Finite Group Databasebeta

← C2×#79084 #11660287

Subgroups — C2×#79084 #11660287

Order 768.

1982 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5528C211yesmaximal, characteristic
2C2×C3×#424C211yesmaximal, characteristic, complemented
3C2×#5127C211yesmaximal, characteristic, complemented
4C2×#5128C211yesmaximal, characteristic, complemented
5C2×C8×#67C211yesmaximal, characteristic, complemented
6C2×C8×#67C211yesmaximal, characteristic, complemented
7C2×#5000C211yesmaximal, characteristic, complemented
8#79084C2116yesmaximal, direct product factor
9C2×#4839C211yesmaximal, characteristic, complemented
10C2×D3×C4⋊C8C211yesmaximal, characteristic, complemented
11C2×#4828C211yesmaximal, characteristic, complemented
12C2×#4830C211yesmaximal, characteristic, complemented
13C2×#4836C211yesmaximal, characteristic, complemented
14C2×#4834C211yesmaximal, characteristic, complemented
15C2×#4840C211yesmaximal, characteristic, complemented
16C2×#4833C211yesmaximal, characteristic, complemented
17C2×#2994—31nomaximal, Sylow
18C22×C3×M16C2211yescharacteristic
19C23×C3×C8C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C2×C4×#67C2211yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C22×ΓL(1,𝔽25)C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27#5528C418yes—
28#5528C2218yes—
29C2×#898C411yescharacteristic
30C2×#896C411yescharacteristic
31C2×#894C411yescharacteristic
32C2×#889C411yescharacteristic
33C2×#885C411yescharacteristic
34C2×#884C411yescharacteristic
35C2×#883C411yescharacteristic
36C2×#879C411yescharacteristic
37C2×C4×D12C2211yescharacteristic
38C2×#872C2211yescharacteristic
39C2×C42×D3C2211yescharacteristic
40C2×C4×Dic6C2211yescharacteristic
41C3×#424C2218yescomplemented
42C2×C3×C4⋊C8C2211yescharacteristic
43C2×C3×C4⋊C8C2211yescharacteristic
44C2×C3×C4⋊C8C2211yescharacteristic
45C2×C3×C4⋊C8C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5128C2218yescomplemented
49#5127C2218yescomplemented
50C8×#67C2218yescomplemented
51C8×#67C2218yescomplemented
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56C2×#815C2211yescharacteristic
57C2×Dic3⋊C8C2211yescharacteristic
58C2×Dic3⋊C8C2211yescharacteristic
59C2×Dic3⋊C8C2211yescharacteristic
60C2×Dic3⋊C8C2211yescharacteristic
61C2×C8×Dic3C2211yescharacteristic
62C2×C8×Dic3C2211yescharacteristic
63C2×C8×Dic3C2211yescharacteristic
64#5000C2218yescomplemented
65C2×C4⋊(C3⋊C8)C2211yescharacteristic
66C2×C4⋊(C3⋊C8)C2211yescharacteristic
67C2×#803C2211yescharacteristic
68C2×C4×C3⋊C8C2211yescharacteristic
69#4840C2218yescomplemented
70#4839C2218yescomplemented
71#4836C2218yescomplemented
72#4834C2218yescomplemented
73#4833C2218yescomplemented
74D3×C4⋊C8C2218yescomplemented
