Finite Group Databasebeta

← #11867776

Subgroups — #11867776

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic, complemented
2#10595398C211yesmaximal, characteristic
3#10595397C211yesmaximal, characteristic, complemented
4C2×#63805C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6C3×#5189C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591634C211yesmaximal, characteristic, complemented
9#10591600C211yesmaximal, characteristic, complemented
10#10591590C211yesmaximal, characteristic, complemented
11#10591556C211yesmaximal, characteristic, complemented
12D3×#835C211yesmaximal, characteristic, complemented
13#10590843C211yesmaximal, characteristic, complemented
14#10590833C211yesmaximal, characteristic, complemented
15#10590681C211yesmaximal, characteristic, complemented
16#83986—31nomaximal
17#80907—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3798C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22#64155C2211yescharacteristic
23#64155C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#918—24no—
30C2×C3×#204C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63916C2211yescharacteristic
34#63908C2211yescharacteristic
35#63907—21no—
36#63906—21no—
37#63905—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63886—21no—
40#63885—21no—
41#63871C2211yescharacteristic
42#63856C2211yescharacteristic
43#63851—21no—
44#63850—21no—
45#63841C2211yescharacteristic
46#63839—21no—
47C2×#3712C2211yescharacteristic
48C2×D3×C3⋊C8C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50#63805—24no—
51#63662C2211yescharacteristic
52#63662C2211yescharacteristic
53#63645C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#817C2211yescharacteristic
57#63575C2211yescharacteristic
58#63573C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×#137—31no—
64#5833—31no—
65#5816—31no—
66C2×#918D311yescharacteristic, complemented
67C2×#907—31no—
68C2×#907—31no—
69#5629—31no—
70#5628—31no—
71C3×#470—31no—
72#5233—31no—
73C2×#835—31no—
74#5189—31no—
75#5189D311yescharacteristic, complemented
76#5188—31no—
77#5188—31no—
78#5188—31no—
79#5188—61no—
80#5174—31no—
81#5174—31no—
82#5171—31no—
83#5171—31no—
84#5134—31no—
85#5121—31no—
86#5051—31no—
87#5048—31no—
88#4864—31no—
89#4861—31no—
90#4816—31no—
91#4812—31no—
92#4804—31no—
93D3×#103—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C3×#239—22no—
98C3×#239—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#627D411yescharacteristic
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#626D411yescharacteristic
113C2×#625—21no—
114C2×#625D411yescharacteristic
115C2×D3×Dic3—21no—
116#3798—22no—
117#3798—22no—
118C32×Q16—22no—
119C2×C32×C8C2311yescharacteristic
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C8×C3⋊D3—22no—
128C3×#216—22no—
129C3×#215—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×ΓL(1,𝔽25)—22no—
140C3×ΓL(1,𝔽25)D414yescomplemented
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32—21no—
150#3712—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#3063—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8C2×D311yescharacteristic
158C2×#235—31no—
159C2×#235—31no—
160C3×#137—64no—
161C2×C3×Q16—21no—
162C2×C3×Q16—31no—
163C2×C3×Q16C2×D311yescharacteristic
164C2×C3×Q16C2×D311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×M16—31no—
168C2×C3×M16—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171#947—61no—
172#946—31no—
173#946—31no—
174#946—31no—
175#946—31no—
176#946—31no—
177#946—31no—
178#946—61no—
179#946—61no—
180#946C2×D311yescharacteristic
181#946C2×D311yescharacteristic
182#944—61no—
183C2×#216C2×D311yescharacteristic
184C2×#215C2×D311yescharacteristic
185#939—61no—
186#939—61no—
187#938—31no—
188#938—31no—
189#930—31no—
190#930—61no—
191#929—61no—
192#929—61no—
193#926—31no—
194C2×C4⋊Dic3—31no—
195#924—31no—
196#924—61no—
197C22×C3⋊C8—31no—
198C22×C3⋊C8—31no—
199#918—24no—
200#907—64no—
201#907—64no—
202C2×#204C2×D311yescharacteristic
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)C2×D311yescharacteristic
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8—31no—
211C2×D3×C8—61no—
212#897—31no—
213#896—61no—
214#895—31no—
215#895—61no—
216#894—61no—
217#892—31no—
218D3×C4⋊C4—31no—
219#888—61no—
220#885—61no—
221#884—61no—
222#884—61no—
