Finite Group Databasebeta

← C2×#13072197 #14921653

Subgroups — C2×#13072197 #14921653

Order 2816.

5062 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×#66992C211yesmaximal, characteristic, complemented
5C22×#66991C211yesmaximal, characteristic, complemented
6C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
7#13072197C2116yesmaximal, direct product factor
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic
28C23×D44C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C2×#66993—28no—
38C2×#66993C2218yescomplemented
39C2×#66992—28no—
40C2×#66992—28no—
41C2×#66992—28no—
42C2×#66992C2218yescomplemented
43C2×#66992C2218yescomplemented
44C2×#66992C2218yescomplemented
45C2×#66991—28no—
46C2×#66991C2218yescomplemented
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×C4⋊Dic11C2211yescharacteristic
53C22×Dic11⋊C4C2211yescharacteristic
54C22×Dic11⋊C4C2211yescharacteristic
55C22×Dic11⋊C4C2211yescharacteristic
56C22×C4×Dic11C2211yescharacteristic
57C22×C4×Dic11C2211yescharacteristic
58C2×(C22⋊D11)⋊C4—28no—
59C2×(C22⋊D11)⋊C4C2218yescomplemented
60C11×#392C2218yescomplemented
61C2×C11×#95C2211yescharacteristic
62#10622833C2218yescomplemented
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622574C2218yescomplemented
67#10622573C2218yescomplemented
68#10622572C2218yescomplemented
69#10622570C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71#10622278C2218yescomplemented
72#10622260C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C25×C11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C24×D11C2311yescharacteristic
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—42no—
85C22×D4×C11—42no—
86C22×D4×C11—42no—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C22×D4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—24no—
105C22×C22⋊D11—24no—
106C22×C22⋊D11—24no—
107C22×C22⋊D11—42no—
108C22×C22⋊D11—42no—
109C22×C22⋊D11—42no—
110C22×C22⋊D11—42no—
111C22×C22⋊D11D418yescomplemented
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yes—
115C22×C22⋊D11C2314yes—
116C22×C22⋊D11C2314yes—
117C22×C22⋊D11C2314yes—
118C23×Dic11—24no—
119C23×Dic11—24no—
120C23×Dic11—24no—
121C23×Dic11—24no—
122C23×Dic11—24no—
123C23×Dic11—42no—
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C23×Dic11C2314yes—
127C23×Dic11C2314yes—
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×D44—24no—
133C22×D44—24no—
134C22×D44—42no—
135C22×D44C2314yes—
136C22×C4×D11—24no—
137C22×C4×D11—24no—
138C22×C4×D11—42no—
139C22×C4×D11C2314yes—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—42no—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11—24no—
148C2×C22⋊Dic11—24no—
149C2×C22⋊Dic11D418yescomplemented
150C2×C22⋊Dic11C2314yes—
151C2×C22⋊Dic11C2314yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2314yes—
154#66993—232no—
155#66992—232no—
156#66992—232no—
157#66992—232no—
158#66991—232no—
159C2×(C2×D11)⋊C4—24no—
160C2×(C2×D11)⋊C4—24no—
161C2×(C2×D11)⋊C4—24no—
162C2×(C2×D11)⋊C4—24no—
163C2×(C2×D11)⋊C4—42no—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×C4⋊Dic11—24no—
170C2×C4⋊Dic11C2314yes—
171C2×Dic11⋊C4—24no—
172C2×Dic11⋊C4—24no—
173C2×Dic11⋊C4D418yescomplemented
174C2×Dic11⋊C4C2314yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2314yes—
177C2×C4×Dic11—24no—
178C2×C4×Dic11—24no—
179C2×C4×Dic11C2314yes—
180C2×C4×Dic11C2314yes—
181(C22⋊D11)⋊C4—232no—
182C11×#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C2×#2428—111nomaximal, Sylow
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—22no—
200C24×C11—22no—