75#4830C2218yescomplemented
76#4828C2218yescomplemented
77C2×#529—31no—
78#2994—316no—
79C2×#446—31no—
80C2×C8×Q8—31no—
81C2×#436—31no—
82C2×#435—31no—
83C2×#435—31no—
84C2×C8×D4—31no—
85C2×C8×D4—31no—
86C2×C8×D4—31no—
87C2×#433—31no—
88C2×#433—31no—
89C2×#431—31no—
90C2×#424—31no—
91C2×#424D311yescharacteristic, complemented
92C22×C4⋊C8—31no—
93C23×C3×C4C2311yescharacteristic
94C22×#67C2×C411yescharacteristic
95C22×#67C2×C411yescharacteristic
96C22×D12C2×C411yescharacteristic
97C22×C4×D3C2×C411yescharacteristic
98C22×C4×D3C2×C411yescharacteristic
99C22×C4×D3C2311yescharacteristic
100C22×C4×D3C2311yescharacteristic
101C22×Dic6C2×C411yescharacteristic
102C2×C3×M16—42no—
103C2×C3×M16C2314yes—
104C22×C3×C8—42no—
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2314yes—
110C3×#117C2×C414yes—
111C3×#117C2314yes—
112C2×C3×C4⋊C4C2×C411yescharacteristic
113C2×C3×C4⋊C4C2×C411yescharacteristic
114C2×C3×C22⋊C4C2×C411yescharacteristic
115C2×C3×C22⋊C4C2×C411yescharacteristic
116C2×C3×C42C2311yescharacteristic
117C2×C3×C42C2311yescharacteristic
118C2×#217C2×C411yescharacteristic
119C2×#217C2×C411yescharacteristic
120C4×#67C2×C414yes—
121C4×#67C2×C414yes—
122C4×#67C2314yes—
123C4×#67C2314yes—
124C2×(C2×D3)⋊C4C2×C411yescharacteristic
125C2×(C2×D3)⋊C4C2×C411yescharacteristic
126C2×(C2×D3)⋊C4C2×C411yescharacteristic
127C2×(C2×D3)⋊C4C2×C411yescharacteristic
128C2×(C2×D3)⋊C4C2×C411yescharacteristic
129C2×(C2×D3)⋊C4C2×C411yescharacteristic
130C2×C4⋊Dic3C2×C411yescharacteristic
131C2×C4⋊Dic3C2×C411yescharacteristic
132C2×Dic3⋊C4C2×C411yescharacteristic
133C2×Dic3⋊C4C2×C411yescharacteristic
134C2×Dic3⋊C4C2×C411yescharacteristic
135C2×Dic3⋊C4C2×C411yescharacteristic
136C2×Dic3⋊C4C2×C411yescharacteristic
137C2×Dic3⋊C4C2×C411yescharacteristic
138C2×C4×Dic3C2×C411yescharacteristic
139C2×C4×Dic3C2×C411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C2×ΓL(1,𝔽25)—42no—
147C2×ΓL(1,𝔽25)C2314yes—
148C2×D3×C8—42no—
149C2×D3×C8—42no—
150C2×D3×C8—42no—
151C2×D3×C8C2314yes—
152C2×D3×C8C2314yes—
153C2×D3×C8C2314yes—
154#898C2×C418yes—
155#896C2×C418yes—
156#894C2×C418yes—
157#889C2×C418yes—
158#885C2×C418yes—
159#884C2×C418yes—
160#883C2×C418yes—
161#879C2×C418yes—
162C4×D12C2×C414yes—
163C4×D12C2314yes—
164#872C2×C414yes—
165#872C2314yes—
166C42×D3C2×C414yes—
167C42×D3C2314yes—
168C4×Dic6C2×C414yes—
169C4×Dic6C2314yes—
170C3×C4⋊C8C2314yes—
171C3×C4⋊C8C2314yes—
172C3×C4⋊C8C2314yes—
173C3×C4⋊C8C2314yes—
174#830C2314yes—
175#830C2314yes—
176(C2×D3)⋊C8C2314yes—
177(C2×D3)⋊C8C2314yes—
178(C2×D3)⋊C8C2314yes—
179(C2×D3)⋊C8C2314yes—
180#815C2314yes—
181Dic3⋊C8C2314yes—
182Dic3⋊C8C2314yes—
183Dic3⋊C8C2314yes—
184Dic3⋊C8C2314yes—
185C8×Dic3C2314yes—
186C8×Dic3C2314yes—
