Finite Group Databasebeta

← C2×#13071747 #14913488

Subgroups — C2×#13071747 #14913488

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2#13071747C2116yesmaximal, direct product factor
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622558C211yesmaximal, characteristic, complemented
5C2×#10622553C211yesmaximal, characteristic, complemented
6C2×#10622282C211yesmaximal, characteristic, complemented
7C2×#10622557C211yesmaximal, characteristic, complemented
8C2×#10622546C211yesmaximal, characteristic, complemented
9C2×#10622265C211yesmaximal, characteristic, complemented
10C2×#10622569C211yesmaximal, characteristic
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C2×#10622262C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#66982C4116yescomplemented
28C2×#66982C2218yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C4×C11×C22⋊C4C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C4×C22⋊Dic11C2218yescomplemented
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56#10622570C2218yes—
57#10622569C2218yes—
58#10622558C2218yescomplemented
59#10622557C2218yescomplemented
60#10622553C2218yescomplemented
61C4×(C2×D11)⋊C4C2218yescomplemented
62#10622546C2218yescomplemented
63C4×Dic11⋊C4C2218yescomplemented
64#10622282C2218yescomplemented
65#10622279C2218yescomplemented
66#10622265C2218yescomplemented
67#10622262C2218yescomplemented
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C23×C4×C11—42no—
71C23×C4×C11—42no—
72C23×C4×C11C2×C418yescomplemented
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2314yes—
80C22×C22⋊D11—42no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11C2×C418yes—
83C22×C22⋊D11C2314yes—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×C4×D11—24no—
92C22×C4×D11—24no—
93C22×C4×D11—42no—
94C22×C4×D11C2314yes—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C42×C11—42no—
100C2×C42×C11—42no—
101C2×C42×C11C2314yes—
102C2×C42×C11C2314yes—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11C2×C418yescomplemented
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109#66982C2×C4164yescomplemented
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—24no—
112C2×(C2×D11)⋊C4—42no—
113C2×(C2×D11)⋊C4C2×C418yes—
114C2×(C2×D11)⋊C4C2×C418yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—42no—
123C2×Dic11⋊C4C2×C418yescomplemented
124C2×Dic11⋊C4C2×C418yescomplemented
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×C4×Dic11—24no—
131C2×C4×Dic11—24no—
132C2×C4×Dic11—42no—
133C2×C4×Dic11—42no—
134C2×C4×Dic11—42no—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2374—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11C22×C414yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11C22×C414yes—
167C23×D11C2412yes—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—416no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11C22×C414yes—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C22×C4116yescomplemented
188C22×C4×C11#4114yes—
189C22×C4×C11#4114yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C2×C22⋊D11—416no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11—44no—
199C2×C22⋊D11C22×C4116yes—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11C22×C414yes—
217C22×Dic11C22×C414yes—
218C22×Dic11C22×C414yes—
219C22×Dic11#4114yes—
220C22×Dic11#4114yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C2×C4×D11—28no—
229C2×C4×D11—28no—
230C2×C4×D11—44no—
231C2×C4×D11—416no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C42×C11—44no—
235C42×C11—44no—
236C22⋊Dic11—28no—
237C22⋊Dic11—28no—
238C22⋊Dic11C22×C4116yescomplemented
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—44no—
242(C2×D11)⋊C4C22×C4116yes—
243(C2×D11)⋊C4C22×C4116yes—
244Dic11⋊C4—28no—
245Dic11⋊C4—28no—
246Dic11⋊C4—44no—
247Dic11⋊C4C22×C4116yescomplemented
248Dic11⋊C4C22×C4116yescomplemented
249C4×Dic11—28no—
250C4×Dic11—28no—
251C4×Dic11—44no—
252C4×Dic11—44no—
253C4×Dic11—44no—
254C22×#123—111no—
255#2374—1116no—
256C2×#390—111no—
257C2×#388—111no—
258C2×#388—111no—
259C2×#388—111no—
260C2×#388—111no—
261C2×#387—111no—
262C2×#387—111no—
263C2×#386—111no—
264C2×C4×C4⋊C4—111no—
265C2×C4×C4⋊C4—111no—
266C2×C4×C22⋊C4—111no—
267C2×C4×C22⋊C4—111no—
268C2×C4×C22⋊C4—111no—
269C2×C4×C22⋊C4D1111yescharacteristic, complemented
270C23×C11—28no—
271C23×C11—28no—
272C23×C11—28no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11C23×C414yes—
