Finite Group Databasebeta

← #11861489

Subgroups — #11861489

Order 1152.

759 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic
2#10592723C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590334C211yesmaximal, characteristic
5#10590324C211yesmaximal, characteristic
6#10590324C211yesmaximal, characteristic
7D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
8#10590319C211yesmaximal, characteristic
9#10590318C211yesmaximal, characteristic
10#10590252C211yesmaximal, characteristic, complemented
11#10590252C211yesmaximal, characteristic, complemented
12#10590251C211yesmaximal, characteristic, complemented
13#10590251C211yesmaximal, characteristic, complemented
14#10590250C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
16#83330—31nomaximal
17#79961—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19C3×#946C411yescharacteristic
20C3×#944C411yescharacteristic
21C3×#897C411yescharacteristic
22C3×#896C411yescharacteristic
23C3×#896C411yescharacteristic
24C3×#889C411yescharacteristic
25C3×#889C411yescharacteristic
26C3×#888C411yescharacteristic
27C3×#872C2211yescharacteristic
28C3×#872C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33C2×#3711C2211yescharacteristic
34C2×#3711C2211yescharacteristic
35C2×D3×C3⋊C8C2211yescharacteristic
36C2×D3×C3⋊C8C2211yescharacteristic
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
40#63630C2211yescharacteristic
41#63630C2211yescharacteristic
42C4×C3⋊(C3⋊C8)C2211yescharacteristic
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C3×#803C2211yescharacteristic
47C3×#803C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49Dic3⋊(C3⋊C8)C2211yescharacteristic
50Dic3⋊(C3⋊C8)C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63554C2211yescharacteristic
56#63554C2211yescharacteristic
57Dic3×C3⋊C8C2211yescharacteristic
58Dic3×C3⋊C8C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#533—31no—
62#5578D311yescharacteristic
63C3×#446—31no—
64#5024—31no—
65#5024—31no—
66#5024—31no—
67#5024—31no—
68#5024—31no—
69#5024—31no—
70#5024—61no—
71#5024D311yescharacteristic, complemented
72Q8×C3⋊C8—31no—
73Q8×C3⋊C8—31no—
74#4999—31no—
75#4999—31no—
76#4997—31no—
77#4997—31no—
78C2×C4⋊(C3⋊C8)—31no—
79C4×#208—31no—
80#4839—31no—
81#4839—31no—
82D3×C4⋊C8—31no—
83#4830—31no—
84#4828—31no—
85#4828—31no—
86#4708—31no—
87#4707—31no—
88#4701—31no—
89#4701—31no—
90#4689—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2×C411yescharacteristic
93C2×C3×C4×D3C2×C411yescharacteristic
94C2×C3×C4×D3C2×C411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2×C411yescharacteristic
97C2×C3×Dic6C2×C411yescharacteristic
98C2×C3×Dic6C2×C411yescharacteristic
99C32×C4⋊C4C2×C411yescharacteristic
100C32×C4⋊C4C2×C411yescharacteristic
101C32×C4⋊C4C2×C411yescharacteristic
102C32×C42C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C32×C42C2311yescharacteristic
105C2×C3⋊(C3⋊C8)C2311yescharacteristic
106C2×C3⋊(C3⋊C8)C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×(C2×D3)⋊C4C2×C411yescharacteristic
110C3×(C2×D3)⋊C4C2×C411yescharacteristic