187C8×Dic3C2314yes—
188C4⋊(C3⋊C8)C2314yes—
189C4⋊(C3⋊C8)C2314yes—
190#803C2314yes—
191C4×C3⋊C8C2314yes—
192C22×M16—31no—
193C22×M16C2×D311yescharacteristic
194C23×C8—31no—
195C23×C8—31no—
196C23×C8—31no—
197C23×C8C2×D311yescharacteristic
198#529—38no—
199#529—38no—
200C2×#126—31no—
201C2×#126—31no—
202C2×#125—31no—
203C2×#124—31no—
204C2×#123—31no—
205C2×#123—31no—
206C2×C22⋊Q8—31no—
207C2×#121—31no—
208C2×C4×Q8—31no—
209C2×C4×D4—31no—
210C2×C4×D4—31no—
211C2×C4×D4—31no—
212C2×#117—31no—
213C2×#117C2×D311yescharacteristic
214C22×C42—31no—
215#446—38no—
216C8×Q8—38no—
217#436—38no—
218#435—38no—
219#435—38no—
220C8×D4—38no—
221C8×D4—38no—
222C8×D4—38no—
223#433—38no—
224#433—38no—
225#431—38no—
226#424—38no—
227#424C2×D318yescomplemented
228C2×C4⋊C8—31no—
229C2×C4⋊C8—31no—
230C2×C4⋊C8—31no—
231C2×C4⋊C8—31no—
232C2×C4⋊C8—31no—
233C2×C4⋊C8—31no—
234C2×C4⋊C8—38no—
235C2×C4⋊C8C2×D311yescharacteristic
236C2×C4⋊C8C2×D311yescharacteristic
237C2×C4⋊C8C2×D311yescharacteristic
238C2×C4⋊C8C2×D311yescharacteristic
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8—31no—
245C2×#97—31no—
246C2×#97—31no—
247C2×C4×C8—31no—
248C2×C4×C8—31no—
249C2×C4×C8—31no—
250C2×C4×C8—31no—
251C24×C3C22×C411yescharacteristic
252C23×D3C22×C411yescharacteristic
253C23×D3C22×C411yescharacteristic
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C22×C411yescharacteristic
258C22×C3×C4C22×C411yescharacteristic
259C22×C3×C4C22×C411yescharacteristic
260C22×C3×C4C22×C411yescharacteristic
261C22×C3×C4C22×C412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2411yescharacteristic
264C2×#67—24no—
265C2×#67—24no—
266C2×#67C22×C414yes—
267C2×#67C22×C414yes—
268C22×Dic3C22×C411yescharacteristic
269C22×Dic3C22×C411yescharacteristic
270C22×Dic3C22×C411yescharacteristic
271C22×Dic3C22×C411yescharacteristic
272C22×Dic3C22×C411yescharacteristic
273C22×Dic3C22×C411yescharacteristic
274C2×D12—24no—
275C2×D12C22×C414yes—
276C2×C4×D3—24no—
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—24no—
282C2×C4×D3C22×C412yes—
283C2×C4×D3C22×C414yes—
284C2×C4×D3C22×C414yes—
285C2×C4×D3C22×C412yes—
286C2×C4×D3C2412yes—
287C2×C4×D3C2412yes—
288C2×Dic6—24no—
289C2×Dic6C22×C414yes—
290C3×M16—44no—
291C2×C3×C8—22no—
292C2×C3×C8—22no—
293C2×C3×C8—22no—
294C2×C3×C8—22no—
295C2×C3×C8—44no—
296C2×C3×C8C2412yes—
297C2×C3×C8C2412yes—
298C2×C3×C8C2412yes—
299C2×C3×C8C2412yes—
300C3×C4⋊C4C22×C414yes—
301C3×C4⋊C4C22×C414yes—
302C3×C22⋊C4C22×C414yes—
303C3×C22⋊C4C22×C414yes—
304C3×C42C22×C412yes—
305C3×C42C22×C412yes—
306C3×C42C2412yes—
307C3×C42C2412yes—
308#217C22×C414yes—
309#217C22×C414yes—
310(C2×D3)⋊C4C22×C414yes—
311(C2×D3)⋊C4C22×C414yes—
312(C2×D3)⋊C4C22×C414yes—
313(C2×D3)⋊C4C22×C414yes—
