Finite Group Databasebeta

← C2×#21448891 #29839621

Subgroups — C2×#21448891 #29839621

Order 15616.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D61C211yesmaximal, characteristic
4#21448891C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839662C211yesmaximal, characteristic
7C2×#16839656C211yesmaximal, characteristic, complemented
8C2×#16839655C211yesmaximal, characteristic, complemented
9C2×#16839653C211yesmaximal, characteristic, complemented
10C2×#16839653C211yesmaximal, characteristic, complemented
11C2×#16839636C211yesmaximal, characteristic, complemented
12C2×#16839635C211yesmaximal, characteristic, complemented
13C2×C4×#11758196C211yesmaximal, characteristic, complemented
14C2×#16839613C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519763C4116yescomplemented
21C2×#14519763C2218yes—
22C2×C4×Dic122—28no—
23C2×C4×Dic122C2218yescomplemented
24C2×C4×C22⋊D61—28no—
25C2×C4×C22⋊D61C2218yes—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45#16839666C2218yescomplemented
46#16839662C2218yes—
47#16839656C2218yescomplemented
48#16839655C2218yescomplemented
49#16839653C2218yescomplemented
50#16839653C2218yescomplemented
51#16839636C2218yescomplemented
52#16839635C2218yescomplemented
53C4×#11758196C2218yescomplemented
54#16839613C2218yescomplemented
55#16839609C2218yescomplemented
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C24×C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C4×C22⋊C4×C61C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122C2×C418yescomplemented
74C22×Dic122C2314yes—
75C22×C22⋊D61—24no—
76C22×C22⋊D61—24no—
77C22×C22⋊D61C2×C418yes—
78C22×C22⋊D61C2314yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—42no—
89C22×C4×D61C2314yes—
90#14519763C2×C4164yescomplemented
91C4×Dic122—232no—
92C4×C22⋊D61—232no—
93C2×C4⋊Dic61—24no—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196D418yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61—42no—
107C2×C22⋊Dic61C2×C418yescomplemented
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—42no—
114C2×#11758198C2×C418yescomplemented
115C2×#11758198C2×C418yescomplemented
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×#11758198C2314yes—
121C2×C4×Dic61—24no—
122C2×C4×Dic61—24no—
123C2×C4×Dic61—24no—
124C2×C4×Dic61—42no—
125C2×C4×Dic61C2×C418yescomplemented
126C2×C4×Dic61C2314yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137C25×C61C2311yescharacteristic
138C23×C4×C61—24no—
139C23×C4×C61—24no—
140C23×C4×C61—42no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2314yes—
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—24no—
149C2×C22⋊C4×C61C2×C418yescomplemented
150C2×C22⋊C4×C61C2314yes—
151C2×C22⋊C4×C61C2314yes—
152C2×C42×C61—24no—
153C2×C42×C61—42no—
154C2×C42×C61C2314yes—
155C2×C42×C61C2314yes—
156#95×C61C2314yes—
157#95×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61C22×C414yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61C22×C414yes—
174C23×D61C2412yes—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—28no—
189C22×C4×C61—28no—
190C22×C4×C61—44no—
191C22×C4×C61—416no—
192C22×C4×C61C22×C414yes—
193C22×C4×C61C22×C414yes—
194C22×C4×C61C2×D414yes—
195C22×C4×C61#4114yes—
196C22×C4×C61#4114yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C2×C22⋊D61—232no—
204C2×C22⋊D61—28no—
205C2×C22⋊D61—28no—
206C2×C22⋊D61C22×C4116yes—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61C22×C414yes—
