Finite Group Databasebeta

← C2×#21462318 #30624634

Subgroups — C2×#21462318 #30624634

Order 15616.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462318C2116yesmaximal, direct product factor
2C2×#16840714C211yesmaximal, characteristic
3C2×#16840713C211yesmaximal, characteristic, complemented
4C2×#16840712C211yesmaximal, characteristic, complemented
5C2×#16840712C211yesmaximal, characteristic, complemented
6C2×#16840712C211yesmaximal, characteristic, complemented
7C2×#16840712C211yesmaximal, characteristic, complemented
8C2×#16840711C211yesmaximal, characteristic, complemented
9C2×#16840711C211yesmaximal, characteristic, complemented
10C2×#16840710C211yesmaximal, characteristic
11C2×#16840709C211yesmaximal, characteristic, complemented
12C2×#16840704C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×#6923C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#6923C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
16C2×#123×D61C211yesmaximal, characteristic
17C24×#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22C22×C4⋊#6923C2211yescharacteristic
23C22×C22⋊#6923C2211yescharacteristic
24C22×C22⋊#6923C2211yescharacteristic
25C22×C22⋊#6923C2211yescharacteristic
26C22×C22⋊#6923C2211yescharacteristic
27C22×C22⋊#6923C2211yescharacteristic
28C22×C22⋊#6923C2211yescharacteristic
29C22×C22⋊#6923C2211yescharacteristic
30C22×C4×#6923C2211yescharacteristic
31C22×C4×#6923C2211yescharacteristic
32C22×C4×#6923C2211yescharacteristic
33C22×C4×#6923C2211yescharacteristic
34C22×C4×#6923C2211yescharacteristic
35#16840714C2218yes—
36#16840713C2218yescomplemented
37#16840712C2218yescomplemented
38#16840712C2218yescomplemented
39#16840712C2218yescomplemented
40#16840712C2218yescomplemented
41#16840711C2218yescomplemented
42#16840711C2218yescomplemented
43#16840710C2218yes—
44#16840709C2218yescomplemented
45#16840704C2218yescomplemented
46C4⋊C4×#6923C2218yescomplemented
47C22⋊C4×#6923C2218yescomplemented
48C4×C22⋊#6923C2218yescomplemented
49C2×(C2×#6923)⋊C4C2211yescharacteristic
50C2×(C2×#6923)⋊C4C2211yescharacteristic
51C2×(C2×#6923)⋊C4C2211yescharacteristic
52C2×(C2×#6923)⋊C4C2211yescharacteristic
53C2×(C2×#6923)⋊C4C2211yescharacteristic
54C2×(C2×#6923)⋊C4C2211yescharacteristic
55C2×(C2×#6923)⋊C4C2211yescharacteristic
56C2×(C2×#6923)⋊C4C2211yescharacteristic
57C2×(C2×#6923)⋊C4C2211yescharacteristic
58C2×(C2×#6923)⋊C4C2211yescharacteristic
59C22×D4×D61C2211yescharacteristic
60C23×C4×D61C2211yescharacteristic
61C2×#14519762C411yescharacteristic, complemented
62C2×#14519762C411yescharacteristic, complemented
63C2×#14519761C411yescharacteristic, complemented
64C2×#14519760C411yescharacteristic, complemented
65C2×#14519759C411yescharacteristic, complemented
66C2×#14519759C411yescharacteristic, complemented
67C2×#14519758C411yescharacteristic, complemented
68#123×D61C418yescomplemented
69#123×D61C2218yes—
70C2×C4⋊C4×D61C2211yescharacteristic
71C2×C4⋊C4×D61C2211yescharacteristic
72C2×C22⋊C4×D61C2211yescharacteristic
73C2×C22⋊C4×D61C2211yescharacteristic
74C2×C22⋊C4×D61C2211yescharacteristic
75C2×#123×C61C411yescharacteristic, complemented
76C23×#6923—24no—
77C23×#6923—42no—
78C23×#6923—42no—
79C23×#6923C2311yescharacteristic
80C23×#6923C2311yescharacteristic
