Finite Group Databasebeta

← C2×#13072203 #14921658

Subgroups — C2×#13072203 #14921658

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×#66983C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×#66937C211yesmaximal, characteristic, complemented
5C22×#66937C211yesmaximal, characteristic, complemented
6C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
7#13072203C2116yesmaximal, direct product factor
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622284C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622570C211yesmaximal, characteristic, complemented
13C2×#10622260C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×D44C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66993—28no—
36C2×#66993C2218yescomplemented
37C2×#66983—28no—
38C2×#66983C2218yescomplemented
39C2×C4×C22⋊D11—28no—
40C2×C4×C22⋊D11C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
48C22×C4⋊Dic11C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×Dic11⋊C4C2211yescharacteristic
52C22×C4×Dic11C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C2×#66937—28no—
55C2×#66937—28no—
56C2×#66937—28no—
57C2×#66937C2218yescomplemented
58C2×#66937C2218yescomplemented
59C2×#66937C2218yescomplemented
60C11×#386C2218yescomplemented
61C2×C11×#95C2211yescharacteristic
62C2×C11×#95C2211yescharacteristic
63#10622836C2218yescomplemented
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622574C2218yescomplemented
67#10622572C2218yescomplemented
68#10622570C2218yescomplemented
69#10622284C2218yescomplemented
70#10622279C2218yescomplemented
71#10622278C2218yescomplemented
72#10622260C2218yescomplemented
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×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11—42no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
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—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—42no—
105C22×C22⋊D11—42no—
106C22×C22⋊D11—42no—
107C22×C22⋊D11—42no—
108C22×C22⋊D11D418yescomplemented
109C22×C22⋊D11C2314yes—
110C22×C22⋊D11C2314yes—
111C22×C22⋊D11C2314yes—
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yes—
115C23×Dic11C2311yescharacteristic
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×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—24no—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11—42no—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150#66993—232no—
151#66983—232no—
152C4×C22⋊D11—232no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4—42no—
159C2×(C2×D11)⋊C4D418yescomplemented
160C2×(C2×D11)⋊C4C2314yes—
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×C4⋊Dic11—24no—
168C2×C4⋊Dic11C2314yes—
169C2×Dic11⋊C4—24no—
170C2×Dic11⋊C4—24no—
171C2×Dic11⋊C4D418yescomplemented
172C2×Dic11⋊C4C2314yes—
173C2×Dic11⋊C4C2314yes—
174C2×Dic11⋊C4C2314yes—
175C2×C4×Dic11—24no—
176C2×C4×Dic11—24no—
177C2×C4×Dic11C2314yes—
178C2×C4×Dic11C2314yes—
179#66937—232no—
180#66937—232no—
181#66937—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—28no—
245C22×C4×C11—28no—
246C22×C4×C11—44no—
247C22×C4×C11—416no—
248C22×C4×C11C2×D414yes—
249C22×C4×C11C2×D414yes—
250C22×C4×C11#4114yes—
251C22×C4×C11C2412yes—
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—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11C2×D414yes—
291C22×Dic11C2×D414yes—
292C22×Dic11C2×D414yes—
293C22×Dic11C2×D414yes—
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×C22⋊C4—28no—
321C11×C22⋊C4—28no—
322C11×C22⋊C4—28no—
323C22⋊Dic11—28no—
324C22⋊Dic11—44no—
325(C2×D11)⋊C4—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—44no—
331(C2×D11)⋊C4C2×D4116yescomplemented
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×#392—111no—
349C2×#390—111no—
350C2×#389—111no—
351C2×#386—111no—
352C2×#386D1111yescharacteristic, complemented
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—28no—
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—416no—
449C2×C4×C11—44no—
450C2×C4×C11—44no—
451C2×C4×C11C22×D414yes—
452C2×C4×C11C22×D414yes—
453C2×C4×C11C2×#4114yes—
454C22⋊D11—232no—
455C22⋊D11—416no—
456C22⋊D11—416no—
457C22⋊D11—416no—
458C22⋊D11—416no—
459C22⋊D11—416no—
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—22no—
472C2×Dic11—44no—
473C2×Dic11—44no—
474C2×Dic11#121116yescomplemented
475C2×Dic11C22×D414yes—
476C2×Dic11C22×D414yes—
477C2×Dic11C22×D414yes—
478C2×Dic11C22×D414yes—
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×C4C2×D1111yescharacteristic
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#392—118no—
532#390—118no—
533#389—118no—
