Finite Group Databasebeta

← C2×#19137374 #25255479

Subgroups — C2×#19137374 #25255479

Order 11008.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137374C2116yesmaximal, direct product factor
2C2×#14582798C211yesmaximal, characteristic, complemented
3C2×#14582798C211yesmaximal, characteristic, complemented
4C2×#14582792C211yesmaximal, characteristic
5C2×#14582792C211yesmaximal, characteristic
6C2×#14582792C211yesmaximal, characteristic
7C2×#14582785C211yesmaximal, characteristic, complemented
8C2×#14582785C211yesmaximal, characteristic, complemented
9C2×#14582785C211yesmaximal, characteristic, complemented
10C2×#14582774C211yesmaximal, characteristic
11C2×#14582774C211yesmaximal, characteristic
12C2×#14582765C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic43C211yesmaximal, characteristic
16C22×#126×C43C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582798C2218yescomplemented
34#14582798C2218yescomplemented
35#14582792C2218yes—
36#14582792C2218yes—
37#14582792C2218yes—
38#14582785C2218yescomplemented
39#14582785C2218yescomplemented
40#14582785C2218yescomplemented
41#14582774C2218yes—
42#14582774C2218yes—
43#14582765C2218yescomplemented
44C4⋊C4×Dic43C2218yescomplemented
45C4×C4⋊Dic43C2218yescomplemented
46C22⋊C4×Dic43C2218yes—
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×#126×C43C4116yescomplemented
60C2×#126×C43C2218yes—
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C42×C43C2211yescharacteristic
68C23×Dic43—24no—
69C23×Dic43—42no—
70C23×Dic43—42no—
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2314yes—
80C2×C4⋊Dic43—24no—
81C2×C4⋊Dic43—24no—
82C2×C4⋊Dic43—24no—
83C2×C4⋊Dic43—42no—
84C2×C4⋊Dic43—42no—
85C2×C4⋊Dic43—42no—
86C2×C4⋊Dic43—42no—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2314yes—
91C2×C4⋊Dic43C2314yes—
92C2×C4⋊Dic43C2314yes—
93C2×C4⋊Dic43C2314yes—
94C2×C22⋊Dic43—24no—
95C2×C22⋊Dic43—42no—
96C2×C22⋊Dic43—42no—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×C22⋊Dic43C2314yes—
100C2×C4×Dic43—24no—
101C2×C4×Dic43—42no—
102C2×C4×Dic43—42no—
103C2×C4×Dic43—42no—
104C2×C4×Dic43—42no—
105C2×C4×Dic43C2314yes—
106C2×C4×Dic43C2314yes—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2314yes—
109C2×C4×Dic43C2314yes—
110C43⋊#95C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C25×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129#126×C43C2×C4164yescomplemented
130C2×C4⋊C4×C43C2×C418yescomplemented
131C2×C4⋊C4×C43C2×C418yescomplemented
132C2×C4⋊C4×C43C2×C418yescomplemented
133C2×C4⋊C4×C43C2314yes—
134C2×C4⋊C4×C43C2314yes—
135C2×C4⋊C4×C43C2314yes—
136C2×C22⋊C4×C43C2×C418yes—
137C2×C22⋊C4×C43C2×C418yes—
138C2×C22⋊C4×C43C2×C418yes—
139C2×C22⋊C4×C43C2314yes—
140C2×C22⋊C4×C43C2314yes—
141C2×C22⋊C4×C43C2314yes—
142C2×C42×C43C2×C418yescomplemented
143C2×C42×C43C2314yes—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43C22×C414yes—
151C24×C43C2412yes—
152C24×C43C2411yescharacteristic
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43C22×C414yes—
166C22×C4×C43C22×C414yes—
167C22×C4×C43C22×C414yes—
168C22×C4×C43C22×C414yes—
169C22×C4×C43C22×C414yes—
170C22×C4×C43C22×C414yes—
171C22×C4×C43C2412yes—
172C22×C4×C43C2412yes—
173C22×C4×C43C2412yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×Dic43—28no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—44no—
