Finite Group Databasebeta

← #11858507

Subgroups — #11858507

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic
2#10594602C211yesmaximal, characteristic
3D3×#892C211yesmaximal, characteristic
4#10592560C211yesmaximal, characteristic, complemented
5C3×#4861C211yesmaximal, characteristic, complemented
6C3×#4860C211yesmaximal, characteristic, complemented
7#10590707C211yesmaximal, characteristic, complemented
8#10590688C211yesmaximal, characteristic, complemented
9#10590681C211yesmaximal, characteristic, complemented
10#10590583C211yesmaximal, characteristic, complemented
11#10590582C211yesmaximal, characteristic, complemented
12#10590580C211yesmaximal, characteristic, complemented
13#10590572C211yesmaximal, characteristic, complemented
14#10590571C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16#79208—31nomaximal
17#79177—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20#64101C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#63921—21no—
29D3×(C2×D3)⋊C4—21no—
30#63900C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32C4×#624—21no—
33#63878—21no—
34#63877—21no—
35#63877—21no—
36C4×D3×Dic3—21no—
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41#63836—21no—
42C2×#3712C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45D3×ΓL(1,𝔽25)C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63574C2211yescharacteristic, complemented
59#63573C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63573C2211yescharacteristic, complemented
62C2×D3×M16—31no—
63C22×ΓL(1,𝔽25)—31no—
64D3×#117—31no—
65D3×#117—31no—
66D3×#117—31no—
67C2×#892—31no—
68C3×#428—31no—
69C3×#427—31no—
70#5121—31no—
71#5106—31no—
72#4998—31no—
73#4998—31no—
74#4995—31no—
75#4964—31no—
76#4881—31no—
77#4881—31no—
78#4881—31no—
79#4881—31no—
80#4881—31no—
81#4881—31no—
82#4880—31no—
83#4880—31no—
84#4861—31no—
85#4861—31no—
86#4861—31no—
87#4861—31no—
88#4861—31no—
89#4861—61no—
90#4861D311yescharacteristic, complemented
91#4860—31no—
92#4860D311yescharacteristic, complemented
93C22×D32D411yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×#624—21no—
100C2×#624D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3D411yescharacteristic
103C2×D3×Dic3D411yescharacteristic
104C4×D32C2×C414yes—
105C4×D32Q814yes—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109#3752—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115#3743C2×C414yescomplemented
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×ΓL(1,𝔽25)C2×C414yescomplemented
130C3×D3×C8C2×C414yescomplemented
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141#3712C2×C414yescomplemented
142#3711C2×C414yescomplemented
143D3×C3⋊C8C2×C414yescomplemented
144#2911—91noSylow
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C2×C3×M16—31no—
148C22×C3×C8—31no—
149C3×#117—31no—
150C3×#117—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153C2×(C2×D3)⋊C4—61no—
154#926—31no—
155#926—31no—
156#926—31no—
157C2×C4⋊Dic3—31no—
158C2×C4×Dic3—61no—
159C2×#208—31no—
160C22×C3⋊C8—31no—
161D3×M16—38no—
162C2×ΓL(1,𝔽25)—31no—
163C2×ΓL(1,𝔽25)—31no—
164C2×ΓL(1,𝔽25)—31no—
165C2×ΓL(1,𝔽25)—31no—
166C2×ΓL(1,𝔽25)—31no—
167C2×ΓL(1,𝔽25)—38no—
168C2×ΓL(1,𝔽25)—61no—
169C2×ΓL(1,𝔽25)C2×D311yescharacteristic
170C2×D3×C8—31no—
171C2×D3×C8C2×D311yescharacteristic
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—31no—
177#892—31no—
178#892—31no—
179#892—61no—
180#892—61no—
181#892—61no—
182#892C2×D311yescharacteristic
183#892C2×D311yescharacteristic
184#892C2×D311yescharacteristic
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4C2×D311yescharacteristic
192D3×C22⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#877—61no—
196#877—61no—
197#877—61no—
198#872—61no—
199#872—61no—
200#872—61no—
201C42×D3—61no—
202C42×D3—61no—
203C42×D3—61no—
204C3×#107—31no—
205C3×#107—31no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—21no—
209C3×#106—31no—
210C3×#106—31no—
211C3×#106C2×D311yescharacteristic, complemented
212C3×#106C2×D311yescharacteristic, complemented
213#818—31no—
214#818—31no—
215#818—31no—
216#818—61no—
217#818C2×D311yescharacteristic, complemented
218#817—31no—
219#817—31no—
220#817—31no—
221#817C2×D311yescharacteristic, complemented
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237#807C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239#807C2×D311yescharacteristic, complemented
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—41no—
244C2×D32—41no—
245C2×D32C4⋊C414yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4×C3⋊D3—42no—
