Finite Group Databasebeta

← C2×#13073687 #14923844

Subgroups — C2×#13073687 #14923844

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4#13073687C2116yesmaximal, direct product factor
5C2×#10622842C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×#124C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#124—28no—
27C2×C11×#124C2218yescomplemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#67000—28no—
37C2×#67000C2218yescomplemented
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×#66937—28no—
53C2×#66937C2218yescomplemented
54#10622842C2218yescomplemented
55#10622836C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622573C2218yescomplemented
63#10622572C2218yescomplemented
64#10622571C2218yescomplemented
65#10622570C2218yescomplemented
66#10622569C2218yescomplemented
67#10622558C2218yescomplemented
68C22⋊C4×Dic11C2218yescomplemented
69#10622553C2218yescomplemented
70C4×(C2×D11)⋊C4C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×Q8×C11—24no—
76C22×Q8×C11—24no—
77C22×Q8×C11—42no—
78C22×Q8×C11C2314yes—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—42no—
82C22×D4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
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—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11—42no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11—24no—
105C23×Dic11—24no—
106C23×Dic11—42no—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2314yes—
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×D44—24no—
115C22×D44—24no—
116C22×D44—42no—
117C22×D44C2314yes—
118C22×C4×D11—24no—
119C22×C4×D11—24no—
120C22×C4×D11—42no—
121C22×C4×D11C2314yes—
122C11×#124—232no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4D418yescomplemented
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C42×C11—24no—
132C2×C42×C11C2314yes—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11—24no—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139#67000—232no—
140#66992—232no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4D418yescomplemented
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11—42no—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165#66937—232no—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2555—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11C2×D414yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11C2×D414yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×Q8×C11—28no—
207C2×Q8×C11—28no—
208C2×Q8×C11—44no—
209C2×Q8×C11—416no—
210C2×D4×C11—28no—
211C2×D4×C11—28no—
212C2×D4×C11—44no—
213C2×D4×C11—416no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11C2×D414yes—
227C22×C4×C11C2×D414yes—
228C22×C4×C11C2×D414yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—416no—
247C2×C22⋊D11—416no—
248C2×C22⋊D11—416no—
249C2×C22⋊D11—416no—
250C22×Dic11—28no—
251C22×Dic11—28no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—44no—
267C22×Dic11—416no—
268C22×Dic11C2×D414yes—
269C22×Dic11#4114yes—
270C22×Dic11#4114yes—
271C22×Dic11#4114yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C2×D44—28no—
279C2×D44—28no—
280C2×D44—44no—
281C2×D44—416no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—416no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4C2×D4116yescomplemented
290C42×C11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4C2×D4116yescomplemented
301Dic11⋊C4—28no—
302Dic11⋊C4—28no—
303Dic11⋊C4—44no—
304C4×Dic11—28no—
305C4×Dic11—44no—
306C22×#124—111no—
307C22×#124D1111yescharacteristic, complemented
308C22×#121—111no—
309C22×#121—111no—
310#2555—1116no—
311C2×#395—111no—
312C2×#394—111no—
313C2×#392—111no—
314C2×#392—111no—
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×C4×C22⋊C4—111no—
321C2×C4×C22⋊C4—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11C22×D412yes—
350C23×C11C22×D414yes—
351C23×C11C22×D412yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11C2×#4112yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11C2511yescharacteristic
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11C22×D414yes—
386Q8×C11—416no—
387D4×C11—416no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C22×D414yes—
407C2×C4×C11C22×D414yes—
408C22⋊D11—416no—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C22⋊D11—416no—
412C2×Dic11—28no—
413C2×Dic11—28no—
414C2×Dic11—28no—
415C2×Dic11—28no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—416no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11C22×D414yes—
434C2×Dic11C2×#4114yes—
435C2×Dic11C2×#4114yes—
436C2×Dic11C2×#4114yes—
437D44—416no—
438C4×D11—416no—
439C23×Q8C2×D1111yescharacteristic
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C23×D4C2×D1111yescharacteristic
446C24×C4—111no—
447C24×C4—111no—
448C2×#124—28no—
449C2×#124—118no—
450C2×#124—228no—
451C2×#124C2×D1118yescomplemented
452C2×#121—118no—
453C2×#121—118no—
454C2×#121—228no—
455C2×#121—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4C2×D1111yescharacteristic
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42C2×D1111yescharacteristic
476#395—118no—
477#394—118no—
478#392—118no—
479#392—118no—
480#390—118no—
481#388—118no—
482#388—118no—
483#386—118no—
484#386—118no—
485C4×C22⋊C4—118no—
486C4×C22⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—88no—
509C22×C11#53214yes—
510C22×C11#53214yes—
511C22×C11#53814yes—
512C22×C11D4214yes—
513C22×C11#54614yes—
514C22×C11#54614yes—
515C22×C11#55514yes—
516C22×C11C23×D411yescharacteristic
517C22×C11C23×D411yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—416no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—42no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—24no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×Q8—24no—
555C22×Q8—24no—
556C22×Q8—42no—
557C22×Q8C22×D1114yes—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—114no—
562C22×D4—114no—