201C22×Dic43—44no—
202C22×Dic43—416no—
203C22×Dic43#4114yes—
204C22×Dic43#4114yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C4⋊C4×C43C22×C4116yescomplemented
214C4⋊C4×C43C22×C4116yescomplemented
215C4⋊C4×C43C22×C4116yescomplemented
216C22⋊C4×C43C22×C4116yes—
217C22⋊C4×C43C22×C4116yes—
218C22⋊C4×C43C22×C4116yes—
219C42×C43C22×C4116yescomplemented
220C22⋊Dic43—28no—
221C22⋊Dic43—44no—
222C22⋊Dic43—44no—
223C4⋊Dic43—28no—
224C4⋊Dic43—28no—
225C4⋊Dic43—28no—
226C4⋊Dic43—44no—
227C4⋊Dic43—44no—
228C4⋊Dic43—44no—
229C4⋊Dic43—44no—
230C4×Dic43—28no—
231C4×Dic43—44no—
232C4×Dic43—44no—
233C4×Dic43—44no—
234C4×Dic43—44no—
235C23×C43—28no—
236C23×C43—28no—
237C23×C43—28no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—44no—
245C23×C43—44no—
246C23×C43—44no—
247C23×C43—44no—
248C23×C43C23×C414yes—
249C23×C43C23×C412yes—
250C23×C43C2×#4112yes—
251C23×C43C2×#4112yes—
252C23×C43H(5,𝔽2)12yes—
253C23×C43H(5,𝔽2)12yes—
254C23×C432−1+412yes—
255C23×C432−1+412yes—
256C23×C43C2511yescharacteristic
257C2×C4×C43—28no—
258C2×C4×C43—28no—
259C2×C4×C43—28no—
260C2×C4×C43—28no—
261C2×C4×C43—28no—
262C2×C4×C43—28no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43C23×C414yes—
276C2×C4×C43C23×C414yes—
277C2×C4×C43C23×C414yes—
278C2×C4×C43C23×C414yes—
279C2×C4×C43C23×C414yes—
280C2×C4×C43C23×C414yes—
281C2×Dic43—28no—
282C2×Dic43—28no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—416no—
306C2×Dic43—44no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43—44no—
310C2×Dic43—44no—
311C2×Dic43—44no—
312C2×Dic43C2×#4114yes—
313C2×Dic43C2×#4114yes—
314C2×#2334—431nomaximal, Sylow
315C22×C43—24no—
316C22×C43—24no—
317C22×C43—24no—
318C22×C43—416no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43C4×#4114yes—
324C22×C43#52014yes—
325C22×C43#52014yes—
326C22×C43#53814yes—
327C22×C43#53914yes—
328C22×C43#54114yes—
329C22×C43#54214yes—
330C22×C43C24×C411yescharacteristic
331C22×C43C22×#4111yescharacteristic
332C22×C43C22×#4111yescharacteristic
333C22×C43C2×H(5,𝔽2)11yescharacteristic
334C22×C43C2×H(5,𝔽2)11yescharacteristic
335C22×C43C2×2−1+411yescharacteristic
336C22×C43C2×2−1+411yescharacteristic
337C4×C43—24no—
338C4×C43—24no—
339C4×C43—24no—
340C4×C43—24no—
341C4×C43—24no—
342C4×C43—24no—
343Dic43—24no—
344Dic43—24no—
345Dic43—42no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351C22×#126D4311yescharacteristic
352#2334—4316no—
353C2×#389—431no—
354C2×#389—431no—
355C2×#388—431no—
356C2×#388—431no—
357C2×#388—431no—
358C2×#387—431no—
359C2×#387—431no—
360C2×#387—431no—
361C2×#385—431no—
362C2×#385—431no—
363C2×#382—431no—
364C2×C4×C4⋊C4—431no—
365C2×C4×C4⋊C4—431no—
366C2×C4×C22⋊C4—431no—
367C2×C43—44no—
368C2×C43#233418yescomplemented
369C2×C43C2×C4×#4111yescharacteristic
370C2×C43C2×#52011yescharacteristic
371C2×C43C2×#52011yescharacteristic
372C2×C43C2×#53811yescharacteristic
373C2×C43C2×#53911yescharacteristic
374C2×C43C2×#54111yescharacteristic
375C2×C43C2×#54211yescharacteristic
376C24×C4—431no—
377C2×#126Dic43116yescomplemented
378C2×#126C2×D4318yes—
379C22×C4⋊C4—431no—
380C22×C4⋊C4—431no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—431no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4C2×D4311yescharacteristic
387C22×C4⋊C4C2×D4311yescharacteristic
