Finite Group Databasebeta

← C2×#21454755 #30544381

Subgroups — C2×#21454755 #30544381

Order 15616.

1894 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21454755C2116yesmaximal, direct product factor
3C2×#16839893C211yesmaximal, characteristic, complemented
4C2×#16839892C211yesmaximal, characteristic, complemented
5C2×#16839891C211yesmaximal, characteristic, complemented
6C2×#16839891C211yesmaximal, characteristic, complemented
7C2×#16839890C211yesmaximal, characteristic, complemented
8C2×#16839890C211yesmaximal, characteristic, complemented
9C2×#16839889C211yesmaximal, characteristic, complemented
10C2×#16839787C211yesmaximal, characteristic
11C2×#16839787C211yesmaximal, characteristic
12C2×#16839784C211yesmaximal, characteristic
13C2×#16839719C211yesmaximal, characteristic
14C2×#16839716C211yesmaximal, characteristic
15C2×#97×D61C211yesmaximal, characteristic
16C2×C61×#446C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840316C418yes—
22#16840316C2218yes—
23C2×#14519776C411yescharacteristic
24C2×#14519775C411yescharacteristic
25C2×#14519767C411yescharacteristic
26C2×#14519767C411yescharacteristic
27C2×#14519757C411yescharacteristic
28C2×#14519755C411yescharacteristic
29C2×#14519755C411yescharacteristic
30C2×#14519753C411yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×C4×Dic122C2211yescharacteristic
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×#14519734C2211yescharacteristic
36C2×C42×D61C2211yescharacteristic
37#16839893C2218yescomplemented
38#16839892C2218yescomplemented
39#16839891C2218yescomplemented
40#16839891C2218yescomplemented
41#16839890C2218yescomplemented
42#16839890C2218yescomplemented
43#16839889C2218yescomplemented
44#16839787C2218yes—
45#16839787C2218yes—
46#16839784C2218yes—
47C2×C4⋊#92418C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49C2×C4⋊#92418C2211yescharacteristic
50C2×#14519706C2211yescharacteristic
51C2×#14519706C2211yescharacteristic
52C2×#14519706C2211yescharacteristic
53C2×#14519706C2211yescharacteristic
54C2×#14519706C2211yescharacteristic
55C2×#14519706C2211yescharacteristic
56#16839719C2218yes—
57#16839716C2218yes—
58C2×#14519688C2211yescharacteristic
59C2×#14519688C2211yescharacteristic
60C2×#14519687C2211yescharacteristic
61C2×#14519687C2211yescharacteristic
62C2×#14519687C2211yescharacteristic
63C2×#14519687C2211yescharacteristic
64#97×D61C2218yes—
65C2×C4×#92418C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C4×Q8×C61C2211yescharacteristic
69C61×#446C2218yescomplemented
70C2×C4⋊C8×C61C2211yescharacteristic
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×#97×C61C2211yescharacteristic
74C2×#97×C61C2211yescharacteristic
75C2×C4×C8×C61C2211yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×Dic122C2×C411yescharacteristic
78C22×Dic122C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C2×#11758189—24no—
83C2×#11758189—24no—
84C2×#11758189C2314yes—
85C2×#11758189C2314yes—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—24no—
91C2×C8×D61Q818yescomplemented
92C2×C8×D61C2314yes—
