Finite Group Databasebeta

← C2×#79462 #11660245

Subgroups — C2×#79462 #11660245

Order 768.

2210 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#237C211yesmaximal, characteristic
2C2×C3×#435C211yesmaximal, characteristic, complemented
3C2×#5127C211yesmaximal, characteristic, complemented
4C2×#5118C211yesmaximal, characteristic, complemented
5C2×C8×#67C211yesmaximal, characteristic, complemented
6C22×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#5011C211yesmaximal, characteristic, complemented
8#79462C2116yesmaximal, direct product factor
9C2×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C2×#4828C211yesmaximal, characteristic, complemented
11C2×#4728C211yesmaximal, characteristic, complemented
12C2×#67⋊C8C211yesmaximal, characteristic, complemented
13C2×#4719C211yesmaximal, characteristic, complemented
14C2×#4718C211yesmaximal, characteristic, complemented
15C2×#4705C211yesmaximal, characteristic, complemented
16C2×#4701C211yesmaximal, characteristic, complemented
17C2×#2990—31nomaximal, Sylow
18C22×#237C411yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×D4×Dic3C411yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×#208C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C4×#237C418yes—
32C4×#237C2218yes—
33C2×#892C411yescharacteristic
34C2×#887C411yescharacteristic
35C2×#67⋊C4C411yescharacteristic
36C2×#67⋊C4C411yescharacteristic
37C2×#877C411yescharacteristic
38C2×#877C411yescharacteristic
39C2×C42×D3C2211yescharacteristic
40C2×C4×Dic6C2211yescharacteristic
41C3×#435C2218yescomplemented
42C2×C3×C4⋊C8C2211yescharacteristic
43C2×C3×C22⋊C8C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×#97C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5127C2218yescomplemented
49#5118C2218yescomplemented
50C8×#67C2218yescomplemented
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×#815C2211yescharacteristic
54C2×#815C2211yescharacteristic
55C2×Dic3⋊C8C2211yescharacteristic
56C2×Dic3⋊C8C2211yescharacteristic
57C2×Dic3⋊C8C2211yescharacteristic
58C2×Dic3⋊C8C2211yescharacteristic
59C2×Dic3⋊C8C2211yescharacteristic
60C2×Dic3⋊C8C2211yescharacteristic
61C2×Dic3⋊C8C2211yescharacteristic
62C2×Dic3⋊C8C2211yescharacteristic
63C2×Dic3⋊C8C2218yescomplemented
64C2×C8×Dic3C2211yescharacteristic
65C2×C8×Dic3C2211yescharacteristic
66#5011C2218yescomplemented
67C2×C4⋊(C3⋊C8)C2211yescharacteristic
68C2×#803C2211yescharacteristic
69D3×C4⋊C8C2218yescomplemented
70#4828C2218yescomplemented
71#4728C2218yescomplemented
72#67⋊C8C2218yescomplemented
73#4719C2218yescomplemented
74#4718C2218yescomplemented
75#4705C2218yescomplemented
76#4701C2218yescomplemented
77C2×C4×#41—31no—
78#2990—316no—
79C2×#446—31no—
80C2×#446—31no—
81C2×#435—31no—
82C2×#435—31no—
83C2×#435—31no—