81C23×#6923C2311yescharacteristic
82C23×#6923C2311yescharacteristic
83C23×#6923C2311yescharacteristic
84C23×#6923C2311yescharacteristic
85C23×#6923C2311yescharacteristic
86C23×#6923C2311yescharacteristic
87C23×#6923C2314yes—
88C2×C4⋊#6923—24no—
89C2×C4⋊#6923—42no—
90C2×C4⋊#6923—42no—
91C2×C4⋊#6923—42no—
92C2×C4⋊#6923—42no—
93C2×C4⋊#6923C2314yes—
94C2×C4⋊#6923C2314yes—
95C2×C4⋊#6923C2314yes—
96C2×C4⋊#6923C2314yes—
97C2×C4⋊#6923C2314yes—
98C2×C22⋊#6923—24no—
99C2×C22⋊#6923—24no—
100C2×C22⋊#6923—24no—
101C2×C22⋊#6923—42no—
102C2×C22⋊#6923—42no—
103C2×C22⋊#6923—42no—
104C2×C22⋊#6923—42no—
105C2×C22⋊#6923C2314yes—
106C2×C22⋊#6923C2314yes—
107C2×C22⋊#6923C2314yes—
108C2×C22⋊#6923C2314yes—
109C2×C22⋊#6923C2314yes—
110C2×C22⋊#6923C2314yes—
111C2×C22⋊#6923C2314yes—
112C2×C4×#6923—24no—
113C2×C4×#6923—42no—
114C2×C4×#6923—42no—
115C2×C4×#6923—42no—
116C2×C4×#6923—42no—
117C2×C4×#6923C2314yes—
118C2×C4×#6923C2314yes—
119C2×C4×#6923C2314yes—
120C2×C4×#6923C2314yes—
121C2×C4×#6923C2314yes—
122(C2×#6923)⋊C4C2314yes—
123(C2×#6923)⋊C4C2314yes—
124(C2×#6923)⋊C4C2314yes—
125(C2×#6923)⋊C4C2314yes—
126(C2×#6923)⋊C4C2314yes—
127(C2×#6923)⋊C4C2314yes—
128(C2×#6923)⋊C4C2314yes—
129(C2×#6923)⋊C4C2314yes—
130(C2×#6923)⋊C4C2314yes—
131(C2×#6923)⋊C4C2314yes—
132C24×D61C2311yescharacteristic
133C24×D61C2311yescharacteristic
134C22×D244C2×C411yescharacteristic
135C22×C22⋊D61C2×C411yescharacteristic
136C22×C22⋊D61C2×C411yescharacteristic
137C2×D4×D61—42no—
138C2×D4×D61—42no—
139C2×D4×D61C2×C414yes—
140C2×D4×D61C2314yes—
141C23×Dic61C2×C411yescharacteristic, complemented
142C22×C4×D61—42no—
143C22×C4×D61—42no—
144C22×C4×D61C2×C414yescomplemented
145C22×C4×D61C2×C411yescharacteristic, complemented
146C22×C4×D61C2×C411yescharacteristic, complemented
147C22×C4×D61C2311yescharacteristic
148C22×C4×D61C2311yescharacteristic
149C22×C4×D61C2311yescharacteristic
150C22×C4×D61C2311yescharacteristic
151C22×C4×D61C2311yescharacteristic
152C22×C4×D61C2314yes—
153#14519762C2×C418yescomplemented
154#14519762C2×C418yescomplemented
155#14519761C2×C418yescomplemented
156#14519760C2×C418yescomplemented
157#14519759C2×C418yescomplemented
158#14519759C2×C418yescomplemented
159#14519758C2×C418yescomplemented
160C2×C4⋊Dic61C2×C411yescharacteristic, complemented
161C2×C4⋊Dic61C2×C411yescharacteristic, complemented
162C2×#11758196C2×C411yescharacteristic, complemented
163C2×#11758196C2×C411yescharacteristic, complemented
164C2×#11758196C2×C411yescharacteristic, complemented
165C2×#11758196C2×C411yescharacteristic, complemented
166C4⋊C4×D61C2×C414yescomplemented
167C4⋊C4×D61C2×C414yescomplemented
168C4⋊C4×D61C2314yes—
169C4⋊C4×D61C2314yes—
170C2×C22⋊Dic61C2×C411yescharacteristic
171C2×C22⋊Dic61C2×C411yescharacteristic
172C2×C22⋊Dic61C2×C411yescharacteristic, complemented
173C2×#11758198C2×C411yescharacteristic
174C2×#11758198C2×C411yescharacteristic
175C2×#11758198C2×C411yescharacteristic
176C2×#11758198C2×C411yescharacteristic
177C2×#11758198C2×C411yescharacteristic, complemented
178C2×#11758198C2×C411yescharacteristic, complemented
179C22⋊C4×D61C2×C414yes—
180C22⋊C4×D61C2×C414yes—
181C22⋊C4×D61C2×C414yescomplemented
182C22⋊C4×D61C2314yes—
183C22⋊C4×D61C2314yes—
184C22⋊C4×D61C2314yes—
185C22×D4×C61C2×C411yescharacteristic