93C2×C8×D61C2314yes—
94#14519776C2×C418yes—
95#14519775C2×C418yes—
96#14519767C2×C418yes—
97#14519767C2×C418yes—
98#14519757C2×C418yes—
99#14519755C2×C418yes—
100#14519755C2×C418yes—
101#14519753C2×C418yes—
102C4×Dic122C2×C414yes—
103C4×Dic122C2×C414yes—
104C4×Dic122C2×C414yes—
105C4×Dic122C2314yes—
106C4×Dic122C2314yes—
107C4×Dic122C2314yes—
108#14519734C2×C414yes—
109#14519734C2×C414yes—
110#14519734C2314yes—
111#14519734C2314yes—
112C2×C4⋊Dic61C2×C411yescharacteristic
113C2×C4⋊Dic61C2×C411yescharacteristic
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×C4×Dic61C2×C411yescharacteristic
130C2×C4×Dic61C2×C411yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132C2×C4×Dic61C2311yescharacteristic
133C2×C4×Dic61C2311yescharacteristic
134C42×D61C2×C414yes—
135C42×D61C2314yes—
136C4⋊#92418C2314yes—
137C4⋊#92418C2314yes—
138C4⋊#92418C2314yes—
139#14519706C2314yes—
140#14519706C2314yes—
141#14519706C2314yes—
142#14519706C2314yes—
143#14519706C2314yes—
144#14519706C2314yes—
145#14519688C2314yes—
146#14519688C2314yes—
147#14519687C2314yes—
148#14519687C2314yes—
149#14519687C2314yes—
150#14519687C2314yes—
151C4×#92418C2314yes—
152C8×Dic61C2314yes—
153C8×Dic61C2314yes—
154C22×Q8×C61C2×C411yescharacteristic
155C22×C8×C61C2311yescharacteristic
156C22×C8×C61C2311yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C4×Q8×C61C2×C414yes—
160C4×Q8×C61C2314yes—
161C2×C4⋊C4×C61C2×C411yescharacteristic
162C2×C4⋊C4×C61C2×C411yescharacteristic
163C2×C4⋊C4×C61C2×C411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C2×C42×C61C2311yescharacteristic
167C4⋊C8×C61C2314yes—
168C4⋊C8×C61C2314yes—
169C4⋊C8×C61C2314yes—
170#97×C61C2314yes—
171#97×C61C2314yes—
172C4×C8×C61C2314yes—
173C23×D61C22×C411yescharacteristic
174C2×Q8×C61—42no—
175C2×Q8×C61C22×C414yes—
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61C22×C414yes—
193C2×C4×D61C22×C414yes—
194C2×C4×D61C22×C412yes—
195C2×C4×D61C2×Q814yes—
196C2×C4×D61#4114yes—
197C2×C4×D61C2412yes—
198C2×Dic122—42no—
199C2×Dic122—42no—
200C2×Dic122—42no—
201C2×Dic122C22×C414yes—
202C2×Dic122C22×C414yes—
203C2×Dic122C22×C414yes—
204C2×C8×C61—22no—
205C2×C8×C61—22no—
206C2×C8×C61—22no—
207C2×C8×C61C2×Q814yes—
208C2×C8×C61C2412yes—
209C2×C8×C61C2412yes—
210C2×C8×C61C2412yes—
211C2×C8×C61C2412yes—
212C4⋊C4×C61C22×C414yes—
213C4⋊C4×C61C22×C414yes—
214C4⋊C4×C61C22×C414yes—
215C42×C61C22×C412yes—
216C42×C61C22×C412yes—
217C42×C61C22×C412yes—
218C42×C61C2412yes—
219C42×C61C2412yes—
220C42×C61C2412yes—
221#11758198C22×C414yes—
222#11758198C22×C414yes—
223#11758198C22×C414yes—
224#11758198C22×C414yes—
225C4⋊Dic61C22×C414yes—
226C4⋊Dic61C22×C414yes—
227C4⋊Dic61C22×C414yes—
228#11758196C22×C414yes—
229#11758196C22×C414yes—
230#11758196C22×C414yes—
231#11758196C22×C414yes—
232#11758196C22×C414yes—
233#11758196C22×C414yes—
234#11758196C22×C414yes—
235#11758196C22×C414yes—
236#11758196C22×C414yes—
237#11758196C22×C414yes—
238C4×Dic61C22×C412yes—
239C4×Dic61C22×C414yes—
240C4×Dic61C22×C414yes—
241C4×Dic61C22×C412yes—
242C4×Dic61C22×C412yes—
243C4×Dic61C2412yes—