223#883—61no—
224C3×#106—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#835—61no—
235#835C2×D311yescharacteristic
236#835C2×D311yescharacteristic
237#832—31no—
238#832—31no—
239#821—31no—
240#818—31no—
241#818—31no—
242#818—31no—
243#818—61no—
244#817—31no—
245#817C2×D311yescharacteristic
246#816—31no—
247#810—31no—
248#809—31no—
249#808—31no—
250#807—31no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8—21no—
257C32×Q8—21no—
258C32×Q8—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2411yescharacteristic
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—42no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×C4×D3—42no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—42no—
284#627—22no—
285#626—22no—
286#626—22no—
287#626—81no—
288#625—22no—
289#625—81no—
290D3×Dic3—81no—
291C32×C8C2×D412yes—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8C2×D412yes—
295C2×#137—31no—
296C2×#131—91no—
297#537—91no—
298#536—91no—
299#470—31no—
300#470—91no—
301#468—91no—
302#468—91no—
303#467—91no—
304#467—91no—
305#465—91no—
306#465—91no—
307#428—91no—
308#416—91no—
309C2×#103—91no—
310C3×#41—62no—
311C3×#41—62no—
312C2×C3×Q8—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—31no—
331C2×#67—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C22×Dic3—61no—
336#239—22no—
337#239—22no—
338D3×Q8—22no—
339D3×Q8—22no—
340#235—62no—
341#235—62no—
342#235—62no—
343#235—62no—
344C2×D12—21no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3C22×D311yescharacteristic
356C2×C4×D3C22×D311yescharacteristic
357C2×Dic6—21no—
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—22no—
362C3×Q16—22no—
363C3×Q16—42no—
364C3×Q16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×M16—34no—
368C3×M16—62no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#216—22no—
385#215—22no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4—121no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—121no—
421Dic3⋊C4—121no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C2×C3⋊C8—31no—
425C2×C3⋊C8—31no—
426C2×C3⋊C8—61no—
427C2×C3⋊C8—62no—
428C2×C3⋊C8—62no—
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431#204—22no—
432ΓL(1,𝔽25)—22no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)#6714yescomplemented
436D3×C8—62no—
437D3×C8—62no—
438D3×C8—62no—
439D3×C8—62no—
440D3×C8—122no—
441C22×C32C22×D411yescharacteristic
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3#12112yes—
454C32×C4—41no—
455C32×C4—41no—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C2×#41—31no—
467C2×#41—91no—
468C22×Q8—31no—
469#137—64no—
470C2×Q16—31no—
471C2×Q16D3211yescharacteristic
472C2×SD16—31no—
473C2×SD16—31no—
474#131—184no—
475C2×M16—31no—
476C2×M16—31no—
477C2×M16—91no—
478C22×C8—91no—
479C22×C8—91no—
480C22×C8—91no—
481C4⋊Q8—181no—
482#124—181no—
483#123—181no—
484#123—181no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C22⋊Q8—91no—
490C22⋊Q8—91no—
491C22⋊Q8—181no—
492#121—91no—
493#121—91no—
494#121—181no—
495#121—181no—
496#121—181no—
497#117—91no—
498C2×C4⋊C4—91no—
499#107—91no—
500#107—91no—
501#106—31no—
502#106—91no—
503#103—31no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—91no—
510#102—91no—
511C23×C3—31no—
512C23×C3—31no—
513C23×C3—61no—
514C22×D3—21no—
515C22×D3—31no—
516C22×D3—31no—
517C22×D3—61no—
518C22×D3D3×D411yescharacteristic
519C22×D3D3×D411yescharacteristic
520C3×Q8—21no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—41no—
531C3×Q8—41no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×Q8—122no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—31no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—122no—
555C2×C3×C4—122no—
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—62no—
559#67—62no—
560#67—62no—
561#67—62no—
562#67—241no—
563#67—241no—
564#67—241no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—241no—
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580D12—21no—
581D12—21no—
582D12—42no—
583D12—62no—
584D12—62no—
585D12—241no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—42no—
589C4×D3—42no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—121no—
595C4×D3—121no—
596C4×D3—241no—
597C4×D3#23712yes—
598C4×D3C2×#6712yes—
599Dic6—21no—
600Dic6—21no—
601Dic6—42no—
