Finite Group Databasebeta

← C2×#21454779 #30544449

Subgroups — C2×#21454779 #30544449

Order 15616.

2286 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×#11758224C211yesmaximal, characteristic
2#21454779C2116yesmaximal, direct product factor
3C2×#16839891C211yesmaximal, characteristic, complemented
4C2×#16839890C211yesmaximal, characteristic, complemented
5C2×#16839838C211yesmaximal, characteristic, complemented
6C2×#16839837C211yesmaximal, characteristic, complemented
7C2×#16839834C211yesmaximal, characteristic, complemented
8C2×#16839833C211yesmaximal, characteristic, complemented
9C2×#16839830C211yesmaximal, characteristic, complemented
10C2×#16839814C211yesmaximal, characteristic, complemented
11C2×#16839812C211yesmaximal, characteristic, complemented
12C2×#16839812C211yesmaximal, characteristic, complemented
13C2×#16839714C211yesmaximal, characteristic, complemented
14C2×M16×Dic61C211yesmaximal, characteristic, complemented
15C22×C8×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758224C411yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22C4×#11758224C418yes—
23C4×#11758224C2218yes—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742C411yescharacteristic
26C2×D4×Dic61C411yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737C411yescharacteristic
30C2×#14519737C411yescharacteristic
31C2×#14519735C411yescharacteristic
32C2×#14519733C411yescharacteristic
33C2×#14519733C411yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C2×C42×D61C2211yescharacteristic
37#16839891C2218yescomplemented
38#16839890C2218yescomplemented
39#16839838C2218yescomplemented
40#16839837C2218yescomplemented
41#16839834C2218yescomplemented
42#16839833C2218yescomplemented
43#16839830C2218yescomplemented
44#16839814C2218yescomplemented
45#16839812C2218yescomplemented
46#16839812C2218yescomplemented
47C2×C4⋊#92418C2211yescharacteristic
48C2×#14519706C2211yescharacteristic
49C2×#14519706C2211yescharacteristic
50C2×#14519706C2211yescharacteristic
51C2×#14519706C2211yescharacteristic
52C2×C22⋊#92418C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55C2×#14519689C2211yescharacteristic
56#16839714C2218yescomplemented
57M16×Dic61C2218yescomplemented
58C2×#14519688C2211yescharacteristic
59C2×#14519687C2211yescharacteristic
60C2×#14519687C2211yescharacteristic
61C2×C8×Dic61C2211yescharacteristic
62C2×C8×Dic61C2211yescharacteristic
63C2×C8×Dic61C2211yescharacteristic
64C2×C8×Dic61C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2218yescomplemented
68C22×M16×C61C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#435C2218yescomplemented
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×#11758224—28no—
77C2×#11758224C2×C418yes—
78C22×Dic122C2×C411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C23×Dic61C2×C411yescharacteristic
82C23×Dic61C2×C411yescharacteristic
83C23×Dic61C2×C411yescharacteristic
84C23×Dic61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758194—24no—
89C2×#11758194C2314yes—
90C2×#11758189—24no—
91C2×#11758189—24no—
92C2×#11758189C2314yes—
93C2×#11758189C2314yes—
94C22×#92418—24no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2314yes—
99C22×#92418C2311yescharacteristic
100C4×Dic122C2×C414yes—
101C4×Dic122C2314yes—
102#14519742C2×C418yes—
103D4×Dic61C2×C418yes—
104C4×C22⋊D61C2×C414yes—
105C4×C22⋊D61C2×C414yes—
106C4×C22⋊D61C2314yes—