186C23×C4×C61C2×C411yescharacteristic, complemented
187#123×C61C2×C418yescomplemented
188C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
189C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
190C2×C22⋊C4×C61C2×C411yescharacteristic
191C2×C22⋊C4×C61C2×C411yescharacteristic
192C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
193C24×C61C22×C411yescharacteristic
194C24×C61C22×C411yescharacteristic
195C23×D61—22no—
196C23×D61—22no—
197C23×D61—22no—
198C23×D61—22no—
199C23×D61—22no—
200C23×D61—22no—
201C23×D61—22no—
202C23×D61—22no—
203C23×D61—22no—
204C23×D61—22no—
205C23×D61—22no—
206C23×D61—22no—
207C23×D61C22×C412yes—
208C23×D61C22×C411yescharacteristic
209C23×D61C22×C412yes—
210C23×D61C22×C411yescharacteristic
211C23×D61C2412yes—
212C23×D61C2412yes—
213C23×D61C2411yescharacteristic
214C22×#6923—22no—
215C22×#6923—22no—
216C22×#6923—22no—
217C22×#6923—22no—
218C22×#6923—22no—
219C22×#6923—22no—
220C22×#6923—22no—
221C22×#6923—22no—
222C22×#6923—22no—
223C22×#6923—22no—
224C22×#6923—22no—
225C22×#6923—22no—
226C22×#6923—22no—
227C22×#6923—22no—
228C22×#6923—22no—
229C22×#6923—22no—
230C22×#6923—22no—
231C22×#6923—22no—
232C22×#6923—22no—
233C22×#6923—22no—
234C22×#6923—22no—
235C22×#6923—22no—
236C22×#6923—28no—
237C22×#6923—44no—
238C22×#6923—44no—
239C22×#6923—416no—
240C22×#6923#4114yes—
241C22×#6923#4114yes—
242C22×#6923C2412yes—
243C22×#6923C2412yes—
244C22×#6923C2412yes—
245C22×#6923C2412yes—
246C22×#6923C2412yes—
247C22×#6923C2412yes—
248C22×#6923C2412yes—
249C22×#6923C2412yes—
250C2×D4×C61—42no—
251C2×D4×C61C22×C414yes—
252C22×C4×C61—42no—
253C22×C4×C61C22×C411yescharacteristic
254C22×C4×C61C22×C411yescharacteristic
255C22×C4×C61C22×C411yescharacteristic
256C22×C4×C61C22×C411yescharacteristic
257C22×C4×C61C22×C411yescharacteristic
258C22×C4×C61C22×C414yescomplemented
259C2×C22⋊D61—42no—
260C2×C22⋊D61—42no—
261C2×C22⋊D61C22×C414yes—
262C2×C22⋊D61C22×C414yes—
263C22×Dic61—42no—
264C22×Dic61C22×C411yescharacteristic
265C22×Dic61C22×C411yescharacteristic
266C22×Dic61C22×C411yescharacteristic
267C22×Dic61C22×C411yescharacteristic
268C22×Dic61C22×C411yescharacteristic
269C22×Dic61C22×C414yescomplemented
270D4×D61—48no—
271D4×D61—44no—
272D4×D61—44no—
273C2×D244—42no—
274C2×D244C22×C414yes—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—22no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—22no—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61—48no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—42no—
289C2×C4×D61—42no—
290C2×C4×D61C22×C412yes—
291C2×C4×D61C22×C412yes—
292C2×C4×D61C22×C412yes—
293C2×C4×D61C22×C412yes—
294C2×C4×D61C22×C412yes—
295C2×C4×D61C22×C414yescomplemented
296C2×C4×D61C22×C414yescomplemented
297C2×C4×D61C2412yes—
298C2×C4×D61C2412yes—
299C2×C4×D61C2412yes—
300C2×C4×D61C2412yes—
301C2×C4×D61C2412yes—
302C22⋊#6923—28no—
303C22⋊#6923—28no—
304C22⋊#6923—28no—
305C22⋊#6923—44no—
306C22⋊#6923—44no—
307C22⋊#6923—44no—
308C22⋊#6923—44no—
309C4⋊#6923—28no—
310C4⋊#6923—44no—
311C4⋊#6923—44no—
312C4⋊#6923—44no—
313C4⋊#6923—44no—
314C4×#6923—28no—
315C4×#6923—44no—
316C4×#6923—44no—
317C4×#6923—44no—
318C4×#6923—44no—
319C4⋊C4×C61C22×C414yescomplemented
320C4⋊C4×C61C22×C414yescomplemented
321C22⋊C4×C61C22×C414yes—
