Finite Group Databasebeta

← C4×#10623261 #14913752

Subgroups — C4×#10623261 #14913752

Order 2816.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic
2#13071717C212yesmaximal, complemented
3#13071706C211yesmaximal, characteristic, complemented
4#13071695C214yesmaximal, complemented
5#13071620C212yesmaximal, complemented
6#13071575C211yesmaximal, characteristic, complemented
7#13071525C212yesmaximal
8#13071516C211yesmaximal, characteristic
9#13071492C212yesmaximal, complemented
10C4×#66943C212yesmaximal, complemented
11C4×#66950C212yesmaximal, complemented
12C4×#66999C214yesmaximal, complemented
13C42×Dic22C211yesmaximal, characteristic, complemented
14C42×D44C211yesmaximal, characteristic
15C4×#66946C212yesmaximal
16C4×C4⋊C4×D11C212yesmaximal, complemented
17C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2212yes—
20C2×#66999C2214yes—
21#10623261C4116yesdirect product factor
22C2×#66950C2212yes—
23C2×#66946C2212yes—
24C2×#66946C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×C4⋊C4×D11C2212yes—
27C2×#66943C2212yes—
28C2×C4×D44C2211yescharacteristic
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C2×C42×D11C2212yes—
32C2×C42×D11C2214yes—
33C2×C4×Dic22C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C11×#391C2212yes—
37C11×#389C2212yes—
38C11×#389C2212yes—
39C11×#384C2211yescharacteristic
40C4×C11×C4⋊C4C2212yes—
41C4×C11×C4⋊C4C2212yes—
42C43×C11C2211yescharacteristic
43#10622843C2214yes—
44#10622602C2214yes—
45#10622602C2214yes—
46#10622600C2214yes—
47#10622600C2212yes—
48#10622598C2212yes—
49#10622598C2212yes—
50#10622591C2214yes—
51#10622591C2214yes—
52#10622590C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57#10622587C2212yes—
58#10622586C2214yes—
59#10622586C2212yes—
60C4×(C2×D11)⋊C4C2212yes—
61C4×(C2×D11)⋊C4C2212yes—
62C4×(C2×D11)⋊C4C2214yes—
63C4×(C2×D11)⋊C4C2212yes—
64C4×C4⋊Dic11C2214yes—
65C4×C4⋊Dic11C2211yescharacteristic
66C4×C4⋊Dic11C2211yescharacteristic
67C4×C4⋊Dic11C2211yescharacteristic
68C4×C4⋊Dic11C2211yescharacteristic
69C4×C4⋊Dic11C2211yescharacteristic
70C4×C4⋊Dic11C2211yescharacteristic
71C4×Dic11⋊C4C2212yes—
72C4×Dic11⋊C4C2214yes—
73C4×Dic11⋊C4C2212yes—
74C4×Dic11⋊C4C2212yes—
75C42×Dic11C2212yes—
76#10622281C2214yes—
77#10622279C2214yes—
78#10622279C2214yes—
79D11×#95C2214yes—
80#10622268C2214yes—
81#10622267C2214yes—
82#10622266C2214yes—
83#10622262C2214yes—
84C22×Q8×C11C2312yes—
85C22×D44C2311yescharacteristic
86C22×C4×D11C2312yes—
87C22×C4×D11C2314yes—
88C22×C4×D11C2312yes—
89C22×C4×D11C2312yes—
90C22×C4×D11C2314yes—
91C22×Dic22C2311yescharacteristic
92C11×C4⋊Q8C2×C418yescomplemented
93C4×Q8×C11—44no—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2314yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108#66999C2×C4132yescomplemented
