Finite Group Databasebeta

← #11889747

Subgroups — #11889747

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2#10594003C211yesmaximal, characteristic
3#10592727C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591589C211yesmaximal, characteristic, complemented
9#10590607C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic, complemented
11#10590427C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590326C211yesmaximal, characteristic, complemented
14#10590294C211yesmaximal, characteristic, complemented
15#10590269C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#79802—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C2×#3756C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23#64084C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#896—21no—
28C3×#896—21no—
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic, complemented
31C3×C4×D12—21no—
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×#870—21no—
35C3×#869C2211yescharacteristic, complemented
36#63922—21no—
37D3×(C2×D3)⋊C4—21no—
38#63909C2211yescharacteristic
39#63906—21no—
40#63890—21no—
41#63857C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#554—31no—
62#5579D311yescharacteristic, complemented
63#5554—31no—
64#5550—31no—
65C3×#440—31no—
66#5173—31no—
67#5169—31no—
68#5089—31no—
69#5087—31no—
70#5051—31no—
71#5049—31no—
72#5047—31no—
73#5046—31no—
74#5028—31no—
75#5028—31no—
76#5028—61no—
77#5026D311yescharacteristic, complemented
78#5011—31no—
79#5007—31no—
80#4970—31no—
81#4967—31no—
82#4966—31no—
83C2×#809—31no—
84#4884—31no—
85#4882—31no—
86#4813—31no—
87#4812—31no—
88#4771—31no—
89D3×#102—31no—
90#4714—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3795—22no—
111#3795—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3756—41no—
117#3755—41no—
118#3752—21no—
119#3752—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×SD16—31no—
150C3×C4⋊Q8—31no—
151C3×#125—61no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—21no—
157C3×C4×Q8C2×D311yescharacteristic, complemented
158C3×C4×Q8C2×D311yescharacteristic, complemented
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164#946C2×D311yescharacteristic
165#946C2×D311yescharacteristic, complemented
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—61no—
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—61no—
172C2×#215C2×D311yescharacteristic
173#937—61no—
174#930—31no—
175#930—61no—
176C2×(C2×D3)⋊C4—61no—
177#924—31no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#897—31no—
183#896—21no—
184#896—21no—
185#895—31no—
186#894—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188D3×C4⋊C4C2×D311yescharacteristic, complemented
189#886—61no—
190#884—61no—
191#882—61no—
192D3×C22⋊C4—61no—
193#875—31no—
194#875—31no—
195#875—61no—
196C4×D12—21no—
197C4×D12C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic
199#870—21no—
200#869C2×D311yescharacteristic, complemented
201C3×#107—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#97—31no—
205#835C2×D311yescharacteristic, complemented
206#832—31no—
207#832—31no—
208#830—31no—
209#830—31no—
210#821—31no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214#816—31no—
215#816—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×Dic6—81no—
273#626—42no—
274#626—81no—
275#625—42no—
276D3×Dic3—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—31no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—61no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314#237—62no—
315#237—121no—
316D3×D4—62no—
317D3×D4—121no—
318#235—62no—
319#235—121no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—121no—
327C2×D12#6711yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—21no—
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—61no—
339C3×SD16—62no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—41no—
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368#217—61no—
369#216—121no—
370#216—121no—
371#216—122no—
372#215—22no—
373#215—121no—
374#215—121no—
375#215—122no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—121no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4#6711yescharacteristic
389(C2×D3)⋊C4#6711yescharacteristic
390C4⋊Dic3—21no—
391C4⋊Dic3—61no—
392C4⋊Dic3#6711yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401#208—121no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411ΓL(1,𝔽25)—121no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yes—
426D32—84no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447#125—61no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—61no—
453C22⋊Q8—61no—
454C22⋊Q8—91no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8D3211yescharacteristic, complemented
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—61no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—31no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3C2×#6711yescharacteristic
496C22×D3C2×#6711yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—241no—
504C3×D4—32no—
505C3×D4—62no—
506C3×D4—61no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4—241no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—122no—
535#67—122no—
536#67—122no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—122no—
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547D12—22no—
548D12—21no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12—121no—
555D12—122no—
556D12—241no—
557D12#23512yes—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—81no—
563C4×D3—81no—
564C4×D3—81no—
565C4×D3—122no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—81no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3⋊D3—81no—
587C3×D3—22no—
588C3×D3—42no—
589C3×D3—41no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—61no—
594C2×Q8—91no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610Q16—361no—
611SD16—62no—
612SD16—361no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—91no—
618C2×C8—361no—
619C4⋊C4—21no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—21no—
641C42C2×D3211yescharacteristic
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C22×#6711yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—22no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
673C2×D3#94212yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—42no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—81no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4C2×#23511yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4#100911yescharacteristic
696C3×C4#100911yescharacteristic
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—121no—
703Dic3—121no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—31no—
708C23—61no—
709C23—181no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—21no—
714Q8—21no—
715Q8—181no—
716Q8—181no—
717Q8—241no—
718D4—32no—
719D4—62no—
720D4—61no—
721D4—181no—
722D4—181no—
723D4—362no—
724D4—362no—
725D4—721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—362no—
742C2×C4D3×#6711yescharacteristic
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—122no—
754C2×C3—121no—
755C2×C3#555011yescharacteristic
756C2×C3#577411yescharacteristic
757C2×C3D3×#13711yescharacteristic
758C2×C3C2×#94211yescharacteristic
759C2×C3#582911yescharacteristic
760C2×C3#583511yescharacteristic
761D3—22no—
762D3—41no—
763D3—42no—
764D3—241no—
765D3—241no—
766D3—481no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—724no—
780C22C2×D3×#6711yescharacteristic
781C4—21no—
782C4—21no—
783C4—41no—
784C4—41no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—361no—
791C4D3×#23511yescharacteristic
792C4#6430811yescharacteristic
793C3—21no—
794C3#7980211yescharacteristic, complemented
795C3#8363511yescharacteristic, complemented
796C2—62no—
797C2—121no—
798C2—122no—
799C2—721no—
800C2#1059506711yescharacteristic
801C2D3×#94211yescharacteristic
802C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594003C2
hypercenterC4×Q8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
3. #10592727C2semidirect
4. C3×#5026C2semidirect
5. #10591655C2semidirect
6. #10591651C2semidirect
7. #10591596C2semidirect
8. #10591589C2semidirect
9. #10590607C2semidirect
10. D3×#809C2semidirect
11. #10590427C2semidirect
12. #10590422C2semidirect
13. #10590326C2semidirect
14. #10590294C2semidirect
15. #10590269C2semidirect
20. C32×C4×Q8C22semidirect
21. C2×#3756C22semidirect
25. C3×#946C22semidirect
30. C3×D3×C4⋊C4C22semidirect
35. C3×#869C22semidirect
42. C2×#3711C22semidirect
44. #63637C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#835C22semidirect
49. C3×#807C22semidirect
50. C3×#803C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5579D3semidirect
77. #5026D3semidirect
157. C3×C4×Q8C2×D3semidirect
158. C3×C4×Q8C2×D3semidirect
165. #946C2×D3semidirect
188. D3×C4⋊C4C2×D3semidirect
200. #869C2×D3semidirect
205. #835C2×D3semidirect
233. #807C2×D3semidirect
237. #803C2×D3semidirect
458. C4×Q8D32semidirect
705. C32#3314semidirect
794. C3#79802semidirect
795. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
#105940032
#105927272
C3×#50262
#105916552
#105916512
#105915962
#105915892
#105906072
D3×#8092
#105904272
#105904222
#105903262
#105902942
#105902692
#836353
#798023