Finite Group Databasebeta

← #11889709

Subgroups — #11889709

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic
3C3×#5011C211yesmaximal, characteristic, complemented
4#10591187C211yesmaximal, characteristic, complemented
5#10591176C211yesmaximal, characteristic, complemented
6#10591173C211yesmaximal, characteristic, complemented
7#10591172C211yesmaximal, characteristic, complemented
8#10591103C211yesmaximal, characteristic, complemented
9#10591094C211yesmaximal, characteristic, complemented
10#10591088C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590378C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590276C211yesmaximal, characteristic, complemented
15#10590272C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#79503—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25#64133C2211yescharacteristic, complemented
26#64099—21no—
27#64087—21no—
28#64087—21no—
29#64078C2211yescharacteristic, complemented
30C4×#634C2211yescharacteristic, complemented
31C3×#937—21no—
32C3×#930C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic
36C3×#894—21no—
37C3×#884—21no—
38C3×D3×C22⋊C4—21no—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C2×#3719C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
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#63566C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#546—31no—
62#5550D311yescharacteristic
63#5543—31no—
64#5543—31no—
65#5543—61no—
66C3×#435—31no—
67#5239—31no—
68#5232—31no—
69#5218—31no—
70C2×#832—31no—
71#5134—31no—
72#5133—31no—
73#5116—31no—
74C2×#821—31no—
75#5055—31no—
76#5054—31no—
77#5051—31no—
78#5044—31no—
79#5042—31no—
80#5033—31no—
81#5018—31no—
82#5011D311yescharacteristic, complemented
83#5007—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
96C22×C3⋊Dic3—21no—
97C22×C3⋊Dic3—21no—
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×Dic6C2311yescharacteristic
112C32×C4⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3757—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126#3750—21no—
127C4×C3⋊Dic3—21no—
128C3×#217—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—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#3716—22no—
143#3716—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C2×C3×M16—31no—
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×#120—61no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C2×C3×C22⋊C4—61no—
162C2×#216—31no—
163#937—21no—
164D4×Dic3—62no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167C2×#214—31no—
168C2×#214—31no—
169#930C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175C2×C4⋊Dic3—61no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—31no—
180#924—61no—
181#924—61no—
182#924C2×D311yescharacteristic
183C2×#208C2×D311yescharacteristic, complemented
184C22×C3⋊C8C2×D311yescharacteristic
185C2×Dic12—31no—
186C2×#204—31no—
187C2×#204—31no—
188#894—21no—
189#890—62no—
190#890—61no—
191#890—61no—
192#884—21no—
193D3×C22⋊C4—21no—
194#878—62no—
195#878—62no—
196#878—61no—
197#878—61no—
198#878—61no—
199#878—61no—
200#875C2×D311yescharacteristic
201C4×D12C2×D311yescharacteristic
202#869—31no—
203#869—31no—
204#869—61no—
205C4×Dic6—31no—
206C4×Dic6—31no—
207C4×Dic6—61no—
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#830C2×D311yescharacteristic
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#818—31no—
230#818—31no—
231#818—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—31no—
236#810—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
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—81no—
264C2×C3⋊Dic3—81no—
265#634—21no—
266#634—21no—
267#634—81no—
268C3×#67—42no—
269C3×#67—81no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—42no—
276C3×D12#4112yes—
277C3×C4×D3—42no—
278C3×C4×D3—81no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—91no—
286#546—31no—
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—
300C24×C3—61no—
301C23×D3—21no—
302C3×#41—62no—
303C3×#41—121no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4D1211yescharacteristic
314C2×C3×D4#6711yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—21no—
324C2×#67—21no—
325C22×Dic3—62no—
326C22×Dic3—62no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331#235—22no—
332#235—41no—
333C2×D12—22no—
334C2×D12—21no—
335C2×D12—41no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C2×Dic6—62no—
344C2×Dic6—61no—
345C2×Dic6—61no—
346C2×Dic6C22×D311yescharacteristic
347C3×M16—121no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4D1211yescharacteristic
357C3×C4⋊C4#6711yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4D1211yescharacteristic
366C3×C22⋊C4D1211yescharacteristic
367C3×C22⋊C4#6711yescharacteristic
368C3×C22⋊C4#6711yescharacteristic
369C3×C42—21no—
370C3×C42C22×D311yescharacteristic
371C3×C42C22×D311yescharacteristic
372#217—21no—
373#217—62no—
374#217—62no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#216—121no—
380#214—62no—
381#214—121no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—62no—
396C4⋊Dic3—62no—
397C4⋊Dic3—62no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3—62no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418#208—41no—
419C2×C3⋊C8—41no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424Dic12—121no—
425#204—62no—
426#204—121no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32#13712yes—
433C22×C32C22×D411yescharacteristic
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—84no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4C2×#4111yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—31no—
454C22×D4—31no—
455C2×Q16—91no—
456C2×SD16—91no—
457C2×SD16—91no—
458C2×M16—31no—
459C22×C8—31no—
460C4⋊Q8—91no—
461#125—181no—
462#124—31no—
463#123—61no—
464C22⋊Q8—31no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8—181no—
468C22⋊Q8—181no—
469#121—31no—
470#121—61no—
471#120—61no—
472C4×Q8—91no—
473C4×D4—31no—
474C4×D4—181no—
475C4×D4D3211yescharacteristic
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—61no—
479#107—91no—
480#107—91no—
481#107—91no—
482C4⋊C8—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#103—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493C22⋊C8—31no—