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2314yes—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2314yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2312yes—
138#66950C2×C4116yescomplemented
139#66946—28no—
140#66946C2×C4116yes—
141C4⋊C4×D11—28no—
142C4⋊C4×D11C2×C4116yescomplemented
143#66943C2×C4116yescomplemented
144C4×D44—24no—
145C4×D44C2×C418yes—
146C4×D44Q818yescomplemented
147C42×D11—28no—
148C42×D11—48no—
149C4×Dic22—24no—
150C4×Dic22—24no—
151C4×Dic22C2×C418yescomplemented
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165C11⋊#95C2312yes—
166C4×#554—111nomaximal, Sylow
167C23×D11C2412yes—
168C2×Q8×C11—42no—
169C2×Q8×C11—42no—
170C2×Q8×C11C22×C418yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2414yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C2×D44C22×C414yes—
188C2×D44C2×Q814yes—
189C2×D44#4114yes—
190C2×C4×D11—28no—
191C2×C4×D11—24no—
192C2×C4×D11—28no—
193C2×C4×D11—24no—
194C2×C4×D11—24no—
195C2×C4×D11—24no—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—44no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—42no—
202C2×C4×D11C22×C418yes—
203C2×C4×D11C22×C4116yes—
204C2×C4×D11C2×Q818yes—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22C22×C414yes—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—44no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4C22×C418yes—
213C11×C4⋊C4C22×C418yes—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—28no—
217C42×C11—22no—
218C42×C11—41no—
219C42×C11C22×C414yes—
220C42×C11C2×Q814yes—
221C42×C11#4114yes—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—28no—
224(C2×D11)⋊C4C22×C418yes—
225(C2×D11)⋊C4C22×C4116yes—
226(C2×D11)⋊C4C2×Q818yes—
227C4⋊Dic11—22no—
228C4⋊Dic11—22no—
229C4⋊Dic11—44no—
230C4⋊Dic11C22×C414yes—
231C4⋊Dic11C22×C414yes—
232C4⋊Dic11C22×C4116yes—
233C4⋊Dic11C2×Q814yes—
234C4⋊Dic11#4114yes—
235Dic11⋊C4—24no—
236Dic11⋊C4—28no—
237Dic11⋊C4—24no—
238Dic11⋊C4C22×C418yes—
239Dic11⋊C4C22×C4116yes—
240C4×Dic11—24no—
241C4×Dic11—24no—
242C4×Dic11—24no—
243C4×Dic11—24no—
244C4×Dic11—24no—
245C4×Dic11—24no—
246C4×Dic11—24no—
247C4×Dic11—44no—
248C4×Dic11—44no—
249C4×Dic11—42no—
250C4×Dic11C22×C418yes—
251C2×#554—111no—
252#2370—112no—
253#2369—111no—
254#2368—114no—
255#2360—112no—
256#2355—111no—
257#2349—112no—
258D4×C4⋊C4—111no—
259#2345—112no—
260C4×C4⋊Q8D1111yescharacteristic, complemented
261C4×#125—112no—
262C4×C22⋊Q8—112no—
263C4×C22⋊Q8—114no—
264C42×Q8—111no—
265C42×D4—112no—
266C42×D4—111no—
267C2×C4×C4⋊C4—112no—
268C23×C11C2511yescharacteristic
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11C23×C414yes—
274C22×D11C22×Q814yes—
275C22×D11C2×#4114yes—
276Q8×C11—48no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—24no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—24no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—24no—
287C2×C4×C11—21no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—21no—
291C2×C4×C11C23×C412yes—
