Finite Group Databasebeta

← C2×#13072199 #14921657

Subgroups — C2×#13072199 #14921657

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×#66948C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×#66937C211yesmaximal, characteristic, complemented
5C22×#66992C211yesmaximal, characteristic, complemented
6C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
7#13072199C2116yesmaximal, direct product factor
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622585C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×D44C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#66993—28no—
37C2×#66993C2218yescomplemented
38C2×#66992—28no—
39C2×#66992C2218yescomplemented
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66948—28no—
53C2×#66948C2218yescomplemented
54C2×#66937—28no—
55C2×#66937—28no—
56C2×#66937C2218yescomplemented
57C2×#66937C2218yescomplemented
58C2×(C22⋊D11)⋊C4—28no—
59C2×(C22⋊D11)⋊C4C2218yescomplemented
60C11×#394C2218yescomplemented
61C2×C11×#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622585C2218yescomplemented
66#10622573C2218yescomplemented
67#10622573C2218yescomplemented
68#10622571C2218yescomplemented
69#10622570C2218yescomplemented
70#10622569C2218yescomplemented
71#10622285C2218yescomplemented
72#10622279C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C24×D11C2311yescharacteristic
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—42no—
81C22×D4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
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—42no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11D418yescomplemented
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yes—
107C22×C22⋊D11C2314yes—
108C22×C22⋊D11C2314yes—
109C22×C22⋊D11C2314yes—
110C22×C22⋊D11C2314yes—
111C23×Dic11—24no—
112C23×Dic11—24no—
113C23×Dic11—42no—
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2314yes—
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2311yescharacteristic
120C22×D44—24no—
121C22×D44—24no—
122C22×D44—24no—
123C22×D44—24no—
124C22×D44—24no—
125C22×D44—24no—
126C22×D44—42no—
127C22×D44—42no—
128C22×D44—42no—
129C22×D44C2314yes—
130C22×D44C2314yes—
131C22×D44C2314yes—
132C22×C4×D11—24no—
133C22×C4×D11—24no—
134C22×C4×D11—24no—
135C22×C4×D11—24no—
136C22×C4×D11—24no—
137C22×C4×D11—42no—
138C22×C4×D11C2314yes—
139C22×C4×D11C2314yes—
140C2×C11×C4⋊C4—24no—
141C2×C11×C4⋊C4C2314yes—
142C2×C11×C22⋊C4—24no—
143C2×C11×C22⋊C4—24no—
144C2×C11×C22⋊C4—24no—
145C2×C11×C22⋊C4—42no—
146C2×C11×C22⋊C4C2314yes—
147C2×C11×C22⋊C4C2314yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C11×C22⋊C4C2314yes—
150C2×C22⋊Dic11—24no—
151C2×C22⋊Dic11C2314yes—
152#66993—232no—
153#66992—232no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4—24no—
159C2×(C2×D11)⋊C4—42no—
160C2×(C2×D11)⋊C4D418yescomplemented
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×Dic11⋊C4—24no—
169C2×Dic11⋊C4—24no—
170C2×Dic11⋊C4D418yescomplemented
171C2×Dic11⋊C4C2314yes—
172C2×Dic11⋊C4C2314yes—
173C2×Dic11⋊C4C2314yes—
174C2×C4×Dic11—24no—
175C2×C4×Dic11—24no—
176C2×C4×Dic11C2314yes—
177C2×C4×Dic11C2314yes—
178#66948—232no—
179#66937—232no—
180#66937—232no—
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×C11C2×D414yes—
201C24×C11C2412yes—
202C24×C11C2412yes—
203C24×C11C2411yescharacteristic
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
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×D11C2×D414yes—
224C23×D11C2×D414yes—
225C23×D11C2412yes—
226C23×D11C2412yes—
227C23×D11C2412yes—
228C2×D4×C11—28no—
229C2×D4×C11—28no—
230C2×D4×C11—44no—
231C2×D4×C11—416no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11C2×D414yes—
246C22×C4×C11C2×D414yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C2×C22⋊D11—232no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—28no—
