Finite Group Databasebeta

← #11858870

Subgroups — #11858870

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#926C211yesmaximal, characteristic
2#10592419C211yesmaximal, characteristic, complemented
3C3×#4726C211yesmaximal, characteristic
4C3×#4720C211yesmaximal, characteristic, complemented
5#10591154C211yesmaximal, characteristic
6#10591062C211yesmaximal, characteristic, complemented
7#10591056C211yesmaximal, characteristic, complemented
8#10590699C211yesmaximal, characteristic, complemented
9#10590698C211yesmaximal, characteristic, complemented
10#10590697C211yesmaximal, characteristic, complemented
11#10590696C211yesmaximal, characteristic, complemented
12#10590667C211yesmaximal, characteristic, complemented
13#10590663C211yesmaximal, characteristic, complemented
14#10590663C211yesmaximal, characteristic, complemented
15Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16#79371—31nomaximal
17#78620—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19#64135C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23D3×#217C411yescharacteristic
24D3×#217C411yescharacteristic
25#63955C411yescharacteristic
26#63955C411yescharacteristic
27D3×C4⋊Dic3C411yescharacteristic
28D3×C4⋊Dic3C411yescharacteristic
29C4×D3×Dic3C2211yescharacteristic
30C4×D3×Dic3C2211yescharacteristic
31#63855C2211yescharacteristic
32#63855C2211yescharacteristic
33#63841C411yescharacteristic
34#63841C411yescharacteristic
35C2×#3711C2211yescharacteristic
36C2×#3711C2211yescharacteristic
37C32×C22⋊C8C2211yescharacteristic
38#63657C2211yescharacteristic
39#63642C2211yescharacteristic, complemented
40#63641C2211yescharacteristic, complemented
41#63641C2211yescharacteristic, complemented
42C8×C3⋊Dic3C2211yescharacteristic, complemented
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×(C2×D3)⋊C8C2211yescharacteristic
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×#815C2211yescharacteristic, complemented
48C3×Dic3⋊C8C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51#63572C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
56(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
57#63555C2211yescharacteristic, complemented
58#63554C2211yescharacteristic, complemented
59#63553C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#926—31no—
62D3×#117—31no—
63C3×#433—31no—
64C3×#407—31no—
65#5207—31no—
66#5118—31no—
67#5118—31no—
68Dic3×M16—31no—
69Dic3×M16—31no—
70#5000—31no—
71#4840—31no—
72#4840—31no—
73#4837—31no—
74#4837—31no—
75#4726—31no—
76#4726D311yescharacteristic
77#4720—31no—
78#4720—31no—
79#4720—31no—
80#4720—31no—
81#4720—31no—
82#4720—31no—
83#4720—31no—
84#4720—31no—
85#4720—31no—
86#4720—61no—
87#4720D311yescharacteristic, complemented
88#4709—31no—
89#4707—31no—
90#4690—31no—
91C4×ΓL(1,𝔽25)—31no—
92C23×C3×D3C2×C411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3C2×C411yescharacteristic
95C2×C3×C4×D3—22no—
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3C2×C411yescharacteristic
98C2×C3×C4×D3C2×C411yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×D3×Dic3C2×C411yescharacteristic
102C2×D3×Dic3C2×C411yescharacteristic
103C2×D3×Dic3C2×C411yescharacteristic
104C2×D3×Dic3C2×C411yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107#3757C2×C411yescharacteristic
108#3757C2×C411yescharacteristic
109C4⋊(C3⋊Dic3)C2×C411yescharacteristic
110C4⋊(C3⋊Dic3)C2×C411yescharacteristic
111C4×C3⋊Dic3C2311yescharacteristic
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217C2×C411yescharacteristic
116C3×#217C2×C411yescharacteristic
117C3×C4⋊Dic3C2×C411yescharacteristic
118C3×C4⋊Dic3C2×C411yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×ΓL(1,𝔽25)—22no—