534#386—118no—
535#386C2×D1118yescomplemented
536C4×C22⋊C4—118no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95C2×D1111yescharacteristic
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—24no—
598C4×C11—42no—
599C4×C11—42no—
600Dic11—24no—
601Dic11—24no—
602Dic11—42no—
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—24no—
651C23×C4—24no—
652C23×C4—42no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—114no—
659C23×C4—114no—
660C23×C4—224no—
661C23×C4—224no—
662C23×C4—224no—
663C23×C4—224no—
664C23×C4—224no—
665C23×C4—442no—
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1114yes—
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—24no—
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—442no—
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#95C22×D1114yes—
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—28no—
825C22×C4—28no—
826C22×C4—44no—
827C22×C4—416no—
828C22×C4—114no—
829C22×C4—114no—
830C22×C4—114no—
831C22×C4—112no—
832C22×C4—114no—
833C22×C4—114no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
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—222no—
852C22×C4—228no—
853C22×C4—444no—
854C22×C4—4416no—
855C22×C4—4416no—
856C22×C4#433914yes—
857C22×C4D4×D1114yes—
858C22×C4D4×D1114yes—
859C22×C4C23×D1112yes—
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—28no—
871C22⋊C4—1116no—
872C22⋊C4—228no—
873C22⋊C4—228no—
874C22⋊C4—228no—
875C22⋊C4—228no—
876C22⋊C4—228no—
877C22⋊C4—228no—
878C22⋊C4—444no—
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—228no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—222no—
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×#433912yes—
953C23C2×D4×D1114yes—
954C23C2×D4×D1112yes—
955C23C2×D4×D1112yes—
956C23C2×D4×D1112yes—
957C23#6703712yes—
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—28no—
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—416no—
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—228no—
996C2×C4—228no—
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—444no—
1010C2×C4—444no—
1011C2×C4C2×#433914yes—
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#1062302114yes—
1055C22#1062307914yes—
1056C22#1062308414yes—
1057C22#1062312114yes—
1058C22D11×#12114yes—
1059C22#1062314014yes—
1060C22#1062319414yes—
1061C22C22×#433911yescharacteristic
1062C22C22×D4×D1111yescharacteristic
1063C22C22×D4×D1111yescharacteristic
1064C22C22×D4×D1111yescharacteristic
1065C22C2×#6703711yescharacteristic
1066C22C2×#41×D1111yescharacteristic
1067C22C2×#6704211yescharacteristic
1068C4—24no—
1069C4—24no—
1070C4—24no—
1071C4—42no—
1072C4—42no—
1073C4—118no—
1074C4—224no—
1075C4—224no—
1076C4—442no—
1077C4—442no—
1078C2—44no—
1079C2—82no—
1080C2—444no—
1081C2—444no—
1082C2—882no—
1083C2#1307220318yesdirect product factor
1084C2C2×D11×#12111yescharacteristic
1085C2C2×#1062307911yescharacteristic
1086C2C2×#1062319411yescharacteristic
1087C2C2×#1062312111yescharacteristic
1088C2C2×#1062314011yescharacteristic
1089C2C2×#1062302111yescharacteristic
1090C2C2×#1062308411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66993C2semidirect
2. C22×#66983C2semidirect
3. C22×#66937C2semidirect
4. C22×#66937C2semidirect
5. C22×#66937C2semidirect
6. C22×C4×C22⋊D11C2semidirect
7. #13072203C2direct (N × H)
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622284C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622570C2semidirect
13. C2×#10622260C2semidirect
14. C2×#10622278C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#386C2semidirect
36. C2×#66993C22semidirect
38. C2×#66983C22semidirect
40. C2×C4×C22⋊D11C22semidirect
57. C2×#66937C22semidirect
58. C2×#66937C22semidirect
59. C2×#66937C22semidirect
60. C11×#386C22semidirect
63. #10622836C22semidirect
66. #10622574C22semidirect
67. #10622572C22semidirect
68. #10622570C22semidirect
69. #10622284C22semidirect
70. #10622279C22semidirect
71. #10622278C22semidirect
72. #10622260C22semidirect
108. C22×C22⋊D11D4semidirect
159. C2×(C2×D11)⋊C4D4semidirect
171. C2×Dic11⋊C4D4semidirect
279. C2×C22⋊D11C2×D4semidirect
331. (C2×D11)⋊C4C2×D4semidirect
335. Dic11⋊C4C2×D4semidirect
352. C2×#386D11semidirect
474. C2×Dic11#121semidirect
535. #386C2×D11semidirect
604. Dic11C2×#121semidirect
720. C2×C11#2428semidirect
882. C11C2×#2428semidirect
1083. C2#13072203direct (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×#669832
C22×#669372
C22×C4×C22⋊D112
#130722032
C2×#106225742
C2×#106225722
C2×#106222842
C2×#106228362
C2×#106225702
C2×#106222602
C2×#106222782
C2×#106222792
C2×C11×#3862
C2×#242811