314(C2×D3)⋊C4C22×C414yes—
315(C2×D3)⋊C4C22×C414yes—
316C4⋊Dic3C22×C414yes—
317C4⋊Dic3C22×C414yes—
318Dic3⋊C4C22×C414yes—
319Dic3⋊C4C22×C414yes—
320Dic3⋊C4C22×C414yes—
321Dic3⋊C4C22×C414yes—
322Dic3⋊C4C22×C414yes—
323Dic3⋊C4C22×C414yes—
324C4×Dic3C22×C412yes—
325C4×Dic3C22×C412yes—
326C4×Dic3C22×C414yes—
327C4×Dic3C22×C414yes—
328C4×Dic3C2412yes—
329C4×Dic3C2412yes—
330C2×C3⋊C8—22no—
331C2×C3⋊C8—22no—
332C2×C3⋊C8—22no—
333C2×C3⋊C8—22no—
334C2×C3⋊C8C2412yes—
335C2×C3⋊C8C2412yes—
336C2×C3⋊C8C2412yes—
337C2×C3⋊C8C2412yes—
338ΓL(1,𝔽25)—44no—
339D3×C8—44no—
340D3×C8—44no—
341D3×C8—44no—
342C22×Q8—31no—
343C22×D4—31no—
344C22×D4—31no—
345C22×D4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4C22×D311yescharacteristic
351C2×M16—34no—
352C2×M16—42no—
353C2×M16—122no—
354C2×M16C22×D314yes—
355C22×C8—31no—
356C22×C8—31no—
357C22×C8—31no—
358C22×C8—31no—
359C22×C8—34no—
360C22×C8—34no—
361C22×C8—34no—
362C22×C8—42no—
363C22×C8—122no—
364C22×C8—122no—
365C22×C8—122no—
366C22×C8C22×D311yescharacteristic
367C22×C8C22×D311yescharacteristic
368C22×C8C22×D311yescharacteristic
369C22×C8C22×D311yescharacteristic
370C22×C8C22×D314yes—
371#126—38no—
372#126—38no—
373#125—38no—
374#124—38no—
375#123—38no—
376#123—38no—
377C22⋊Q8—38no—
378#121—38no—
379C4×Q8—34no—
380C4×Q8—34no—
381C4×D4—34no—
382C4×D4—34no—
383C4×D4—34no—
384C4×D4—34no—
385C4×D4—34no—
386C4×D4—34no—
387#117—34no—
388#117—34no—
389#117C4×D314yes—
390#117C22×D314yes—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4C4×D311yescharacteristic
400C2×C4⋊C4C4×D311yescharacteristic
401C2×C22⋊C4—31no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4C4×D311yescharacteristic
410C2×C22⋊C4C4×D311yescharacteristic
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—34no—
416C2×C42—34no—
417C2×C42C22×D311yescharacteristic
418C2×C42C22×D311yescharacteristic
419C4⋊C8—34no—
420C4⋊C8—34no—
421C4⋊C8—34no—
422C4⋊C8—34no—
423C4⋊C8—34no—
424C4⋊C8—34no—
425C4⋊C8C22×D314yes—
426C4⋊C8C22×D314yes—
427C4⋊C8C22×D314yes—
428C4⋊C8C22×D314yes—
429C22⋊C8—34no—
430C22⋊C8—34no—
431C22⋊C8—34no—
432C22⋊C8—34no—
433C22⋊C8—34no—
434C22⋊C8—34no—
435#97—34no—
436#97—34no—
437C4×C8—34no—
438C4×C8—34no—
439C4×C8—34no—
440C4×C8—34no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3C23×C412yes—
445C23×C3C23×C411yescharacteristic
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3#13114yes—
452C22×D3C23×C412yes—
453C22×D3C23×C412yes—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4C23×C412yes—
463C2×C3×C4C23×C412yes—
464C2×C3×C4C23×C412yes—
465C2×C3×C4C23×C412yes—
466C2×C3×C4C23×C412yes—
467C2×C3×C4C23×C411yescharacteristic
468C2×C3×C4H(5,𝔽2)12yes—
469C2×C3×C42−1+412yes—
470C2×C3×C4C2511yescharacteristic
471#67—28no—