126C3×ΓL(1,𝔽25)—22no—
127Dic3⋊Dic3C2×C411yescharacteristic
128Dic3⋊Dic3C2×C411yescharacteristic
129Dic3⋊Dic3C2×C411yescharacteristic
130Dic3⋊Dic3C2×C411yescharacteristic
131(C2×D3)⋊Dic3C2×C411yescharacteristic
132(C2×D3)⋊Dic3C2×C411yescharacteristic
133(C2×D3)⋊Dic3C2×C411yescharacteristic
134(C2×D3)⋊Dic3C2×C411yescharacteristic
135Dic32C2×C411yescharacteristic
136Dic32C2×C411yescharacteristic
137Dic32C2×C411yescharacteristic
138Dic32C2×C411yescharacteristic
139#3711—22no—
140#3711—22no—
141#2921—91noSylow
142C23×C3×C4—31no—
143C22×C4×D3C2×D311yescharacteristic
144C2×C3×M16—31no—
145C2×C3×M16—31no—
146C3×#117—31no—
147C2×#217—31no—
148C2×#217—31no—
149#926—31no—
150#926—31no—
151#926—31no—
152#926—31no—
153#926—31no—
154#926—31no—
155#926—31no—
156#926—31no—
157#926—61no—
158#926C2×D311yescharacteristic
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×#208—31no—
164C2×#208—31no—
165C2×ΓL(1,𝔽25)—31no—
166C2×ΓL(1,𝔽25)—31no—
167C2×ΓL(1,𝔽25)C2×D311yescharacteristic
168C2×ΓL(1,𝔽25)C2×D311yescharacteristic
169#892—31no—
170#892—31no—
171D3×C4⋊C4—31no—
172D3×C4⋊C4—31no—
173D3×C22⋊C4—31no—
174D3×C22⋊C4—31no—
175#877—31no—
176#877—31no—
177#872—31no—
178#872—31no—
179C42×D3—31no—
180C42×D3—31no—
181C3×C4⋊C8—31no—
182C3×C4⋊C8—31no—
183C3×C22⋊C8—21no—
184C3×C22⋊C8—31no—
185C3×C22⋊C8—31no—
186C3×C22⋊C8—31no—
187C3×C22⋊C8—31no—
188C3×C22⋊C8C2×D311yescharacteristic
189C3×C22⋊C8C2×D311yescharacteristic
190C3×#97—31no—
191C3×C4×C8—31no—
192#830—31no—
193#830—31no—
194#830—31no—
195#830—31no—
196#830—61no—
197#830C2×D311yescharacteristic
198#830C2×D311yescharacteristic
199(C2×D3)⋊C8—31no—
200(C2×D3)⋊C8—31no—
201(C2×D3)⋊C8C2×D311yescharacteristic
202(C2×D3)⋊C8C2×D311yescharacteristic
203#815—31no—
204#815—31no—
205#815—31no—
206#815—31no—
207#815—31no—
208#815—61no—
209#815C2×D311yescharacteristic, complemented
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221Dic3⋊C8—61no—
222Dic3⋊C8C2×D311yescharacteristic, complemented
223Dic3⋊C8C2×D311yescharacteristic, complemented
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230C8×Dic3C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C22×C411yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—41no—
238C22×C3×D3—41no—
239C22×C3×D3C22×C411yescharacteristic
240C22×C3×D3C22×C411yescharacteristic
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C22×C411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3C22×C411yescharacteristic
246C2×C3⋊Dic3C22×C411yescharacteristic
247C2×C3⋊Dic3C22×C411yescharacteristic
248C2×C3⋊Dic3C22×C411yescharacteristic
249C2×C3×Dic3—22no—
250C2×C3×Dic3C22×C411yescharacteristic
251C2×C3×Dic3C22×C411yescharacteristic
252C2×C3×Dic3C22×C411yescharacteristic
253C2×C3×Dic3C22×C411yescharacteristic
254C2×C3×Dic3C22×C411yescharacteristic
255C2×C3×Dic3C22×C411yescharacteristic
256C3×C4×D3—22no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—22no—
260C3×C4×D3#4112yes—
261C3×C4×D3#4112yes—
262D3×Dic3—41no—
263D3×Dic3—41no—
264D3×Dic3—41no—
265D3×Dic3—41no—
266C32×C8—21no—
267C32×C8—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C2×#117—91no—
275#433—31no—
276#433—91no—
277#433—91no—
278#433—91no—
279#433—91no—
280#433—91no—
281#433—91no—
282#433—91no—
283#423—91no—
284#423—91no—
285#407—31no—
286#407—91no—
287C4×M16—91no—
288C4×M16—91no—
289C24×C3—31no—
290C23×D3C4×D311yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—62no—
298C22×C3×C4—62no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3C4×D311yescharacteristic
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3C4×D311yescharacteristic