563C22×D4—114no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4—442no—
576C22×D4—442no—
577C22×D4—442no—
578C22×D4—442no—
579C22×D4—442no—
580C22×D4—442no—
581C22×D4C22×D1114yes—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—114no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#124—232no—
602#124—2232no—
603#121—2232no—
604#121—2232no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—224no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4—442no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—118no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—224no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4C22⋊D1118yescomplemented
635C2×C22⋊C4C22×D1114yes—
636C2×C22⋊C4C22×D1114yes—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C42—24no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—224no—
643C2×C42—442no—
644C2×C42C22×D1114yes—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11#255518yescomplemented
654C2×C11C2×#53211yescharacteristic
655C2×C11C2×#53211yescharacteristic
656C2×C11C2×#53811yescharacteristic
657C2×C11C2×D4211yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#55511yescharacteristic
661D11—44no—
662D11—82no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—114no—
677C24—112no—
678C24—112no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24C2×C22⋊D1114yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×Q8—28no—
697C2×Q8—28no—
698C2×Q8—44no—
699C2×Q8—416no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—44no—
703C2×D4—416no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—444no—
714C2×D4—4416no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—444no—
719C2×D4—444no—
720C2×D4—4416no—
721C2×D4—4416no—
722C2×D4—4416no—
723C2×D4—4416no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—114no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—114no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—228no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—228no—
764C22×C4—444no—
765C22×C4—4416no—
766C22×C4—444no—
767C22×C4—4416no—
768C22×C4D4×D1114yes—
769C22×C4C2×C22⋊D1114yes—
770C22×C4C2×C22⋊D1114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—228no—
777C4⋊C4—228no—
778C4⋊C4—444no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—1116no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4C2×C22⋊D11116yescomplemented
793C42—28no—
794C42—228no—
795C42—444no—
796C11C2×#255511yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—228no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—228no—
832C23—222no—
833C23—228no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×D4×D1112yes—
853C23#6703712yes—
854C23#41×D1112yes—
855C23#41×D1112yes—
856C23#41×D1112yes—
857C23#6704212yes—
858C23C22×C22⋊D1114yes—
859C23C22×C22⋊D1112yes—
860C23C24×D1111yescharacteristic
861Q8—416no—
862D4—416no—
863D4—4416no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867D4—4416no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—114no—
889C2×C4—228no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—228no—
899C2×C4—228no—
900C2×C4—228no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—4416no—
908C2×C4—4416no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4C2×D4×D1114yes—
912C2×C4C22×C22⋊D1114yes—
913C2×C4C22×C22⋊D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—416no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—88no—
930C22—224no—
931C22—224no—
932C22—224no—
933C22—4416no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—888no—
946C22#1062319914yes—
947C22#1062320114yes—
948C22#1062320714yes—
949C22#1062320914yes—
950C22D4×C22⋊D1114yes—
951C22#1062336014yes—
952C22#1062336314yes—
953C22C22×D4×D1111yescharacteristic
954C22C2×#6703711yescharacteristic
955C22C2×#41×D1111yescharacteristic
956C22C2×#41×D1111yescharacteristic
957C22C2×#41×D1111yescharacteristic
958C22C2×#6704211yescharacteristic
959C22C23×C22⋊D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—42no—
964C4—42no—
965C4—224no—
966C4—224no—
967C4—224no—
968C4—224no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—82no—
973C2—444no—
974C2—882no—
975C2#1307368718yesdirect product factor
976C2C2×#1062336311yescharacteristic
977C2C2×#1062319911yescharacteristic
978C2C2×#1062320911yescharacteristic
979C2C2×D4×C22⋊D1111yescharacteristic
980C2C2×#1062336011yescharacteristic
981C2C2×#1062320711yescharacteristic
982C2C2×#1062320111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#124C2
socleC24×C11C24
hypercenterC22×#124D11
hypocenterC11C2×#2555
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66937C2semidirect
3. C22×#66992C2semidirect
4. #13073687C2direct (N × H)
5. C2×#10622842C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622569C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C22×C11×#124C2semidirect
27. C2×C11×#124C22semidirect
37. C2×#67000C22semidirect
39. C2×#66992C22semidirect
53. C2×#66937C22semidirect
54. #10622842C22semidirect
55. #10622836C22semidirect
62. #10622573C22semidirect
63. #10622572C22semidirect
64. #10622571C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622558C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. #10622553C22semidirect
70. C4×(C2×D11)⋊C4C22semidirect
126. C2×C11×C22⋊C4D4semidirect
147. C2×(C2×D11)⋊C4D4semidirect
289. C11×C22⋊C4C2×D4semidirect
300. (C2×D11)⋊C4C2×D4semidirect
307. C22×#124D11semidirect
451. C2×#124C2×D11semidirect
634. C2×C22⋊C4C22⋊D11semidirect
653. C2×C11#2555semidirect
792. C22⋊C4C2×C22⋊D11semidirect
796. C11C2×#2555semidirect
975. C2#13073687direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669372
C22×#669922
#130736872
C2×#106228422
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225702
C2×#106225582
C2×#106225532
C2×#106225712
C2×#106225692
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C22×C11×#1242
C2×#255511