107C4×C22⋊D61C2314yes—
108#14519737C2×C418yes—
109#14519737C2×C418yes—
110#14519735C2×C418yes—
111#14519733C2×C418yes—
112#14519733C2×C418yes—
113C2×C4⋊Dic61C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×C4×Dic61C2×C411yescharacteristic
123C2×C4×Dic61C2×C411yescharacteristic
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2×C414yes—
129C2×C4×Dic61C2×C414yes—
130C2×C4×Dic61C2311yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132C2×C4×Dic61C2314yes—
133C2×C4×Dic61C2311yescharacteristic
134C2×C4×Dic61C2314yes—
135C42×D61C2×C414yes—
136C42×D61C2314yes—
137C4⋊#92418C2314yes—
138#14519706C2314yes—
139#14519706C2314yes—
140#14519706C2314yes—
141#14519706C2314yes—
142C22⋊#92418C2314yes—
143C22⋊#92418C2314yes—
144#14519689C2314yes—
145#14519689C2314yes—
146#14519688C2314yes—
147#14519687C2314yes—
148#14519687C2314yes—
149C8×Dic61C2314yes—
150C8×Dic61C2314yes—
151C8×Dic61C2314yes—
152C8×Dic61C2314yes—
153C8×Dic61C2314yes—
154C8×Dic61C2314yes—
155C22×D4×C61C2×C411yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C2×M16×C61—24no—
159C2×M16×C61C2314yes—
160C22×C8×C61—24no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C4×D4×C61C2×C414yes—
167C4×D4×C61C2314yes—
168C2×C4⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170C2×C22⋊C4×C61C2×C411yescharacteristic
171C2×C42×C61C2311yescharacteristic
172C4⋊C8×C61C2314yes—
173C22⋊C8×C61C2314yes—
174C22⋊C8×C61C2314yes—
175#97×C61C2314yes—
176C24×C61C22×C411yescharacteristic
177C24×C61C22×C411yescharacteristic
178C23×D61C22×C411yescharacteristic
179C2×D4×C61—24no—
180C2×D4×C61C22×C414yes—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C22×C412yes—
190C22×C4×C61C22×C412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61C22×C414yes—
197C2×C22⋊D61C22×C414yes—
198C22×Dic61—24no—
199C22×Dic61—24no—
200C22×Dic61—24no—
201C22×Dic61M1618yescomplemented
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C22×C411yescharacteristic
204C22×Dic61C22×C414yes—
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C22×C414yes—
208C22×Dic61C22×C414yes—
209C22×Dic61C22×C411yescharacteristic
210C22×Dic61C22×C411yescharacteristic
211C22×Dic61C22×C414yes—
212C22×Dic61C22×C411yescharacteristic
213#11758224—232no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61C22×C414yes—
219C2×C4×D61C22×C414yes—
220C2×C4×D61C22×C412yes—
221C2×C4×D61C2412yes—
222C2×Dic122—24no—
223C2×Dic122C22×C414yes—
224M16×C61—28no—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—28no—
229C2×C8×C61#4114yescomplemented
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61C22×C414yes—
235C22⋊C4×C61C22×C414yes—
236C22⋊C4×C61C22×C414yes—
237C42×C61C22×C412yes—
238C42×C61C2412yes—
239C22⋊Dic61C22×C414yes—
240C22⋊Dic61C22×C414yes—
241#11758198C22×C414yes—
242#11758198C22×C414yes—
243C4⋊Dic61C22×C414yes—
244#11758196C22×C414yes—
245#11758196C22×C414yes—
246#11758196C22×C414yes—
247#11758196C22×C414yes—
248C4×Dic61C22×C412yes—
249C4×Dic61C22×C414yes—
250C4×Dic61C22×C414yes—
251C4×Dic61C22×C414yes—
252C4×Dic61C22×C414yes—
253C4×Dic61C22×C414yes—
254C4×Dic61C22×C414yes—
255C4×Dic61C22×C412yes—
256C4×Dic61C22×C412yes—
257C4×Dic61C2412yes—
258C4×Dic61C2412yes—
259C4×Dic61C2412yes—
260#11758194—28no—
261C2×#92418—22no—
262C2×#92418—22no—
263C2×#92418—22no—
264C2×#92418—28no—
265C2×#92418#4114yescomplemented
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270#11758189—28no—