111C3×(C2×D3)⋊C4C2×C411yescharacteristic
112C3×(C2×D3)⋊C4C2×C411yescharacteristic
113C3×C4⋊Dic3C2×C411yescharacteristic
114C3×C4⋊Dic3C2×C411yescharacteristic
115C3×C4⋊Dic3C2×C411yescharacteristic
116C3×Dic3⋊C4C2×C411yescharacteristic
117C3×Dic3⋊C4C2×C411yescharacteristic
118C3×Dic3⋊C4C2×C411yescharacteristic
119C3×Dic3⋊C4C2×C411yescharacteristic
120C3×Dic3⋊C4C2×C411yescharacteristic
121C3×Dic3⋊C4C2×C411yescharacteristic
122C3×Dic3⋊C4C2×C411yescharacteristic
123C3×Dic3⋊C4C2×C411yescharacteristic
124C3×Dic3⋊C4C2×C411yescharacteristic
125C3×Dic3⋊C4C2×C411yescharacteristic
126C3×C4×Dic3C2×C411yescharacteristic
127C3×C4×Dic3C2×C411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3711—22no—
136#3711Q814yescomplemented
137D3×C3⋊C8—22no—
138D3×C3⋊C8—22no—
139#2962—91noSylow
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×#125—31no—
143C3×#125—31no—
144C3×C22⋊Q8—31no—
145C3×C22⋊Q8—31no—
146C3×C22⋊Q8—31no—
147C3×C22⋊Q8—31no—
148C3×C4×Q8—21no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8C2×D311yescharacteristic
153C3×C4×Q8C2×D311yescharacteristic
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C42—31no—
157#946Dic311yescharacteristic
158#944Dic311yescharacteristic
159C2×#208—31no—
160C2×#208—31no—
161C22×C3⋊C8—31no—
162C22×C3⋊C8—31no—
163C2×ΓL(1,𝔽25)—31no—
164C2×ΓL(1,𝔽25)—31no—
165C2×D3×C8—31no—
166C2×D3×C8—31no—
167#897Dic311yescharacteristic
168#896Dic311yescharacteristic
169#896Dic311yescharacteristic
170#889Dic311yescharacteristic
171#889Dic311yescharacteristic
172#888Dic311yescharacteristic
173#872C2×D311yescharacteristic
174#872C2×D311yescharacteristic
175C42×D3C2×D311yescharacteristic
176C4×Dic6C2×D311yescharacteristic
177C4×Dic6C2×D311yescharacteristic
178C4×Dic6C2×D311yescharacteristic
179C3×C4⋊C8—31no—
180C3×C4⋊C8—31no—
181C3×C4⋊C8—31no—
182C3×#97—31no—
183C3×#97—31no—
184C3×C4×C8—31no—
185#815—31no—
186#815—31no—
187Dic3⋊C8—31no—
188Dic3⋊C8—31no—
189Dic3⋊C8—31no—
190Dic3⋊C8—31no—
191Dic3⋊C8—31no—
192Dic3⋊C8—31no—
193C8×Dic3—31no—
194C8×Dic3—31no—
195C8×Dic3—31no—
196C8×Dic3—31no—
197C4⋊(C3⋊C8)—31no—
198C4⋊(C3⋊C8)—31no—
199C4⋊(C3⋊C8)—31no—
200C4⋊(C3⋊C8)—31no—
201C4⋊(C3⋊C8)—31no—
202C4⋊(C3⋊C8)—31no—
203C4⋊(C3⋊C8)—31no—
204C4⋊(C3⋊C8)—31no—
205C4⋊(C3⋊C8)—31no—
206C4⋊(C3⋊C8)—31no—
207C4⋊(C3⋊C8)—31no—
208C4⋊(C3⋊C8)—31no—
209C4⋊(C3⋊C8)—61no—
210C4⋊(C3⋊C8)—61no—
211C4⋊(C3⋊C8)—61no—
212C4⋊(C3⋊C8)C2×D311yescharacteristic
213C4⋊(C3⋊C8)C2×D311yescharacteristic
214C4⋊(C3⋊C8)C2×D311yescharacteristic
215#803—31no—
216#803—31no—
217#803—31no—
218#803—31no—
219#803—31no—
220#803—31no—
221#803—61no—
222#803—61no—
223#803C2×D311yescharacteristic
224#803C2×D311yescharacteristic
225C4×C3⋊C8—31no—
226C4×C3⋊C8—31no—
227C4×C3⋊C8—31no—
228C4×C3⋊C8—31no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8—61no—
232C4×C3⋊C8C2×D311yescharacteristic
233C22×C3×D3C22×C411yescharacteristic
234C32×Q8—41no—
235C2×C32×C4C22×C411yescharacteristic
236C2×C32×C4C22×C411yescharacteristic
237C2×C32×C4C22×C411yescharacteristic
238C2×C32×C4C22×C411yescharacteristic
239C2×C32×C4C22×C411yescharacteristic