223C22×Dic61C22×C414yes—
224C22×Dic61C22×C414yes—
225C22×Dic61C2×D414yes—
226C22×Dic61C2×D414yes—
227C22×Dic61#4114yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—28no—
236C2×C4×D61—28no—
237C2×C4×D61—44no—
238C2×C4×D61—416no—
239C2×Dic122—232no—
240C2×Dic122—28no—
241C2×Dic122—28no—
242C2×Dic122C22×C4116yescomplemented
243C22⋊C4×C61—28no—
244C22⋊C4×C61C22×C4116yescomplemented
245C42×C61—28no—
246C42×C61—44no—
247C22⋊Dic61—28no—
248C22⋊Dic61—44no—
249C22⋊Dic61C22×C4116yescomplemented
250#11758198—28no—
251#11758198—28no—
252#11758198—44no—
253#11758198C22×C4116yescomplemented
254#11758198C22×C4116yescomplemented
255C4⋊Dic61—28no—
256#11758196—28no—
257#11758196—28no—
258#11758196—28no—
259#11758196—28no—
260#11758196C2×D4116yes—
261C4×Dic61—28no—
262C4×Dic61—28no—
263C4×Dic61—28no—
264C4×Dic61—44no—
265C4×Dic61C22×C4116yescomplemented
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61C23×C414yes—
280C23×C61C23×C412yes—
281C23×C61C22×D412yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C612−1+412yes—
287C23×C61C2511yescharacteristic
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61C23×C414yes—
302C2×C4×C61—28no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—28no—
306C2×C4×C61—28no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—416no—
321C2×C4×C61—44no—
322C2×C4×C61C23×C414yes—
323C2×C4×C61C23×C414yes—
324C2×C4×C61C22×D414yes—
325C2×C4×C61C2×#4114yes—
326C2×C4×C61C2×#4114yes—
327C22⋊D61—232no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—44no—
347C2×Dic61—44no—
348C2×Dic61—44no—
349C2×Dic61C4×D4116yes—
350C2×Dic61C23×C414yes—
351C2×Dic61C23×C414yes—
352C2×Dic61C23×C414yes—
353C2×Dic61C22×D414yes—
354C2×Dic61C22×D414yes—
355C2×Dic61C2×#4114yes—
356C4×D61—416no—
357Dic122—232no—
358C2×#2367—611nomaximal, Sylow
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—416no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61C2×C4×D414yes—
368C22×C61C4×#4114yes—
369C22×C61#52014yes—
370C22×C61#54614yes—
371C22×C61#54814yes—
372C22×C61#55614yes—
373C22×C61#55914yes—
374C22×C61C24×C411yescharacteristic
375C22×C61C23×D411yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×2−1+411yescharacteristic
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—416no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61C2×C4×D418yes—
402C22×#124—611no—
403C22×C4×Q8—611no—
404C22×C4×D4—611no—
405#2367—6116no—
406C2×#391—611no—
407C2×#390—611no—
408C2×#388—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#388—611no—
412C2×#385—611no—
413C2×#385—611no—
414C2×C4×C4⋊C4—611no—
415C2×C4×C4⋊C4—611no—
416C2×C4×C22⋊C4—611no—
417C2×C4×C22⋊C4D6111yescharacteristic, complemented
418C2×C61—44no—
419C2×C61#236718yescomplemented
420C2×C61C22×C4×D411yescharacteristic
421C2×C61C2×C4×#4111yescharacteristic
422C2×C61C2×#52011yescharacteristic
423C2×C61C2×#54611yescharacteristic
424C2×C61C2×#54811yescharacteristic
425C2×C61C2×#55611yescharacteristic
426C2×C61C2×#55911yescharacteristic
427D61—44no—
428C23×Q8—611no—
429C23×D4—611no—
430C24×C4—611no—
431C24×C4C2×D6111yescharacteristic
432C2×#124—6116no—
433C2×#124—618no—
434C2×C4×Q8—618no—
435C2×C4×Q8—1228no—
436C2×C4×D4—618no—
437C2×C4×D4—1228no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4C2×D6111yescharacteristic
453C22×C22⋊C4C2×D6111yescharacteristic
454C22×C42—611no—
455C22×C42—611no—