292C2×C4×C11C23×C418yes—
293C2×C4×C11C23×C412yes—
294C2×C4×C11C23×C412yes—
295C2×C4×C11C22×Q812yes—
296C2×C4×C11C22×Q812yes—
297C2×C4×C11C22×Q812yes—
298C2×C4×C11C2×#4112yes—
299C2×C4×C11C2×#4112yes—
300C2×C4×C11C2×#4112yes—
301C2×C4×C11C2×#4112yes—
302C2×C4×C11C2×#4112yes—
303C2×C4×C11H(5,𝔽2)12yes—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11C23×C414yes—
321C2×Dic11C23×C414yes—
322C2×Dic11C23×C414yes—
323C2×Dic11C22×Q814yes—
324C2×Dic11C2×#4114yes—
325D44C4×Q8116yescomplemented
326C4×D11—216no—
327C4×D11—216no—
328C4×D11—416no—
329C4×D11—416no—
330C4×D11—48no—
331Dic22—28no—
332#554—1116no—
333C2×C4⋊Q8C2×D1111yescharacteristic
334C2×#125—112no—
335C2×C22⋊Q8—114no—
336C2×C22⋊Q8—112no—
337C2×C4×Q8—111no—
338C2×C4×Q8—111no—
339C2×C4×Q8—111no—
340C2×C4×Q8C2×D1112yes—
341C2×C4×D4—112no—
342C2×C4×D4—112no—
343C2×C4×D4—111no—
344C2×C4×D4—111no—
345C2×C4×D4—111no—
346C22×C4⋊C4—112no—
347C22×C4⋊C4—112no—
348C22×C42—112no—
349C22×C42—114no—
350#391—114no—
351#391—112no—
352#391C2×D1112yes—
353#389—112no—
354#389—112no—
355#389—112no—
356#389—114no—
357#389C2×D1112yes—
358#389C2×D1112yes—
359#387—114no—
360#387—114no—
361#387—114no—
362#387—114no—
363#387—114no—
364#385—114no—
365#385—114no—
366#385—114no—
367#384C2×D1111yescharacteristic
368#382—112no—
369#380—112no—
370#380—114no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4—112no—
374C4×C4⋊C4—112no—
375C4×C4⋊C4—111no—
376C4×C4⋊C4—114no—
377C4×C4⋊C4—114no—
378C4×C4⋊C4—111no—
379C4×C4⋊C4—111no—
380C4×C4⋊C4—112no—
381C4×C4⋊C4—111no—
382C4×C4⋊C4—112no—
383C4×C4⋊C4—111no—
384C4×C4⋊C4—112no—
385C4×C4⋊C4—111no—
386C4×C4⋊C4—114no—
387C4×C4⋊C4C2×D1112yes—
388C4×C4⋊C4C2×D1112yes—
389C4×C22⋊C4—112no—
390C4×C22⋊C4—112no—
391C4×C22⋊C4—112no—
392C4×C22⋊C4—114no—
393C4×C22⋊C4—114no—
394C4×C22⋊C4—114no—
395C2×#95—114no—
396C43—112no—
397C43C2×D1111yescharacteristic
398C22×C11C24×C411yescharacteristic
399C22×C11C23×Q811yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C22×#4111yescharacteristic
403C22×C11C2×H(5,𝔽2)11yescharacteristic
404C22×C11#58511yescharacteristic
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—24no—
410C2×D11—24no—
411C2×D11C2×C4×Q818yes—
412C4×C11—22no—
413C4×C11—28no—
414C4×C11—22no—
415C4×C11—22no—
416C4×C11—41no—
417C4×C11—44no—
418C4×C11C2×C4×Q814yes—
419C4×C11C4×#4114yes—
420C4×C11#55414yescomplemented
421Dic11—24no—
422Dic11—24no—
423Dic11—24no—
424Dic11—24no—
425Dic11—24no—
426Dic11—42no—
427Dic11—42no—
428C22×Q8—111no—
429C22×Q8C22×D1112yes—
430C22×D4—111no—
431C23×C4—112no—
432C23×C4—112no—
433C23×C4—114no—
434C23×C4—114no—
435C23×C4—112no—
436C4⋊Q8C4×D1118yescomplemented
437#125—1116no—
438C22⋊Q8—1132no—
439C22⋊Q8—1116no—
440C4×Q8—44no—
441C4×Q8—118no—
442C4×Q8—224no—
443C4×Q8—224no—
444C4×D4—1116no—
445C4×D4—118no—
446C4×D4—118no—
447C4×D4—224no—
