Finite Group Databasebeta

← #11860433

Subgroups — #11860433

Order 1152.

1028 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#237C211yesmaximal, characteristic
2C2×#63929C211yesmaximal, characteristic
3D3×#887C211yesmaximal, characteristic, complemented
4#10592456C211yesmaximal, characteristic, complemented
5C3×#4771C211yesmaximal, characteristic
6C3×#4758C211yesmaximal, characteristic, complemented
7#10591446C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590948C211yesmaximal, characteristic, complemented
10#10590793C211yesmaximal, characteristic, complemented
11#10590791C211yesmaximal, characteristic, complemented
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590581C211yesmaximal, characteristic, complemented
14#10590485C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16C4×#915—31nomaximal
17#78867—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30#63955—21no—
31C2×Dic32—21no—
32#63929C418yescomplemented
33D3×Dic3⋊C4—21no—
34C4×D3×Dic3—21no—
35C4×D3×Dic3C2211yescharacteristic
36#63844C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63838—21no—
42#63837—21no—
43C2×#3719C2211yescharacteristic
44C2×#3718C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63643C2211yescharacteristic
48#63642C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63575C2211yescharacteristic
57#63574C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62Dic3×#41—31no—
63C2×#951—31no—
64C2×#915—31no—
65C4×D3×Q8—31no—
66C4×#237—31no—
67C2×#887—31no—
68C3×C4×SD16—31no—
69C3×#417—31no—
70#5164—31no—
71#5120—31no—
72Dic3×M16—31no—
73C4×#216—31no—
74C4×#214—31no—
75#4964—31no—
76#4861—31no—
77#4853—31no—
78#4802—31no—
79#4790—31no—
80#4790—31no—
81#4789—31no—
82#4789—31no—
83#4789—31no—
84#4771D311yescharacteristic
85#4758—31no—
86#4758D311yescharacteristic, complemented
87#4757—31no—
88#4757—31no—
89#4757—31no—
90#4757—61no—
91C4×Dic12—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237C2×C414yes—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109D3×Dic6—22no—
110D3×Dic6C2×C414yescomplemented
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114#3754C2×C414yescomplemented
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#214C2×C414yescomplemented
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3719C2×C414yescomplemented
144#3718C2×C414yescomplemented
145#3711C2×C414yescomplemented
146C4×#137—91noSylow
147C2×C3×#41—31no—
148C2×D3×Q8—31no—
149C2×#237C2×D311yescharacteristic
150C22×Dic6—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—31no—
156#951—38no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#216—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—61no—
172C2×#214C2×D311yescharacteristic
173C4×#67—61no—
174#926—31no—
175#926—61no—
176C2×Dic3⋊C4—61no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—61no—
179C2×C4×Dic3—61no—
180C2×C4×Dic3—61no—
181C2×#208—31no—
182#915—38no—
183C2×Dic12—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×ΓL(1,𝔽25)C2×D311yescharacteristic
186#892—31no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4C2×D311yescharacteristic
189#887—31no—
190#887—31no—
191#887—31no—
192#887—31no—
193#887—31no—
194#887—61no—
195#887—61no—
196#887—61no—
197#887—61no—
198#887C2×D311yescharacteristic
199#67⋊C4—61no—
200#877—61no—
201C42×D3—31no—
202C42×D3—61no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×C4×C8—31no—
215#835—31no—
216#832C2×D311yescharacteristic
217#818—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—61no—
230C8×Dic3—31no—
231C8×Dic3C2×D311yescharacteristic
232#810—31no—
233#810C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808C2×D311yescharacteristic
237#807—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×D4—21no—
245C32×D4C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634C22×C412yes—
255C3×#67—24no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—42no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6C22×C412yes—
271C3×Dic6C22×C412yes—
272#627—24no—
273D3×Dic3—24no—
274D3×Dic3—22no—
275D3×Dic3—41no—
276C32×C8—21no—
277C3⋊(C3⋊C8)C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—91no—
286#440—91no—
287C4×Q16—91no—
288C4×Q16—91no—
289C4×SD16—31no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—31no—
294C4×M16—91no—
295C3×#41—34no—
296C3×#41—62no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316D3×Q8—34no—
317D3×Q8—62no—
318#237—22no—
319#237C4×D314yes—
320C2×C4×D3—21no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×SD16—34no—
335C3×M16—62no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351#217—21no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—121no—
356#216—34no—
357#216—34no—
358#216—34no—
359#214—34no—
360#214—34no—
361#214—64no—
362#214C4×D314yescomplemented
363(C2×D3)⋊C4—61no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382C4×Dic3—21no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404#208—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410Dic12—34no—
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)—34no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3C4×D412yes—
420C32×C4—41no—
421C32×C4C23×C411yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—22no—
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3⋊Dic3—41no—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3C4×D412yes—