253C4×C3⋊D3C22×C412yes—
254C4×C3⋊D3C2×Q812yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—42no—
262C3×C4×D3C22×C412yes—
263C3×C4×D3C22×C412yes—
264C3×C4×D3C2×Q812yes—
265C3×C4×D3C2×Q812yes—
266#624—42no—
267#624C4⋊C414yes—
268D3×Dic3—42no—
269D3×Dic3C4⋊C414yes—
270D3×Dic3C4⋊C414yes—
271C32×C8C22×C412yes—
272C3⋊(C3⋊C8)C22×C412yes—
273C3×C3⋊C8C22×C412yes—
274C3×C3⋊C8C22×C412yes—
275C22×M16—91no—
276C2×#117—91no—
277C2×#117—91no—
278#428—31no—
279#428—91no—
280#428—91no—
281#428—91no—
282#428—91no—
283#428—91no—
284#428—91no—
285#428—91no—
286#427—31no—
287#427—91no—
288#427—91no—
289#427—91no—
290C23×D3—31no—
291C23×D3—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—61no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C2×C4×D3—21no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×C4×D3—34no—
306C2×C4×D3—34no—
307C2×C4×D3—34no—
308C2×C4×D3—34no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—121no—
316C2×C4×D3C22×D311yescharacteristic
317C2×C4×D3C22×D311yescharacteristic
318C3×M16—34no—
319C2×C3×C8—21no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8—34no—
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—61no—
340C3×C42—61no—
341C3×C42—61no—
342#217—61no—
343#217—61no—
344#217—61no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—21no—
347(C2×D3)⋊C4—21no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—121no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365C4⋊Dic3C22×D311yescharacteristic
366C4⋊Dic3C22×D311yescharacteristic
367Dic3⋊C4—21no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—121no—
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—121no—
388#208—34no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—34no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395ΓL(1,𝔽25)—34no—
396ΓL(1,𝔽25)—34no—
397ΓL(1,𝔽25)—34no—
398ΓL(1,𝔽25)—34no—
399ΓL(1,𝔽25)—34no—
400ΓL(1,𝔽25)—64no—
401ΓL(1,𝔽25)C4×D314yescomplemented
402D3×C8—34no—
403D3×C8C4×D314yescomplemented
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—21no—
406C2×C3⋊D3—21no—
407C2×C3⋊D3C2×C4⋊C412yes—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3C2×C4⋊C412yes—
413C2×C3×D3C2×C4⋊C412yes—
414D32—44no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C23×C411yescharacteristic
418C32×C4C22×Q811yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3C2×C4⋊C412yes—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3C2×C4⋊C412yes—
427C3×Dic3C2×C4⋊C412yes—
428C23×C4—91no—
429C2×M16—31no—
430C2×M16—91no—
431C2×M16—98no—
432C2×M16—91no—
433C2×M16—91no—
434C22×C8—31no—
435C22×C8—91no—
436#117—31no—
437#117—31no—
438#117—31no—
439#117—91no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—91no—
444#117—181no—
445#117—181no—
446#117—181no—
447#117—181no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C22⋊C4—181no—
453C2×C22⋊C4—181no—
454C2×C42—181no—
455C2×C42—181no—
456#107—31no—
457#107—31no—
458#107—31no—
459#107—31no—
460#107—91no—
461#107—91no—
462#107—91no—
463#107—91no—
464#106—31no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#106—91no—
470#106—91no—
471#106D3211yescharacteristic, complemented
472C23×C3—31no—
473C23×C3—31no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—34no—
477C22×D3—34no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3—121no—
481C22×D3—121no—
482C22×D3—121no—
483C22×D3D3×D411yescharacteristic
484C22×D3D3×D411yescharacteristic
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—122no—
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—34no—
512C2×Dic3—34no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—122no—
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523C4×D3—34no—
524C4×D3—34no—
525C4×D3—32no—
526C4×D3—32no—
527C4×D3—32no—
528C4×D3—32no—
529C4×D3—34no—
530C4×D3—34no—
531C4×D3—42no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—122no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3—122no—
538C4×D3—122no—
539C4×D3—242no—
540C4×D3C2×C4×D312yes—
541C4×D3C2×C4×D312yes—
542C4×D3D3×Q812yes—
543C4×D3D3×Q812yes—
544C3×C8—22no—
545C3×C8—32no—
546C3×C8—32no—
547C3×C8C2×C4×D312yes—
548C3×C8C2×C4×D312yes—
549C3⋊C8—32no—
550C3⋊C8—32no—
551C3⋊C8—62no—
552C3⋊C8C2×C4×D312yes—
553C3⋊C8C2×C4×D312yes—
554C2×C32C22×C4⋊C411yescharacteristic
555C2×C32#57511yescharacteristic
556C2×C32#57511yescharacteristic
557C3⋊D3—22no—
558C3×D3—22no—
559C3×D3—22no—
560C24—91no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—61no—
564C22×C4—91no—
565C22×C4—94no—
566C22×C4—94no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—181no—