322C22⋊C4×C61C22×C414yes—
323C22⋊C4×C61C22×C414yescomplemented
324C22⋊Dic61C22×C414yes—
325C22⋊Dic61C22×C414yes—
326C22⋊Dic61C22×C414yescomplemented
327#11758198C22×C414yes—
328#11758198C22×C414yes—
329#11758198C22×C414yes—
330#11758198C22×C414yes—
331#11758198C22×C414yescomplemented
332#11758198C22×C414yescomplemented
333C4⋊Dic61C22×C414yescomplemented
334C4⋊Dic61C22×C414yescomplemented
335#11758196C22×C414yescomplemented
336#11758196C22×C414yescomplemented
337#11758196C22×C414yescomplemented
338#11758196C22×C414yescomplemented
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61C23×C412yes—
346C23×C61C23×C412yes—
347C23×C61C23×C411yescharacteristic
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—24no—
355C22×D61—24no—
356C22×D61—24no—
357C22×D61—24no—
358C22×D61—24no—
359C22×D61—24no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—44no—
373C22×D61—44no—
374C22×D61—44no—
375C22×D61—44no—
376C22×D61—44no—
377C22×D61—44no—
378C22×D61—44no—
379C22×D61—44no—
380C22×D61C23×C412yes—
381C22×D61C23×C412yes—
382C22×D61C23×C411yescharacteristic
383C22×D61C2×#4112yes—
384C22×D61C2×#4112yes—
385C22×D61H(5,𝔽2)12yes—
386C22×D61H(5,𝔽2)12yes—
387C22×D61H(5,𝔽2)12yes—
388C22×D612−1+412yes—
389C22×D61C2511yescharacteristic
390C2×#6923—28no—
391C2×#6923—28no—
392C2×#6923—22no—
393C2×#6923—22no—
394C2×#6923—22no—
395C2×#6923—22no—
396C2×#6923—22no—
397C2×#6923—22no—
398C2×#6923—22no—
399C2×#6923—22no—
400C2×#6923—22no—
401C2×#6923—22no—
402C2×#6923—22no—
403C2×#6923—22no—
404C2×#6923—22no—
405C2×#6923—22no—
406C2×#6923—22no—
407C2×#6923—22no—
408C2×#6923—22no—
409C2×#6923—22no—
410C2×#6923—22no—
411C2×#6923—22no—
412C2×#6923—22no—
413C2×#6923—22no—
414C2×#6923—416no—
415C2×#6923—44no—
416C2×#6923—44no—
417C2×#6923—44no—
418C2×#6923—44no—
419C2×#6923—44no—
420C2×#6923—44no—
421C2×#6923C2×#4114yes—
422C2×#6923C2×#4114yes—
423D4×C61—44no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—44no—
430C2×C4×C61C23×C412yes—
431C2×C4×C61C23×C412yes—
432C2×C4×C61C23×C412yes—
433C2×C4×C61C23×C412yes—
434C2×C4×C61C23×C412yes—
435C22⋊D61—44no—
436C22⋊D61—44no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—44no—
443C2×Dic61C23×C412yes—
444C2×Dic61C23×C412yes—
445C2×Dic61C23×C412yes—
446C2×Dic61C23×C412yes—
447C2×Dic61C23×C412yes—
448D244—44no—
449C4×D61—24no—
450C4×D61—24no—
451C4×D61—24no—
452C4×D61—24no—
453C4×D61—24no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—44no—
465C4×D61—44no—
466C2×#2335—611nomaximal, Sylow
467C22×C61—22no—
468C22×C61—22no—
469C22×C61—22no—
470C22×C61—22no—
471C22×C61—22no—
472C22×C61—22no—
473C22×C61—44no—
474C22×C61—44no—
475C22×C61C4×#4112yes—
476C22×C61#51812yes—
477C22×C61#52012yes—
478C22×C61C24×C411yescharacteristic
479C2×D61—22no—
480C2×D61—22no—
481C2×D61—22no—
482C2×D61—22no—
483C2×D61—22no—
484C2×D61—22no—
485C2×D61—44no—
486C2×D61—44no—
487C2×D61—48no—
488C2×D61—48no—
489C2×D61—42no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—42no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—42no—
497C2×D61C4×#4112yes—
498C2×D61#51812yes—
499C2×D61#52012yes—
500C2×D61#53814yes—
501C2×D61#53914yes—
502C2×D61#54014yes—
503C2×D61#54214yes—
504C2×D61C22×#4111yescharacteristic
505C2×D61C22×#4111yescharacteristic
506C2×D61C2×H(5,𝔽2)11yescharacteristic
