Finite Group Databasebeta

← #11889710

Subgroups — #11889710

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596021C211yesmaximal, characteristic
2C3×#5543C211yesmaximal, characteristic, complemented
3C3×#5011C211yesmaximal, characteristic, complemented
4#10591187C211yesmaximal, characteristic, complemented
5#10591184C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591178C211yesmaximal, characteristic, complemented
8#10591135C211yesmaximal, characteristic, complemented
9#10591133C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590368C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic, complemented
15#10590294C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#79503—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64146—21no—
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic
24#64103—21no—
25#64093—21no—
26C22⋊C4×C3⋊D3—21no—
27#64084C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C3×D4×Dic3—21no—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic
36C3×#890—21no—
37C3×#878—21no—
38C3×#878—21no—
39C3×#869C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#830C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#803C2211yescharacteristic, complemented
48#63575C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63567C2211yescharacteristic, complemented
52#63567C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61C3×#554—31no—
62#5550—31no—
63#5550—31no—
64#5550—61no—
65#5543D311yescharacteristic, complemented
66C3×#435—31no—
67#5134—31no—
68#5133—31no—
69#5116—31no—
70C2×#821—31no—
71#5089—31no—
72#5087—31no—
73#5051—31no—
74#5049—31no—
75#5047—31no—
76#5046—31no—
77#5028—31no—
78#5026—31no—
79#5011D311yescharacteristic, complemented
80#4970—31no—
81#4967—31no—
82#4966—31no—
83C2×#809—31no—
84#4846—31no—
85#4845—31no—
86#4736—31no—
87#4733—31no—
88#4731—31no—
89#4722—31no—
90#4714—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C32×C4⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×#208—41no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3719—41no—
142#3717—22no—
143#3717—41no—
144#3314—91noSylow
145C2×#235—31no—
146C2×#235—31no—
147C2×#235—61no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—61no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×C4⋊Q8—31no—
154C3×#125—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—61no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C2×D311yescharacteristic
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×#216—31no—
167C2×#215—31no—
168C2×#215—31no—
169#937—62no—
170#937—61no—
171#937—61no—
172D4×Dic3—21no—
173#930—31no—
174#930—31no—
175#930—61no—
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×C4⋊Dic3C2×D311yescharacteristic, complemented
178#924—31no—
179#924—31no—
180#924—61no—
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic, complemented
183C2×#208C2×D311yescharacteristic, complemented
184C22×C3⋊C8C2×D311yescharacteristic
185C2×Dic12—31no—
186C2×#204—31no—
187C2×#204—31no—
188#894—62no—
189#894—61no—
190#894—61no—
191#890—21no—
192#884—62no—
193#884—61no—
194#884—61no—
195D3×C22⋊C4—62no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#878—21no—
199#878—21no—
200#875—31no—
201#875—31no—
202#875—61no—
203C4×D12—31no—
204C4×D12—31no—
205C4×D12—61no—
206#869C2×D311yescharacteristic, complemented
207C4×Dic6C2×D311yescharacteristic, complemented
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#835—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic, complemented
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#818—31no—
222#818—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241#803C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3—81no—
249C32×D4—22no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259#638—42no—
260#638—81no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—42no—
267C4⋊(C3⋊D3)#4112yes—
268C4×C3⋊D3—42no—
269C4×C3⋊D3—81no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—81no—
277C2×C3×Dic3—81no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280C3×Dic6—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—31no—
286#546—91no—
287#489—91no—
288#484—91no—
289#480—91no—
290#474—91no—
291#468—91no—
292#467—91no—
293#464—91no—
294#452—91no—
295#450—91no—
296#440—91no—
297#435—31no—
298#417—91no—
299C2×#102—91no—
300C23×D3—62no—
301C23×D3—61no—
302C23×D3—61no—
303C2×C3×Q8—31no—
304C2×C3×Q8—61no—
305C2×C3×D4—21no—
306C2×C3×D4D1211yescharacteristic