240C2×C32×C4C22×C411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3×Dic3C22×C411yescharacteristic
243C2×C3×Dic3C22×C411yescharacteristic
244C2×C3×Dic3C22×C411yescharacteristic
245C2×C3×Dic3C22×C411yescharacteristic
246C2×C3×Dic3C22×C411yescharacteristic
247C2×C3×Dic3C22×C411yescharacteristic
248C2×C3×Dic3C22×C411yescharacteristic
249C3×C4×D3—22no—
250C3×C4×D3—41no—
251C3×C4×D3C2×Q812yes—
252C3×C4×D3#4112yes—
253C3×Dic6—22no—
254C3×Dic6—22no—
255C3×Dic6—41no—
256C3⋊(C3⋊C8)—21no—
257C3⋊(C3⋊C8)—21no—
258C3⋊(C3⋊C8)—21no—
259C3⋊(C3⋊C8)C2×Q812yes—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8C2×Q812yes—
264#533—31no—
265#446—31no—
266#446—91no—
267#446—91no—
268#446—91no—
269#446—91no—
270#446—91no—
271C8×Q8—91no—
272C8×Q8—91no—
273#424—91no—
274#424—91no—
275C2×C4⋊C8—91no—
276#405—91no—
277#405—91no—
278C4×M16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8C4×D311yescharacteristic
284C2×C3×Q8C2×Dic311yescharacteristic
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C2×C4×D3C2×Dic311yescharacteristic
289C2×C4×D3C2×Dic311yescharacteristic
290C2×C4×D3C22×D311yescharacteristic
291C2×Dic6C2×Dic311yescharacteristic
292C2×Dic6C2×Dic311yescharacteristic
293C2×Dic6C2×Dic311yescharacteristic
294C2×C3×C8—31no—
295C2×C3×C8—31no—
296C2×C3×C8—31no—
297C2×C3×C8—31no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—31no—
302C3×C4⋊C4—31no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4C4×D311yescharacteristic
315C3×C4⋊C4C4×D311yescharacteristic
316C3×C4⋊C4C4×D311yescharacteristic
317C3×C4⋊C4C2×Dic311yescharacteristic
318C3×C4⋊C4C2×Dic311yescharacteristic
319C3×C4⋊C4C2×Dic311yescharacteristic
320C3×C22⋊C4—31no—
321C3×C22⋊C4—31no—
322C3×C22⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—31no—
328C3×C42—31no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—31no—
332C3×C42C22×D311yescharacteristic
333C3×C42C22×D311yescharacteristic
334C3×C42C22×D311yescharacteristic
335C3×C42C22×D311yescharacteristic
336C3×C42C22×D311yescharacteristic
337C3×C42C22×D311yescharacteristic
338(C2×D3)⋊C4C2×Dic311yescharacteristic
339(C2×D3)⋊C4C2×Dic311yescharacteristic
340(C2×D3)⋊C4C2×Dic311yescharacteristic
341(C2×D3)⋊C4C2×Dic311yescharacteristic
342C4⋊Dic3C2×Dic311yescharacteristic
343C4⋊Dic3C2×Dic311yescharacteristic
344C4⋊Dic3C2×Dic311yescharacteristic
345Dic3⋊C4C2×Dic311yescharacteristic
346Dic3⋊C4C2×Dic311yescharacteristic
347Dic3⋊C4C2×Dic311yescharacteristic
348Dic3⋊C4C2×Dic311yescharacteristic
349Dic3⋊C4C2×Dic311yescharacteristic
350Dic3⋊C4C2×Dic311yescharacteristic
351Dic3⋊C4C2×Dic311yescharacteristic
352Dic3⋊C4C2×Dic311yescharacteristic
353Dic3⋊C4C2×Dic311yescharacteristic
354Dic3⋊C4C2×Dic311yescharacteristic
355C4×Dic3C2×Dic311yescharacteristic
356C4×Dic3C2×Dic311yescharacteristic
357C4×Dic3C22×D311yescharacteristic
358C4×Dic3C22×D311yescharacteristic
359C4×Dic3C22×D311yescharacteristic
360#208—34no—
361#208—62no—
362C2×C3⋊C8—31no—
363C2×C3⋊C8—31no—
364C2×C3⋊C8—31no—
365C2×C3⋊C8—31no—
366C2×C3⋊C8—31no—
367C2×C3⋊C8—31no—
368C2×C3⋊C8—31no—
369C2×C3⋊C8—31no—
370C2×C3⋊C8—61no—