84C2×#435D311yescharacteristic, complemented
85C2×C8×D4—31no—
86C2×C8×D4—31no—
87C2×#432—31no—
88C2×#432—31no—
89C2×#431—31no—
90C2×#423—31no—
91C22×C4⋊C8—31no—
92C22×C4⋊C8—31no—
93C22×C3×D4C2×C411yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67C2×C411yescharacteristic
97C22×#67C2×C411yescharacteristic
98C23×Dic3C2×C411yescharacteristic
99C23×Dic3C2×C411yescharacteristic
100C23×Dic3C2×C411yescharacteristic
101C23×Dic3C2×C411yescharacteristic
102C2×#237—28no—
103C2×#237C2×C418yes—
104C22×C4×D3C2×C411yescharacteristic
105C22×C4×D3C2×C411yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×Dic6C2×C411yescharacteristic
108C2×C3×M16—42no—
109C2×C3×M16C2314yes—
110C22×C3×C8—42no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2314yes—
116C3×C4×D4C2×C414yes—
117C3×C4×D4C2314yes—
118C2×C3×C4⋊C4C2×C411yescharacteristic
119C2×C3×C22⋊C4C2×C411yescharacteristic
120C2×C3×C22⋊C4C2×C411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×#217C2×C411yescharacteristic
123C2×#217C2×C411yescharacteristic
124D4×Dic3C2×C418yes—
125C4×#67C2×C414yes—
126C4×#67C2×C414yes—
127C4×#67C2314yes—
128C4×#67C2314yes—
129C2×(C2×D3)⋊C4C2×C411yescharacteristic
130C2×(C2×D3)⋊C4C2×C411yescharacteristic
131C2×C4⋊Dic3C2×C411yescharacteristic
132C2×Dic3⋊C4C2×C411yescharacteristic
133C2×Dic3⋊C4C2×C411yescharacteristic
134C2×Dic3⋊C4C2×C411yescharacteristic
135C2×Dic3⋊C4C2×C411yescharacteristic
136C2×C4×Dic3C2×C411yescharacteristic
137C2×C4×Dic3C2×C411yescharacteristic
138C2×C4×Dic3C2×C411yescharacteristic
139C2×C4×Dic3C2×C411yescharacteristic
140C2×C4×Dic3C2×C411yescharacteristic
141C2×C4×Dic3C2×C411yescharacteristic
142C2×C4×Dic3C2×C414yes—
143C2×C4×Dic3C2×C414yes—
144C2×C4×Dic3C2311yescharacteristic
145C2×C4×Dic3C2311yescharacteristic
146C2×C4×Dic3C2311yescharacteristic
147C2×C4×Dic3C2314yes—
148C2×C4×Dic3C2314yes—
149C2×#208—42no—
150C2×#208C2314yes—
151C22×C3⋊C8—42no—
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2314yes—
157C2×D3×C8—42no—
158C2×D3×C8—42no—
159C2×D3×C8C2314yes—
160C2×D3×C8C2314yes—
161#892C2×C418yes—
162#887C2×C418yes—
163#67⋊C4C2×C418yes—
164#67⋊C4C2×C418yes—
165#877C2×C418yes—
166#877C2×C418yes—
167C42×D3C2×C414yes—
168C42×D3C2314yes—
169C4×Dic6C2×C414yes—
170C4×Dic6C2314yes—
171C3×C4⋊C8C2314yes—
172C3×C22⋊C8C2314yes—
173C3×C22⋊C8C2314yes—
174C3×#97C2314yes—
175#830C2314yes—
176#830C2314yes—
177(C2×D3)⋊C8C2314yes—
178(C2×D3)⋊C8C2314yes—
179#815C2314yes—
180#815C2314yes—
181Dic3⋊C8C2314yes—
182Dic3⋊C8C2314yes—
183Dic3⋊C8C2314yes—
184Dic3⋊C8C2314yes—
185Dic3⋊C8C2314yes—
186Dic3⋊C8C2314yes—
187Dic3⋊C8C2314yes—
188Dic3⋊C8C2314yes—
189C8×Dic3C2314yes—
190C8×Dic3C2314yes—
191C4⋊(C3⋊C8)C2314yes—
192#803C2314yes—
193C22×#41—31no—
194C22×M16—31no—
195C22×M16C2×D311yescharacteristic
196C23×C8—31no—
197C23×C8—31no—
198C23×C8—31no—