307C2×C3×D4#6711yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—62no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—62no—
320C2×#67—61no—
321C2×#67—61no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324#235—62no—
325#235—62no—
326#235—122no—
327#235—121no—
328#235—121no—
329#235—122no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—122no—
342C2×D12—121no—
343C2×D12—121no—
344C2×D12—122no—
345C2×C4×D3—62no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—62no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×Dic6—21no—
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C3×M16—121no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—121no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4D1211yescharacteristic
373C3×C4⋊C4#6711yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4D1211yescharacteristic
379C3×C22⋊C4D1211yescharacteristic
380C3×C22⋊C4#6711yescharacteristic
381C3×C22⋊C4#6711yescharacteristic
382C3×C42—21no—
383C3×C42—61no—
384C3×C42C22×D311yescharacteristic
385C3×C42C22×D311yescharacteristic
386#217—21no—
387#217—21no—
388#217—62no—
389#217—61no—
390#217—61no—
391#216—121no—
392#215—62no—
393#215—121no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406C4⋊Dic3—21no—
407C4⋊Dic3—21no—
408C4⋊Dic3—21no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—61no—
412C4⋊Dic3C22×D311yescharacteristic
413C4⋊Dic3C22×D311yescharacteristic
414C4⋊Dic3C22×D311yescharacteristic
415Dic3⋊C4—21no—
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—62no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421C4×Dic3—21no—
422#208—41no—
423C2×C3⋊C8—41no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428Dic12—121no—
429#204—62no—
430#204—121no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32#13712yes—
437C22×C32C22×D411yescharacteristic
438C2×C3⋊D3—22no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—84no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—41no—
452C3⋊Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C2×#41—91no—
458C22×D4—91no—
459C2×Q16—91no—
460C2×SD16—91no—
461C2×SD16—91no—
462C2×M16—31no—
463C22×C8—31no—
464C4⋊Q8—31no—
465#125—61no—
466#124—91no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—31no—
470C22⋊Q8—61no—
471C22⋊Q8—61no—
472C22⋊Q8—91no—
473#121—91no—
474#121—181no—
475#120—181no—
476C4×Q8—31no—
477C4×D4—61no—
478C4×D4—91no—
479C4×D4D3211yescharacteristic
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C22⋊C4—181no—
483#107—91no—
484#107—91no—
485#107—91no—
486C4⋊C8—31no—
487#103—91no—
488#103—91no—
489#103—91no—
490#103—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497C22⋊C8—31no—
498C22⋊C8—31no—
499#97—31no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3C2×D1211yescharacteristic
503C23×C3C2×D1211yescharacteristic
504C23×C3C2×#6711yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C22×D3—62no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—62no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—124no—
515C22×D3—124no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—242no—
521C3×Q8—61no—
522C3×Q8—61no—
523C3×Q8—241no—
524C3×D4—22no—
525C3×D4—22no—
526C3×D4—42no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—241no—
549C2×C3×C4—241no—
550C2×C3×C4C2×D1211yescharacteristic
551C2×C3×C4C2×D1211yescharacteristic
552C2×C3×C4C2×D1211yescharacteristic
553C2×C3×C4C2×D1211yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C2×#6711yescharacteristic
556C2×C3×C4C2×#6711yescharacteristic
557C2×C3×C4C2×#6711yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560#67—122no—
561#67—122no—
562#67—124no—
563#67—241no—
564#67—241no—
565#67—242no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—62no—
571C2×Dic3—62no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—81no—
577C2×Dic3—81no—
578D12—32no—
579D12—32no—
580D12—62no—
581D12—62no—
582D12—61no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—121no—
589D12—121no—
590D12—122no—
591D12—122no—
592D12—124no—
593C4×D3—122no—
594C4×D3—122no—
595C4×D3—124no—
596C4×D3—241no—
597C4×D3—241no—
598C4×D3—242no—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—81no—
606Dic6—121no—
607Dic6—121no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32—22no—
617C2×C32—41no—
618C2×C32#54611yescharacteristic
619C2×C32C2×#13711yescharacteristic
620C2×C32#57611yescharacteristic
621C3⋊D3—42no—
622C3⋊D3—81no—
623C24—181no—
624#41—182no—
625#41—361no—
626C2×Q8—31no—
627C2×Q8—61no—
628C2×Q8—91no—