201C24×C11—22no—
202C24×C11—22no—
203C24×C11—22no—
204C24×C11—22no—
205C24×C11—22no—
206C24×C11C2×D414yes—
207C24×C11C2×D414yes—
208C24×C11C2412yes—
209C24×C11C2412yes—
210C24×C11C2412yes—
211C24×C11C2411yescharacteristic
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11C2×D414yes—
226C23×D11C2412yes—
227C23×D11C2412yes—
228C2×D4×C11—28no—
229C2×D4×C11—28no—
230C2×D4×C11—28no—
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C2×D4×C11—416no—
238C2×D4×C11—416no—
239C2×D4×C11—416no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11C2×D414yes—
251C22×C4×C11#4114yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C2×C22⋊D11—232no—
257C2×C22⋊D11—28no—
258C2×C22⋊D11—28no—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—28no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—416no—
275C2×C22⋊D11—416no—
276C2×C22⋊D11—416no—
277C2×C22⋊D11—416no—
278C2×C22⋊D11—416no—
279C2×C22⋊D11C2×D4116yescomplemented
280C22×Dic11—28no—
281C22×Dic11—28no—
282C22×Dic11—28no—
283C22×Dic11—28no—
284C22×Dic11—28no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—44no—
298C22×Dic11—416no—
299C22×Dic11—416no—
300C22×Dic11C2×D414yes—
301C22×Dic11C2×D414yes—
302C22×Dic11C2×D414yes—
303C22×Dic11C2×D414yes—
304C22×Dic11C2×D414yes—
305C22×Dic11#4114yes—
306C22×Dic11C2412yes—
307C22×Dic11C2412yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C2×D44—28no—
313C2×D44—28no—
314C2×D44—44no—
315C2×D44—416no—
316C2×C4×D11—28no—
317C2×C4×D11—28no—
318C2×C4×D11—44no—
319C2×C4×D11—416no—
320C11×C22⋊C4—28no—
321C11×C22⋊C4—28no—
322C11×C22⋊C4—44no—
323C22⋊Dic11—28no—
324C22⋊Dic11—28no—
325C22⋊Dic11—28no—
326C22⋊Dic11C2×D4116yescomplemented
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—44no—
332C4⋊Dic11—28no—
333Dic11⋊C4—28no—
334Dic11⋊C4—28no—
335Dic11⋊C4C2×D4116yescomplemented
336C4×Dic11—28no—
337C4×Dic11—28no—
338C22×#127—111no—
339C22×#121—111no—
340C22×#121—111no—
341C22×#121—111no—
342C22×#121—111no—
343C22×C4×D4—111no—
344#2428—1116no—
345C2×#394—111no—
346C2×#394—111no—
347C2×#392—111no—
348C2×#392D1111yescharacteristic, complemented
349C2×#390—111no—
350C2×#389—111no—
351C2×#386—111no—
352C2×#386—111no—
353C2×C4×C22⋊C4—111no—
354C23×C11—28no—
355C23×C11—28no—
356C23×C11—28no—
357C23×C11—28no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11—44no—
385C23×C11—44no—
386C23×C11—44no—
387C23×C11—44no—
388C23×C11—44no—
389C23×C11—44no—
390C23×C11—44no—
391C23×C11—44no—
392C23×C11—44no—
393C23×C11—44no—
394C23×C11C22×D414yes—
395C23×C11C22×D414yes—
396C23×C11C22×D412yes—
397C23×C11C22×D412yes—
398C23×C11C22×D412yes—
399C23×C11C2×#4112yes—
400C23×C11C2×#4112yes—
401C23×C11H(5,𝔽2)12yes—
402C23×C11H(5,𝔽2)12yes—
403C23×C11C2511yescharacteristic
404C22×D11—28no—
405C22×D11—28no—
406C22×D11—28no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—44no—
421C22×D11—44no—
422C22×D11—44no—
423C22×D11—44no—
424C22×D11—44no—
425C22×D11—44no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—44no—
431C22×D11C22×D414yes—
432D4×C11—416no—
433D4×C11—416no—
434D4×C11—416no—
435C2×C4×C11—28no—
436C2×C4×C11—28no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—44no—
448C2×C4×C11—44no—
449C2×C4×C11C22×D414yes—
450C2×C4×C11C2×#4114yes—
451C22⋊D11—232no—
452C22⋊D11—416no—
453C22⋊D11—416no—
454C22⋊D11—416no—
455C22⋊D11—416no—
456C22⋊D11—416no—
457C2×Dic11—28no—
458C2×Dic11—28no—
459C2×Dic11—28no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—416no—
473C2×Dic11—44no—
474C2×Dic11—44no—
475C2×Dic11—416no—
476C2×Dic11#121116yescomplemented
477C2×Dic11C22×D414yes—