371C2×C3⋊C8—61no—
372C2×C3⋊C8—61no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8—62no—
375C2×C3⋊C8—62no—
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380ΓL(1,𝔽25)—34no—
381ΓL(1,𝔽25)—62no—
382D3×C8—62no—
383D3×C8—62no—
384C22×C32C23×C411yescharacteristic
385C2×C3×D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3C4×Q812yes—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4C22×Q811yescharacteristic
395C32×C4C2×#4111yescharacteristic
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3C4×Q812yes—
402C3×Dic3#13112yes—
403C2×M16—91no—
404C2×M16—91no—
405C22×C8—91no—
406C22×C8—91no—
407C4⋊Q8—31no—
408C4⋊Q8—31no—
409#125—31no—
410#125—31no—
411C22⋊Q8—31no—
412C22⋊Q8—31no—
413C22⋊Q8—31no—
414C22⋊Q8—31no—
415C4×Q8—31no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8D3211yescharacteristic
419#117—31no—
420#117—31no—
421C2×C42—31no—
422C4⋊C8—31no—
423C4⋊C8—31no—
424C4⋊C8—31no—
425C4⋊C8—91no—
426C4⋊C8—91no—
427C4⋊C8—91no—
428C4⋊C8—91no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#97—31no—
435#97—31no—
436#97—91no—
437#97—91no—
438#97—91no—
439#97—91no—
440C4×C8—31no—
441C4×C8—91no—
442C4×C8—91no—
443C4×C8—91no—
444C4×C8—91no—
445C4×C8—91no—
446C23×C3—31no—
447C22×D3C22×Dic311yescharacteristic
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—42no—
451C3×Q8—62no—
452C3×Q8—62no—
453C3×Q8—121no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—62no—
471C2×C3×C4—121no—
472C2×C3×C4C2×C4×D311yescharacteristic
473C2×C3×C4C2×C4×D311yescharacteristic
474C2×C3×C4C2×C4×D311yescharacteristic
475C2×C3×C4C2×C4×D311yescharacteristic
476C2×C3×C4C2×C4×D311yescharacteristic
477C2×C3×C4C2×C4×D311yescharacteristic
478C2×C3×C4C22×Dic311yescharacteristic
479C2×C3×C4C22×Dic311yescharacteristic
480C2×C3×C4C22×Dic311yescharacteristic
481C2×C3×C4C22×Dic311yescharacteristic
482C2×C3×C4C22×Dic311yescharacteristic
483C2×C3×C4C22×Dic311yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486C2×Dic3C22×Dic311yescharacteristic
487C2×Dic3C22×Dic311yescharacteristic
488C2×Dic3C22×Dic311yescharacteristic
489C2×Dic3C22×Dic311yescharacteristic
490C2×Dic3C22×Dic311yescharacteristic
491C2×Dic3C22×Dic311yescharacteristic
492C2×Dic3C22×Dic311yescharacteristic
493C4×D3—22no—
494C4×D3—41no—
495C4×D3D3×Q812yes—
496C4×D3#23912yes—
497Dic6—22no—
498Dic6—22no—
499Dic6—41no—
500C3×C8—32no—
501C3×C8—61no—
502C3×C8—61no—
503C3×C8—61no—
504C3⋊C8—21no—
505C3⋊C8—21no—
506C3⋊C8—21no—
507C3⋊C8—32no—
508C3⋊C8—32no—
509C3⋊C8—62no—
510C3⋊C8—61no—
511C3⋊C8—61no—
512C3⋊C8—61no—
513C3⋊C8—61no—
514C3⋊C8—61no—
515C3⋊C8—61no—
516C3⋊C8—121no—
517C3⋊C8—121no—
518C3⋊C8—121no—
519C3⋊C8D3×Q812yes—
520C2×C32C2×C4×Q811yescharacteristic
521C2×C32C2×#13111yescharacteristic
522C2×C32#56811yescharacteristic
523C3×D3—22no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8—31no—
527C2×Q8D3×Dic311yescharacteristic
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531M16—94no—
532M16—182no—
533C2×C8—31no—
534C2×C8—31no—
535C2×C8—31no—
536C2×C8—31no—
537C2×C8—91no—
538C2×C8—91no—
539C2×C8—91no—
540C2×C8—91no—
541C2×C8—182no—