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—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—416no—
271C2×C22⋊D11—416no—
272C2×C22⋊D11—416no—
273C2×C22⋊D11—416no—
274C2×C22⋊D11—416no—
275C2×C22⋊D11C2×D4116yescomplemented
276C22×Dic11—28no—
277C22×Dic11—28no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—44no—
288C22×Dic11—416no—
289C22×Dic11C2×D414yes—
290C22×Dic11C2×D414yes—
291C22×Dic11C2×D414yes—
292C22×Dic11C2×D414yes—
293C22×Dic11#4114yes—
294C22×Dic11#4114yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C2×D44—28no—
301C2×D44—28no—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44—28no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—416no—
310C2×D44—416no—
311C2×D44—416no—
312C2×C4×D11—28no—
313C2×C4×D11—28no—
314C2×C4×D11—28no—
315C2×C4×D11—28no—
316C2×C4×D11—28no—
317C2×C4×D11—44no—
318C2×C4×D11—416no—
319C2×C4×D11—416no—
320C11×C4⋊C4—28no—
321C11×C22⋊C4—28no—
322C11×C22⋊C4—28no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—44no—
325C22⋊Dic11—28no—
326(C2×D11)⋊C4—28no—
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—
332(C2×D11)⋊C4C2×D4116yescomplemented
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×#394D1111yescharacteristic, complemented
347C2×#392—111no—
348C2×#392—111no—
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—22no—
358C23×C11—22no—
359C23×C11—22no—
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—44no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11—44no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11C22×D414yes—
382C23×C11C22×D412yes—
383C23×C11C22×D412yes—
384C23×C11C22×D412yes—
385C23×C11C2×#4112yes—
386C23×C11C2×#4112yes—
387C23×C11H(5,𝔽2)12yes—
388C23×C11H(5,𝔽2)12yes—
389C23×C11C2511yescharacteristic
390C22×D11—28no—
391C22×D11—28no—
392C22×D11—28no—
393C22×D11—28no—
394C22×D11—28no—
395C22×D11—28no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
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—44no—
416C22×D11—44no—
417C22×D11—44no—
418C22×D11—44no—
419C22×D11—44no—
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×D11C22×D414yes—
431C22×D11C22×D414yes—
432D4×C11—416no—
433C2×C4×C11—28no—
434C2×C4×C11—28no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
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—22no—
448C2×C4×C11—44no—
449C2×C4×C11—44no—
450C2×C4×C11—44no—
451C2×C4×C11C22×D414yes—
452C2×C4×C11C22×D414yes—
453C22⋊D11—232no—
454C22⋊D11—416no—
455C22⋊D11—416no—
456C22⋊D11—416no—
457C22⋊D11—416no—
458C22⋊D11—416no—
459C2×Dic11—28no—
460C2×Dic11—28no—
461C2×Dic11—28no—
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—416no—
472C2×Dic11—44no—
473C2×Dic11#121116yescomplemented
474C2×Dic11C22×D414yes—
475C2×Dic11C22×D414yes—
476C2×Dic11C22×D414yes—
477C2×Dic11C22×D414yes—
478C2×Dic11C2×#4114yes—
479C2×Dic11C2×#4114yes—
480D44—416no—
481D44—416no—
482D44—416no—
483C4×D11—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×D4—111no—
493C23×D4—111no—
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⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
523C22×C22⋊C4C2×D1111yescharacteristic
524C22×C22⋊C4C2×D1111yescharacteristic
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C42—111no—
527C22×C42—111no—
528#394—118no—
529#394C2×D1118yescomplemented
530#392—118no—
531#392—118no—
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—42no—
545C22×C11—416no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—88no—
557C22×C11C2×#12114yes—
558C22×C11#53214yes—
559C22×C11#54014yes—
560C22×C11D4214yes—
561C22×C11D4214yes—
562C22×C11#54614yes—
563C22×C11#55014yes—
564C22×C11C23×D411yescharacteristic
565C22×C11C23×D411yescharacteristic
566C22×C11C23×D411yescharacteristic
567C22×C11C22×#4111yescharacteristic
568C22×C11C22×#4111yescharacteristic
569C22×C11C2×H(5,𝔽2)11yescharacteristic