478C2×Dic11C22×D414yes—
479C2×Dic11C22×D414yes—
480C2×Dic11C22×D414yes—
481C2×Dic11C22×D414yes—
482C2×Dic11C2×#4114yes—
483D44—416no—
484C4×D11—416no—
485C23×D4—111no—
486C23×D4—111no—
487C23×D4—111no—
488C23×D4—111no—
489C23×D4—111no—
490C23×D4—111no—
491C23×D4—111no—
492C23×D4C2×D1111yescharacteristic
493C23×D4C2×D1111yescharacteristic
494C23×D4C2×D1111yescharacteristic
495C24×C4—111no—
496C24×C4—111no—
497C24×C4—111no—
498C2×#127—118no—
499C2×#127—228no—
500C2×#121—118no—
501C2×#121—118no—
502C2×#121—118no—
503C2×#121—118no—
504C2×#121—228no—
505C2×#121—228no—
506C2×#121—228no—
507C2×#121—228no—
508C2×C4×D4—118no—
509C2×C4×D4—228no—
510C22×C4⋊C4—111no—
511C22×C4⋊C4—111no—
512C22×C4⋊C4—111no—
513C22×C4⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4C2×D1111yescharacteristic
524C22×C22⋊C4C2×D1111yescharacteristic
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C42—111no—
527C22×C42—111no—
528#394—118no—
529#394—118no—
530#392—118no—
531#392C2×D1118yescomplemented
532#390—118no—
533#389—118no—
534#386—118no—
535#386—118no—
536C4×C22⋊C4—118no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95C2×D1111yescharacteristic
541C22×C11—24no—
542C22×C11—24no—
543C22×C11—24no—
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—416no—
550C22×C11—416no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—88no—
565C22×C11C2×#12114yes—
566C22×C11#53214yes—
567C22×C11#54014yes—
568C22×C11D4214yes—
569C22×C11D4214yes—
570C22×C11#54614yes—
571C22×C11#55014yes—
572C22×C11C23×D411yescharacteristic
573C22×C11C23×D411yescharacteristic
574C22×C11C23×D411yescharacteristic
575C22×C11C22×#4111yescharacteristic
576C22×C11C22×#4111yescharacteristic
577C22×C11C2×H(5,𝔽2)11yescharacteristic
578C22×C11C2×H(5,𝔽2)11yescharacteristic
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—42no—
583C2×D11—416no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—88no—
595C4×C11—24no—
596C4×C11—24no—
597C4×C11—42no—
598C4×C11—42no—
599Dic11—24no—
600Dic11—24no—
601Dic11—24no—
602Dic11—42no—
603Dic11—42no—
604Dic11C2×#12118yescomplemented
605C25—111no—
606C25—111no—
607C25C22×D1111yescharacteristic
608C25C22×D1111yescharacteristic
609C25C22×D1111yescharacteristic
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—24no—
615C22×D4—24no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—118no—
620C22×D4—114no—
621C22×D4—114no—
622C22×D4—114no—
623C22×D4—114no—
624C22×D4—114no—
625C22×D4—114no—
626C22×D4—114no—
627C22×D4—224no—
628C22×D4—224no—
629C22×D4—224no—
630C22×D4—224no—
631C22×D4—224no—
632C22×D4—224no—
633C22×D4—224no—
634C22×D4—224no—
635C22×D4—224no—
636C22×D4—224no—
637C22×D4—224no—
638C22×D4—224no—
639C22×D4—224no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—442no—
643C22×D4—442no—
644C22×D4—442no—
645C22×D4—442no—
646C22×D4—442no—
647C22×D4C22×D1114yes—
648C22×D4C22×D1114yes—
649C22×D4C22×D1114yes—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—114no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—114no—
658C23×C4—114no—
659C23×C4—224no—
660C23×C4—224no—
661C23×C4—224no—
662C23×C4—224no—
663C23×C4—224no—
664C23×C4—224no—
665C23×C4—224no—
666C23×C4—442no—
667C23×C4—442no—
668C23×C4C22×D1111yescharacteristic
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672#127—2232no—
673#121—2232no—
674#121—2232no—
675#121—2232no—
676#121—2232no—
677C4×D4—2232no—
678C2×C4⋊C4—118no—
679C2×C4⋊C4—114no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—114no—
682C2×C4⋊C4—114no—
683C2×C4⋊C4—224no—
684C2×C4⋊C4—224no—
