic
690C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
691C2×C32#57511yescharacteristic
692C3⋊D3—22no—
693C3⋊D3—41no—
694C3⋊D3—81no—
695C3×D3—81no—
696C24—91no—
697C24—181no—
698#41—182no—
699#41—182no—
700C2×Q8—31no—
701C2×D4—21no—
702C2×D4—31no—
703C2×D4—61no—
704C2×D4—91no—
705C2×D4—181no—
706C2×D4—181no—
707C2×D4—181no—
708C2×D4—182no—
709C2×D4—182no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—364no—
714C2×D4C2×D3211yescharacteristic
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—181no—
723C22×C4—181no—
724C22×C4C2×D3211yescharacteristic
725SD16—62no—
726SD16—182no—
727D8—62no—
728D8—182no—
729M16—94no—
730M16—182no—
731M16—182no—
732M16—182no—
733C2×C8—31no—
734C2×C8—31no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—62no—
738C2×C8—62no—
739C4⋊C4—31no—
740C4⋊C4—31no—
741C4⋊C4—61no—
742C4⋊C4—91no—
743C4⋊C4—181no—
744C4⋊C4—181no—
745C4⋊C4C2×D3211yescharacteristic
746C22⋊C4—21no—
747C22⋊C4—61no—
748C22⋊C4—61no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C22⋊C4—181no—
755C42—181no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—22no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3#91112yescomplemented
777C22×C3#91412yescomplemented
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×D3×D411yescharacteristic
780C2×D3—32no—
781C2×D3—32no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—62no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—124no—
802C2×D3—124no—
803C2×D3—128no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—122no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—248no—
814C2×D3—244no—
815C2×D3—244no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—41no—
821C3×C4—42no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4—121no—
827C3×C4C2×D3×D411yescharacteristic
828C3×C4C2×D3×D411yescharacteristic
829C3×C4D3×#4111yescharacteristic
830C3×C4D3×#4111yescharacteristic
831Dic3—32no—
832Dic3—32no—
833Dic3—41no—
834Dic3—41no—
835Dic3—41no—
836Dic3—62no—
837Dic3—61no—
838Dic3—61no—
839Dic3—121no—
840Dic3—122no—
841Dic3—121no—
842Dic3—121no—
843C32#305511yescharacteristic, complemented, Sylow
844C23—21no—
845C23—61no—
846C23—91no—
847C23—91no—
848C23—182no—
849C23—182no—
850C23—181no—
851C23—361no—
852C23—362no—
853C23—362no—
854C23—362no—
855C23#381111yescharacteristic
856Q8—61no—
857Q8—61no—
858D4—21no—
859D4—21no—
860D4—42no—
861D4—61no—
862D4—61no—
863D4—122no—
864D4—181no—
865D4—181no—
866D4—362no—
867D4—362no—
868D4—362no—
869D4—362no—
870D4—362no—
871D4—362no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—91no—
879C2×C4—92no—
880C2×C4—92no—
881C2×C4—91no—
882C2×C4—182no—
883C2×C4—182no—
884C2×C4—182no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—362no—
889C2×C4—362no—
890C2×C4#381111yescharacteristic
891C2×C4C22×D3211yescharacteristic
892C8—32no—
893C8—32no—
894C8—61no—
895C8—61no—
896C2×C3—22no—
897C2×C3—22no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—42no—
902C2×C3—82no—
903C2×C3—81no—
904C2×C3—81no—
905C2×C3—241no—
906C2×C3D3×#12111yescharacteristic
907C2×C3D3×#12111yescharacteristic
908C2×C3C2×#91111yescharacteristic
909C2×C3C2×#91411yescharacteristic
910C2×C3#576811yescharacteristic
911C2×C3#576811yescharacteristic
912D3—64no—
913D3—62no—
914D3—62no—
915D3—81no—
916D3—122no—
917D3—121no—
918D3—121no—
919D3—242no—
920D3—241no—
921D3—241no—
922C22—21no—
923C22—21no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—92no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—181no—
932C22—181no—
933C22—181no—
934C22—181no—
935C22—181no—
936C22—364no—
937C22—361no—
938C22—361no—
939C22—361no—
940C22—724no—
941C22#6393712yescomplemented
942C22C2×#381111yescharacteristic
943C4—21no—
944C4—41no—
945C4—92no—
946C4—121no—
947C4—121no—
948C4—121no—
949C4—181no—
950C4—361no—
951C4D32×D411yescharacteristic
952C4#6431211yescharacteristic
953C3—21no—
954C3#8065711yescharacteristic, complemented
955C3#8071511yescharacteristic, complemented
956C2—22no—
957C2—81no—
958C2—182no—
959C2—241no—
960C2—361no—
961C2—721no—
962C2C2×#6393711yescharacteristic
963C2#1059529811yescharacteristic
964C2#1059546011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#121C2semidirect
2. C2×#63937C2semidirect
3. #10594922C2semidirect
4. C22×#3712C2semidirect
5. C3×#5041C2semidirect
6. C3×#5038C2semidirect
7. #10591464C2semidirect
8. #10591454C2semidirect
9. #10591426C2semidirect
10. #10591177C2semidirect
11. #10591164C2semidirect
12. #10590612C2semidirect
13. #10590583C2semidirect
14. #10590522C2semidirect
15. #10590508C2semidirect
30. C2×C3×#214C22semidirect
31. C2×C3×#213C22semidirect
32. C3×#930C22semidirect
33. C3×#924C22semidirect
34. C22×C3×C3⋊C8C22semidirect
35. C22×C3×C3⋊C8C22semidirect
39. #63916C22semidirect
41. #63871C22semidirect
44. C2×#3717C22semidirect
45. C2×#3714C22semidirect
49. C2×#3712C22semidirect
50. C2×#3712C22semidirect
51. C3×#832C22semidirect
52. C3×#832C22semidirect
53. C3×#810C22semidirect
54. C3×#809C22semidirect
55. C3×#808C22semidirect
56. C3×#807C22semidirect
57. #63575C22semidirect
58. #63573C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
79. #5041D3semidirect
81. #5038D3semidirect
153. #3712D4semidirect
186. C2×#214C2×D3semidirect
188. C2×#213C2×D3semidirect
192. #930C2×D3semidirect
193. #924C2×D3semidirect
194. C22×C3⋊C8C2×D3semidirect
195. C22×C3⋊C8C2×D3semidirect
240. #832C2×D3semidirect
241. #832C2×D3semidirect
248. #810C2×D3semidirect
251. #809C2×D3semidirect
253. #808C2×D3semidirect
255. #807C2×D3semidirect
306. C3×C3⋊C8C2×D4semidirect
307. C3×C3⋊C8C2×D4semidirect
476. C22×C32AGL(1,ℤ/8)semidirect
685. C3⋊C8D3×D4semidirect
686. C3⋊C8D3×D4semidirect
776. C22×C3#911semidirect
777. C22×C3#914semidirect
843. C32#3055semidirect
941. C22#63937semidirect
954. C3#80657semidirect
955. C3#80715semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
C2×#639372
#105949222
C22×#37122
C3×#50412
C3×#50382
#105914642
#105914542
#105914262
#105911772
#105911642
#105906122
#105905832
#105905222
#105905082
#807153
#806573