388C22×C4⋊C4C2×D4311yescharacteristic
389C22×C22⋊C4—431no—
390C22×C22⋊C4—431no—
391C22×C22⋊C4—431no—
392C22×C22⋊C4C2×D4311yescharacteristic
393C22×C22⋊C4C2×D4311yescharacteristic
394C22×C22⋊C4C2×D4311yescharacteristic
395C22×C42—431no—
396C22×C42—431no—
397C22×C42—431no—
398C22×C42—431no—
399C22×C42—431no—
400C22×C42C2×D4311yescharacteristic
401#389—438no—
402#389—438no—
403#388—438no—
404#388—438no—
405#388—438no—
406#387—438no—
407#387—438no—
408#387—438no—
409#385—438no—
410#385—438no—
411#382—438no—
412C4×C4⋊C4—438no—
413C4×C4⋊C4—438no—
414C4×C22⋊C4—438no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—431no—
425C2×#95—431no—
426C2×#95—431no—
427C43C2×#233411yescharacteristic, complemented, Sylow
428C25C22×D4311yescharacteristic
429C23×C4—431no—
430C23×C4—431no—
431C23×C4—431no—
432C23×C4—431no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—434no—
438C23×C4—864no—
439C23×C4—1722no—
440C23×C4—1722no—
441C23×C4C22×D4311yescharacteristic
442C23×C4C22×D4311yescharacteristic
443C23×C4C22×D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447#126C2×Dic43164yescomplemented
448C2×C4⋊C4—434no—
449C2×C4⋊C4—434no—
450C2×C4⋊C4—434no—
451C2×C4⋊C4—434no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—434no—
454C2×C4⋊C4—434no—
455C2×C4⋊C4—864no—
456C2×C4⋊C4—864no—
457C2×C4⋊C4—864no—
458C2×C4⋊C4—1722no—
459C2×C4⋊C4—1722no—
460C2×C4⋊C4—1722no—
461C2×C4⋊C4—1722no—
462C2×C4⋊C4C2×Dic4318yescomplemented
463C2×C4⋊C4C2×Dic4318yescomplemented
464C2×C4⋊C4C2×Dic4318yescomplemented
465C2×C4⋊C4C22×D4314yes—
466C2×C4⋊C4C22×D4314yes—
467C2×C4⋊C4C22×D4314yes—
468C2×C22⋊C4—434no—
469C2×C22⋊C4—434no—
470C2×C22⋊C4—434no—
471C2×C22⋊C4—864no—
472C2×C22⋊C4—1722no—
473C2×C22⋊C4—1722no—
474C2×C22⋊C4C2×Dic4318yes—
475C2×C22⋊C4C2×Dic4318yes—
476C2×C22⋊C4C2×Dic4318yes—
477C2×C22⋊C4C22×D4314yes—
478C2×C22⋊C4C22×D4314yes—
479C2×C22⋊C4C22×D4314yes—
480C2×C42—434no—
481C2×C42—434no—
482C2×C42—434no—
483C2×C42—434no—
484C2×C42—434no—
485C2×C42—864no—
486C2×C42—1722no—
487C2×C42—1722no—
488C2×C42—1722no—
489C2×C42—1722no—
490C2×C42C2×Dic4318yescomplemented
491C2×C42C22×D4314yes—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95—434no—
503#95—434no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C22×Dic4314yes—
511C24C23×D4312yes—
512C24C23×D4311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—434no—
526C22×C4—434no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—432no—
532C22×C4—432no—
533C22×C4—432no—
534C22×C4—432no—
535C22×C4—868no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—1724no—
559C22×C4—1724no—
560C22×C4—17216no—
561C22×C4C22×Dic4314yes—
562C22×C4C22×Dic4314yes—
563C22×C4C22×Dic4314yes—
564C22×C4C22×Dic4314yes—
565C22×C4C22×Dic4314yes—
566C22×C4C22×Dic4314yes—
567C22×C4C23×D4312yes—
568C22×C4C23×D4312yes—
569C22×C4C23×D4312yes—
570C22×C4C23×D4312yes—
571C22×C4C23×D4312yes—
572C22×C4C23×D4312yes—
573C4⋊C4—868no—
574C4⋊C4—868no—
575C4⋊C4—868no—
576C4⋊C4—1724no—
577C4⋊C4—1724no—
578C4⋊C4—1724no—
579C4⋊C4—1724no—
580C4⋊C4C22×Dic43116yescomplemented
581C4⋊C4C22×Dic43116yescomplemented
582C4⋊C4C22×Dic43116yescomplemented
583C22⋊C4—868no—
584C22⋊C4—1724no—
585C22⋊C4—1724no—
586C22⋊C4C22×Dic43116yes—
587C22⋊C4C22×Dic43116yes—
588C22⋊C4C22×Dic43116yes—
589C42—868no—
590C42—1724no—
591C42—1724no—
592C42—1724no—