433C3×Dic3#13712yescomplemented
434C2×#41—31no—
435C22×Q8—91no—
436#137—98no—
437C2×Q16—91no—
438C2×Q16—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×M16—31no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—181no—
459C2×C42—91no—
460C2×C42—181no—
461C2×C42—181no—
462#107—91no—
463#107—91no—
464#106—31no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102D3211yescharacteristic
474#97—91no—
475#97—91no—
476C4×C8—31no—
477C4×C8—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—41no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—32no—
484C3×Q8—32no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—41no—
491C3×D4—64no—
492C3×D4C2×C4×D312yes—
493C3×D4C2×C4×D312yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—64no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—24no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—24no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—42no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—64no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—62no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3—122no—
536C2×Dic3—242no—
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540C4×D3—42no—
541C4×D3—62no—
542C4×D3—64no—
543C4×D3—121no—
544C4×D3C2×C4×D312yes—
545C4×D3#23712yes—
546Dic6—21no—
547Dic6—21no—
548Dic6—32no—
549Dic6—32no—
550Dic6—62no—
551Dic6—64no—
552Dic6—61no—
553Dic6—61no—
554Dic6—64no—
555Dic6—121no—
556Dic6C2×C4×D312yes—
557Dic6C2×C4×D312yes—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—32no—
561C3×C8—41no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—32no—
565C3⋊C8—32no—
566C3⋊C8—62no—
567C3⋊C8C2×C4×D312yes—
568C2×C32—42no—
569C2×C32C2×C4×D411yescharacteristic
570C2×C32C2×#13711yescharacteristic
571C2×C32#57511yescharacteristic
572C3×D3—22no—
573#41—34no—
574#41—62no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×Q8—94no—
578C2×Q8—91no—
579C2×Q8—181no—
580C2×Q8—182no—
581C2×D4—61no—
582C2×D4C2×D3211yescharacteristic
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—181no—
590C22×C4—181no—
591Q16—94no—
592Q16—94no—
593SD16—34no—
594SD16—94no—
595M16—62no—
596M16—94no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8C2×D3211yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—32no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3#67⋊C412yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—32no—
647C3×C4—32no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—62no—
651C3×C4—61no—
652C3×C4—62no—
653C3×C4—81no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C22×C4×D311yescharacteristic
657C3×C4C22×C4×D311yescharacteristic
658C3×C4C2×#23711yescharacteristic
659C3×C4D3×#4111yescharacteristic
660Dic3—22no—
661Dic3—21no—
662Dic3—22no—
663Dic3—41no—
664Dic3—41no—
665Dic3—62no—
666Dic3—61no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—62no—
671Dic3—122no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—241no—
677Dic3#67⋊C412yes—
678Dic3#91512yescomplemented
679C32C4×#13711yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682Q8—32no—
683Q8—32no—
684Q8—61no—
685Q8—61no—
686Q8—92no—
687Q8—184no—
688Q8—181no—
689D4—21no—
690D4—64no—
691D4C4×D3212yes—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—31no—
698C2×C4—64no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—182no—
708C2×C4—184no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—361no—
712C2×C4—362no—
713C2×C4C22×D3211yescharacteristic
714C8—21no—
715C8—32no—
716C8—61no—
717C8—92no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3—42no—
723C2×C3—62no—
724C2×C3—82no—
725C2×C3C2×#67⋊C411yescharacteristic
726C2×C3C4×D3×D411yescharacteristic
727C2×C3C2×#91511yescharacteristic
728C2×C3#576811yescharacteristic
729C2×C3#577311yescharacteristic
730C2×C3D3×#13711yescharacteristic
731D3—22no—
732C22—22no—
733C22—32no—
734C22—41no—
735C22—41no—
736C22—61no—
737C22—61no—
738C22D32×D411yescharacteristic
739C4—32no—
740C4—32no—
741C4—41no—
742C4—61no—
743C4—62no—
744C4—62no—
745C4—121no—
746C4—121no—
747C4—181no—
748C4—181no—
749C4—182no—
750C4—361no—
751C4C2×C4×D3211yescharacteristic
752C4D3×#23711yescharacteristic
753C3—21no—
754C3#7886711yescharacteristic, complemented
755C3C4×#91511yescharacteristic, complemented
756C2—42no—
757C2—62no—
758C2D3×#67⋊C411yescharacteristic
759C2#1059472911yescharacteristic
760C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. D3×#887C2semidirect
4. #10592456C2semidirect
6. C3×#4758C2semidirect
7. #10591446C2semidirect
8. #10591401C2semidirect
9. #10590948C2semidirect
10. #10590793C2semidirect
11. #10590791C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
13. #10590581C2semidirect
14. #10590485C2semidirect
15. #10590476C2semidirect
32. #63929C4semidirect
86. #4758D3semidirect
110. D3×Dic6C2×C4semidirect
114. #3754C2×C4semidirect
121. C3×#214C2×C4semidirect
143. #3719C2×C4semidirect
144. #3718C2×C4semidirect
145. #3711C2×C4semidirect
362. #214C4×D3semidirect
433. C3×Dic3#137semidirect
678. Dic3#915semidirect
679. C32C4×#137semidirect
754. C3#78867semidirect
755. C3C4×#915semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2372
C2×#639292
D3×#8872
#105924562
C3×#47712
C3×#47582
#105914462
#105914012
#105909482
#105907932
#105907912
Dic3×ΓL(1,𝔽25)2
#105905812
#105904852
#105904762
C4×#9153
#788673