570C22×C11C2×H(5,𝔽2)11yescharacteristic
571C2×D11—24no—
572C2×D11—24no—
573C2×D11—24no—
574C2×D11—24no—
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—416no—
580C2×D11—416no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
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—
599C4×C11—42no—
600Dic11—24no—
601Dic11—24no—
602Dic11—24no—
603Dic11—42no—
604Dic11C2×#12118yescomplemented
605C25—111no—
606C25—111no—
607C25—111no—
608C25C22×D1111yescharacteristic
609C25C22×D1111yescharacteristic
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—42no—
613C22×D4—118no—
614C22×D4—114no—
615C22×D4—114no—
616C22×D4—114no—
617C22×D4—114no—
618C22×D4—114no—
619C22×D4—114no—
620C22×D4—114no—
621C22×D4—114no—
622C22×D4—114no—
623C22×D4—224no—
624C22×D4—224no—
625C22×D4—224no—
626C22×D4—224no—
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×D4—442no—
648C22×D4—442no—
649C22×D4C22×D1114yes—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—114no—
656C23×C4—114no—
657C23×C4—114no—
658C23×C4—224no—
659C23×C4—224no—
660C23×C4—224no—
661C23×C4—224no—
662C23×C4—224no—
663C23×C4—224no—
664C23×C4—224no—
665C23×C4—442no—
666C23×C4—442no—
667C23×C4C22×D1111yescharacteristic
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—24no—
679C2×C4⋊C4—118no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—114no—
682C2×C4⋊C4—114no—
683C2×C4⋊C4—224no—
684C2×C4⋊C4—224no—
685C2×C4⋊C4C22×D1114yes—
686C2×C22⋊C4—24no—
687C2×C22⋊C4—24no—
688C2×C22⋊C4—24no—
689C2×C22⋊C4—42no—
690C2×C22⋊C4—118no—
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—442no—
706C2×C22⋊C4C22×D1114yes—
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—82no—
720C2×C11#242818yescomplemented
721C2×C11C22×#12111yescharacteristic
722C2×C11C2×#53211yescharacteristic
723C2×C11C2×#54011yescharacteristic
724C2×C11C2×D4211yescharacteristic
725C2×C11C2×D4211yescharacteristic
726C2×C11C2×#54611yescharacteristic
727C2×C11C2×#55011yescharacteristic
728D11—44no—
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—114no—
745C24—114no—
746C24—112no—
747C24—112no—
748C24—112no—
749C24—222no—
750C24—222no—
751C24—222no—
752C24—222no—
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—
766C24—222no—
767C24—222no—
768C24D4×D1114yes—
769C24C23×D1112yes—
770C24C23×D1112yes—
771C24C23×D1111yescharacteristic
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—44no—
775C2×D4—416no—
776C2×D4—1116no—
777C2×D4—228no—
778C2×D4—228no—
779C2×D4—228no—
780C2×D4—228no—
781C2×D4—228no—
782C2×D4—2232no—
783C2×D4—228no—
784C2×D4—228no—
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—228no—
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—444no—
798C2×D4—444no—
799C2×D4—444no—
800C2×D4—4416no—
801C2×D4—4416no—
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—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—114no—
826C22×C4—114no—
827C22×C4—114no—
828C22×C4—112no—
829C22×C4—114no—
830C22×C4—114no—
831C22×C4—114no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—228no—
837C22×C4—228no—
838C22×C4—228no—
839C22×C4—228no—
840C22×C4—228no—
841C22×C4—228no—
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—228no—
852C22×C4—444no—
853C22×C4—4416no—
854C22×C4—4416no—
855C22×C4—444no—
856C22×C4—4416no—
857C22×C4D4×D1114yes—
858C22×C4D4×D1114yes—
859C22×C4C23×D1112yes—
860C22×C4C23×D1112yes—
861C22×C4C23×D1112yes—
862C22×C4C23×D1112yes—
863C22×C4C23×D1112yes—
864C4⋊C4—28no—
865C4⋊C4—1116no—
866C4⋊C4—228no—
867C4⋊C4—228no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—44no—
872C22⋊C4—1116no—
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—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—44no—
900C23—44no—
901C23—44no—
902C23—44no—
903C23—44no—
904C23—44no—
905C23—44no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—114no—