593C42—1724no—
594C42C22×Dic43116yescomplemented
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C23×Dic4314yes—
609C23C23×Dic4312yes—
610C23#41×D4312yes—
611C23#41×D4312yes—
612C23#1306337112yes—
613C23#1306337112yes—
614C23#1306337212yes—
615C23#1306337212yes—
616C23C24×D4311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—434no—
636C2×C4—434no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—868no—
642C2×C4—868no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—17216no—
662C2×C4—1724no—
663C2×C4—1724no—
664C2×C4—1724no—
665C2×C4—1724no—
666C2×C4—1724no—
667C2×C4—1724no—
668C2×C4C23×Dic4314yes—
669C2×C4C23×Dic4314yes—
670C2×C4C23×Dic4314yes—
671C2×C4C23×Dic4314yes—
672C2×C4C23×Dic4314yes—
673C2×C4C23×Dic4314yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#41×Dic4314yes—
683C22#1458338214yes—
684C22#1458338214yes—
685C22#1458348814yes—
686C22#1458349014yes—
687C22#1458350614yes—
688C22#1458351514yes—
689C22C24×Dic4311yescharacteristic
690C22C2×#41×D4311yescharacteristic
691C22C2×#41×D4311yescharacteristic
692C22C2×#1306337111yescharacteristic
693C22C2×#1306337111yescharacteristic
694C22C2×#1306337211yescharacteristic
695C22C2×#1306337211yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—864no—
703C4—864no—
704C4—1722no—
705C4—1722no—
706C4—1722no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C2—44no—
711C2#1913737418yesdirect product factor
712C2C2×#41×Dic4311yescharacteristic
713C2C2×#1458338211yescharacteristic
714C2C2×#1458338211yescharacteristic
715C2C2×#1458348811yescharacteristic
716C2C2×#1458349011yescharacteristic
717C2C2×#1458350611yescharacteristic
718C2C2×#1458351511yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×#126×C43C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC22×#126D43
hypocenterC43C2×#2334
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #19137374C2direct (N × H)
2. C2×#14582798C2semidirect
3. C2×#14582798C2semidirect
7. C2×#14582785C2semidirect
8. C2×#14582785C2semidirect
9. C2×#14582785C2semidirect
12. C2×#14582765C2semidirect
13. C2×C4⋊C4×Dic43C2semidirect
14. C2×C4×C4⋊Dic43C2semidirect
33. #14582798C22semidirect
34. #14582798C22semidirect
38. #14582785C22semidirect
39. #14582785C22semidirect
40. #14582785C22semidirect
43. #14582765C22semidirect
44. C4⋊C4×Dic43C22semidirect
45. C4×C4⋊Dic43C22semidirect
59. C2×#126×C43C4semidirect
129. #126×C43C2×C4semidirect
130. C2×C4⋊C4×C43C2×C4semidirect
131. C2×C4⋊C4×C43C2×C4semidirect
132. C2×C4⋊C4×C43C2×C4semidirect
142. C2×C42×C43C2×C4semidirect
213. C4⋊C4×C43C22×C4semidirect
214. C4⋊C4×C43C22×C4semidirect
215. C4⋊C4×C43C22×C4semidirect
219. C42×C43C22×C4semidirect
368. C2×C43#2334semidirect
377. C2×#126Dic43semidirect
427. C43C2×#2334semidirect
447. #126C2×Dic43semidirect
462. C2×C4⋊C4C2×Dic43semidirect
463. C2×C4⋊C4C2×Dic43semidirect
464. C2×C4⋊C4C2×Dic43semidirect
490. C2×C42C2×Dic43semidirect
580. C4⋊C4C22×Dic43semidirect
581. C4⋊C4C22×Dic43semidirect
582. C4⋊C4C22×Dic43semidirect
594. C42C22×Dic43semidirect
711. C2#19137374direct (N × H)

Maximal subgroups

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

subgroupindex
#191373742
C2×#145827982
C2×#145827922
C2×#145827852
C2×#145827742
C2×#145827652
C2×C4⋊C4×Dic432
C2×C4×C4⋊Dic432
C2×C22⋊C4×Dic432
C22×#126×C432
C2×#233443