Finite Group Databasebeta

← C2×#13072233 #14922104

Subgroups — C2×#13072233 #14922104

Order 2816.

6278 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C22×#66993C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×#66937C211yesmaximal, characteristic, complemented
5#13072233C2116yesmaximal, direct product factor
6C2×#10622284C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, 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
25C22×#4339—28no—
26C22×#4339—28no—
27C22×#4339—28no—
28C22×#4339C2218yescomplemented
29C23×D44C2211yescharacteristic
30C23×D44C2211yescharacteristic
31C23×D44C2211yescharacteristic
32C23×C4×D11C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic
34C23×Dic22C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C2×#66993—28no—
41C2×#66993C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66938—28no—
53C2×#66938C2218yescomplemented
54C2×#66937—28no—
55C2×#66937C2218yescomplemented
56C11×#386C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59#10622836C2218yescomplemented
60#10622826C2218yescomplemented
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622573C2218yescomplemented
66#10622573C2218yescomplemented
67#10622570C2218yescomplemented
68#10622569C2218yescomplemented
69#10622284C2218yescomplemented
70#10622279C2218yescomplemented
71#10622278C2218yescomplemented
72#10622259C2218yescomplemented
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—24no—
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
120C2×#4339—2128no—
121C2×#4339—232no—
122C2×#4339—232no—
123C2×#4339—232no—
124C22×D44—24no—
125C22×D44—24no—
126C22×D44—24no—
127C22×D44—24no—
128C22×D44—24no—
129C22×D44—24no—
130C22×D44—42no—
131C22×D44—42no—
132C22×D44—42no—
133C22×D44C2314yes—
134C22×D44C2314yes—
135C22×D44C2314yes—
136C22×C4×D11—24no—
137C22×C4×D11—24no—
138C22×C4×D11—24no—
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11D418yescomplemented
142C22×C4×D11C2314yes—
143C22×C4×D11C2314yes—
144C22×Dic22—24no—
145C22×Dic22—24no—
146C22×Dic22D418yescomplemented
147C22×Dic22C2314yes—
148C2×C11×C22⋊C4—24no—
149C2×C11×C22⋊C4—24no—
150C2×C11×C22⋊C4—42no—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2314yes—
154C2×C22⋊Dic11—24no—
155C2×C22⋊Dic11—42no—
156C2×C22⋊Dic11C2314yes—
157C2×C22⋊Dic11C2314yes—
158#66993—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—24no—
164C2×(C2×D11)⋊C4—42no—
165C2×(C2×D11)⋊C4—42no—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×Dic11⋊C4—24no—
174C2×Dic11⋊C4C2314yes—
175C2×C4×Dic11—24no—
176C2×C4×Dic11—24no—
177C2×C4×Dic11C2314yes—
178C2×C4×Dic11C2314yes—
179#66938—232no—
180#66937—232no—
181C11×#95C2314yes—
182C11×#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C11⋊#95C2314yes—
187C2×#2431—111nomaximal, Sylow
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×C11C2×D414yes—
202C24×C11C2412yes—
203C24×C11C2412yes—
204C24×C11C2411yescharacteristic
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×D11—22no—
224C23×D11C2×D414yes—
225C23×D11C2×D414yes—
226C23×D11C2412yes—
227C23×D11C2412yes—
228C23×D11C2412yes—
229C2×D4×C11—28no—
230C2×D4×C11—28no—
231C2×D4×C11—44no—
232C2×D4×C11—416no—
233C22×C4×C11—232no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—28no—
240C22×C4×C11—22no—
241C22×C4×C11—28no—
242C22×C4×C11—28no—
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×C11C2×D414yes—
250C22×C4×C11C2×D414yes—
251C22×C4×C11#4114yescomplemented