685C2×C4⋊C4—224no—
686C2×C22⋊C4—24no—
687C2×C22⋊C4—24no—
688C2×C22⋊C4—42no—
689C2×C22⋊C4—118no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—114no—
692C2×C22⋊C4—114no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—224no—
700C2×C22⋊C4—224no—
701C2×C22⋊C4—224no—
702C2×C22⋊C4—224no—
703C2×C22⋊C4—224no—
704C2×C22⋊C4—224no—
705C2×C22⋊C4—224no—
706C2×C22⋊C4—442no—
707C2×C22⋊C4C22×D1114yes—
708C2×C22⋊C4C22×D1114yes—
709C2×C22⋊C4C22×D1114yes—
710C2×C42—114no—
711C2×C42—114no—
712C2×C42—224no—
713C2×C42—224no—
714#95—114no—
715#95—114no—
716#95—114no—
717#95C22×D1114yes—
718C2×C11—44no—
719C2×C11—44no—
720C2×C11—82no—
721C2×C11#242818yescomplemented
722C2×C11C22×#12111yescharacteristic
723C2×C11C2×#53211yescharacteristic
724C2×C11C2×#54011yescharacteristic
725C2×C11C2×D4211yescharacteristic
726C2×C11C2×D4211yescharacteristic
727C2×C11C2×#54611yescharacteristic
728C2×C11C2×#55011yescharacteristic
729D11—44no—
730D11—82no—
731C24—22no—
732C24—22no—
733C24—22no—
734C24—22no—
735C24—22no—
736C24—22no—
737C24—22no—
738C24—22no—
739C24—22no—
740C24—22no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—114no—
751C24—112no—
752C24—112no—
753C24—222no—
754C24—222no—
755C24—222no—
756C24—222no—
757C24—222no—
758C24—222no—
759C24—222no—
760C24—222no—
761C24—222no—
762C24—222no—
763C24—222no—
764C24—222no—
765C24—222no—
766C24D4×D1114yes—
767C24D4×D1114yes—
768C24C23×D1112yes—
769C24C23×D1112yes—
770C24C23×D1112yes—
771C24C23×D1111yescharacteristic
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—416no—
782C2×D4—416no—
783C2×D4—416no—
784C2×D4—1116no—
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—2232no—
788C2×D4—228no—
789C2×D4—228no—
790C2×D4—228no—
791C2×D4—228no—
792C2×D4—228no—
793C2×D4—228no—
794C2×D4—228no—
795C2×D4—228no—
796C2×D4—228no—
797C2×D4—228no—
798C2×D4—228no—
799C2×D4—228no—
800C2×D4—228no—
801C2×D4—444no—
802C2×D4—4416no—
803C2×D4—4416no—
804C2×D4—444no—
805C2×D4—444no—
806C2×D4—444no—
807C2×D4—444no—
808C2×D4—4416no—
809C2×D4—4416no—
810C2×D4—4416no—
811C2×D4—4416no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—114no—
823C22×C4—114no—
824C22×C4—114no—
825C22×C4—112no—
826C22×C4—114no—
827C22×C4—114no—
828C22×C4—114no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—228no—
835C22×C4—228no—
836C22×C4—228no—
837C22×C4—228no—
838C22×C4—228no—
839C22×C4—228no—
840C22×C4—222no—
841C22×C4—222no—
842C22×C4—222no—
843C22×C4—222no—
844C22×C4—222no—
845C22×C4—222no—
846C22×C4—222no—
847C22×C4—222no—
848C22×C4—222no—
849C22×C4—222no—
850C22×C4—222no—
851C22×C4—222no—
852C22×C4—228no—
853C22×C4—444no—
854C22×C4—4416no—
855C22×C4—4416no—
856C22×C4—444no—
857C22×C4—4416no—
858C22×C4D4×D1114yes—
859C22×C4#434114yes—
860C22×C4C23×D1112yes—
861C22×C4C23×D1112yes—
862C22×C4C23×D1112yes—
863C22×C4C23×D1112yes—
864C4⋊C4—1116no—
865C4⋊C4—228no—
866C4⋊C4—228no—
867C4⋊C4—228no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—1116no—
872C22⋊C4—228no—
873C22⋊C4—228no—
874C22⋊C4—228no—
875C22⋊C4—228no—
876C22⋊C4—228no—
877C22⋊C4—228no—
878C22⋊C4—228no—
879C22⋊C4—444no—
880C42—228no—
881C42—228no—
882C11C2×#242811yescharacteristic, complemented, Sylow
883C23—28no—
884C23—28no—
885C23—28no—
886C23—28no—
887C23—28no—
888C23—28no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—44no—
922C23—44no—
923C23—114no—
924C23—228no—
925C23—228no—
926C23—228no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—444no—
941C23—444no—
942C23—444no—
943C23—444no—
944C23—444no—
945C23—444no—
946C23—444no—
947C23—444no—
948C23—444no—
949C23—444no—