199C23×C8C2×D311yescharacteristic
200C4×#41—38no—
201C4×#41—38no—
202C2×C4×Q8—31no—
203C2×C4×Q8—31no—
204C2×C4×D4—31no—
205C2×C4×D4—31no—
206C2×C4×D4—31no—
207C2×C4×D4—31no—
208C2×C4×D4—31no—
209C2×C4×D4C2×D311yescharacteristic
210C2×#117—31no—
211C2×#117—31no—
212C2×#117—31no—
213C22×C42—31no—
214C22×C42—31no—
215C22×C42—31no—
216#446—38no—
217#446—38no—
218#435—38no—
219#435—38no—
220#435—38no—
221#435C2×D318yescomplemented
222C8×D4—38no—
223C8×D4—38no—
224#432—38no—
225#432—38no—
226#431—38no—
227#423—38no—
228C2×C4⋊C8—31no—
229C2×C4⋊C8—31no—
230C2×C4⋊C8—31no—
231C2×C4⋊C8—31no—
232C2×C4⋊C8—31no—
233C2×C4⋊C8—38no—
234C2×C4⋊C8—31no—
235C2×C4⋊C8—31no—
236C2×C4⋊C8—31no—
237C2×C4⋊C8—31no—
238C2×C4⋊C8—38no—
239C2×C4⋊C8C2×D311yescharacteristic
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8C2×D311yescharacteristic
245C2×C22⋊C8C2×D311yescharacteristic
246C2×#97—31no—
247C2×#97—31no—
248C2×#97—31no—
249C2×#97C2×D311yescharacteristic
250C2×C4×C8—31no—
251C2×C4×C8—31no—
252C24×C3C22×C411yescharacteristic
253C24×C3C22×C411yescharacteristic
254C23×D3C22×C411yescharacteristic
255C2×C3×D4—24no—
256C2×C3×D4C22×C414yes—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4C22×C411yescharacteristic
262C22×C3×C4C22×C411yescharacteristic
263C22×C3×C4C22×C412yes—
264C22×C3×C4C22×C412yes—
265C22×C3×C4C22×C411yescharacteristic
266C22×C3×C4C22×C411yescharacteristic
267C22×C3×C4C2412yes—
268C22×C3×C4C2412yes—
269C22×C3×C4C2411yescharacteristic
270C2×#67—24no—
271C2×#67M1618yescomplemented
272C2×#67C22×C414yes—
273C2×#67C22×C414yes—
274C22×Dic3—24no—
275C22×Dic3—24no—
276C22×Dic3—24no—
277C22×Dic3—24no—
278C22×Dic3C22×C414yes—
279C22×Dic3C22×C414yes—
280C22×Dic3C22×C414yes—
281C22×Dic3C22×C414yes—
282C22×Dic3C22×C411yescharacteristic
283C22×Dic3C22×C411yescharacteristic
284C22×Dic3C22×C411yescharacteristic
285C22×Dic3C22×C411yescharacteristic
286C22×Dic3C22×C411yescharacteristic
287C22×Dic3C22×C411yescharacteristic
288C22×Dic3C22×C411yescharacteristic
289#237—232no—
290C2×C4×D3—24no—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3—24no—
294C2×C4×D3C22×C412yes—
295C2×C4×D3C22×C414yes—
296C2×C4×D3C22×C414yes—
297C2×C4×D3C2412yes—
298C2×Dic6—24no—
299C2×Dic6C22×C414yes—
300C3×M16—44no—
301C2×C3×C8—22no—
302C2×C3×C8—22no—
303C2×C3×C8—22no—
304C2×C3×C8—22no—
305C2×C3×C8—44no—
306C2×C3×C8C2412yes—
307C2×C3×C8C2412yes—
308C2×C3×C8C2412yes—
309C2×C3×C8C2412yes—
310C3×C4⋊C4C22×C414yes—
311C3×C22⋊C4C22×C414yes—
312C3×C22⋊C4C22×C414yes—
313C3×C42C22×C412yes—
314C3×C42C2412yes—
315#217C22×C414yes—
316#217C22×C414yes—
317(C2×D3)⋊C4C22×C414yes—
318(C2×D3)⋊C4C22×C414yes—
319C4⋊Dic3C22×C414yes—
320Dic3⋊C4C22×C414yes—
321Dic3⋊C4C22×C414yes—
322Dic3⋊C4C22×C414yes—
323Dic3⋊C4C22×C414yes—
324C4×Dic3C22×C412yes—