911C23—114no—
912C23—228no—
913C23—228no—
914C23—228no—
915C23—228no—
916C23—228no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—228no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—444no—
938C23—444no—
939C23—444no—
940C23—444no—
941C23—444no—
942C23—444no—
943C23—444no—
944C23—444no—
945C23—444no—
946C23—444no—
947C23—444no—
948C23—444no—
949C23—444no—
950C23—444no—
951C23—444no—
952C23C2×D4×D1114yes—
953C23C2×D4×D1112yes—
954C23C2×D4×D1112yes—
955C23C2×D4×D1112yes—
956C23#6703712yes—
957C23#41×D1112yes—
958C23#41×D1112yes—
959C23#6704212yes—
960C23C24×D1111yescharacteristic
961D4—416no—
962D4—2232no—
963D4—4416no—
964D4—4416no—
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—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—1116no—
990C2×C4—114no—
991C2×C4—114no—
992C2×C4—114no—
993C2×C4—114no—
994C2×C4—114no—
995C2×C4—114no—
996C2×C4—228no—
997C2×C4—228no—
998C2×C4—228no—
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—222no—
1008C2×C4—4416no—
1009C2×C4—4416no—
1010C2×C4—4416no—
1011C2×C4—444no—
1012C2×C4C2×D4×D1114yes—
1013C2×C4C2×D4×D1114yes—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—42no—
1018C22—416no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—88no—
1030C22—224no—
1031C22—224no—
1032C22—224no—
1033C22—224no—
1034C22—224no—
1035C22—224no—
1036C22—442no—
1037C22—4416no—
1038C22—4416no—
1039C22—442no—
1040C22—442no—
1041C22—442no—
1042C22—442no—
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#1062313014yes—
1056C22D11×#12114yes—
1057C22#1062314014yes—
1058C22#1062318514yes—
1059C22#1062319414yes—
1060C22#1062319914yes—
1061C22C22×D4×D1111yescharacteristic
1062C22C22×D4×D1111yescharacteristic
1063C22C22×D4×D1111yescharacteristic
1064C22C2×#6703711yescharacteristic
1065C22C2×#41×D1111yescharacteristic
1066C22C2×#41×D1111yescharacteristic
1067C22C2×#6704211yescharacteristic
1068C4—24no—
1069C4—24no—
1070C4—42no—
1071C4—42no—
1072C4—42no—
1073C4—118no—
1074C4—224no—
1075C4—224no—
1076C4—224no—
1077C4—442no—
1078C2—44no—
1079C2—82no—
1080C2—444no—
1081C2—444no—
1082C2—882no—
1083C2#1307219918yesdirect product factor
1084C2C2×D11×#12111yescharacteristic
1085C2C2×#1062319911yescharacteristic
1086C2C2×#1062319411yescharacteristic
1087C2C2×#1062312111yescharacteristic
1088C2C2×#1062314011yescharacteristic
1089C2C2×#1062318511yescharacteristic
1090C2C2×#1062313011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66993C2semidirect
2. C22×#66948C2semidirect
3. C22×#66937C2semidirect
4. C22×#66937C2semidirect
5. C22×#66992C2semidirect
6. C22×(C22⋊D11)⋊C4C2semidirect
7. #13072199C2direct (N × H)
8. C2×#10622285C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622585C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#394C2semidirect
37. C2×#66993C22semidirect
39. C2×#66992C22semidirect
53. C2×#66948C22semidirect
56. C2×#66937C22semidirect
57. C2×#66937C22semidirect
59. C2×(C22⋊D11)⋊C4C22semidirect
60. C11×#394C22semidirect
65. #10622585C22semidirect
66. #10622573C22semidirect
67. #10622573C22semidirect
68. #10622571C22semidirect
69. #10622570C22semidirect
70. #10622569C22semidirect
71. #10622285C22semidirect
72. #10622279C22semidirect
104. C22×C22⋊D11D4semidirect
160. C2×(C2×D11)⋊C4D4semidirect
170. C2×Dic11⋊C4D4semidirect
275. C2×C22⋊D11C2×D4semidirect
332. (C2×D11)⋊C4C2×D4semidirect
335. Dic11⋊C4C2×D4semidirect
346. C2×#394D11semidirect
473. C2×Dic11#121semidirect
529. #394C2×D11semidirect
604. Dic11C2×#121semidirect
720. C2×C11#2428semidirect
882. C11C2×#2428semidirect
1083. C2#13072199direct (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×#669482
C22×#669372
C22×#669922
C22×(C22⋊D11)⋊C42
#130721992
C2×#106222852
C2×#106225732
C2×#106225702
C2×#106225852
C2×#106225712
C2×#106225692
C2×#106222792
C2×C11×#3942
C2×#242811