271#11758189—28no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61C2×M1614yes—
278C23×C61C23×C412yes—
279C23×C61C23×C412yes—
280C23×C61C23×C411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61C23×C412yes—
285D4×C61—28no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61C23×C412yes—
297C2×C4×C61C23×C412yes—
298C2×C4×C61C23×C412yes—
299C2×C4×C61C23×C412yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C2×#4112yes—
302C2×C4×C61C2×#4112yes—
303C2×C4×C61C2511yescharacteristic
304C22⋊D61—28no—
305C22⋊D61—28no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—28no—
311C2×Dic61—28no—
312C2×Dic61—28no—
313C2×Dic61C2×M1614yes—
314C2×Dic61C2×M1614yes—
315C2×Dic61C2×M16116yescomplemented
316C2×Dic61#13114yes—
317C2×Dic61C23×C412yes—
318C2×Dic61C23×C412yes—
319C2×Dic61C23×C412yes—
320C2×Dic61C23×C412yes—
321C2×Dic61C23×C412yes—
322C2×Dic61C23×C412yes—
323C2×Dic61C23×C412yes—
324C4×D61—24no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—28no—
328C4×D61—28no—
329Dic122—28no—
330C8×C61—22no—
331C8×C61—22no—
332C8×C61—22no—
333C8×C61C2×#4114yescomplemented
334#92418—22no—
335#92418—22no—
336#92418—22no—
337#92418C2×#4114yescomplemented
338C2×#2965—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—28no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—44no—
346C22×C61C4×#4112yes—
347C22×C61C22×M1614yes—
348C22×C61C22×M1612yes—
349C22×C61C2×#13112yes—
350C22×C61C24×C411yescharacteristic
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—44no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61C4×#4112yes—
360C4×C61C22×#4111yescharacteristic
361C4×C61C22×#4111yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—22no—
366Dic61C22×M1614yes—
367Dic61C22×M1614yes—
368Dic61C2×#13114yes—
369C2×C4×#41—611no—
370#2965—6116no—
371C2×#446—611no—
372C2×#446—611no—
373C2×#436—611no—
374C2×#436—611no—
375C2×#435—611no—
376C2×#435—611no—
377C2×#435—611no—
378C2×#435D6111yescharacteristic, complemented
379C2×#431—611no—
380C2×#431—611no—
381C2×#431—611no—
382C2×C4×M16—611no—
383C2×C4×M16—611no—
384C22×C4×C8—611no—
385C2×C61—24no—
386C2×C61—42no—
387C2×C61#296514yescomplemented
388C2×C61C2×C4×#4111yescharacteristic
389C2×C61C23×M1611yescharacteristic
390C2×C61C22×#13111yescharacteristic
391D61—42no—
392C22×#41—611no—
393C22×M16—611no—
394C22×M16—611no—
395C22×M16—611no—
396C22×M16C2×D6111yescharacteristic
397C23×C8—611no—
398C23×C8C2×D6111yescharacteristic
399C4×#41—618no—
400C4×#41—618no—
401C2×C4×Q8—611no—
402C2×C4×Q8—611no—
403C2×C4×D4—611no—
404C2×C4×D4—611no—
405C2×C4×D4—611no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4C2×D6111yescharacteristic
409C2×#117—611no—
410C2×#117—611no—
411C2×#117—611no—
412C22×C42—611no—
413C22×C42—611no—
414C22×C42—611no—
415#446—618no—
416#446—618no—
417#436—618no—
418#436—618no—
419#435—618no—
420#435—618no—
421#435—618no—
422#435C2×D6118yescomplemented
423#431—618no—
424#431—618no—
425#431—618no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8—611no—
429C2×C4⋊C8—611no—
430C2×C4⋊C8—611no—
431C2×C4⋊C8C2×D6111yescharacteristic
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×C22⋊C8C2×D6111yescharacteristic
438C4×M16—618no—
439C4×M16—618no—
440C2×#97—611no—
441C2×#97—611no—
442C2×#97—611no—
443C2×#97C2×D6111yescharacteristic
444C2×C4×C8—611no—
445C2×C4×C8—611no—
446C2×C4×C8—611no—
447C2×C4×C8—611no—