602Dic6—62no—
603Dic6—62no—
604C3×C8—22no—
605C3×C8—32no—
606C3×C8—61no—
607C3×C8D3×D412yes—
608C3×C8C2×#6712yes—
609C3⋊C8—21no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—121no—
613C3⋊C8C2×#6712yes—
614C2×C32C2×#12111yescharacteristic
615C2×C32#57711yescharacteristic
616C2×C32#57811yescharacteristic
617C3⋊D3—41no—
618C3×D3—22no—
619C3×D3—41no—
620C3×D3—81no—
621#41—62no—
622#41—62no—
623#41—182no—
624#41—182no—
625C2×Q8—31no—
626C2×Q8—61no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8—91no—
630C2×Q8C2×D3211yescharacteristic
631C2×Q8C2×D3211yescharacteristic
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—91no—
635C2×D4—91no—
636C2×D4—91no—
637C2×D4—181no—
638C2×D4—181no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—91no—
644C22×C4—181no—
645Q16—22no—
646Q16—62no—
647SD16—62no—
648SD16—62no—
649M16—34no—
650M16—62no—
651M16—182no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—91no—
655C2×C8—182no—
656C2×C8—182no—
657C2×C8—182no—
658C2×C8C2×D3211yescharacteristic
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—91no—
664C4⋊C4—91no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—181no—
680C22×C3—21no—
681C22×C3—32no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3C2×D3×D411yescharacteristic
691C22×C3C2×D3×D411yescharacteristic
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—62no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3#93812yes—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—32no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—61no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4C2×D3×D411yescharacteristic
724C3×C4C2×#23711yescharacteristic
725C3×C4D3×#4111yescharacteristic
726C3×C4C22×#6711yescharacteristic
727Dic3—21no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—61no—
732Dic3—61no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—241no—
739Dic3—241no—
740Dic3#93812yes—
741C32#306311yescharacteristic, complemented, Sylow
742C23—31no—
743C23—31no—
744C23—61no—
745C23—91no—
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—61no—
751Q8—61no—
752Q8—122no—
753Q8—182no—
754D4—61no—
755D4—61no—
756D4—122no—
757D4—182no—
758D4—182no—
759D4—182no—
760D4—721no—
761D4—721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—31no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—91no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—721no—
781C2×C4C22×D3211yescharacteristic
782C8—32no—
783C8—61no—
784C8—181no—
785C8D3×#6712yes—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—62no—
790C2×C3—121no—
791C2×C3—241no—
792C2×C3D3×#12111yescharacteristic
793C2×C3#577811yescharacteristic
794C2×C3#577811yescharacteristic
795C2×C3#577911yescharacteristic
796C2×C3#577911yescharacteristic
797C2×C3C2×#93811yescharacteristic
798D3—22no—
799D3—41no—
800D3—81no—
801D3—122no—
802D3—121no—
803D3—121no—
804C22—32no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—181no—
814C22—181no—
815C22—181no—
816C22D32×D411yescharacteristic
817C4—32no—
818C4—41no—
819C4—41no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—361no—
826C4—361no—
827C4D3×#23711yescharacteristic
828C4C2×D3×#6711yescharacteristic
829C3—21no—
830C3#8090711yescharacteristic, complemented
831C3#8398611yescharacteristic, complemented
832C2—62no—
833C2—121no—
834C2—241no—
835C2—361no—
836C2#1059476711yescharacteristic
837C2#1059476911yescharacteristic
838C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595398C2
hypercenterC2×Q16D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#918C2semidirect
3. #10595397C2semidirect
4. C2×#63805C2semidirect
5. #10592887C2semidirect
6. C3×#5189C2semidirect
7. #10591635C2semidirect
8. #10591634C2semidirect
9. #10591600C2semidirect
10. #10591590C2semidirect
11. #10591556C2semidirect
12. D3×#835C2semidirect
13. #10590843C2semidirect
14. #10590833C2semidirect
15. #10590681C2semidirect
66. C2×#918D3semidirect
75. #5189D3semidirect
140. C3×ΓL(1,𝔽25)D4semidirect
435. ΓL(1,𝔽25)#67semidirect
741. C32#3063semidirect
830. C3#80907semidirect
831. C3#83986semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
#105953982
#105953972
C2×#638052
#105928872
C3×#51892
#105916352
#105916342
#105916002
#105915902
#105915562
D3×#8352
#105908432
#105908332
#105906812
#839863
#809073