507C2×D61C2×H(5,𝔽2)11yescharacteristic
508C2×D61C2×H(5,𝔽2)11yescharacteristic
509C2×D61C2×2−1+411yescharacteristic
510#6923—24no—
511#6923—24no—
512#6923—42no—
513#6923—42no—
514#6923—42no—
515#6923—42no—
516#6923—42no—
517#6923—42no—
518C4×C61—22no—
519C4×C61—22no—
520C4×C61—22no—
521C4×C61—22no—
522C4×C61—22no—
523Dic61—22no—
524Dic61—22no—
525Dic61—22no—
526Dic61—22no—
527Dic61—22no—
528C22×#123—611no—
529#2335—6116no—
530C2×#390—611no—
531C2×#389—611no—
532C2×#388—611no—
533C2×#388—611no—
534C2×#388—611no—
535C2×#388—611no—
536C2×#387—611no—
537C2×#387—611no—
538C2×#386—611no—
539C2×#385—611no—
540C2×#380—611no—
541C2×C4×C4⋊C4—611no—
542C2×C4×C22⋊C4—611no—
543C2×C4×C22⋊C4—611no—
544C2×C61—42no—
545C2×C61—42no—
546C2×C61#233514yescomplemented
547C2×C61C2×C4×#4111yescharacteristic
548C2×C61C2×#51811yescharacteristic
549C2×C61C2×#52011yescharacteristic
550D61—42no—
551D61—42no—
552D61#233514yescomplemented
553D61C2×#53811yescharacteristic
554D61C2×#53911yescharacteristic
555D61C2×#54011yescharacteristic
556D61C2×#54211yescharacteristic
557C23×D4—611no—
558C24×C4—611no—
559C24×C4—611no—
560C2×#123—611no—
561C2×#123—611no—
562C2×#123—618no—
563C2×#123—618no—
564C2×#123—611no—
565C2×#123—611no—
566C2×#123—611no—
567C2×#123—611no—
568C2×#123—611no—
569C2×#123#692311yescharacteristic, complemented
570C22×C4⋊C4—611no—
571C22×C4⋊C4—611no—
572C22×C4⋊C4—611no—
573C22×C4⋊C4—611no—
574C22×C4⋊C4—611no—
575C22×C4⋊C4—611no—
576C22×C4⋊C4—611no—
577C22×C22⋊C4—611no—
578C22×C22⋊C4—611no—
579C22×C22⋊C4—611no—
580C22×C22⋊C4—611no—
581C22×C22⋊C4—611no—
582C22×C22⋊C4—611no—
583C22×C22⋊C4—611no—
584C22×C22⋊C4—611no—
585C22×C22⋊C4—611no—
586C22×C22⋊C4—611no—
587C22×C42—611no—
588C22×C42—611no—
589C22×C42—611no—
590C22×C42—611no—
591C22×C42—611no—
592#390—618no—
593#389—618no—
594#388—618no—
595#388—618no—
596#388—618no—
597#388—618no—
598#387—618no—
599#387—618no—
600#386—618no—
601#385—618no—
602#380—618no—
603C4×C4⋊C4—618no—
604C4×C22⋊C4—618no—
605C4×C22⋊C4—618no—
606C2×#95—611no—
607C2×#95—611no—
608C2×#95—611no—
609C2×#95—611no—
610C2×#95—611no—
611C2×#95—611no—
612C2×#95—611no—
613C2×#95—611no—
614C2×#95—611no—
615C2×#95—611no—
616C61C2×#233511yescharacteristic, complemented, Sylow
617C25—611no—
618C25—611no—
619C22×D4—611no—
620C22×D4—611no—
621C22×D4—614no—
622C22×D4—614no—
623C22×D4—611no—
624C22×D4—2442no—
625C22×D4—2442no—
626C22×D4C2×#692311yescharacteristic
627C23×C4—611no—
628C23×C4—611no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—611no—
636C23×C4—611no—
637C23×C4—614no—
638C23×C4—614no—
639C23×C4—611no—
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C23×C4—611no—
644C23×C4—611no—
645C23×C4—614no—
646C23×C4—1224no—
647C23×C4—2442no—
648C23×C4—2442no—
649C23×C4—2442no—
650C23×C4—2442no—
651C23×C4C2×#692311yescharacteristic, complemented
652#123—618no—
653#123—618no—
654#123—618no—
655#123—618no—
656#123—618no—
657#123—618no—
658#123—618no—
659#123C2×#692318yescomplemented
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—611no—
663C2×C4⋊C4—611no—
664C2×C4⋊C4—611no—
665C2×C4⋊C4—611no—
666C2×C4⋊C4—614no—
667C2×C4⋊C4—614no—
668C2×C4⋊C4—614no—
669C2×C4⋊C4—614no—
670C2×C4⋊C4—614no—
671C2×C4⋊C4—614no—
672C2×C4⋊C4—614no—
673C2×C4⋊C4—614no—
