Finite Group Databasebeta

← C2×#13076737 #14960120

Subgroups — C2×#13076737 #14960120

Order 2816.

2822 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076737C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic, complemented
3C2×#10622287C211yesmaximal, characteristic, complemented
4C2×#10622285C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622284C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622573C211yesmaximal, characteristic, complemented
12C2×#10622573C211yesmaximal, characteristic, complemented
13C2×#10622570C211yesmaximal, characteristic, complemented
14C2×#10622283C211yesmaximal, characteristic, complemented
15C2×#10622603C211yesmaximal, characteristic, complemented
16C2×C11×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#397C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622604C2218yescomplemented
54#10622603C2218yescomplemented
55#10622574C2218yescomplemented
56#10622573C2218yescomplemented
57#10622573C2218yescomplemented
58#10622573C2218yescomplemented
59#10622572C2218yescomplemented
60#10622570C2218yescomplemented
61#10622287C2218yescomplemented
62#10622285C2218yescomplemented
63#10622285C2218yescomplemented
64#10622284C2218yescomplemented
65#10622283C2218yescomplemented
66#10622271C2218yescomplemented
67C25×C11C2311yescharacteristic
68C24×D11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—24no—
78C22×C22⋊D11—42no—
79C22×C22⋊D11—42no—
80C22×C22⋊D11—42no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—42no—
95C22×D44—42no—
96C22×D44—42no—
97C22×D44—42no—
98C22×D44—42no—
99C22×D44—42no—
100C22×D44—42no—
101C22×D44—42no—
102C22×D44—42no—
103C22×D44C2314yes—
104C22×D44C2314yes—
105C22×D44C2314yes—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C22⋊Dic11—42no—
115C2×C22⋊Dic11C2314yes—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—42no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4—42no—
127C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×C4⋊Dic11—42no—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4—42no—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2828—111nomaximal, Sylow
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
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—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11C2412yes—
188C23×D11C2412yes—
189C23×D11C2412yes—
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×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—416no—
224C2×C22⋊D11—416no—
225C2×C22⋊D11—416no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11#4114yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C2×D44—44no—
247C2×D44—44no—
248C2×D44—44no—
249C2×D44—44no—
250C2×D44—44no—
251C2×D44—44no—
252C2×D44—44no—
253C2×D44—44no—
254C2×D44—44no—
255C2×D44—416no—
256C2×D44—416no—
257C2×D44—416no—
258C11×C4⋊C4—44no—
259C11×C22⋊C4—44no—
260C11×C22⋊C4—44no—
261C11×C22⋊C4—44no—
262C22⋊Dic11—44no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275C4⋊Dic11—44no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C4×Dic11—44no—
279#2828—1116no—
280C2×#400—111no—
281C2×#397—111no—
282C2×#397D1111yescharacteristic, complemented
283C2×#394—111no—
284C2×#394—111no—
285C2×#394—111no—
286C2×#394—111no—
287C2×#394—111no—
288C2×#392—111no—
289C2×#392—111no—
290C2×#392—111no—
291C2×#392—111no—
292C2×#390—111no—
293C2×#388—111no—
294C2×#388—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11C2×#4112yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11H(5,𝔽2)12yes—
313C23×C11H(5,𝔽2)12yes—
314C23×C11H(5,𝔽2)12yes—
315C23×C11H(5,𝔽2)12yes—
316C23×C11C2511yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—44no—
341C22×D11—44no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C2×C4×C11—44no—
380C2×C4×C11—44no—
381C2×C4×C11—44no—
382C2×C4×C11—44no—
383C22⋊D11—416no—
384C22⋊D11—416no—
385C22⋊D11—416no—
386C2×Dic11—28no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11C2×#4114yes—
406D44—416no—
407D44—416no—
408D44—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C23×D4—111no—
413C23×D4—111no—
414C23×D4—111no—
415C22×C4⋊C4—111no—
416C22×C4⋊C4—111no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C22⋊C4C2×D1111yescharacteristic
435C22×C42—111no—
436#400—118no—
437#397—118no—
438#397C2×D1118yescomplemented
439#394—118no—
440#394—118no—
441#394—118no—
442#394—118no—
443#394—118no—
444#392—118no—
445#392—118no—
446#392—118no—
447#392—118no—
448#390—118no—
449#388—118no—
450#388—118no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—88no—
467C22×C11#53814yes—
468C22×C11#54014yes—
469C22×C11#54014yes—
470C22×C11#56014yes—
471C22×C11#56014yes—
472C22×C11#56014yes—
473C22×C11H(3,𝔽4)14yes—
474C22×C11C22×#4111yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C22×C11C2×H(5,𝔽2)11yescharacteristic
477C22×C11C2×H(5,𝔽2)11yescharacteristic
478C22×C11C2×H(5,𝔽2)11yescharacteristic
479C22×C11C2×H(5,𝔽2)11yescharacteristic
480C22×C11C2×H(5,𝔽2)11yescharacteristic
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—88no—
503C2×D11—88no—
504C2×D11—88no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511Dic11—24no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516C25—111no—
517C25—111no—
518C25—111no—
519C25C22×D1111yescharacteristic
520C22×D4—114no—
521C22×D4—114no—
522C22×D4—114no—
523C22×D4—114no—
524C22×D4—114no—
525C22×D4—114no—
526C22×D4—224no—
527C22×D4—442no—
528C22×D4—442no—
529C22×D4—442no—
530C22×D4—442no—
531C22×D4—442no—