950C23—444no—
951C23C2×D4×D1114yes—
952C23C2×D4×D1114yes—
953C23C2×D4×D1112yes—
954C23C2×D4×D1112yes—
955C23C2×D4×D1112yes—
956C23C2×#434112yes—
957C23#6703712yes—
958C23#6703712yes—
959C23#41×D1112yes—
960C23C24×D1111yescharacteristic
961D4—416no—
962D4—416no—
963D4—416no—
964D4—2232no—
965D4—4416no—
966D4—4416no—
967D4—4416no—
968D4—4416no—
969D4—4416no—
970D4—4416no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—1116no—
986C2×C4—114no—
987C2×C4—114no—
988C2×C4—114no—
989C2×C4—114no—
990C2×C4—114no—
991C2×C4—114no—
992C2×C4—228no—
993C2×C4—228no—
994C2×C4—228no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—4416no—
1008C2×C4—4416no—
1009C2×C4—4416no—
1010C2×C4—444no—
1011C2×C4—444no—
1012C2×C4C2×D4×D1114yes—
1013C2×C4C2×#434114yes—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—42no—
1021C22—416no—
1022C22—416no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—88no—
1038C22—224no—
1039C22—224no—
1040C22—224no—
1041C22—442no—
1042C22—4416no—
1043C22—442no—
1044C22—442no—
1045C22—442no—
1046C22—442no—
1047C22—442no—
1048C22—442no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—442no—
1053C22—888no—
1054C22#1062312114yes—
1055C22#1062312114yes—
1056C22#1062312214yes—
1057C22#1062312714yes—
1058C22D11×#12114yes—
1059C22#1062314614yes—
1060C22#1062324914yes—
1061C22C22×D4×D1111yescharacteristic
1062C22C22×D4×D1111yescharacteristic
1063C22C22×D4×D1111yescharacteristic
1064C22C22×#434111yescharacteristic
1065C22C2×#6703711yescharacteristic
1066C22C2×#6703711yescharacteristic
1067C22C2×#41×D1111yescharacteristic
1068C4—24no—
1069C4—24no—
1070C4—42no—
1071C4—42no—
1072C4—118no—
1073C4—224no—
1074C4—224no—
1075C4—224no—
1076C4—442no—
1077C4—442no—
1078C2—44no—
1079C2—44no—
1080C2—82no—
1081C2—444no—
1082C2—882no—
1083C2#1307219718yesdirect product factor
1084C2C2×D11×#12111yescharacteristic
1085C2C2×#1062312711yescharacteristic
1086C2C2×#1062314611yescharacteristic
1087C2C2×#1062312111yescharacteristic
1088C2C2×#1062312111yescharacteristic
1089C2C2×#1062312211yescharacteristic
1090C2C2×#1062324911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66993C2semidirect
2. C22×#66992C2semidirect
3. C22×#66992C2semidirect
4. C22×#66992C2semidirect
5. C22×#66991C2semidirect
6. C22×(C22⋊D11)⋊C4C2semidirect
7. #13072197C2direct (N × H)
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622260C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622278C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#392C2semidirect
38. C2×#66993C22semidirect
42. C2×#66992C22semidirect
43. C2×#66992C22semidirect
44. C2×#66992C22semidirect
46. C2×#66991C22semidirect
59. C2×(C22⋊D11)⋊C4C22semidirect
60. C11×#392C22semidirect
62. #10622833C22semidirect
66. #10622574C22semidirect
67. #10622573C22semidirect
68. #10622572C22semidirect
69. #10622570C22semidirect
70. C22⋊C4×Dic11C22semidirect
71. #10622278C22semidirect
72. #10622260C22semidirect
111. C22×C22⋊D11D4semidirect
149. C2×C22⋊Dic11D4semidirect
173. C2×Dic11⋊C4D4semidirect
279. C2×C22⋊D11C2×D4semidirect
326. C22⋊Dic11C2×D4semidirect
335. Dic11⋊C4C2×D4semidirect
348. C2×#392D11semidirect
476. C2×Dic11#121semidirect
531. #392C2×D11semidirect
604. Dic11C2×#121semidirect
721. C2×C11#2428semidirect
882. C11C2×#2428semidirect
1083. C2#13072197direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669922
C22×#669912
C22×(C22⋊D11)⋊C42
#130721972
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106225702
C2×#106222602
C2×#106228332
C2×#106222782
C2×C22⋊C4×Dic112
C2×C11×#3922
C2×#242811