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C2×C22⋊D11—232no—
258C2×C22⋊D11—232no—
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—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—416no—
277C2×C22⋊D11—416no—
278C2×C22⋊D11—416no—
279C2×C22⋊D11—416no—
280C2×C22⋊D11C2×D4116yescomplemented
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×Dic11—22no—
291C22×Dic11C2×D414yes—
292C22×Dic11C2×D414yes—
293C22×Dic11C2×D414yes—
294C22×Dic11C2×D414yes—
295C22×Dic11#4114yescomplemented
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301#4339—2256no—
302C2×D44—232no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44—28no—
306C2×D44—28no—
307C2×D44—28no—
308C2×D44—28no—
309C2×D44—44no—
310C2×D44—44no—
311C2×D44—44no—
312C2×D44—416no—
313C2×D44—416no—
314C2×C4×D11—232no—
315C2×C4×D11—232no—
316C2×C4×D11—28no—
317C2×C4×D11—28no—
318C2×C4×D11—28no—
319C2×C4×D11—28no—
320C2×C4×D11—28no—
321C2×C4×D11C2×D4116yescomplemented
322C2×Dic22—232no—
323C2×Dic22—28no—
324C2×Dic22—28no—
325C2×Dic22C2×D4116yescomplemented
326C11×C22⋊C4—28no—
327C11×C22⋊C4—28no—
328C11×C22⋊C4—44no—
329C22⋊Dic11—28no—
330C22⋊Dic11—44no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—28no—
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338Dic11⋊C4—28no—
339C4×Dic11—28no—
340C4×Dic11—28no—
341C23×#41—111no—
342C22×#127—111no—
343C22×#124—111no—
344C22×#121—111no—
345#2431—1116no—
346C2×#392—111no—
347C2×#392—111no—
348C2×#392—111no—
349C2×#392—111no—
350C2×#391—111no—
351C2×#390—111no—
352C2×#386—111no—
353C2×#386—111no—
354C2×#386—111no—
355C2×#386D1111yescharacteristic, complemented
356C2×C4×C22⋊C4—111no—
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—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11—44no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11C22×D414yes—
385C23×C11C22×D412yes—
386C23×C11C22×D412yes—
387C23×C11C22×D412yes—
388C23×C11C2×#4112yes—
389C23×C11C2×#4112yes—
390C23×C11H(5,𝔽2)12yes—
391C23×C11H(5,𝔽2)12yes—
392C23×C11C2511yescharacteristic
393C22×D11—28no—
394C22×D11—28no—
395C22×D11—28no—
396C22×D11—28no—
397C22×D11—28no—
398C22×D11—28no—
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—22no—
416C22×D11—22no—
417C22×D11—22no—
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×D11—44no—
431C22×D11—44no—
432C22×D11—44no—
433C22×D11C22×D414yes—
434C22×D11C22×D414yes—
435D4×C11—416no—
436C2×C4×C11—232no—
437C2×C4×C11—28no—
438C2×C4×C11—28no—
439C2×C4×C11—28no—
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—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—44no—
453C2×C4×C11—44no—
454C2×C4×C11C22×D414yes—
455C2×C4×C11C22×D414yes—
456C2×C4×C11C2×#4114yescomplemented
457C22⋊D11—232no—
458C22⋊D11—232no—
459C22⋊D11—416no—
460C22⋊D11—416no—
461C22⋊D11—416no—
462C22⋊D11—416no—
463C2×Dic11—28no—
464C2×Dic11—28no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—44no—
476C2×Dic11—44no—
477C2×Dic11#120116yes—
478C2×Dic11C22×D414yes—
479C2×Dic11C22×D414yes—
480C2×Dic11C22×D414yes—
481C2×Dic11C22×D414yes—
482C2×Dic11C2×#4114yescomplemented
483D44—232no—
484D44—416no—
485D44—416no—
486C4×D11—232no—
487C4×D11—232no—
488Dic22—232no—
489C22×#41—118no—
490C22×#41—228no—
491C22×#41—228no—
492C22×#41—228no—
493C23×Q8—111no—
494C23×D4—111no—
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4—111no—
500C23×D4—111no—
501C23×D4—111no—
502C23×D4—111no—
503C23×D4C2×D1111yescharacteristic