532C22×D4—442no—
533C22×D4—442no—
534C22×D4—442no—
535C22×D4—442no—
536C22×D4—442no—
537C22×D4—442no—
538C22×D4—442no—
539C22×D4—442no—
540C22×D4—442no—
541C22×D4—442no—
542C22×D4—442no—
543C22×D4—442no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C2×C4⋊C4—42no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—442no—
560C2×C4⋊C4—442no—
561C2×C4⋊C4—442no—
562C2×C4⋊C4C22×D1114yes—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—442no—
582C2×C22⋊C4—442no—
583C2×C22⋊C4—442no—
584C2×C22⋊C4—442no—
585C2×C22⋊C4—442no—
586C2×C22⋊C4—442no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4—442no—
590C2×C22⋊C4—442no—
591C2×C22⋊C4—442no—
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C22⋊C4C22×D1114yes—
595C2×C42—114no—
596C2×C42—442no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602#95C22×D1114yes—
603#95C22×D1114yes—
604#95C22×D1114yes—
605C2×C11—82no—
606C2×C11#282818yescomplemented
607C2×C11C2×#53811yescharacteristic
608C2×C11C2×#54011yescharacteristic
609C2×C11C2×#54011yescharacteristic
610C2×C11C2×#56011yescharacteristic
611C2×C11C2×#56011yescharacteristic
612C2×C11C2×#56011yescharacteristic
613C2×C11C2×H(3,𝔽4)11yescharacteristic
614D11—82no—
615D11—82no—
616D11—82no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—112no—
625C24—112no—
626C24—112no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24—222no—
648C24C23×D1112yes—
649C24C23×D1111yescharacteristic
650C2×D4—228no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—444no—
655C2×D4—444no—
656C2×D4—444no—
657C2×D4—444no—
658C2×D4—444no—
659C2×D4—444no—
660C2×D4—4416no—
661C2×D4—4416no—
662C2×D4—4416no—
663C2×D4—444no—
664C2×D4—444no—
665C2×D4—444no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—4416no—
672C2×D4—4416no—
673C2×D4—4416no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—114no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C4⋊C4—44no—
719C4⋊C4—444no—
720C4⋊C4—444no—
721C4⋊C4—444no—
722C22⋊C4—44no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—228no—
726C22⋊C4—228no—
727C22⋊C4—444no—
728C22⋊C4—444no—
729C22⋊C4—444no—
730C22⋊C4—444no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C22⋊C4—444no—
738C42—444no—
739C11C2×#282811yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23—444no—
782C23—444no—
783C23—444no—
784C23—444no—
785C23—444no—
786C23—444no—
787C23—444no—
788C23—444no—
789C23—444no—
790C23—444no—
791C23—444no—
792C23—444no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23#6703712yes—
797C23#6703712yes—
798C23#41×D1112yes—
799C23#6704212yes—
800C23#6704212yes—
801C23#6704212yes—
802C23#6704212yes—
803C23C24×D1111yescharacteristic
804D4—4416no—
805D4—4416no—
806D4—4416no—
807D4—4416no—
808D4—4416no—
809D4—4416no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—114no—
835C2×C4—228no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—444no—
851C2×C4—444no—
852C2×C4—444no—
853C2×C4—444no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—88no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22—442no—
871C22—442no—
872C22—442no—
873C22—442no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22—442no—
882C22—442no—
883C22—888no—
884C22—888no—
885C22—888no—
886C22#1062315114yes—
887C22#1062319414yes—
888C22#1062319414yes—
889C22#1062319714yes—
890C22#1062321414yes—
891C22#1062323514yes—
892C22#1062324214yes—
893C22C2×#6703711yescharacteristic
894C22C2×#6703711yescharacteristic
895C22C2×#41×D1111yescharacteristic
896C22C2×#6704211yescharacteristic
897C22C2×#6704211yescharacteristic
898C22C2×#6704211yescharacteristic
899C22C2×#6704211yescharacteristic
900C4—42no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—224no—
907C4—442no—
908C4—442no—
909C4—442no—
910C4—442no—
911C2—82no—
912C2—882no—
913C2—882no—
914C2—882no—
915C2#1307673718yesdirect product factor
916C2C2×#1062323511yescharacteristic
917C2C2×#1062319411yescharacteristic
918C2C2×#1062319411yescharacteristic
919C2C2×#1062315111yescharacteristic
920C2C2×#1062319711yescharacteristic
921C2C2×#1062324211yescharacteristic
922C2C2×#1062321411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
hypercenterC2×#397D11
hypocenterC11C2×#2828
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. #13076737C2direct (N × H)
2. C2×#10622271C2semidirect
3. C2×#10622287C2semidirect
4. C2×#10622285C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622284C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622573C2semidirect
12. C2×#10622573C2semidirect
13. C2×#10622570C2semidirect
14. C2×#10622283C2semidirect
15. C2×#10622603C2semidirect
16. C2×C11×#397C2semidirect
44. C11×#397C22semidirect
53. #10622604C22semidirect
54. #10622603C22semidirect
55. #10622574C22semidirect
56. #10622573C22semidirect
57. #10622573C22semidirect
58. #10622573C22semidirect
59. #10622572C22semidirect
60. #10622570C22semidirect
61. #10622287C22semidirect
62. #10622285C22semidirect
63. #10622285C22semidirect
64. #10622284C22semidirect
65. #10622283C22semidirect
66. #10622271C22semidirect
282. C2×#397D11semidirect
438. #397C2×D11semidirect
606. C2×C11#2828semidirect
739. C11C2×#2828semidirect
915. C2#13076737direct (N × H)

Maximal subgroups

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

subgroupindex
#130767372
C2×#106222712
C2×#106222872
C2×#106222852
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222842
C2×#106225732
C2×#106225702
C2×#106222832
C2×#106226032
C2×C11×#3972
C2×#282811