472#67—28no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3#13114yes—
479C2×Dic3C23×C412yes—
480C2×Dic3C23×C412yes—
481C2×Dic3C23×C412yes—
482C2×Dic3C23×C412yes—
483C2×Dic3C23×C412yes—
484C2×Dic3C23×C412yes—
485D12—28no—
486C4×D3—28no—
487C4×D3—24no—
488C4×D3—24no—
489C4×D3—22no—
490C4×D3—22no—
491C4×D3—22no—
492C4×D3—22no—
493C4×D3—28no—
494Dic6—28no—
495C3×C8—22no—
496C3×C8—22no—
497C3×C8—22no—
498C3×C8—22no—
499C3⋊C8—22no—
500C3⋊C8—22no—
501C3⋊C8—22no—
502C3⋊C8—22no—
503C24—31no—
504C24—31no—
505C24C2×C4×D311yescharacteristic
506C2×Q8—34no—
507C2×Q8—64no—
508C2×D4—34no—
509C2×D4—34no—
510C2×D4—34no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—64no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—32no—
523C22×C4—34no—
524C22×C4—34no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4C2×C4×D311yescharacteristic
535C22×C4C2×C4×D311yescharacteristic
536C22×C4C2×C4×D311yescharacteristic
537C22×C4C2×C4×D311yescharacteristic
538C22×C4C2×C4×D311yescharacteristic
539C22×C4C2×C4×D312yes—
540C22×C4C23×D312yes—
541C22×C4C23×D311yescharacteristic
542M16—44no—
543M16—124no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—32no—
549C2×C8—32no—
550C2×C8—32no—
551C2×C8—32no—
552C2×C8—44no—
553C2×C8—62no—
554C2×C8—62no—
555C2×C8—62no—
556C2×C8—62no—
557C2×C8—124no—
558C2×C8—124no—
559C2×C8—124no—
560C2×C8C23×D312yes—
561C2×C8C23×D312yes—
562C2×C8C23×D312yes—
563C2×C8C23×D312yes—
564C4⋊C4—34no—
565C4⋊C4—34no—
566C4⋊C4—34no—
567C4⋊C4—34no—
568C4⋊C4—34no—
569C4⋊C4—34no—
570C4⋊C4—34no—
571C4⋊C4—34no—
572C4⋊C4C2×C4×D314yes—
573C4⋊C4C2×C4×D314yes—
574C22⋊C4—34no—
575C22⋊C4—34no—
576C22⋊C4—34no—
577C22⋊C4—34no—
578C22⋊C4—34no—
579C22⋊C4—34no—
580C22⋊C4—34no—
581C22⋊C4—34no—
582C22⋊C4C2×C4×D314yes—
583C22⋊C4C2×C4×D314yes—
584C42—32no—
585C42—34no—
586C42—34no—
587C42—32no—
588C42—32no—
589C42—32no—
590C42C2×C4×D312yes—
591C42C2×C4×D312yes—
592C42C23×D312yes—
593C42C23×D312yes—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—44no—
598C22×C3#52012yes—
599C22×C3C2×#13112yes—
600C22×C3C2×#13112yes—
601C22×C3C24×C411yescharacteristic
602C2×D3—22no—
603C2×D3—28no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—44no—
609C2×D3C2×#13114yes—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4#52012yes—
616C3×C4C2×H(5,𝔽2)11yescharacteristic
617C3×C4C2×2−1+411yescharacteristic
618Dic3—22no—
619Dic3—22no—
620Dic3—22no—
621Dic3—22no—
622Dic3—22no—
623Dic3C2×#13114yes—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—32no—
628C23—34no—
629C23—32no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23C22×C4×D312yes—
636C23C22×C4×D311yescharacteristic
637Q8—68no—
638D4—68no—
639D4—68no—
640D4—68no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—32no—