284C23×C11C23×C412yes—
285C23×C11C2×#4112yes—
286C23×C11C2×#4112yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11H(5,𝔽2)12yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C11C2511yescharacteristic
292C22×D11—28no—
293C22×D11—28no—
294C22×D11—28no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11C23×C414yes—
306C2×C4×C11—28no—
307C2×C4×C11—28no—
308C2×C4×C11—28no—
309C2×C4×C11—28no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—416no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11C23×C414yes—
328C2×C4×C11C23×C414yes—
329C2×C4×C11C2×#4114yes—
330C2×C4×C11C2×#4114yes—
331C22⋊D11—416no—
332C2×Dic11—28no—
333C2×Dic11—28no—
334C2×Dic11—28no—
335C2×Dic11—28no—
336C2×Dic11—28no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—44no—
354C2×Dic11—44no—
355C2×Dic11C23×C414yes—
356C2×Dic11C23×C414yes—
357C2×Dic11C23×C414yes—
358C2×Dic11C2×#4114yes—
359C2×Dic11C2×#4114yes—
360C4×D11—416no—
361C23×D4—111no—
362C24×C4—111no—
363C24×C4C2×D1111yescharacteristic
364C2×#123—118no—
365C2×#123—1116no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—111no—
376C22×C22⋊C4—111no—
377C22×C22⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4C2×D1111yescharacteristic
380C22×C22⋊C4C2×D1111yescharacteristic
381C22×C42—111no—
382C22×C42—111no—
383C22×C42—111no—
384C22×C42—111no—
385C22×C42—111no—
386C22×C42C2×D1111yescharacteristic
387C22×C42C2×D1111yescharacteristic
388#390—118no—
389#388—118no—
390#388—118no—
391#388—118no—
392#388—118no—
393#387—118no—
394#387—118no—
395#386—118no—
396C4×C4⋊C4—118no—
397C4×C4⋊C4—118no—
398C4×C22⋊C4—118no—
399C4×C22⋊C4—118no—
400C4×C22⋊C4—118no—
401C4×C22⋊C4C2×D1118yescomplemented
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95C2×D1111yescharacteristic
411C2×#95C2×D1111yescharacteristic
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—416no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11C4×#4114yes—
421C22×C11C4×#4114yes—
422C22×C11#51814yes—
423C22×C11#55114yes—
424C22×C11#55314yes—
425C22×C11#55314yes—
426C22×C11#55914yes—
427C22×C11C24×C411yescharacteristic
428C22×C11C22×#4111yescharacteristic
429C22×C11C22×#4111yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C22×#4111yescharacteristic
432C22×C11C2×H(5,𝔽2)11yescharacteristic
433C22×C11C2×H(5,𝔽2)11yescharacteristic
434C2×D11—24no—
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—416no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C4×C11—24no—
443C4×C11—24no—
444C4×C11—24no—
445C4×C11—24no—
446C4×C11—42no—
447C4×C11—42no—
448Dic11—24no—
449Dic11—24no—
450Dic11—24no—
451Dic11—24no—
452Dic11—24no—
453Dic11—42no—
454Dic11—42no—
455C25—111no—
456C25C22×D1111yescharacteristic
457C22×D4—118no—
458C22×D4—114no—
459C22×D4—442no—
460C22×D4—442no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—114no—
471C23×C4—224no—
472C23×C4—224no—
473C23×C4—442no—
474C23×C4C4×D1118yescomplemented
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1114yes—
482#123—1164no—
483C2×C4⋊C4—118no—
484C2×C4⋊C4—118no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—442no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—118no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—118no—
498C2×C22⋊C4—118no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—224no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—442no—
511C2×C22⋊C4C22×D1114yes—
512C2×C22⋊C4C22×D1114yes—
513C2×C42—42no—
514C2×C42—42no—
515C2×C42—114no—
516C2×C42—114no—
517C2×C42—114no—
518C2×C42—114no—
519C2×C42—114no—
520C2×C42—224no—
521C2×C42—224no—
522C2×C42—442no—
523C2×C42—442no—
524C2×C42—442no—
525C2×C42C22×D1114yes—
526C2×C42C22×D1114yes—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95C22×D1114yes—
536#95C22×D1114yes—
537C2×C11—44no—
538C2×C11#237418yescomplemented
539C2×C11C2×C4×#4111yescharacteristic
540C2×C11C2×C4×#4111yescharacteristic
541C2×C11C2×#51811yescharacteristic
542C2×C11C2×#55111yescharacteristic
543C2×C11C2×#55311yescharacteristic
544C2×C11C2×#55311yescharacteristic
545C2×C11C2×#55911yescharacteristic
546D11—44no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—114no—
554C24—112no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24C2×C4×D1114yes—
562C24C23×D1112yes—
563C24C23×D1111yescharacteristic
564C2×D4—1116no—
565C2×D4—4416no—
566C2×D4—444no—