448C2×C4×C8—611no—
449C2×C4×C8—611no—
450C2×C4×C8—618no—
451C61C2×#296511yescharacteristic, complemented, Sylow
452C2×#41—618no—
453C2×#41—1228no—
454C22×Q8—611no—
455C22×D4—611no—
456C22×D4—611no—
457C22×D4C4×D6111yescharacteristic
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×M16—24no—
468C2×M16—614no—
469C2×M16—614no—
470C2×M16—614no—
471C2×M16—1224no—
472C2×M16—1224no—
473C2×M16—1224no—
474C2×M16C22×D6114yes—
475C22×C8—24no—
476C22×C8—611no—
477C22×C8—614no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—1224no—
482C22×C8C22×D6114yes—
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486C22×C8C22×D6111yescharacteristic
487C4×Q8—618no—
488C4×Q8—614no—
489C4×Q8—614no—
490C4×D4—618no—
491C4×D4—614no—
492C4×D4—614no—
493C4×D4—614no—
494C4×D4—614no—
495C4×D4—618no—
496C4×D4—618no—
497C4×D4C4×D6114yes—
498C4×D4C22×D6114yes—
499#117—618no—
500#117—618no—
501#117—618no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4C4×D6111yescharacteristic
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4C4×D6111yescharacteristic
513C2×C22⋊C4C4×D6111yescharacteristic
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—611no—
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—614no—
521C2×C42—614no—
522C2×C42—614no—
523C2×C42—614no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42—614no—
528C2×C42—614no—
529C2×C42C22×D6111yescharacteristic
530C4⋊C8—614no—
531C4⋊C8—614no—
532C4⋊C8—614no—
533C4⋊C8—614no—
534C4⋊C8—614no—
535C4⋊C8C22×D6114yes—
536C22⋊C8—614no—
537C22⋊C8—614no—
538C22⋊C8—614no—
539C22⋊C8—614no—
540C22⋊C8C22×D6114yes—
541C22⋊C8C22×D6114yes—
542#97—614no—
543#97—614no—
544#97—614no—
545#97C22×D6114yes—
546C4×C8—614no—
547C4×C8—614no—
548C4×C8—614no—
549C4×C8—614no—
550C4×C8—614no—
551C4×C8—614no—
552C24—611no—
553C24C2×C4×D6111yescharacteristic
554C24C2×C4×D6111yescharacteristic
555#41—12232no—
556C2×Q8—614no—
557C2×Q8—1224no—
558C2×D4—24no—
559C2×D4—614no—
560C2×D4—614no—
561C2×D4—1224no—
562C2×D4—1224no—
563C2×D4C2×C4×D6114yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—614no—
572C22×C4—618no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—614no—
578C22×C4—614no—
579C22×C4—614no—
580C22×C4—614no—
581C22×C4—614no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1224no—
588C22×C4—1224no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4C2×C4×D6111yescharacteristic
592C22×C4C2×C4×D6111yescharacteristic
593C22×C4C2×C4×D6112yes—
594C22×C4C2×C4×D6112yes—
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C23×D6112yes—
598C22×C4C23×D6112yes—
599C22×C4C23×D6111yescharacteristic
600M16—28no—
601M16—1228no—
602M16—1228no—
603M16—1228no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8—614no—
609C2×C8—612no—
610C2×C8—612no—
611C2×C8—612no—
612C2×C8—612no—
613C2×C8—1228no—
614C2×C8—1222no—
615C2×C8—1222no—
616C2×C8—1222no—
617C2×C8#1175822414yescomplemented
618C2×C8C23×D6112yes—
619C2×C8C23×D6112yes—
620C2×C8C23×D6112yes—
621C2×C8C23×D6112yes—
622C4⋊C4—614no—
623C4⋊C4—614no—
624C4⋊C4—614no—
625C4⋊C4—614no—
626C4⋊C4—614no—
627C4⋊C4C2×C4×D6114yes—
628C22⋊C4—614no—
629C22⋊C4—614no—
630C22⋊C4—614no—
631C22⋊C4—614no—
632C22⋊C4C2×C4×D6114yes—
633C22⋊C4C2×C4×D6114yes—
634C42—612no—
635C42—614no—
636C42—614no—
637C42—614no—
638C42—614no—
639C42—614no—
640C42—614no—
641C42—612no—
642C42—612no—
643C42—612no—
644C42—612no—
645C42—612no—