571C22×C4—181no—
572C22×C4—181no—
573M16—34no—
574M16—94no—
575M16—94no—
576M16—94no—
577C2×C8—31no—
578C2×C8—31no—
579C2×C8—34no—
580C2×C8—94no—
581C2×C8—91no—
582C2×C8C2×D3211yescharacteristic
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—61no—
588C4⋊C4—91no—
589C4⋊C4—91no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4C2×D3211yescharacteristic
594C4⋊C4C2×D3211yescharacteristic
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—181no—
599C22⋊C4—181no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C42—61no—
604C42—61no—
605C42—61no—
606C42—181no—
607C42—181no—
608C42—181no—
609C42—181no—
610C42—181no—
611C22×C3—21no—
612C22×C3—32no—
613C22×C3—32no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C2×D3×D411yescharacteristic
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—32no—
625C2×D3—32no—
626C2×D3—62no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—124no—
634C2×D3—124no—
635C2×D3D3×C4⋊C412yes—
636C2×D3D3×C4⋊C412yes—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—32no—
640C3×C4—32no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4C22×C4×D311yescharacteristic
652C3×C4C22×C4×D311yescharacteristic
653C3×C4C2×D3×Q811yescharacteristic
654C3×C4C2×D3×Q811yescharacteristic
655Dic3—32no—
656Dic3—32no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—62no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667Dic3—241no—
668Dic3D3×C4⋊C412yes—
669Dic3D3×C4⋊C412yes—
670C32#291111yescharacteristic, complemented, Sylow
671C23—31no—
672C23—31no—
673C23—94no—
674C23—91no—
675C23—361no—
676C23—361no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—94no—
690C2×C4—94no—
691C2×C4—94no—
692C2×C4—91no—
693C2×C4—92no—
694C2×C4—92no—
695C2×C4—122no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—362no—
699C2×C4—362no—
700C2×C4—362no—
701C2×C4C22×D3211yescharacteristic
702C8—32no—
703C8—32no—
704C8—92no—
705C8C4×D3212yes—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—62no—
710C2×C3—62no—
711C2×C3C2×D3×C4⋊C411yescharacteristic
712C2×C3C2×D3×C4⋊C411yescharacteristic
713C2×C3#576811yescharacteristic
714C2×C3#576811yescharacteristic
715C2×C3#577311yescharacteristic
716C2×C3#577711yescharacteristic
717D3—22no—
718D3—22no—
719D3—62no—
720D3—62no—
721D3—122no—
722C22—32no—
723C22—32no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—92no—
729C22—181no—
730C22—181no—
731C22—364no—
732C22D32×D411yescharacteristic
733C4—32no—
734C4—32no—
735C4—41no—
736C4—41no—
737C4—92no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—361no—
743C4—361no—
744C4C2×C4×D3211yescharacteristic
745C4D32×Q811yescharacteristic
746C3—21no—
747C3#7917711yescharacteristic, complemented
748C3#7920811yescharacteristic, complemented
749C2—62no—
750C2—62no—
751C2—182no—
752C2D32×C4⋊C411yescharacteristic
753C2#1059474511yescharacteristic
754C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2911
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
4. #10592560C2semidirect
5. C3×#4861C2semidirect
6. C3×#4860C2semidirect
7. #10590707C2semidirect
8. #10590688C2semidirect
9. #10590681C2semidirect
10. #10590583C2semidirect
11. #10590582C2semidirect
12. #10590580C2semidirect
13. #10590572C2semidirect
14. #10590571C2semidirect
15. #10590436C2semidirect
45. D3×ΓL(1,𝔽25)C4semidirect
46. C32×#106C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
49. #63634C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#808C22semidirect
53. C3×#807C22semidirect
54. C3×#807C22semidirect
55. C3×#807C22semidirect
56. #63576C22semidirect
57. #63575C22semidirect
58. #63574C22semidirect
59. #63573C22semidirect
60. #63573C22semidirect
61. #63573C22semidirect
90. #4861D3semidirect
92. #4860D3semidirect
115. #3743C2×C4semidirect
129. C3×ΓL(1,𝔽25)C2×C4semidirect
130. C3×D3×C8C2×C4semidirect
141. #3712C2×C4semidirect
142. #3711C2×C4semidirect
143. D3×C3⋊C8C2×C4semidirect
211. C3×#106C2×D3semidirect
212. C3×#106C2×D3semidirect
217. #818C2×D3semidirect
221. #817C2×D3semidirect
230. #808C2×D3semidirect
237. #807C2×D3semidirect
238. #807C2×D3semidirect
239. #807C2×D3semidirect
401. ΓL(1,𝔽25)C4×D3semidirect
403. D3×C8C4×D3semidirect
471. #106D32semidirect
670. C32#2911semidirect
747. C3#79177semidirect
748. C3#79208semidirect

Maximal subgroups

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

subgroupindex
C2×D3×ΓL(1,𝔽25)2
#105946022
D3×#8922
#105925602
C3×#48612
C3×#48602
#105907072
#105906882
#105906812
#105905832
#105905822
#105905802
#105905722
#105905712
#105904362
#792083
#791773