567C2×D4—444no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—416no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—228no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—228no—
615C22×C4—444no—
616C22×C4—4416no—
617C22×C4C2×C4×D1114yes—
618C22×C4C2×C4×D1114yes—
619C22×C4C2×C4×D11116yescomplemented
620C22×C4#433914yes—
621C22×C4#433914yes—
622C22×C4C23×D1112yes—
623C22×C4C23×D1112yes—
624C22×C4C23×D1112yes—
625C22×C4C23×D1112yes—
626C22×C4C23×D1112yes—
627C22×C4C23×D1112yes—
628C4⋊C4—1116no—
629C4⋊C4—1116no—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—444no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—1116no—
636C22⋊C4—1116no—
637C22⋊C4—1116no—
638C22⋊C4—228no—
639C22⋊C4—228no—
640C22⋊C4—228no—
641C22⋊C4—228no—
642C22⋊C4—444no—
643C42—44no—
644C42—44no—
645C42—228no—
646C42—228no—
647C42—444no—
648C42—444no—
649C42—444no—
650C11C2×#237411yescharacteristic, complemented, Sylow
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—114no—
665C23—228no—
666C23—228no—
667C23—228no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—222no—
673C23—222no—
674C23—444no—
675C23—444no—
676C23—444no—
677C23—444no—
678C23C22×C4×D1114yes—
679C23C22×C4×D1112yes—
680C23C2×#433912yes—
681C23C2×#433912yes—
682C23#6703712yes—
683C23#6703712yes—
684C23#41×D1112yes—
685C23#41×D1112yes—
686C23C24×D1111yescharacteristic
687D4—4416no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—416no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—114no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—114no—
713C2×C4—114no—
714C2×C4—228no—
715C2×C4—228no—
716C2×C4—228no—
717C2×C4—228no—
718C2×C4—228no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—4416no—
736C2×C4—444no—
737C2×C4—444no—
738C2×C4C22×C4×D1114yes—
739C2×C4C22×C4×D1114yes—
740C2×C4C2×#433914yes—
741C2×C4C2×#433914yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—416no—
750C22—224no—
751C22—224no—
752C22—224no—
753C22—442no—
754C22—442no—
755C22—442no—
756C22—442no—
757C22—4416no—
758C22C4×#433914yes—
759C22#1062301714yes—
760C22#1062305314yes—
761C22#1062307114yes—
762C22#1062308714yes—
763C22#1062308914yes—
764C22#1062309014yes—
765C22C23×C4×D1111yescharacteristic
766C22C22×#433911yescharacteristic
767C22C22×#433911yescharacteristic
768C22C2×#6703711yescharacteristic
769C22C2×#6703711yescharacteristic
770C22C2×#41×D1111yescharacteristic
771C22C2×#41×D1111yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—224no—
779C4—224no—
780C4—224no—
781C4—224no—
782C4—224no—
783C4—442no—
784C4—442no—
785C2—44no—
786C2—444no—
787C2#1307174718yesdirect product factor
788C2C2×#1062305311yescharacteristic
789C2C2×C4×#433911yescharacteristic
790C2C2×#1062301711yescharacteristic
791C2C2×#1062308711yescharacteristic
792C2C2×#1062307111yescharacteristic
793C2C2×#1062308911yescharacteristic
794C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2374
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071747C2direct (N × H)
4. C2×#10622558C2semidirect
5. C2×#10622553C2semidirect
6. C2×#10622282C2semidirect
7. C2×#10622557C2semidirect
8. C2×#10622546C2semidirect
9. C2×#10622265C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
12. C2×#10622262C2semidirect
13. C2×C4×(C2×D11)⋊C4C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
27. C2×#66982C4semidirect
44. C4×C11×C22⋊C4C22semidirect
47. C4×C22⋊Dic11C22semidirect
58. #10622558C22semidirect
59. #10622557C22semidirect
60. #10622553C22semidirect
61. C4×(C2×D11)⋊C4C22semidirect
62. #10622546C22semidirect
63. C4×Dic11⋊C4C22semidirect
64. #10622282C22semidirect
65. #10622279C22semidirect
66. #10622265C22semidirect
67. #10622262C22semidirect
72. C23×C4×C11C2×C4semidirect
105. C2×C22⋊Dic11C2×C4semidirect
109. #66982C2×C4semidirect
123. C2×Dic11⋊C4C2×C4semidirect
124. C2×Dic11⋊C4C2×C4semidirect
187. C22×C4×C11C22×C4semidirect
238. C22⋊Dic11C22×C4semidirect
247. Dic11⋊C4C22×C4semidirect
248. Dic11⋊C4C22×C4semidirect
269. C2×C4×C22⋊C4D11semidirect
401. C4×C22⋊C4C2×D11semidirect
474. C23×C4C4×D11semidirect
538. C2×C11#2374semidirect
619. C22×C4C2×C4×D11semidirect
650. C11C2×#2374semidirect
787. C2#13071747direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
#130717472
C2×#106225702
C2×#106225582
C2×#106225532
C2×#106222822
C2×#106225572
C2×#106225462
C2×#106222652
C2×#106225692
C2×C4×Dic11⋊C42
C2×#106222622
C2×C4×(C2×D11)⋊C42
C2×C4×C22⋊Dic112
C2×#106222792
C2×C4×C11×C22⋊C42
C2×#237411