542C2×C8—182no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4D3×Dic311yescharacteristic
557C4⋊C4D3×Dic311yescharacteristic
558C4⋊C4D3×Dic311yescharacteristic
559C22⋊C4—31no—
560C22⋊C4—31no—
561C22⋊C4—31no—
562C22⋊C4—31no—
563C42—31no—
564C42—31no—
565C42—31no—
566C42—31no—
567C42—31no—
568C42C2×D3211yescharacteristic
569C42C2×D3211yescharacteristic
570C42C2×D3211yescharacteristic
571C22×C3—21no—
572C22×C3—32no—
573C22×C3—61no—
574C22×C3—61no—
575C22×C3C22×C4×D311yescharacteristic
576C22×C3C23×Dic311yescharacteristic
577C2×D3—21no—
578C2×D3—21no—
579C2×D3Q8×Dic312yes—
580C3×C4—22no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—32no—
596C3×C4—32no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4C2×D3×Q811yescharacteristic
608C3×C4C2×D3×Q811yescharacteristic
609C3×C4C2×#23911yescharacteristic
610C3×C4D3×#4111yescharacteristic
611Dic3—21no—
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3Q8×Dic312yes—
617Dic3#94812yes—
618C32#296211yescharacteristic, complemented, Sylow
619C23—31no—
620Q8—41no—
621Q8—62no—
622Q8—62no—
623Q8—121no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—32no—
627C2×C4—32no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—62no—
634C2×C4—121no—
635C2×C4C2×D3×Dic311yescharacteristic
636C2×C4C2×D3×Dic311yescharacteristic
637C2×C4C2×D3×Dic311yescharacteristic
638C2×C4C2×D3×Dic311yescharacteristic
639C2×C4C2×D3×Dic311yescharacteristic
640C2×C4C2×D3×Dic311yescharacteristic
641C2×C4C22×D3211yescharacteristic
642C8—32no—
643C8—61no—
644C8—61no—
645C8—61no—
646C8—92no—
647C8—181no—
648C8—181no—
649C8—181no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—62no—
654C2×C3C4×D3×Q811yescharacteristic
655C2×C3#574511yescharacteristic
656C2×C3D3×#13111yescharacteristic
657C2×C3C2×Q8×Dic311yescharacteristic
658C2×C3C2×#94811yescharacteristic
659C2×C3#581911yescharacteristic
660D3—22no—
661C22—32no—
662C22—61no—
663C22—61no—
664C22C22×D3×Dic311yescharacteristic
665C4—21no—
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—32no—
672C4—32no—
673C4—61no—
674C4—61no—
675C4—61no—
676C4—61no—
677C4—61no—
678C4D32×Q811yescharacteristic
679C4D3×#23911yescharacteristic
680C3—21no—
681C3#7996111yescharacteristic, complemented
682C3#8333011yescharacteristic, complemented
683C2—62no—
684C2#1059477611yescharacteristic
685C2D3×Q8×Dic311yescharacteristic
686C2D3×#94811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×Q8C22
prime radicalC22×C3×D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2962
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10592723C2semidirect
3. C3×#5024C2semidirect
10. #10590252C2semidirect
11. #10590252C2semidirect
12. #10590251C2semidirect
13. #10590251C2semidirect
14. #10590250C2semidirect
15. C3⋊C8×Dic6C2semidirect
71. #5024D3semidirect
136. #3711Q8semidirect
618. C32#2962semidirect
681. C3#79961semidirect
682. C3#83330semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
#105927232
C3×#50242
#105903342
#105903242
D3×C4⋊(C3⋊C8)2
#105903192
#105903182
#105902522
#105902512
#105902502
C3⋊C8×Dic62
#833303
#799613