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—611no—
459C22×C42C2×D6111yescharacteristic
460C22×C42C2×D6111yescharacteristic
461#391—618no—
462#390—618no—
463#388—618no—
464#388—618no—
465#388—618no—
466#388—618no—
467#385—618no—
468#385—618no—
469C4×C4⋊C4—618no—
470C4×C4⋊C4—618no—
471C4×C22⋊C4—618no—
472C4×C22⋊C4C2×D6118yescomplemented
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95C2×D6111yescharacteristic
480C2×#95C2×D6111yescharacteristic
481C61C2×#236711yescharacteristic, complemented, Sylow
482C25—611no—
483C25C22×D6111yescharacteristic
484C22×Q8—618no—
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×D4—618no—
489C22×D4—614no—
490C22×D4—1224no—
491C22×D4—1224no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—614no—
503C23×C4—1224no—
504C23×C4—1224no—
505C23×C4—2442no—
506C23×C4C22×D6111yescharacteristic
507C23×C4C22×D6114yes—
508C23×C4C22×D6111yescharacteristic
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513#124—6164no—
514C4×Q8—12232no—
515C4×D4—12232no—
516C2×C4⋊C4—618no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—1224no—
524C2×C4⋊C4—1224no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—1224no—
527C2×C4⋊C4—1224no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—618no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—618no—
532C2×C22⋊C4—618no—
533C2×C22⋊C4—614no—
534C2×C22⋊C4—614no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—614no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—614no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4—1224no—
542C2×C22⋊C4—1224no—
543C2×C22⋊C4—2442no—
544C2×C22⋊C4—2442no—
545C2×C22⋊C4C4×D6118yescomplemented
546C2×C22⋊C4C22×D6114yes—
547C2×C22⋊C4C22×D6114yes—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42—618no—
551C2×C42—614no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—614no—
556C2×C42—1224no—
557C2×C42—1224no—
558C2×C42—1224no—
559C2×C42—2442no—
560C2×C42C22×D6114yes—
561C2×C42C22×D6114yes—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95C22×D6114yes—
569#95C22×D6114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—614no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24C2×C4×D6114yes—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—6116no—
588C2×Q8—1228no—
589C2×Q8—12232no—
590C2×Q8—1228no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—12232no—
594C2×D4—1228no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—614no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—1228no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1228no—
642C22×C4—2444no—
643C22×C4—24416no—
644C22×C4C2×C4×D6114yes—
645C22×C4C2×C4×D6114yes—
646C22×C4#1175822214yes—
647C22×C4#1175822214yes—
648C22×C4D4×D6114yes—
649C22×C4C23×D6112yes—
650C22×C4C23×D6112yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C4⋊C4—6116no—
656C4⋊C4—1228no—
657C4⋊C4—1228no—
658C4⋊C4—1228no—
659C4⋊C4—1228no—
660C4⋊C4—1228no—
661C22⋊C4—28no—
662C22⋊C4—6116no—
663C22⋊C4—6116no—
664C22⋊C4—6116no—
665C22⋊C4—1228no—
666C22⋊C4—1228no—
667C22⋊C4—1228no—
668C22⋊C4—2444no—
669C22⋊C4—2444no—
670C22⋊C4C2×C4×D61116yescomplemented
671C42—28no—
672C42—44no—
673C42—6116no—
674C42—1228no—
675C42—1228no—
676C42—1228no—
677C42—2444no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—614no—
692C23—1228no—
693C23—1228no—
694C23—1228no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—2444no—
702C23—2444no—
703C23—2444no—
