Finite Group Databasebeta

← C2×#13073679 #14923855

Subgroups — C2×#13073679 #14923855

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3#13073679C2116yesmaximal, direct product factor
4C2×#10622607C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622284C211yesmaximal, characteristic
7C2×#10622601C211yesmaximal, characteristic, complemented
8C2×#10622601C211yesmaximal, characteristic, complemented
9C2×#10622601C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622603C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#398C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66951—28no—
47C2×#66951C2218yescomplemented
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C11×#398C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622607C2218yescomplemented
58#10622603C2218yescomplemented
59#10622603C2218yescomplemented
60#10622601C2218yescomplemented
61#10622601C2218yescomplemented
62#10622601C2218yescomplemented
63#10622285C2218yescomplemented
64#10622284C2218yes—
65#10622283C2218yescomplemented
66#10622279C2218yescomplemented
67#10622278C2218yescomplemented
68#10622262C2218yescomplemented
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×D44—24no—
85C22×D44—24no—
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—42no—
90C22×D44—42no—
91C22×D44—42no—
92C22×D44—42no—
93C22×D44C2314yes—
94C22×D44C2314yes—
95C22×D44C2314yes—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—42no—
99C22×C4×D11C2314yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—42no—
103C2×C11×C4⋊C4—42no—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—24no—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11C2314yes—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4D418yescomplemented
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—42no—
145C2×C4×Dic11—42no—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150#66951—232no—
151#66947—232no—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11×#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2554—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11#4114yes—
181C23×D11C2412yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11#4114yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11C2×D414yes—
225C22×Dic11C2×D414yes—
226C22×Dic11#4114yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C2×D44—28no—
233C2×D44—28no—
234C2×D44—28no—
235C2×D44—28no—
236C2×D44—28no—
237C2×D44—44no—
238C2×D44—44no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—416no—
242C2×D44—416no—
243C2×D44—416no—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—44no—
247C2×C4×D11—416no—
248C11×C4⋊C4—28no—
249C11×C4⋊C4—28no—
250C11×C4⋊C4—44no—
251C11×C4⋊C4—44no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—28no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266C4⋊Dic11—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4C2×D4116yescomplemented
269C4×Dic11—28no—
270C4×Dic11—28no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#126—111no—
274C22×#123—111no—
275#2554—1116no—
276C2×#398D1111yescharacteristic, complemented
277C2×#396—111no—
278C2×#394—111no—
279C2×#392—111no—
280C2×#390—111no—
281C2×#390—111no—
282C2×#390—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#388—111no—
286C2×#386—111no—
287C2×C4×C4⋊C4—111no—
288C2×C4×C22⋊C4—111no—
289C23×C11C22×D412yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292C23×C11C2×#4112yes—
293C23×C11C2×#4112yes—
294C23×C11H(5,𝔽2)12yes—
295C23×C11H(5,𝔽2)12yes—
296C23×C11C2511yescharacteristic
297C22×D11—28no—
298C22×D11—28no—
299C22×D11—28no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—44no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11C2×#4114yes—
339C2×C4×C11—28no—
340C2×C4×C11—28no—
341C2×C4×C11—28no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C2×C4×C11C22×D414yes—
365C2×C4×C11C2×#4114yes—
366C2×C4×C11C2×#4114yes—
367C2×Dic11—28no—
368C2×Dic11—28no—
369C2×Dic11—28no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—44no—
383C2×Dic11—44no—
384C2×Dic11C22×D414yes—
385C2×Dic11C22×D414yes—
386C2×Dic11C2×#4114yes—
387D44—416no—
388D44—416no—
389D44—416no—
390C4×D11—416no—
391C23×D4—111no—
392C23×D4—111no—
393C23×D4—111no—
394C24×C4—111no—
395C2×#126—118no—
396C2×#126—228no—
397C2×#123—118no—
398C2×#123—228no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4C2×D1111yescharacteristic
403C22×C4⋊C4C2×D1111yescharacteristic
404C22×C4⋊C4C2×D1111yescharacteristic
405C22×C4⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C42—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#398C2×D1118yescomplemented
425#396—118no—
426#394—118no—
427#392—118no—
428#390—118no—
429#390—118no—
430#390—118no—
431#388—118no—
432#388—118no—
433#388—118no—
434#386—118no—
435C4×C4⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95C2×D1111yescharacteristic
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C22×C11#52914yes—
444C22×C11#53214yes—
445C22×C11#53814yes—
446C22×C11#54614yes—
447C22×C11#55014yes—
448C22×C11#55114yes—
449C22×C11#55314yes—
450C22×C11C23×D411yescharacteristic
451C22×C11C22×#4111yescharacteristic
452C22×C11C22×#4111yescharacteristic
453C22×C11C22×#4111yescharacteristic
454C22×C11C22×#4111yescharacteristic
455C22×C11C2×H(5,𝔽2)11yescharacteristic
456C22×C11C2×H(5,𝔽2)11yescharacteristic
457C2×D11—24no—
458C2×D11—24no—
459C2×D11—24no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—416no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—88no—
480C2×D11—88no—
481C4×C11—24no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—24no—
490Dic11—24no—
491Dic11—42no—
492Dic11—42no—