650C2×C4—34no—
651C2×C4—32no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—68no—
657C2×C4—68no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—64no—
668C2×C4—64no—
669C2×C4C22×C4×D312yes—
670C2×C4C22×C4×D312yes—
671C2×C4C22×C4×D312yes—
672C2×C4C22×C4×D312yes—
673C2×C4C22×C4×D312yes—
674C2×C4C22×C4×D311yescharacteristic
675C2×C4#100412yes—
676C2×C4#100712yes—
677C2×C4C24×D311yescharacteristic
678C8—22no—
679C8—22no—
680C8—22no—
681C8—22no—
682C8—62no—
683C8—62no—
684C8—62no—
685C8—62no—
686C2×C3—42no—
687C2×C3#299414yescomplemented
688C2×C3C2×#52011yescharacteristic
689C2×C3C22×#13111yescharacteristic
690C2×C3C22×#13111yescharacteristic
691D3—24no—
692D3—42no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—34no—
697C22—44no—
698C22—62no—
699C22—62no—
700C22—68no—
701C22—62no—
702C22—62no—
703C22—62no—
704C22—124no—
705C22#550412yes—
706C22D3×#13112yes—
707C22D3×#13112yes—
708C22C23×C4×D311yescharacteristic
709C4—22no—
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—34no—
715C4—62no—
716C4—62no—
717C4—62no—
718C4—62no—
719C4—62no—
720C4#550412yes—
721C4C2×#100411yescharacteristic
722C4C2×#100711yescharacteristic
723C3C2×#299411yescharacteristic, complemented, Sylow
724C2—42no—
725C2—64no—
726C2—122no—
727C2#7908414yesdirect product factor
728C2C2×#550411yescharacteristic
729C2C2×D3×#13111yescharacteristic
730C2C2×D3×#13111yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutatorC22×C3C24×C4
FrattiniC2×C4C24×D3
FittingC2×C3×#424C2
socleC23×C3C23×C4
prime radicalC2×#884C4
cosocleC2×C3×C4C25
hypercenterC2×#424D3
hypocenterC3C2×#2994
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×C3×#424C2semidirect
3. C2×#5127C2semidirect
4. C2×#5128C2semidirect
5. C2×C8×#67C2semidirect
6. C2×C8×#67C2semidirect
7. C2×#5000C2semidirect
8. #79084C2direct (N × H)
9. C2×#4839C2semidirect
10. C2×D3×C4⋊C8C2semidirect
11. C2×#4828C2semidirect
12. C2×#4830C2semidirect
13. C2×#4836C2semidirect
14. C2×#4834C2semidirect
15. C2×#4840C2semidirect
16. C2×#4833C2semidirect
41. C3×#424C22semidirect
48. #5128C22semidirect
49. #5127C22semidirect
50. C8×#67C22semidirect
51. C8×#67C22semidirect
64. #5000C22semidirect
69. #4840C22semidirect
70. #4839C22semidirect
71. #4836C22semidirect
72. #4834C22semidirect
73. #4833C22semidirect
74. D3×C4⋊C8C22semidirect
75. #4830C22semidirect
76. #4828C22semidirect
91. C2×#424D3semidirect
227. #424C2×D3semidirect
687. C2×C3#2994semidirect
723. C3C2×#2994semidirect
727. C2#79084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55282
C2×C3×#4242
C2×#51272
C2×#51282
C2×C8×#672
C2×#50002
#790842
C2×#48392
C2×D3×C4⋊C82
C2×#48282
C2×#48302
C2×#48362
C2×#48342
C2×#48402
C2×#48332
C2×#29943