448C4×D4—228no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—1116no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—114no—
463C2×C4⋊C4—228no—
464C2×C4⋊C4C22×D1112yes—
465C2×C4⋊C4C22×D1112yes—
466C2×C4⋊C4C22×D1114yes—
467C2×C4⋊C4C22×D1112yes—
468C2×C4⋊C4C22×D1112yes—
469C2×C4⋊C4C22×D1112yes—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—112no—
472C2×C22⋊C4—112no—
473C2×C22⋊C4—112no—
474C2×C22⋊C4—114no—
475C2×C42—112no—
476C2×C42—112no—
477C2×C42—112no—
478C2×C42—112no—
479C2×C42—112no—
480C2×C42—112no—
481C2×C42—112no—
482C2×C42—112no—
483C2×C42—112no—
484C2×C42—114no—
485C2×C42—114no—
486C2×C42—228no—
487C2×C42—448no—
488C2×C42C22×D1111yescharacteristic
489C2×C42C22×D1111yescharacteristic
490C2×C42C22×D1111yescharacteristic
491C2×C42C22×D1114yes—
492C2×C42C22×D1111yescharacteristic
493C2×C42C22×D1111yescharacteristic
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496#95—112no—
497#95—114no—
498#95—114no—
499#95—112no—
500#95—112no—
501#95—114no—
502#95—114no—
503#95—112no—
504#95—112no—
505#95—112no—
506#95—114no—
507#95—114no—
508#95C22×D1114yes—
509#95C22×D1114yes—
510C2×C11C22×C4×Q811yescharacteristic
511C2×C11C2×C4×#4111yescharacteristic
512C2×C11C4×H(5,𝔽2)11yescharacteristic
513C2×C11C2×#55411yescharacteristic
514C2×C11#347511yescharacteristic
515C2×C11Q8×#4111yescharacteristic
516C2×C11#348111yescharacteristic
517D11—28no—
518C24—112no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—114no—
522C2×Q8—222no—
523C2×Q8—222no—
524C2×Q8C2×C4×D1118yes—
525C2×D4—114no—
526C2×D4—114no—
527C2×D4—114no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—118no—
534C22×C4—118no—
535C22×C4—1116no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—228no—
539C22×C4—224no—
540C22×C4—228no—
541C22×C4—224no—
542C22×C4—224no—
543C22×C4—224no—
544C22×C4—224no—
545C22×C4—224no—
546C22×C4—444no—
547C22×C4—444no—
548C22×C4—442no—
549C22×C4—444no—
550C22×C4C23×D1114yes—
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1111yescharacteristic
553C22×C4C23×D1114yes—
554C22×C4C23×D1111yescharacteristic
555C22×C4C23×D1111yescharacteristic
556C22×C4C23×D1111yescharacteristic
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1111yescharacteristic
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—44no—
562C4⋊C4—42no—
563C4⋊C4—114no—
564C4⋊C4—1116no—
565C4⋊C4—114no—
566C4⋊C4—118no—
567C4⋊C4—1116no—
568C4⋊C4—114no—
569C4⋊C4—114no—
570C4⋊C4—228no—
571C4⋊C4—224no—
572C4⋊C4—224no—
573C4⋊C4—222no—
574C4⋊C4—222no—
575C4⋊C4—444no—
576C4⋊C4C2×C4×D1118yes—
577C4⋊C4C2×C4×D1118yes—
578C22⋊C4—1116no—
579C22⋊C4—118no—
580C22⋊C4—118no—
581C22⋊C4—224no—
582C22⋊C4—228no—
583C42—28no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—41no—
588C42—118no—
589C42—224no—
590C42—224no—
591C42—224no—
592C42—224no—
593C42—224no—
594C42—224no—
595C42—224no—
596C42—444no—
597C42—444no—
598C42—442no—
599C42C2×C4×D1114yes—
600C42Q8×D1114yes—