504C24×C4—111no—
505C24×C4—111no—
506C24×C4C2×D1111yescharacteristic
507C2×#127—118no—
508C2×#127—228no—
509C2×#124—118no—
510C2×#124—228no—
511C2×#121—118no—
512C2×#121—228no—
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#392—118no—
529#392—118no—
530#392—118no—
531#392—118no—
532#391—118no—
533#390—118no—
534#386—118no—
535#386—118no—
536#386—118no—
537#386C2×D1118yescomplemented
538C4×C22⋊C4—118no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95C2×D1111yescharacteristic
544C2×#95C2×D1111yescharacteristic
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—24no—
548C22×C11—42no—
549C22×C11—42no—
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—88no—
561C22×C11C2×#12014yes—
562C22×C11#53214yes—
563C22×C11#53514yes—
564C22×C11#54614yes—
565C22×C11#54614yes—
566C22×C11#55014yes—
567C22×C11#55014yes—
568C22×C11C23×D411yescharacteristic
569C22×C11C23×D411yescharacteristic
570C22×C11C23×D411yescharacteristic
571C22×C11C22×#4111yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C2×H(5,𝔽2)11yescharacteristic
574C22×C11C2×H(5,𝔽2)11yescharacteristic
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—24no—
578C2×D11—24no—
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—416no—
584C2×D11—416no—
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—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—88no—
599C4×C11—24no—
600C4×C11—24no—
601C4×C11—24no—
602C4×C11—42no—
603C4×C11—42no—
604Dic11—24no—
605Dic11—24no—
606Dic11—42no—
607Dic11—42no—
608Dic11C2×#12018yes—
609C25—111no—
610C25—111no—
611C25—111no—
612C25C22×D1111yescharacteristic
613C25C22×D1111yescharacteristic
614C2×#41—2232no—
615C2×#41—2232no—
616C2×#41—2232no—
617C2×#41—22128no—
618C22×Q8—118no—
619C22×Q8—114no—
620C22×Q8—224no—
621C22×Q8—224no—
622C22×D4—24no—
623C22×D4—24no—
624C22×D4—42no—
625C22×D4—118no—
626C22×D4—114no—
627C22×D4—114no—
628C22×D4—114no—
629C22×D4—114no—
630C22×D4—114no—
631C22×D4—114no—
632C22×D4—114no—
633C22×D4—114no—
634C22×D4—114no—
635C22×D4—224no—
636C22×D4—224no—
637C22×D4—224no—
638C22×D4—224no—
639C22×D4—224no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—224no—
643C22×D4—224no—
644C22×D4—224no—
645C22×D4—224no—
646C22×D4—224no—
647C22×D4—224no—
648C22×D4—224no—
649C22×D4—224no—
650C22×D4—224no—
651C22×D4—224no—
652C22×D4—224no—
653C22×D4—224no—
654C22×D4—442no—
655C22×D4—442no—
656C22×D4—442no—
657C22×D4—442no—
658C22×D4—442no—
659C22×D4—442no—
660C22×D4—442no—
661C22×D4C22×D1114yes—
662C23×C4—24no—
663C23×C4—24no—
664C23×C4—24no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—118no—
669C23×C4—114no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—114no—
673C23×C4—224no—
674C23×C4—224no—
675C23×C4—224no—
676C23×C4—224no—
677C23×C4—224no—
678C23×C4C22×D1114yes—
679C23×C4C22×D1111yescharacteristic
680C23×C4C22×D1111yescharacteristic
681C23×C4C22×D1111yescharacteristic
682C23×C4C22×D1111yescharacteristic
683C23×C4C22×D1111yescharacteristic
684#127—2232no—
685#124—2232no—
686#121—2232no—
687C2×C4⋊C4—114no—
688C2×C4⋊C4—224no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—42no—
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—114no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—224no—
702C2×C22⋊C4—224no—
703C2×C22⋊C4—224no—
704C2×C22⋊C4—224no—
705C2×C22⋊C4—224no—
706C2×C22⋊C4—224no—
707C2×C22⋊C4—442no—
708C2×C22⋊C4—442no—
709C2×C22⋊C4—442no—
710C2×C22⋊C4C22×D1114yes—