646C42C2×C4×D6112yes—
647C42C23×D6112yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—612no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23M16×D6114yes—
658C23C22×C4×D6112yes—
659C23C22×C4×D6112yes—
660C23C22×C4×D6111yescharacteristic
661Q8—1228no—
662D4—28no—
663D4—1228no—
664D4—1228no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—614no—
676C2×C4—614no—
677C2×C4—6116no—
678C2×C4—614no—
679C2×C4—612no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—612no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—1228no—
687C2×C4—1228no—
688C2×C4—1228no—
689C2×C4—1228no—
690C2×C4—1228no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1224no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4C22×C4×D6112yes—
699C2×C4C22×C4×D6112yes—
700C2×C4C22×C4×D6112yes—
701C2×C4C22×C4×D6112yes—
702C2×C4C22×C4×D6111yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4C2×#1175822412yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—614no—
710C8—1222no—
711C8—1222no—
712C8—1222no—
713C8C2×#1175822414yescomplemented
714C22—22no—
715C22—22no—
716C22—28no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—44no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—2444no—
725C22C4×#1175822412yes—
726C22C2×M16×D6114yes—
727C22C2×M16×D6112yes—
728C22#131×D6112yes—
729C22C23×C4×D6111yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—614no—
735C4—614no—
736C4—614no—
737C4—1222no—
738C4—1222no—
739C4—1222no—
740C4—1222no—
741C4C4×#1175822412yes—
742C4C2×#41×D6111yescharacteristic
743C4C22×#1175822411yescharacteristic
744C2—24no—
745C2—42no—
746C2—2442no—
747C2#2145477914yesdirect product factor
748C2C2×C4×#1175822411yescharacteristic
749C2C22×M16×D6111yescharacteristic
750C2C2×#131×D6111yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C23×C4
prime radicalC22×#11758224C4
cosocleC2×C4×C61C25
hypercenterC2×#435D61
hypocenterC61C2×#2965
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #21454779C2direct (N × H)
3. C2×#16839891C2semidirect
4. C2×#16839890C2semidirect
5. C2×#16839838C2semidirect
6. C2×#16839837C2semidirect
7. C2×#16839834C2semidirect
8. C2×#16839833C2semidirect
9. C2×#16839830C2semidirect
10. C2×#16839814C2semidirect
11. C2×#16839812C2semidirect
12. C2×#16839812C2semidirect
13. C2×#16839714C2semidirect
14. C2×M16×Dic61C2semidirect
15. C22×C8×Dic61C2semidirect
16. C2×C61×#435C2semidirect
37. #16839891C22semidirect
38. #16839890C22semidirect
39. #16839838C22semidirect
40. #16839837C22semidirect
41. #16839834C22semidirect
42. #16839833C22semidirect
43. #16839830C22semidirect
44. #16839814C22semidirect
45. #16839812C22semidirect
46. #16839812C22semidirect
56. #16839714C22semidirect
57. M16×Dic61C22semidirect
67. C2×C8×Dic61C22semidirect
71. C61×#435C22semidirect
201. C22×Dic61M16semidirect
229. C2×C8×C61#41semidirect
265. C2×#92418#41semidirect
315. C2×Dic61C2×M16semidirect
333. C8×C61C2×#41semidirect
337. #92418C2×#41semidirect
378. C2×#435D61semidirect
387. C2×C61#2965semidirect
422. #435C2×D61semidirect
451. C61C2×#2965semidirect
617. C2×C8#11758224semidirect
713. C8C2×#11758224semidirect
747. C2#21454779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
#214547792
C2×#168398912
C2×#168398902
C2×#168398382
C2×#168398372
C2×#168398342
C2×#168398332
C2×#168398302
C2×#168398142
C2×#168398122
C2×#168397142
C2×M16×Dic612
C22×C8×Dic612
C2×C61×#4352
C2×#296561