674C2×C4⋊C4—614no—
675C2×C4⋊C4—1224no—
676C2×C4⋊C4—2442no—
677C2×C4⋊C4—2442no—
678C2×C4⋊C4—2442no—
679C2×C4⋊C4—2442no—
680C2×C4⋊C4C2×#692311yescharacteristic, complemented
681C2×C4⋊C4C2×#692311yescharacteristic, complemented
682C2×C22⋊C4—611no—
683C2×C22⋊C4—611no—
684C2×C22⋊C4—611no—
685C2×C22⋊C4—611no—
686C2×C22⋊C4—611no—
687C2×C22⋊C4—611no—
688C2×C22⋊C4—611no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—611no—
691C2×C22⋊C4—614no—
692C2×C22⋊C4—614no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—614no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—614no—
703C2×C22⋊C4—614no—
704C2×C22⋊C4—1224no—
705C2×C22⋊C4—1224no—
706C2×C22⋊C4—1224no—
707C2×C22⋊C4—2442no—
708C2×C22⋊C4—2442no—
709C2×C22⋊C4—2442no—
710C2×C22⋊C4—2442no—
711C2×C22⋊C4C2×#692311yescharacteristic
712C2×C22⋊C4C2×#692311yescharacteristic
713C2×C22⋊C4C2×#692311yescharacteristic, complemented
714C2×C42—614no—
715C2×C42—614no—
716C2×C42—614no—
717C2×C42—614no—
718C2×C42—614no—
719C2×C42—1224no—
720C2×C42—2442no—
721C2×C42—2442no—
722C2×C42—2442no—
723C2×C42—2442no—
724#95—614no—
725#95—614no—
726#95—614no—
727#95—614no—
728#95—614no—
729#95—614no—
730#95—614no—
731#95—614no—
732#95—614no—
733#95—614no—
734C24—611no—
735C24—612no—
736C24—612no—
737C24—612no—
738C24—612no—
739C24—611no—
740C24—611no—
741C24—1222no—
742C24—1222no—
743C24—1222no—
744C24—1222no—
745C24—1222no—
746C24—1222no—
747C24—1222no—
748C24—1222no—
749C24—1222no—
750C24—1222no—
751C24—1222no—
752C24—1222no—
753C24C22×#692311yescharacteristic
754C24C22×#692311yescharacteristic
755C2×D4—42no—
756C2×D4—614no—
757C2×D4—614no—
758C2×D4—614no—
759C2×D4—2442no—
760C2×D4—2444no—
761C2×D4—2444no—
762C2×D4—2448no—
763C2×D4—2442no—
764C2×D4—2442no—
765C2×D4C22×#692314yes—
766C22×C4—42no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—614no—
770C22×C4—614no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—614no—
777C22×C4—612no—
778C22×C4—612no—
779C22×C4—612no—
780C22×C4—612no—
781C22×C4—612no—
782C22×C4—612no—
783C22×C4—612no—
784C22×C4—612no—
785C22×C4—612no—
786C22×C4—612no—
787C22×C4—614no—
788C22×C4—614no—
789C22×C4—612no—
790C22×C4—612no—
791C22×C4—612no—
792C22×C4—612no—
793C22×C4—612no—
794C22×C4—612no—
795C22×C4—1222no—
796C22×C4—1222no—
797C22×C4—1222no—
798C22×C4—1222no—
799C22×C4—1222no—
800C22×C4—1222no—
801C22×C4—1222no—
802C22×C4—1222no—
803C22×C4—1222no—
804C22×C4—1222no—
805C22×C4—1228no—
806C22×C4—1222no—
807C22×C4—1222no—
808C22×C4—1222no—
809C22×C4—1222no—
810C22×C4—1222no—
811C22×C4—1222no—
812C22×C4—1222no—
813C22×C4—1222no—
814C22×C4—1222no—
815C22×C4—1222no—
816C22×C4—1222no—
817C22×C4—1222no—
818C22×C4—1222no—
819C22×C4—1222no—
820C22×C4—1222no—
821C22×C4—1222no—
822C22×C4—1222no—
823C22×C4—1222no—
824C22×C4—1222no—
825C22×C4—1222no—
826C22×C4—1222no—
827C22×C4—1222no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4—2444no—
831C22×C4—2444no—
832C22×C4—2448no—
833C22×C4—2442no—
834C22×C4—2444no—
835C22×C4—2444no—
836C22×C4—24416no—
837C22×C4C22×#692311yescharacteristic
838C22×C4C22×#692311yescharacteristic
839C22×C4C22×#692311yescharacteristic
840C22×C4C22×#692311yescharacteristic
841C22×C4C22×#692311yescharacteristic
842C22×C4C22×#692314yescomplemented
843C4⋊C4—614no—
844C4⋊C4—614no—
845C4⋊C4—614no—