711C2×C22⋊C4C22×D1114yes—
712C2×C22⋊C4C22×D1114yes—
713C2×C42—114no—
714C2×C42—114no—
715C2×C42—224no—
716C2×C42—224no—
717#95—114no—
718#95—114no—
719#95—114no—
720#95—114no—
721#95C22×D1114yes—
722#95C22×D1114yes—
723C2×C11—44no—
724C2×C11—82no—
725C2×C11#243118yescomplemented
726C2×C11C22×#12011yescharacteristic
727C2×C11C2×#53211yescharacteristic
728C2×C11C2×#53511yescharacteristic
729C2×C11C2×#54611yescharacteristic
730C2×C11C2×#54611yescharacteristic
731C2×C11C2×#55011yescharacteristic
732C2×C11C2×#55011yescharacteristic
733D11—44no—
734D11—44no—
735D11—82no—
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—114no—
750C24—114no—
751C24—112no—
752C24—112no—
753C24—112no—
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—
768C24—222no—
769C24—222no—
770C24—222no—
771C24—222no—
772C24—222no—
773C24D4×D1114yes—
774C24C23×D1112yes—
775C24C23×D1112yes—
776C24C23×D1111yescharacteristic
777#41—22256no—
778C2×Q8—1116no—
779C2×Q8—2232no—
780C2×Q8—228no—
781C2×Q8—228no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—44no—
785C2×D4—416no—
786C2×D4—1116no—
787C2×D4—228no—
788C2×D4—228no—
789C2×D4—2232no—
790C2×D4—228no—
791C2×D4—228no—
792C2×D4—2232no—
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—228no—
802C2×D4—2232no—
803C2×D4—228no—
804C2×D4—228no—
805C2×D4—228no—
806C2×D4—228no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—444no—
810C2×D4—444no—
811C2×D4—444no—
812C2×D4—4416no—
813C2×D4—4416no—
814C2×D4—4416no—
815C2×D4—444no—
816C2×D4—444no—
817C2×D4—444no—
818C2×D4—444no—
819C2×D4—4416no—
820C2×D4—4416no—
821C2×D4—4416no—
822C22×C4—232no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—28no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—114no—
839C22×C4—114no—
840C22×C4—114no—
841C22×C4—112no—
842C22×C4—114no—
843C22×C4—114no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—1116no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—2232no—
850C22×C4—228no—
851C22×C4—228no—
852C22×C4—228no—
853C22×C4—228no—
854C22×C4—2232no—
855C22×C4—222no—
856C22×C4—222no—
857C22×C4—222no—
858C22×C4—222no—
859C22×C4—228no—
860C22×C4—222no—
861C22×C4—222no—
862C22×C4—222no—
863C22×C4—222no—
864C22×C4—222no—
865C22×C4—222no—
866C22×C4#433914yescomplemented
867C22×C4D4×D1114yes—
868C22×C4D4×D1114yes—
869C22×C4C23×D1112yes—
870C22×C4C23×D1112yes—
871C22×C4C23×D1112yes—
872C22×C4C23×D1112yes—
873C22×C4C23×D1112yes—
874C4⋊C4—228no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—228no—
879C22⋊C4—228no—
880C22⋊C4—228no—
881C22⋊C4—228no—
882C22⋊C4—228no—
883C22⋊C4—228no—
884C22⋊C4—444no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C42—228no—
888C42—228no—
889C11C2×#243111yescharacteristic, complemented, Sylow
890C23—28no—
891C23—28no—
892C23—28no—
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—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—114no—
918C23—114no—
919C23—228no—
920C23—228no—
921C23—228no—
922C23—228no—
923C23—228no—
924C23—228no—
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—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—444no—
945C23—444no—
946C23—444no—
947C23—444no—
948C23—444no—
949C23—444no—
950C23—444no—
951C23—444no—
952C23—444no—
953C23—444no—
954C23—444no—
955C23—444no—
956C23—444no—
957C23—444no—
958C23—444no—
959C23C2×#433912yes—
960C23C2×D4×D1114yes—
961C23C2×D4×D1112yes—
962C23C2×D4×D1112yes—
963C23C2×D4×D1112yes—
964C23#6703712yes—