629C2×D4—91no—
630C2×D4—91no—
631C2×D4—182no—
632C2×D4—181no—
633C2×D4—181no—
634C2×D4—181no—
635C2×D4—361no—
636C2×D4#62611yescharacteristic
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4C2×D3211yescharacteristic
642C22×C4C2×D3211yescharacteristic
643Q16—361no—
644SD16—182no—
645SD16—361no—
646M16—121no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—121no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—31no—
655C4⋊C4—61no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—91no—
662C4⋊C4—181no—
663C4⋊C4#62611yescharacteristic
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4#62611yescharacteristic
672C22⋊C4#62611yescharacteristic
673C42—61no—
674C42C2×D3211yescharacteristic
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—22no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3#90912yes—
693C22×C3#94212yes—
694C22×C3C22×D1211yescharacteristic
695C22×C3C22×#6711yescharacteristic
696C2×D3—64no—
697C2×D3—62no—
698C2×D3—62no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—122no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3—248no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4#100411yescharacteristic
736C3×C4D3×#4111yescharacteristic
737C3×C4D3×#4111yescharacteristic
738C3×C4#100911yescharacteristic
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—122no—
744Dic3—122no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749C32#331411yescharacteristic, complemented, Sylow
750C23—181no—
751C23—181no—
752C23—362no—
753C23—362no—
754C23—721no—
755C23C2×#62611yescharacteristic
756C23C2×#62611yescharacteristic
757Q8—61no—
758Q8—61no—
759Q8—181no—
760Q8—181no—
761Q8—241no—
762D4—22no—
763D4—92no—
764D4—181no—
765D4—181no—
766D4—181no—
767D4—362no—
768D4—362no—
769D4—721no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—241no—
781C2×C4—241no—
782C2×C4—362no—
783C2×C4—721no—
784C2×C4C2×#62611yescharacteristic
785C2×C4C2×#62611yescharacteristic
786C2×C4C2×#62611yescharacteristic
787C2×C4C2×#62611yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—61no—
790C8—61no—
791C8—61no—
792C8—61no—
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—81no—
802C2×C3#555411yescharacteristic
803C2×C3C2×#90911yescharacteristic
804C2×C3#575211yescharacteristic
805C2×C3C2×#94211yescharacteristic
806C2×C3#582911yescharacteristic
807C2×C3#583511yescharacteristic
808D3—124no—
809D3—122no—
810D3—122no—
811D3—242no—
812D3—241no—
813D3—241no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—182no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22—724no—
826C22#6383312yes—
827C22C22×#62611yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—121no—
836C4—361no—
837C4—361no—
838C4#6431211yescharacteristic
839C4#6431411yescharacteristic
840C3—21no—
841C3#7950311yescharacteristic, complemented
842C3#8363511yescharacteristic, complemented
843C2—22no—
844C2—41no—
845C2—362no—
846C2—721no—
847C2C2×#6383311yescharacteristic
848C2#1059525411yescharacteristic
849C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596021C2
hypercenterC4×D4D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5543C2semidirect
3. C3×#5011C2semidirect
4. #10591187C2semidirect
5. #10591184C2semidirect
6. #10591183C2semidirect
7. #10591178C2semidirect
8. #10591135C2semidirect
9. #10591133C2semidirect
10. #10591106C2semidirect
11. C2×#63564C2semidirect
12. #10590368C2semidirect
13. #10590362C2semidirect
14. #10590313C2semidirect
15. #10590294C2semidirect
31. C2×C3×C4⋊Dic3C22semidirect
33. C3×#924C22semidirect
34. C2×C3×#208C22semidirect
39. C3×#869C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3719C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×#803C22semidirect
48. #63575C22semidirect
49. #63575C22semidirect
50. #63575C22semidirect
51. #63567C22semidirect
52. #63567C22semidirect
53. #63567C22semidirect
54. #63566C22semidirect
65. #5543D3semidirect
79. #5011D3semidirect
177. C2×C4⋊Dic3C2×D3semidirect
182. #924C2×D3semidirect
183. C2×#208C2×D3semidirect
206. #869C2×D3semidirect
207. C4×Dic6C2×D3semidirect
214. #830C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. #803C2×D3semidirect
749. C32#3314semidirect
841. C3#79503semidirect
842. C3#83635semidirect

Maximal subgroups

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

subgroupindex
#105960212
C3×#55432
C3×#50112
#105911872
#105911842
#105911832
#105911782
#105911352
#105911332
#105911062
C2×#635642
#105903682
#105903622
#105903132
#105902942
#836353
#795033