601C42#434314yes—
602C11C4×#55411yescharacteristic, complemented, Sylow
603C23—114no—
604C23—114no—
605C23—114no—
606C23—222no—
607C23—222no—
608C23—222no—
609C23—222no—
610C23C24×D1111yescharacteristic
611Q8—48no—
612Q8—228no—
613D4—1116no—
614C2×C4—24no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—114no—
629C2×C4—114no—
630C2×C4—114no—
631C2×C4—114no—
632C2×C4—114no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—2216no—
644C2×C4—2216no—
645C2×C4—222no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—4416no—
652C2×C4—448no—
653C2×C4—4416no—
654C2×C4C22×C4×D1112yes—
655C2×C4C22×C4×D1118yes—
656C2×C4C22×C4×D1112yes—
657C2×C4C22×C4×D1112yes—
658C2×C4#6703712yes—
659C2×C4C2×Q8×D1112yes—
660C2×C4C2×Q8×D1112yes—
661C2×C4C2×Q8×D1112yes—
662C2×C4C2×#434312yes—
663C2×C4C2×#434312yes—
664C2×C4C2×#434312yes—
665C2×C4#41×D1112yes—
666C2×C4#41×D1112yes—
667C22—118no—
668C22—224no—
669C22—224no—
670C22—224no—
671C22—224no—
672C22—224no—
673C22—224no—
674C22C23×C4×D1111yescharacteristic
675C22C2×#6703711yescharacteristic
676C22C22×Q8×D1111yescharacteristic
677C22C22×#434311yescharacteristic
678C22C2×#41×D1111yescharacteristic
679C22C2×#41×D1111yescharacteristic
680C22#1062345311yescharacteristic
681C4—22no—
682C4—22no—
683C4—28no—
684C4—22no—
685C4—44no—
686C4—41no—
687C4—224no—
688C4—224no—
689C4—224no—
690C4—224no—
691C4—224no—
692C4—442no—
693C4—442no—
694C4C4×Q8×D1114yes—
695C4C4×#434314yes—
696C4#1062326114yesdirect product factor
697C2—228no—
698C2C2×C4×Q8×D1111yescharacteristic
699C2C2×C4×#434311yescharacteristic
700C2C4×#6703711yescharacteristic
701C2C2×#1062326111yescharacteristic
702C2#1308218311yescharacteristic
703C2#1308219411yescharacteristic
704C2#1308222411yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×C4⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC22×D44C23
hypercenterC4×C4⋊Q8D11
hypocenterC11C4×#554
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13071717C2semidirect
3. #13071706C2semidirect
4. #13071695C2semidirect
5. #13071620C2semidirect
6. #13071575C2semidirect
9. #13071492C2semidirect
10. C4×#66943C2semidirect
11. C4×#66950C2semidirect
12. C4×#66999C2semidirect
13. C42×Dic22C2semidirect
16. C4×C4⋊C4×D11C2semidirect
17. C4×C11×C4⋊Q8C2semidirect
21. #10623261C4direct (N × H)
92. C11×C4⋊Q8C2×C4semidirect
108. #66999C2×C4semidirect
138. #66950C2×C4semidirect
142. C4⋊C4×D11C2×C4semidirect
143. #66943C2×C4semidirect
146. C4×D44Q8semidirect
151. C4×Dic22C2×C4semidirect
260. C4×C4⋊Q8D11semidirect
325. D44C4×Q8semidirect
420. C4×C11#554semidirect
436. C4⋊Q8C4×D11semidirect
602. C11C4×#554semidirect
696. C4#10623261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
#130717172
#130717062
#130716952
#130716202
#130715752
#130715252
#130715162
#130714922
C4×#669432
C4×#669502
C4×#669992
C42×Dic222
C42×D442
C4×#669462
C4×C4⋊C4×D112
C4×C11×C4⋊Q82
C4×#55411