244C4×Dic61C2412yes—
245C4×Dic61C2412yes—
246C2×#92418—22no—
247C2×#92418—22no—
248C2×#92418—22no—
249C2×#92418C2×Q814yes—
250C2×#92418C2412yes—
251C2×#92418C2412yes—
252C2×#92418C2412yes—
253C2×#92418C2412yes—
254#11758189—28no—
255#11758189—28no—
256C8×D61—28no—
257C8×D61C2×Q8116yescomplemented
258C23×C61C23×C411yescharacteristic
259C22×D61—22no—
260C22×D61—22no—
261C22×D61C4×Q814yes—
262C22×D61C23×C412yes—
263Q8×C61—44no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61C23×C412yes—
271C2×C4×C61C23×C412yes—
272C2×C4×C61C23×C412yes—
273C2×C4×C61C23×C412yes—
274C2×C4×C61C23×C412yes—
275C2×C4×C61C23×C412yes—
276C2×C4×C61C23×C411yescharacteristic
277C2×C4×C61C22×Q812yes—
278C2×C4×C61C2×#4112yes—
279C2×C4×C61C2511yescharacteristic
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61C4×Q814yes—
287C2×Dic61C23×C412yes—
288C2×Dic61C23×C412yes—
289C2×Dic61C23×C412yes—
290C2×Dic61C23×C412yes—
291C2×Dic61C23×C412yes—
292C2×Dic61C23×C412yes—
293C2×Dic61C23×C412yes—
294C4×D61—44no—
295C4×D61—44no—
296C4×D61C4×Q818yes—
297C4×D61C22×Q814yes—
298C4×D61C2×#4114yes—
299Dic122—44no—
300Dic122—44no—
301Dic122—44no—
302C8×C61—22no—
303C8×C61—22no—
304C8×C61—22no—
305C8×C61C22×Q814yes—
306#92418—22no—
307#92418—22no—
308#92418—22no—
309#92418C22×Q814yes—
310C2×#2961—611nomaximal, Sylow
311C22×C61C2×C4×Q812yes—
312C22×C61#56812yes—
313C22×C61#56812yes—
314C22×C61C24×C411yescharacteristic
315C2×D61—28no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61C2×C4×Q814yes—
319C4×C61—22no—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—22no—
325C4×C61C2×C4×Q812yes—
326C4×C61C23×Q811yescharacteristic
327C4×C61C22×#4111yescharacteristic
328Dic61—22no—
329Dic61—22no—
330Dic61—22no—
331Dic61—22no—
332Dic61—22no—
333Dic61—22no—
334Dic61C2×C4×Q814yes—
335C2×#533—611no—
336#2961—6116no—
337C2×#446—611no—
338C2×#446—611no—
339C2×#446—611no—
340C2×#446—611no—
341C2×#446—611no—
342C2×#446—611no—
343C2×#446—611no—
344C2×#446D6111yescharacteristic, complemented
345C2×#424—611no—
346C2×#424—611no—
347C2×#423—611no—
348C2×#405—611no—
349C2×#405—611no—
350C22×#97—611no—
351C2×C61#296114yescomplemented
352C2×C61C22×C4×Q811yescharacteristic
353C2×C61C2×#56811yescharacteristic
354C2×C61C2×#56811yescharacteristic
355D61—24no—
356C22×M16—611no—
357C22×M16—611no—
358C23×C8—611no—
359C23×C8—611no—
360#533—618no—
361#533—618no—
362C2×C4⋊Q8—611no—
363C2×C4⋊Q8—611no—
364C2×#125—611no—
365C2×#125—611no—
366C2×C22⋊Q8—611no—
367C2×C22⋊Q8—611no—
368C2×C22⋊Q8—611no—
369C2×C22⋊Q8—611no—
370C2×C4×Q8—611no—
371C2×C4×Q8—611no—
372C2×C4×Q8—611no—
373C2×C4×Q8C2×D6111yescharacteristic
374C2×#117—611no—
375C2×#117—611no—
376C22×C42—611no—
377#446—618no—
378#446—618no—
379#446—618no—
380#446—618no—
381#446—618no—
382#446—618no—
383#446—618no—
384#446C2×D6118yescomplemented
385#424—618no—
386#424—618no—
387#423—618no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8—611no—
390C2×C4⋊C8—611no—
391C2×C4⋊C8—611no—
392C2×C4⋊C8—611no—
393C2×C4⋊C8—611no—
394C2×C4⋊C8—611no—
395C2×C4⋊C8—611no—
396C2×C4⋊C8—611no—