325C4×Dic3C22×C412yes—
326C4×Dic3C22×C412yes—
327C4×Dic3C22×C414yes—
328C4×Dic3C22×C414yes—
329C4×Dic3C22×C414yes—
330C4×Dic3C22×C414yes—
331C4×Dic3C22×C414yes—
332C4×Dic3C22×C414yes—
333C4×Dic3C2412yes—
334C4×Dic3C2412yes—
335C4×Dic3C2412yes—
336#208—44no—
337C2×C3⋊C8—22no—
338C2×C3⋊C8—22no—
339C2×C3⋊C8—22no—
340C2×C3⋊C8—22no—
341C2×C3⋊C8—44no—
342C2×C3⋊C8C2412yes—
343C2×C3⋊C8C2412yes—
344C2×C3⋊C8C2412yes—
345C2×C3⋊C8C2412yes—
346D3×C8—44no—
347D3×C8—44no—
348C2×#41—38no—
349C2×#41—68no—
350C22×Q8—31no—
351C22×D4—31no—
352C22×D4—31no—
353C22×D4C4×D311yescharacteristic
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D311yescharacteristic
363C2×M16—34no—
364C2×M16—42no—
365C2×M16—122no—
366C2×M16C22×D314yes—
367C22×C8—31no—
368C22×C8—31no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—34no—
372C22×C8—34no—
373C22×C8—34no—
374C22×C8—42no—
375C22×C8—122no—
376C22×C8—122no—
377C22×C8—122no—
378C22×C8C22×D311yescharacteristic
379C22×C8C22×D311yescharacteristic
380C22×C8C22×D311yescharacteristic
381C22×C8C22×D311yescharacteristic
382C22×C8C22×D314yes—
383C4×Q8—38no—
384C4×Q8—34no—
385C4×Q8—34no—
386C4×D4—38no—
387C4×D4—34no—
388C4×D4—34no—
389C4×D4—34no—
390C4×D4—34no—
391C4×D4—38no—
392C4×D4—38no—
393C4×D4C4×D314yes—
394C4×D4C22×D314yes—
395#117—38no—
396#117—38no—
397#117—38no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4C4×D311yescharacteristic
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4C4×D311yescharacteristic
409C2×C22⋊C4C4×D311yescharacteristic
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—34no—
417C2×C42—34no—
418C2×C42—34no—
419C2×C42—34no—
420C2×C42—31no—
421C2×C42—31no—
422C2×C42—31no—
423C2×C42—34no—
424C2×C42—34no—
425C2×C42C22×D311yescharacteristic
426C4⋊C8—34no—
427C4⋊C8—34no—
428C4⋊C8—34no—
429C4⋊C8—34no—
430C4⋊C8—34no—
431C4⋊C8—34no—
432C4⋊C8—34no—
433C4⋊C8—34no—
434C4⋊C8—34no—
435C4⋊C8C22×D314yes—
436C22⋊C8—34no—
437C22⋊C8—34no—
438C22⋊C8—34no—
439C22⋊C8—34no—
440C22⋊C8C22×D314yes—
441C22⋊C8C22×D314yes—
442#97—34no—
443#97—34no—
444#97—34no—
445#97C22×D314yes—
446C4×C8—34no—
447C4×C8—34no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3C2×M1614yes—
454C23×C3C23×C412yes—
455C23×C3C23×C412yes—
456C23×C3C23×C411yescharacteristic
457C22×D3—22no—
458C22×D3—22no—
459C22×D3C2×M1614yes—
460C22×D3C23×C412yes—
461C3×D4—28no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4C23×C412yes—
473C2×C3×C4C23×C412yes—
474C2×C3×C4C23×C412yes—
475C2×C3×C4C23×C412yes—
476C2×C3×C4C23×C411yescharacteristic
477C2×C3×C4H(5,𝔽2)12yes—
478C2×C3×C42−1+412yes—
479C2×C3×C4C2511yescharacteristic
480#67—28no—
481#67C2×M16116yescomplemented
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—28no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—28no—
489C2×Dic3—28no—
490C2×Dic3—28no—