494C22⋊C8—31no—
495#97—31no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—122no—
501C23×C3—122no—
502C23×C3—241no—
503C23×C3C2×D1211yescharacteristic
504C23×C3C2×D1211yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C23×C3C2×#6711yescharacteristic
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—81no—
512C3×Q8—61no—
513C3×Q8—61no—
514C3×D4—24no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—32no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—122no—
522C3×D4—122no—
523C3×D4—241no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
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—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—122no—
544C2×C3×C4—241no—
545C2×C3×C4C2×D1211yescharacteristic
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4C2×D1211yescharacteristic
548C2×C3×C4C2×D1211yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—42no—
556#67—81no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—241no—
572C2×Dic3—241no—
573C2×Dic3—241no—
574C2×Dic3—241no—
575C2×Dic3—242no—
576C2×Dic3—242no—
577D12—21no—
578D12—21no—
579D12—21no—
580D12—42no—
581D12#23712yes—
582C4×D3—42no—
583C4×D3—81no—
584Dic6—21no—
585Dic6—21no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—61no—
590Dic6—121no—
591Dic6—121no—
592Dic6—241no—
593Dic6—241no—
594Dic6—242no—
595C3×C8—61no—
596C3×C8—61no—
597C3×C8—61no—
598C3×C8—61no—
599C3⋊C8—21no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C2×C32—22no—
604C2×C32—41no—
605C2×C32#54611yescharacteristic
606C2×C32C2×#13711yescharacteristic
607C2×C32#57611yescharacteristic
608C3×D3—42no—
609C3×D3—81no—
610C24—61no—
611#41—62no—
612#41—121no—
613C2×Q8—31no—
614C2×Q8—91no—
615C2×Q8—181no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—62no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—121no—
623C2×D4#62611yescharacteristic
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4C2×D3211yescharacteristic
629C22×C4C2×D3211yescharacteristic
630Q16—361no—
631SD16—182no—
632SD16—361no—
633M16—121no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—121no—
639C4⋊C4—31no—
640C4⋊C4—61no—
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4#62611yescharacteristic
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—61no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4#62611yescharacteristic
659C22⋊C4#62611yescharacteristic
660C42—181no—
661C42C2×D3211yescharacteristic
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—22no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—62no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—244no—
686C22×C3#90912yes—
687C22×C3#95112yes—
688C22×C3C22×D1211yescharacteristic
689C22×C3C22×#6711yescharacteristic
690C2×D3—22no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—84no—
697C3×C4—22no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23711yescharacteristic
714C3×C4#100411yescharacteristic
715C3×C4#100411yescharacteristic
716C3×C4D3×#4111yescharacteristic
717Dic3—41no—
718Dic3—41no—
719Dic3—122no—
720Dic3—122no—
721Dic3—122no—
722Dic3—122no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731C32#331411yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—122no—
735C23—122no—
736C23—241no—
737C23C2×#62611yescharacteristic
738C23C2×#62611yescharacteristic
739Q8—61no—
740Q8—61no—
741Q8—181no—
742Q8—181no—
743Q8—721no—
744D4—22no—
745D4—32no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—122no—
751D4—241no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—122no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—241no—
764C2×C4—721no—
765C2×C4—721no—
766C2×C4C2×#62611yescharacteristic
767C2×C4C2×#62611yescharacteristic
768C2×C4C2×#62611yescharacteristic
769C2×C4C2×#62611yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—61no—
772C8—61no—
773C8—61no—
774C8—61no—
775C2×C3—22no—
776C2×C3—22no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—42no—
781C2×C3—42no—
782C2×C3—41no—
783C2×C3—41no—
784C2×C3—122no—
785C2×C3—241no—
786C2×C3#555411yescharacteristic
787C2×C3C2×#90911yescharacteristic
788C2×C3#575211yescharacteristic
789C2×C3#580611yescharacteristic
790C2×C3C2×#95111yescharacteristic
791C2×C3#583511yescharacteristic
792D3—42no—
793D3—81no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—62no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—244no—
806C22#6383112yes—
807C22C22×#62611yescharacteristic
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—121no—
813C4—121no—
814C4—361no—
815C4—361no—
816C4—361no—
817C4—361no—
818C4D3×#23711yescharacteristic
819C4#6431311yescharacteristic
820C3—21no—
821C3#7950311yescharacteristic, complemented
822C3#8349811yescharacteristic, complemented
823C2—22no—
824C2—41no—
825C2—122no—
826C2—241no—
827C2C2×#6383111yescharacteristic
828C2#1059524611yescharacteristic
829C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5550C2
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
1. #10596014C2semidirect
3. C3×#5011C2semidirect
4. #10591187C2semidirect
5. #10591176C2semidirect
6. #10591173C2semidirect
7. #10591172C2semidirect
8. #10591103C2semidirect
9. #10591094C2semidirect
10. #10591088C2semidirect
11. C2×#63563C2semidirect
12. #10590378C2semidirect
13. #10590360C2semidirect
14. #10590276C2semidirect
15. #10590272C2semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
25. #64133C22semidirect
29. #64078C22semidirect
30. C4×#634C22semidirect
34. C2×C3×#208C22semidirect
41. C2×#3719C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×#803C22semidirect
48. #63575C22semidirect
49. #63575C22semidirect
50. #63575C22semidirect
51. #63567C22semidirect
52. #63566C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
82. #5011D3semidirect
183. C2×#208C2×D3semidirect
222. #830C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. #803C2×D3semidirect
731. C32#3314semidirect
821. C3#79503semidirect
822. C3#83498semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×#55502
C3×#50112
#105911872
#105911762
#105911732
#105911722
#105911032
#105910942
#105910882
C2×#635632
#105903782
#105903602
#105902762
#105902722
#834983
#795033