704C23—2444no—
705C23C22×C4×D6114yes—
706C23C22×C4×D6112yes—
707C23C2×D4×D6112yes—
708C23#41×D6112yes—
709C23C2×#1175822212yes—
710C23C2×#1175822212yes—
711C23#1451982212yes—
712C23#1451982412yes—
713C23C24×D6111yescharacteristic
714Q8—12232no—
715D4—12232no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—6116no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—1228no—
744C2×C4—1228no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1228no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—24416no—
762C2×C4—2444no—
763C2×C4—2444no—
764C2×C4—2444no—
765C2×C4C22×C4×D6114yes—
766C2×C4C22×C4×D6114yes—
767C2×C4C2×D4×D6114yes—
768C2×C4C2×#1175822214yes—
769C2×C4C2×#1175822214yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—24416no—
785C22—2442no—
786C22C4×D4×D6114yes—
787C22C4×#1175822214yes—
788C22#1684024114yes—
789C22#1684040214yes—
790C22#1684042114yes—
791C22#1684048014yes—
792C22#1684049514yes—
793C22C23×C4×D6111yescharacteristic
794C22C22×D4×D6111yescharacteristic
795C22C2×#41×D6111yescharacteristic
796C22C22×#1175822211yescharacteristic
797C22C22×#1175822211yescharacteristic
798C22C2×#1451982211yescharacteristic
799C22C2×#1451982411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—24no—
805C4—42no—
806C4—618no—
807C4—1224no—
808C4—1224no—
809C4—1224no—
810C4—2442no—
811C4—2442no—
812C4—2442no—
813C2—44no—
814C2—2444no—
815C2#2144889118yesdirect product factor
816C2C2×C4×D4×D6111yescharacteristic
817C2C2×C4×#1175822211yescharacteristic
818C2C2×#1684024111yescharacteristic
819C2C2×#1684040211yescharacteristic
820C2C2×#1684042111yescharacteristic
821C2C2×#1684048011yescharacteristic
822C2C2×#1684049511yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#2367
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
4. #21448891C2direct (N × H)
5. C2×#16839666C2semidirect
7. C2×#16839656C2semidirect
8. C2×#16839655C2semidirect
9. C2×#16839653C2semidirect
10. C2×#16839653C2semidirect
11. C2×#16839636C2semidirect
12. C2×#16839635C2semidirect
13. C2×C4×#11758196C2semidirect
14. C2×#16839613C2semidirect
15. C2×#16839609C2semidirect
16. C2×C4×C22⋊C4×C61C2semidirect
20. C2×#14519763C4semidirect
23. C2×C4×Dic122C22semidirect
45. #16839666C22semidirect
47. #16839656C22semidirect
48. #16839655C22semidirect
49. #16839653C22semidirect
50. #16839653C22semidirect
51. #16839636C22semidirect
52. #16839635C22semidirect
53. C4×#11758196C22semidirect
54. #16839613C22semidirect
55. #16839609C22semidirect
67. C4×C22⋊C4×C61C22semidirect
73. C22×Dic122C2×C4semidirect
90. #14519763C2×C4semidirect
107. C2×C22⋊Dic61C2×C4semidirect
114. C2×#11758198C2×C4semidirect
115. C2×#11758198C2×C4semidirect
125. C2×C4×Dic61C2×C4semidirect
149. C2×C22⋊C4×C61C2×C4semidirect
242. C2×Dic122C22×C4semidirect
244. C22⋊C4×C61C22×C4semidirect
249. C22⋊Dic61C22×C4semidirect
253. #11758198C22×C4semidirect
254. #11758198C22×C4semidirect
265. C4×Dic61C22×C4semidirect
417. C2×C4×C22⋊C4D61semidirect
419. C2×C61#2367semidirect
472. C4×C22⋊C4C2×D61semidirect
481. C61C2×#2367semidirect
545. C2×C22⋊C4C4×D61semidirect
670. C22⋊C4C2×C4×D61semidirect
815. C2#21448891direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×C4×Dic1222
C22×C4×C22⋊D612
#214488912
C2×#168396662
C2×#168396622
C2×#168396562
C2×#168396552
C2×#168396532
C2×#168396362
C2×#168396352
C2×C4×#117581962
C2×#168396132
C2×#168396092
C2×C4×C22⋊C4×C612
C2×#236761