491C2×Dic3C2×M1614yes—
492C2×Dic3#13114yes—
493C2×Dic3C23×C412yes—
494C2×Dic3C23×C412yes—
495C2×Dic3C23×C412yes—
496C2×Dic3C23×C412yes—
497C2×Dic3C23×C412yes—
498C2×Dic3C23×C412yes—
499C2×Dic3C23×C412yes—
500C4×D3—28no—
501C4×D3—24no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—28no—
505Dic6—28no—
506C3×C8—22no—
507C3×C8—22no—
508C3×C8—22no—
509C3×C8—22no—
510C3⋊C8—22no—
511C3⋊C8—22no—
512C3⋊C8—22no—
513C3⋊C8—22no—
514C24—31no—
515C24C2×C4×D311yescharacteristic
516C24C2×C4×D311yescharacteristic
517#41—632no—
518C2×Q8—34no—
519C2×Q8—64no—
520C2×D4—24no—
521C2×D4—38no—
522C2×D4—34no—
523C2×D4—34no—
524C2×D4—64no—
525C2×D4C2×C4×D314yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—34no—
543C22×C4—32no—
544C22×C4—32no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—64no—
550C22×C4—64no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4C2×C4×D311yescharacteristic
554C22×C4C2×C4×D311yescharacteristic
555C22×C4C2×C4×D312yes—
556C22×C4C2×C4×D312yes—
557C22×C4C2×C4×D311yescharacteristic
558C22×C4C2×C4×D311yescharacteristic
559C22×C4C23×D312yes—
560C22×C4C23×D312yes—
561C22×C4C23×D311yescharacteristic
562M16—44no—
563M16—124no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—32no—
569C2×C8—32no—
570C2×C8—32no—
571C2×C8—32no—
572C2×C8—44no—
573C2×C8—62no—
574C2×C8—62no—
575C2×C8—62no—
576C2×C8—62no—
577C2×C8—124no—
578C2×C8—124no—
579C2×C8—124no—
580C2×C8C23×D312yes—
581C2×C8C23×D312yes—
582C2×C8C23×D312yes—
583C2×C8C23×D312yes—
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—34no—
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4C2×C4×D314yes—
590C22⋊C4—34no—
591C22⋊C4—34no—
592C22⋊C4—34no—
593C22⋊C4—34no—
594C22⋊C4C2×C4×D314yes—
595C22⋊C4C2×C4×D314yes—
596C42—32no—
597C42—34no—
598C42—34no—
599C42—34no—
600C42—34no—
601C42—34no—
602C42—34no—
603C42—32no—
604C42—32no—
605C42—32no—
606C42—32no—
607C42—32no—
608C42C2×C4×D312yes—
609C42C23×D312yes—
610C22×C3—22no—
611C22×C3—28no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—44no—
617C22×C3#52012yes—
618C22×C3C22×M1614yes—
619C22×C3C22×M1612yes—
620C22×C3C2×#13112yes—
621C22×C3C24×C411yescharacteristic
622C2×D3—22no—
623C2×D3—28no—
624C2×D3—22no—
625C2×D3C22×M1614yes—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4#52012yes—
631C3×C4C2×H(5,𝔽2)11yescharacteristic
632C3×C4C2×2−1+411yescharacteristic
633Dic3—22no—
634Dic3—22no—
635Dic3—22no—
636Dic3—22no—
637Dic3—22no—
638Dic3C22×M1614yes—
639Dic3C2×#13114yes—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—32no—
646C23—34no—
647C23—62no—
648C23—62no—
649C23D3×M1614yes—
650C23C22×C4×D312yes—
651C23C22×C4×D312yes—
652C23C22×C4×D311yescharacteristic
653Q8—68no—
654D4—28no—
655D4—316no—
656D4—68no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—34no—