965C23#41×D1112yes—
966C23#6704212yes—
967C23C24×D1111yescharacteristic
968Q8—2232no—
969D4—416no—
970D4—2232no—
971D4—2232no—
972D4—2232no—
973D4—4416no—
974D4—4416no—
975D4—4416no—
976D4—4416no—
977D4—4416no—
978D4—4416no—
979C2×C4—232no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—1116no—
998C2×C4—114no—
999C2×C4—114no—
1000C2×C4—114no—
1001C2×C4—114no—
1002C2×C4—114no—
1003C2×C4—2232no—
1004C2×C4—2232no—
1005C2×C4—228no—
1006C2×C4—228no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—444no—
1018C2×C4—444no—
1019C2×C4C2×#433914yescomplemented
1020C2×C4C2×D4×D1114yes—
1021C2×C4C2×D4×D1114yes—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—42no—
1026C22—42no—
1027C22—416no—
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—224no—
1042C22—224no—
1043C22—224no—
1044C22—442no—
1045C22—442no—
1046C22—4416no—
1047C22—4416no—
1048C22—442no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—442no—
1053C22—442no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
1061C22—888no—
1062C22#1062302114yes—
1063C22#1062307914yes—
1064C22#1062308414yes—
1065C22D11×#12014yes—
1066C22#1062313014yes—
1067C22#1062313814yes—
1068C22#1062318514yes—
1069C22C22×#433911yescharacteristic
1070C22C22×D4×D1111yescharacteristic
1071C22C22×D4×D1111yescharacteristic
1072C22C22×D4×D1111yescharacteristic
1073C22C2×#6703711yescharacteristic
1074C22C2×#41×D1111yescharacteristic
1075C22C2×#6704211yescharacteristic
1076C4—24no—
1077C4—24no—
1078C4—24no—
1079C4—42no—
1080C4—42no—
1081C4—118no—
1082C4—224no—
1083C4—224no—
1084C4—442no—
1085C4—442no—
1086C2—44no—
1087C2—82no—
1088C2—444no—
1089C2—444no—
1090C2—882no—
1091C2#1307223318yesdirect product factor
1092C2C2×D11×#12011yescharacteristic
1093C2C2×#1062307911yescharacteristic
1094C2C2×#1062313811yescharacteristic
1095C2C2×#1062302111yescharacteristic
1096C2C2×#1062318511yescharacteristic
1097C2C2×#1062313011yescharacteristic
1098C2C2×#1062308411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2431
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C22×#66993C2semidirect
3. C22×#66938C2semidirect
4. C22×#66937C2semidirect
5. #13072233C2direct (N × H)
6. C2×#10622284C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622259C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#386C2semidirect
28. C22×#4339C22semidirect
41. C2×#66993C22semidirect
53. C2×#66938C22semidirect
55. C2×#66937C22semidirect
56. C11×#386C22semidirect
59. #10622836C22semidirect
60. #10622826C22semidirect
65. #10622573C22semidirect
66. #10622573C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622284C22semidirect
70. #10622279C22semidirect
71. #10622278C22semidirect
72. #10622259C22semidirect
108. C22×C22⋊D11D4semidirect
141. C22×C4×D11D4semidirect
146. C22×Dic22D4semidirect
251. C22×C4×C11#41semidirect
280. C2×C22⋊D11C2×D4semidirect
295. C22×Dic11#41semidirect
321. C2×C4×D11C2×D4semidirect
325. C2×Dic22C2×D4semidirect
355. C2×#386D11semidirect
456. C2×C4×C11C2×#41semidirect
482. C2×Dic11C2×#41semidirect
537. #386C2×D11semidirect
725. C2×C11#2431semidirect
866. C22×C4#4339semidirect
889. C11C2×#2431semidirect
1019. C2×C4C2×#4339semidirect
1091. C2#13072233direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669932
C22×#669382
C22×#669372
#130722332
C2×#106222842
C2×#106225732
C2×#106228362
C2×#106222592
C2×#106225702
C2×#106228262
C2×#106222782
C2×#106225692
C2×#106222792
C2×C11×#3862
C2×#243111