397C2×C4⋊C8C2×D6111yescharacteristic
398C2×C4⋊C8C2×D6111yescharacteristic
399C2×C4⋊C8C2×D6111yescharacteristic
400#405—618no—
401#405—618no—
402C2×#97—611no—
403C2×#97—611no—
404C2×#97—611no—
405C2×#97—611no—
406C2×#97—611no—
407C2×#97—611no—
408C2×#97—618no—
409C2×#97C2×D6111yescharacteristic
410C2×#97C2×D6111yescharacteristic
411C2×C4×C8—611no—
412C2×C4×C8—611no—
413C2×C4×C8—611no—
414C2×C4×C8C2×D6111yescharacteristic
415C61C2×#296111yescharacteristic, complemented, Sylow
416C22×Q8—611no—
417C22×Q8—611no—
418C22×Q8—611no—
419C22×Q8C4×D6111yescharacteristic
420C23×C4—611no—
421C23×C4—611no—
422C23×C4—611no—
423C2×M16—614no—
424C2×M16—614no—
425C2×M16—1224no—
426C2×M16—1224no—
427C22×C8—611no—
428C22×C8—618no—
429C22×C8—614no—
430C22×C8—611no—
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—614no—
434C22×C8—1224no—
435C22×C8C22×D6111yescharacteristic
436C22×C8C22×D6111yescharacteristic
437C22×C8C22×D6111yescharacteristic
438C22×C8C22×D6111yescharacteristic
439C4⋊Q8—618no—
440C4⋊Q8—618no—
441#125—618no—
442#125—618no—
443C22⋊Q8—618no—
444C22⋊Q8—618no—
445C22⋊Q8—618no—
446C22⋊Q8—618no—
447C4×Q8—614no—
448C4×Q8—614no—
449C4×Q8—614no—
450C4×Q8—614no—
451C4×Q8—614no—
452C4×Q8—614no—
453C4×Q8C4×D6114yes—
454C4×Q8C22×D6114yes—
455#117—614no—
456#117—614no—
457#117—614no—
458#117—614no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4C4×D6111yescharacteristic
473C2×C4⋊C4C4×D6111yescharacteristic
474C2×C4⋊C4C4×D6111yescharacteristic
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—614no—
485C2×C42—614no—
486C2×C42C22×D6111yescharacteristic
487C2×C42C22×D6111yescharacteristic
488C2×C42C22×D6111yescharacteristic
489C4⋊C8—614no—
490C4⋊C8—614no—
491C4⋊C8—614no—
492C4⋊C8—614no—
493C4⋊C8—614no—
494C4⋊C8—614no—
495C4⋊C8—614no—
496C4⋊C8—614no—
497C4⋊C8—614no—
498C4⋊C8C22×D6114yes—
499C4⋊C8C22×D6114yes—
500C4⋊C8C22×D6114yes—
501#97—614no—
502#97—614no—
503#97—614no—
504#97—614no—
505#97—614no—
506#97—614no—
507#97C22×D6114yes—
508#97C22×D6114yes—
509C4×C8—614no—
510C4×C8—614no—
511C4×C8—614no—
512C4×C8C22×D6114yes—
513C24—611no—
514C2×Q8—42no—
515C2×Q8—614no—
516C2×Q8—614no—
517C2×Q8—614no—
518C2×Q8—2442no—
519C2×Q8—2442no—
520C2×Q8—2442no—
521C2×Q8C2×C4×D6114yes—
522C22×C4—611no—
523C22×C4—612no—
524C22×C4—614no—
525C22×C4—614no—
526C22×C4—612no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—614no—
534C22×C4—614no—
535C22×C4—2442no—
536C22×C4—2442no—
537C22×C4C2×C4×D6111yescharacteristic
538C22×C4C2×C4×D6111yescharacteristic
539C22×C4C2×C4×D6111yescharacteristic
540C22×C4C2×C4×D6111yescharacteristic
541C22×C4C2×C4×D6111yescharacteristic
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4C23×D6111yescharacteristic
544M16—1228no—
545M16—1228no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—614no—
550C2×C8—612no—
551C2×C8—6116no—
552C2×C8—612no—
553C2×C8—612no—
554C2×C8—612no—
555C2×C8—1228no—
556C2×C8—1222no—
557C2×C8—1222no—
558C2×C8—1222no—
559C2×C8Q8×D6114yes—
560C2×C8C23×D6112yes—
561C2×C8C23×D6112yes—
562C2×C8C23×D6112yes—
563C2×C8C23×D6112yes—
564C4⋊C4—614no—