493C25—111no—
494C25—111no—
495C25—111no—
496C22×D4—114no—
497C22×D4—114no—
498C22×D4—114no—
499C22×D4—224no—
500C22×D4—224no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—442no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4—442no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—114no—
514C23×C4—224no—
515C23×C4—224no—
516C23×C4—442no—
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#126—2232no—
525#123—2232no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—42no—
529C2×C4⋊C4—42no—
530C2×C4⋊C4—118no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—224no—
536C2×C4⋊C4C22×D1114yes—
537C2×C4⋊C4C22×D1114yes—
538C2×C4⋊C4C22×D1114yes—
539C2×C4⋊C4C22×D1114yes—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C42—114no—
569C2×C42—114no—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—224no—
573C2×C42—224no—
574C2×C42—442no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95C22×D1114yes—
580#95C22×D1114yes—
581#95C22×D1114yes—
582C2×C11#255418yescomplemented
583C2×C11C2×#52911yescharacteristic
584C2×C11C2×#53211yescharacteristic
585C2×C11C2×#53811yescharacteristic
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#55011yescharacteristic
588C2×C11C2×#55111yescharacteristic
589C2×C11C2×#55311yescharacteristic
590D11—44no—
591D11—82no—
592D11—82no—
593C24—114no—
594C24—112no—
595C24—112no—
596C24—112no—
597C24—222no—
598C24—222no—
599C24—222no—
600C24—222no—
601C24—222no—
602C24—222no—
603C24—222no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24C23×D1111yescharacteristic
618C2×D4—228no—
619C2×D4—228no—
620C2×D4—228no—
621C2×D4—228no—
622C2×D4—228no—
623C2×D4—444no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—4416no—
628C2×D4—4416no—
629C2×D4—4416no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—114no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—228no—
657C22×C4—228no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—444no—
671C22×C4—4416no—
672C22×C4D4×D1114yes—
673C22×C4#434314yes—
674C22×C4#434314yes—
675C22×C4C23×D1112yes—
676C22×C4C23×D1112yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—1116no—
687C4⋊C4—228no—
688C4⋊C4—228no—
689C22⋊C4—228no—
690C22⋊C4—228no—
691C22⋊C4—228no—
692C22⋊C4—228no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—228no—
704C42—228no—
705C42—444no—
706C42—444no—
707C11C2×#255411yescharacteristic, complemented, Sylow
708C23—114no—
709C23—228no—
710C23—228no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—228no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—444no—
733C23—444no—
734C23—444no—
735C23—444no—
736C23—444no—
737C23—444no—
738C23—444no—
739C23—444no—
740C23—444no—
741C23—444no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23C2×D4×D1112yes—
751C23#6703712yes—
752C23C2×#434312yes—
753C23C2×#434312yes—
754C23#41×D1112yes—
755C23#41×D1112yes—
756C23#6704212yes—
757C23C24×D1111yescharacteristic
758D4—4416no—
759D4—4416no—
760D4—4416no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—114no—
789C2×C4—228no—
790C2×C4—228no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—228no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—4416no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4C2×D4×D1114yes—
808C2×C4C2×#434314yes—
809C2×C4C2×#434314yes—
810C22—224no—
811C22—224no—
812C22—224no—
813C22—4416no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—442no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—888no—
833C22—888no—
834C22#1062313014yes—
835C22#1062316814yes—
836C22#1062317514yes—
837C22#1062318514yes—
838C22#1062322214yes—
839C22#1062322614yes—
840C22#1062325614yes—
841C22C22×D4×D1111yescharacteristic
842C22C2×#6703711yescharacteristic
843C22C22×#434311yescharacteristic
844C22C22×#434311yescharacteristic
845C22C2×#41×D1111yescharacteristic
846C22C2×#41×D1111yescharacteristic
847C22C2×#6704211yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—224no—
856C4—224no—
857C4—224no—
858C4—442no—
859C4—442no—
860C2—444no—
861C2—882no—
862C2—882no—
863C2#1307367918yesdirect product factor
864C2C2×#1062322211yescharacteristic
865C2C2×#1062325611yescharacteristic
866C2C2×#1062317511yescharacteristic
867C2C2×#1062318511yescharacteristic
868C2C2×#1062313011yescharacteristic
869C2C2×#1062316811yescharacteristic
870C2C2×#1062322611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×#398D11
hypocenterC11C2×#2554
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66951C2semidirect
2. C22×#66947C2semidirect
3. #13073679C2direct (N × H)
4. C2×#10622607C2semidirect
5. C2×#10622285C2semidirect
7. C2×#10622601C2semidirect
8. C2×#10622601C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622603C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622262C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#398C2semidirect
47. C2×#66951C22semidirect
49. C2×#66947C22semidirect
50. C11×#398C22semidirect
57. #10622607C22semidirect
58. #10622603C22semidirect
59. #10622603C22semidirect
60. #10622601C22semidirect
61. #10622601C22semidirect
62. #10622601C22semidirect
63. #10622285C22semidirect
65. #10622283C22semidirect
66. #10622279C22semidirect
67. #10622278C22semidirect
68. #10622262C22semidirect
139. C2×Dic11⋊C4D4semidirect
268. Dic11⋊C4C2×D4semidirect
276. C2×#398D11semidirect
424. #398C2×D11semidirect
582. C2×C11#2554semidirect
707. C11C2×#2554semidirect
863. C2#13073679direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
C22×#669472
#130736792
C2×#106226072
C2×#106222852
C2×#106222842
C2×#106226012
C2×#106222832
C2×#106226032
C2×#106222782
C2×#106222622
C2×#106222792
C2×C11×#3982
C2×#255411