313C2×C4×D3C4×D311yescharacteristic
314C2×C4×D3C22×D311yescharacteristic
315C2×C4×D3C22×D311yescharacteristic
316C3×M16—62no—
317C3×M16—62no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326C2×C3×C8C22×D311yescharacteristic
327C2×C3×C8C22×D311yescharacteristic
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C22⋊C4—31no—
331C3×C22⋊C4—31no—
332C3×C42—31no—
333C3×C42—31no—
334#217—31no—
335#217—31no—
336#217—31no—
337#217—31no—
338#217—31no—
339#217—31no—
340#217—31no—
341#217—31no—
342#217—61no—
343#217—61no—
344#217C4×D311yescharacteristic
345#217C4×D311yescharacteristic
346(C2×D3)⋊C4—31no—
347(C2×D3)⋊C4—31no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3C4×D311yescharacteristic
361C4⋊Dic3C4×D311yescharacteristic
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382#208—62no—
383#208—62no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394ΓL(1,𝔽25)—22no—
395ΓL(1,𝔽25)—22no—
396ΓL(1,𝔽25)—62no—
397ΓL(1,𝔽25)—62no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32C23×C411yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—44no—
408C2×C3×D3#11712yes—
409C32×C4—21no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—21no—
413C3⋊Dic3—21no—
414C3⋊Dic3—21no—
415C3⋊Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3#11712yes—
422C23×C4—31no—
423C2×M16—31no—
424C2×M16—31no—
425C2×M16—91no—
426C2×M16—91no—
427#117—31no—
428#117—91no—
429#117—91no—
430#117—91no—
431#117—91no—
432#117—91no—
433#117—91no—
434#117—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C42—91no—
440C2×C42—91no—
441C4⋊C8—31no—
442C4⋊C8—31no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447C4⋊C8—91no—
448C4⋊C8—91no—
449C22⋊C8—31no—
450C22⋊C8—31no—
451C22⋊C8—31no—
452C22⋊C8—31no—
453C22⋊C8—91no—
454C22⋊C8—91no—
455C22⋊C8—91no—
456C22⋊C8D3211yescharacteristic
457#97—31no—
458#97—91no—
459#97—91no—
460#97—91no—
461C4×C8—31no—
462C4×C8—91no—
463C4×C8—91no—
464C4×C8—91no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—31no—
468C23×C3—62no—
469C23×C3—121no—
470C23×C3—121no—
471C23×C3C2×C4×D311yescharacteristic
472C23×C3C2×C4×D311yescharacteristic
473C22×D3—22no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3C2×C4×D311yescharacteristic
477C22×D3C2×C4×D311yescharacteristic
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4C2×C4×D311yescharacteristic
500C2×C3×C4C2×C4×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503C2×Dic3—22no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—121no—
517C2×Dic3—121no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3C2×C4×D311yescharacteristic
521C2×Dic3C2×C4×D311yescharacteristic
522C2×Dic3C2×C4×D311yescharacteristic
523C2×Dic3C2×C4×D311yescharacteristic
524C2×Dic3C2×C4×D311yescharacteristic
525C2×Dic3C2×C4×D311yescharacteristic
526C4×D3—22no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—22no—
530C4×D3—121no—
531C4×D3—121no—
532C4×D3—121no—
533C4×D3—121no—
534C4×D3#23712yes—
535C4×D3#23712yes—
536C3×C8—21no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—41no—
541C3×C8—41no—
542C3×C8—61no—
543C3×C8—61no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—121no—
555C3⋊C8—121no—
556C2×C32—41no—
557C2×C32C2×#11711yescharacteristic
558C2×C32#56811yescharacteristic
559C2×C32#56811yescharacteristic
560C3×D3—22no—
561C3×D3—41no—
562C24—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—91no—
571C22×C4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4C2×D3211yescharacteristic
575M16—62no—
576M16—62no—
577M16—182no—
578M16—182no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—91no—
584C2×C8—91no—
585C2×C8C2×D3211yescharacteristic
586C2×C8C2×D3211yescharacteristic