846C4⋊C4—614no—
847C4⋊C4—614no—
848C4⋊C4—614no—
849C4⋊C4—1228no—
850C4⋊C4—2444no—
851C4⋊C4—2444no—
852C4⋊C4—2444no—
853C4⋊C4—2444no—
854C4⋊C4C22×#692314yescomplemented
855C4⋊C4C22×#692314yescomplemented
856C22⋊C4—614no—
857C22⋊C4—614no—
858C22⋊C4—614no—
859C22⋊C4—614no—
860C22⋊C4—614no—
861C22⋊C4—614no—
862C22⋊C4—614no—
863C22⋊C4—614no—
864C22⋊C4—614no—
865C22⋊C4—1228no—
866C22⋊C4—1228no—
867C22⋊C4—1228no—
868C22⋊C4—2444no—
869C22⋊C4—2444no—
870C22⋊C4—2444no—
871C22⋊C4—2444no—
872C22⋊C4C22×#692314yes—
873C22⋊C4C22×#692314yes—
874C22⋊C4C22×#692314yescomplemented
875C42—1228no—
876C42—2444no—
877C42—2444no—
878C42—2444no—
879C42—2444no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—612no—
887C23—612no—
888C23—612no—
889C23—612no—
890C23—612no—
891C23—612no—
892C23—611no—
893C23—611no—
894C23—612no—
895C23—612no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1224no—
906C23—1222no—
907C23—1224no—
908C23—1224no—
909C23—1224no—
910C23—1222no—
911C23—1222no—
912C23—1224no—
913C23—1224no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—2444no—
921C23—2444no—
922C23—2444no—
923C23—2444no—
924C23—2444no—
925C23—2444no—
926C23—2444no—
927C23—2444no—
928C23C23×#692312yes—
929C23C23×#692312yes—
930C23C23×#692311yescharacteristic
931D4—44no—
932D4—2444no—
933D4—2444no—
934D4—2444no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—44no—
941C2×C4—614no—
942C2×C4—614no—
943C2×C4—612no—
944C2×C4—612no—
945C2×C4—612no—
946C2×C4—612no—
947C2×C4—612no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1224no—
958C2×C4—1222no—
959C2×C4—1224no—
960C2×C4—1224no—
961C2×C4—1224no—
962C2×C4—1224no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1228no—
968C2×C4—1228no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—2444no—
993C2×C4—2444no—
994C2×C4—2444no—
995C2×C4—24416no—
996C2×C4—2444no—
997C2×C4—2444no—
998C2×C4—2444no—
999C2×C4—2444no—
1000C2×C4—2444no—
1001C2×C4—2444no—
1002C2×C4C23×#692312yes—
1003C2×C4C23×#692312yes—
1004C2×C4C23×#692312yes—
1005C2×C4C23×#692312yes—
1006C2×C4C23×#692312yes—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—44no—
1014C22—44no—
1015C22—611no—
1016C22—611no—
1017C22—612no—
1018C22—611no—
1019C22—611no—
1020C22—612no—
1021C22—611no—
1022C22—611no—
1023C22—612no—
1024C22—614no—
1025C22—614no—
1026C22—614no—
1027C22—614no—
1028C22—1222no—
1029C22—1222no—
1030C22—1222no—
1031C22—1222no—
1032C22—1222no—
1033C22—1222no—
1034C22—2442no—
1035C22—2442no—
1036C22—2442no—
1037C22—2442no—
1038C22—2442no—
1039C22—2442no—
1040C22—2442no—
1041C22—2442no—
1042C22—2448no—
1043C22—2448no—
1044C22—2444no—
1045C22—2444no—
1046C22#41×#692312yes—
1047C22#1684082912yes—
1048C22#1684083112yes—
1049C22C24×#692311yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—1224no—
1056C4—1224no—
1057C4—1222no—
1058C4—1222no—
1059C4—1222no—
1060C4—1222no—
1061C4—1222no—
1062C4—2442no—
1063C4—2442no—
1064C4—2442no—
1065C4—2442no—
1066C4—2442no—
1067C4—2442no—
1068C2—42no—
1069C2—42no—
1070C2—611no—
1071C2—611no—
1072C2—611no—
1073C2—611no—
1074C2—614no—
1075C2—2442no—
1076C2—2442no—
1077C2#2146231814yesdirect product factor
1078C2C2×#41×#692311yescharacteristic
1079C2C2×#1684082911yescharacteristic
1080C2C2×#1684083111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#123×C61C4