565C4⋊C4—614no—
566C4⋊C4—614no—
567C4⋊C4—614no—
568C4⋊C4—614no—
569C4⋊C4—614no—
570C4⋊C4—614no—
571C4⋊C4—614no—
572C4⋊C4—614no—
573C4⋊C4—614no—
574C4⋊C4—614no—
575C4⋊C4—614no—
576C4⋊C4—614no—
577C4⋊C4C2×C4×D6114yes—
578C4⋊C4C2×C4×D6114yes—
579C4⋊C4C2×C4×D6114yes—
580C22⋊C4—614no—
581C22⋊C4—614no—
582C22⋊C4—614no—
583C22⋊C4—614no—
584C42—612no—
585C42—614no—
586C42—614no—
587C42—612no—
588C42—612no—
589C42—612no—
590C42—612no—
591C42—612no—
592C42C2×C4×D6112yes—
593C42C2×C4×D6112yes—
594C42C2×C4×D6112yes—
595C42C23×D6112yes—
596C42C23×D6112yes—
597C42C23×D6112yes—
598C23—614no—
599C23—612no—
600C23—1222no—
601C23—1222no—
602C23C22×C4×D6111yescharacteristic
603Q8—44no—
604Q8—2444no—
605Q8—2444no—
606Q8—2444no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—614no—
614C2×C4—612no—
615C2×C4—618no—
616C2×C4—614no—
617C2×C4—614no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—612no—
621C2×C4—612no—
622C2×C4—612no—
623C2×C4—612no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—2444no—
631C2×C4—2444no—
632C2×C4C22×C4×D6112yes—
633C2×C4C22×C4×D6112yes—
634C2×C4C22×C4×D6112yes—
635C2×C4C22×C4×D6112yes—
636C2×C4C22×C4×D6112yes—
637C2×C4C22×C4×D6112yes—
638C2×C4C22×C4×D6111yescharacteristic
639C2×C4C2×Q8×D6112yes—
640C2×C4#41×D6112yes—
641C2×C4C24×D6111yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—614no—
646C8—1222no—
647C8—1222no—
648C8—1222no—
649C8C2×Q8×D6114yes—
650C22—614no—
651C22—1222no—
652C22—1222no—
653C22—1228no—
654C22C4×Q8×D6112yes—
655C22#1684052712yes—
656C22#1684052812yes—
657C22C23×C4×D6111yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—614no—
665C4—1222no—
666C4—1222no—
667C4—1222no—
668C4—1222no—
669C4—1222no—
670C4—1222no—
671C4C4×Q8×D6112yes—
672C4C22×Q8×D6111yescharacteristic
673C4C2×#41×D6111yescharacteristic
674C2—1224no—
675C2#2145475514yesdirect product factor
676C2C2×C4×Q8×D6111yescharacteristic
677C2C2×#1684052711yescharacteristic
678C2C2×#1684052811yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#446C2
socleC23×C61C23×C4
prime radicalC23×D61C22×C4
cosocleC2×C4×C61C25
hypercenterC2×#446D61
hypocenterC61C2×#2961
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #21454755C2direct (N × H)
3. C2×#16839893C2semidirect
4. C2×#16839892C2semidirect
5. C2×#16839891C2semidirect
6. C2×#16839891C2semidirect
7. C2×#16839890C2semidirect
8. C2×#16839890C2semidirect
9. C2×#16839889C2semidirect
16. C2×C61×#446C2semidirect
37. #16839893C22semidirect
38. #16839892C22semidirect
39. #16839891C22semidirect
40. #16839891C22semidirect
41. #16839890C22semidirect
42. #16839890C22semidirect
43. #16839889C22semidirect
69. C61×#446C22semidirect
91. C2×C8×D61Q8semidirect
257. C8×D61C2×Q8semidirect
344. C2×#446D61semidirect
351. C2×C61#2961semidirect
384. #446C2×D61semidirect
415. C61C2×#2961semidirect
675. C2#21454755direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403162
#214547552
C2×#168398932
C2×#168398922
C2×#168398912
C2×#168398902
C2×#168398892
C2×#168397872
C2×#168397842
C2×#168397192
C2×#168397162
C2×#97×D612
C2×C61×#4462
C2×#296161