670C2×C4—34no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—68no—
677C2×C4—68no—
678C2×C4—68no—
679C2×C4—68no—
680C2×C4—68no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—68no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4C22×C4×D312yes—
691C2×C4C22×C4×D312yes—
692C2×C4C22×C4×D312yes—
693C2×C4C22×C4×D312yes—
694C2×C4C22×C4×D311yescharacteristic
695C2×C4#100412yes—
696C2×C4#101012yes—
697C2×C4C24×D311yescharacteristic
698C8—22no—
699C8—22no—
700C8—22no—
701C8—22no—
702C8—62no—
703C8—62no—
704C8—62no—
705C8—62no—
706C2×C3—24no—
707C2×C3—42no—
708C2×C3#299014yescomplemented
709C2×C3C2×#52011yescharacteristic
710C2×C3C23×M1611yescharacteristic
711C2×C3C22×#13111yescharacteristic
712D3—24no—
713C22—28no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—34no—
720C22—44no—
721C22—68no—
722C22—62no—
723C22—62no—
724C22#554612yes—
725C22C2×D3×M1614yes—
726C22C2×D3×M1612yes—
727C22D3×#13112yes—
728C22C23×C4×D311yescharacteristic
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—34no—
734C4—34no—
735C4—62no—
736C4—62no—
737C4—62no—
738C4—62no—
739C4—62no—
740C4#554612yes—
741C4C2×#100411yescharacteristic
742C4C2×#101011yescharacteristic
743C3C2×#299011yescharacteristic, complemented, Sylow
744C2—24no—
745C2—42no—
746C2—64no—
747C2#7946214yesdirect product factor
748C2C2×#554611yescharacteristic
749C2C22×D3×M1611yescharacteristic
750C2C2×D3×#13111yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutatorC22×C3C24×C4
FrattiniC2×C4C24×D3
FittingC2×C3×#435C2
socleC23×C3C23×C4
prime radicalC22×#237C4
cosocleC2×C3×C4C25
hypercenterC2×#435D3
hypocenterC3C2×#2990
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×C3×#435C2semidirect
3. C2×#5127C2semidirect
4. C2×#5118C2semidirect
5. C2×C8×#67C2semidirect
6. C22×Dic3⋊C8C2semidirect
7. C2×#5011C2semidirect
8. #79462C2direct (N × H)
9. C2×D3×C4⋊C8C2semidirect
10. C2×#4828C2semidirect
11. C2×#4728C2semidirect
12. C2×#67⋊C8C2semidirect
13. C2×#4719C2semidirect
14. C2×#4718C2semidirect
15. C2×#4705C2semidirect
16. C2×#4701C2semidirect
41. C3×#435C22semidirect
48. #5127C22semidirect
49. #5118C22semidirect
50. C8×#67C22semidirect
63. C2×Dic3⋊C8C22semidirect
66. #5011C22semidirect
69. D3×C4⋊C8C22semidirect
70. #4828C22semidirect
71. #4728C22semidirect
72. #67⋊C8C22semidirect
73. #4719C22semidirect
74. #4718C22semidirect
75. #4705C22semidirect
76. #4701C22semidirect
84. C2×#435D3semidirect
221. #435C2×D3semidirect
271. C2×#67M16semidirect
481. #67C2×M16semidirect
708. C2×C3#2990semidirect
743. C3C2×#2990semidirect
747. C2#79462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#2372
C2×C3×#4352
C2×#51272
C2×#51182
C2×C8×#672
C22×Dic3⋊C82
C2×#50112
#794622
C2×D3×C4⋊C82
C2×#48282
C2×#47282
C2×#67⋊C82
C2×#47192
C2×#47182
C2×#47052
C2×#47012
C2×#29903