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—91no—
590C4⋊C4—91no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—91no—
595C22⋊C4—31no—
596C22⋊C4—31no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4—91no—
603C42—31no—
604C42—31no—
605C42—91no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42—91no—
610C42—91no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—32no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—124no—
628C22×C3C22×C4×D311yescharacteristic
629C22×C3C22×C4×D311yescharacteristic
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—44no—
636C2×D3#87712yes—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—32no—
642C3×C4—41no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4C2×#23711yescharacteristic
649C3×C4C2×#23711yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4D3×#4111yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3#87712yes—
670C32#292111yescharacteristic, complemented, Sylow
671C23—31no—
672C23—31no—
673C23—62no—
674C23—121no—
675C23—121no—
676C23C4×D3211yescharacteristic
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—31no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—361no—
697C2×C4—361no—
698C2×C4—361no—
699C2×C4—361no—
700C2×C4C4×D3211yescharacteristic
701C2×C4C22×D3211yescharacteristic
702C8—21no—
703C8—21no—
704C8—61no—
705C8—61no—
706C8—61no—
707C8—61no—
708C8—181no—
709C8—181no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—41no—
714C2×C3—41no—
715C2×C3—62no—
716C2×C3—81no—
717C2×C3—121no—
718C2×C3C2×#87711yescharacteristic
719C2×C3D3×#11711yescharacteristic
720C2×C3#574511yescharacteristic
721C2×C3#574511yescharacteristic
722C2×C3#575011yescharacteristic
723C2×C3#575011yescharacteristic
724D3—22no—
725D3—41no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—32no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—124no—
736C22C2×C4×D3211yescharacteristic
737C4—21no—
738C4—32no—
739C4—61no—
740C4—61no—
741C4—61no—
742C4—61no—
743C4—61no—
744C4—181no—
745C4—181no—
746C4—181no—
747C4—181no—
748C4D3×#23711yescharacteristic
749C4D3×#23711yescharacteristic
750C3—21no—
751C3#7862011yescharacteristic, complemented
752C3#7937111yescharacteristic, complemented
753C2—41no—
754C2—62no—
755C2—121no—
756C2D3×#87711yescharacteristic
757C2#1059466811yescharacteristic
758C2#1059470611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32#2921
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592419C2semidirect
4. C3×#4720C2semidirect
6. #10591062C2semidirect
7. #10591056C2semidirect
8. #10590699C2semidirect
9. #10590698C2semidirect
10. #10590697C2semidirect
11. #10590696C2semidirect
12. #10590667C2semidirect
13. #10590663C2semidirect
14. #10590663C2semidirect
15. Dic3×ΓL(1,𝔽25)C2semidirect
39. #63642C22semidirect
40. #63641C22semidirect
41. #63641C22semidirect
42. C8×C3⋊Dic3C22semidirect
47. C3×#815C22semidirect
48. C3×Dic3⋊C8C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
51. #63572C22semidirect
52. #63572C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
57. #63555C22semidirect
58. #63554C22semidirect
59. #63553C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. #4720D3semidirect
209. #815C2×D3semidirect
222. Dic3⋊C8C2×D3semidirect
223. Dic3⋊C8C2×D3semidirect
230. C8×Dic3C2×D3semidirect
670. C32#2921semidirect
751. C3#78620semidirect
752. C3#79371semidirect

Maximal subgroups

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

subgroupindex
D3×#9262
#105924192
C3×#47262
C3×#47202
#105911542
#105910622
#105910562
#105906992
#105906982
#105906972
#105906962
#105906672
#105906632
Dic3×ΓL(1,𝔽25)2
#793713
#786203