socleC23×C61C23×C4
prime radicalC22×D4×D61C22
cosocleC22×D61C25
hypercenterC2×#123#6923
hypocenterC61C2×#2335
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462318C2direct (N × H)
3. C2×#16840713C2semidirect
4. C2×#16840712C2semidirect
5. C2×#16840712C2semidirect
6. C2×#16840712C2semidirect
7. C2×#16840712C2semidirect
8. C2×#16840711C2semidirect
9. C2×#16840711C2semidirect
11. C2×#16840709C2semidirect
12. C2×#16840704C2semidirect
13. C2×C4⋊C4×#6923C2semidirect
14. C2×C22⋊C4×#6923C2semidirect
15. C2×C4×C22⋊#6923C2semidirect
36. #16840713C22semidirect
37. #16840712C22semidirect
38. #16840712C22semidirect
39. #16840712C22semidirect
40. #16840712C22semidirect
41. #16840711C22semidirect
42. #16840711C22semidirect
44. #16840709C22semidirect
45. #16840704C22semidirect
46. C4⋊C4×#6923C22semidirect
47. C22⋊C4×#6923C22semidirect
48. C4×C22⋊#6923C22semidirect
61. C2×#14519762C4semidirect
62. C2×#14519762C4semidirect
63. C2×#14519761C4semidirect
64. C2×#14519760C4semidirect
65. C2×#14519759C4semidirect
66. C2×#14519759C4semidirect
67. C2×#14519758C4semidirect
68. #123×D61C4semidirect
75. C2×#123×C61C4semidirect
141. C23×Dic61C2×C4semidirect
144. C22×C4×D61C2×C4semidirect
145. C22×C4×D61C2×C4semidirect
146. C22×C4×D61C2×C4semidirect
153. #14519762C2×C4semidirect
154. #14519762C2×C4semidirect
155. #14519761C2×C4semidirect
156. #14519760C2×C4semidirect
157. #14519759C2×C4semidirect
158. #14519759C2×C4semidirect
159. #14519758C2×C4semidirect
160. C2×C4⋊Dic61C2×C4semidirect
161. C2×C4⋊Dic61C2×C4semidirect
162. C2×#11758196C2×C4semidirect
163. C2×#11758196C2×C4semidirect
164. C2×#11758196C2×C4semidirect
165. C2×#11758196C2×C4semidirect
166. C4⋊C4×D61C2×C4semidirect
167. C4⋊C4×D61C2×C4semidirect
172. C2×C22⋊Dic61C2×C4semidirect
177. C2×#11758198C2×C4semidirect
178. C2×#11758198C2×C4semidirect
181. C22⋊C4×D61C2×C4semidirect
186. C23×C4×C61C2×C4semidirect
187. #123×C61C2×C4semidirect
188. C2×C4⋊C4×C61C2×C4semidirect
189. C2×C4⋊C4×C61C2×C4semidirect
192. C2×C22⋊C4×C61C2×C4semidirect
258. C22×C4×C61C22×C4semidirect
269. C22×Dic61C22×C4semidirect
295. C2×C4×D61C22×C4semidirect
296. C2×C4×D61C22×C4semidirect
319. C4⋊C4×C61C22×C4semidirect
320. C4⋊C4×C61C22×C4semidirect
323. C22⋊C4×C61C22×C4semidirect
326. C22⋊Dic61C22×C4semidirect
331. #11758198C22×C4semidirect
332. #11758198C22×C4semidirect
333. C4⋊Dic61C22×C4semidirect
334. C4⋊Dic61C22×C4semidirect
335. #11758196C22×C4semidirect
336. #11758196C22×C4semidirect
337. #11758196C22×C4semidirect
338. #11758196C22×C4semidirect
546. C2×C61#2335semidirect
552. D61#2335semidirect
569. C2×#123#6923semidirect
616. C61C2×#2335semidirect
651. C23×C4C2×#6923semidirect
659. #123C2×#6923semidirect
680. C2×C4⋊C4C2×#6923semidirect
681. C2×C4⋊C4C2×#6923semidirect
713. C2×C22⋊C4C2×#6923semidirect
842. C22×C4C22×#6923semidirect
854. C4⋊C4C22×#6923semidirect
855. C4⋊C4C22×#6923semidirect
874. C22⋊C4C22×#6923semidirect
1077. C2#21462318direct (N × H)

Maximal subgroups

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

subgroupindex
#214623182
C2×#168407142
C2×#168407132
C2×#168407122
C2×#168407112
C2×#168407102
C2×#168407092
C2×#168407042
C2×C4⋊C4×#69232
C2×C22⋊C4×#69232
C2×C4×C22⋊#69232
C2×#123×D612
C2×#233561