Finite Group Databasebeta

← C2×#13074363 #14920134

Subgroups — C2×#13074363 #14920134

Order 2816.

3718 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic
4C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5#13074363C2116yesmaximal, direct product factor
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622597C211yesmaximal, characteristic, complemented
8C2×#10622561C211yesmaximal, characteristic, complemented
9C2×#10622607C211yesmaximal, characteristic, complemented
10C2×#10622607C211yesmaximal, characteristic, complemented
11C2×#10622574C211yesmaximal, characteristic, complemented
12C2×#10622572C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C2×#66947—28no—
47C2×#66947C2218yescomplemented
48C2×C4⋊C4×D11—28no—
49C2×C4⋊C4×D11C2218yescomplemented
50C2×#66937—28no—
51C2×#66937C2218yes—
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C11×#396C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622607C2218yescomplemented
63#10622600C2218yescomplemented
64#10622597C2218yescomplemented
65#10622574C2218yescomplemented
66#10622572C2218yescomplemented
67#10622569C2218yescomplemented
68#10622561C2218yescomplemented
69#10622278C2218yescomplemented
70#10622270C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—24no—
95C22×D44—24no—
96C22×D44—24no—
97C22×D44C2314yes—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11—42no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11D418yes—
106C22×C4×D11D418yescomplemented
107C22×C4×D11C2314yes—
108C22×C4×D11C2314yes—
109C22×C4×D11C2314yes—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—42no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—42no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4—42no—
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—24no—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11—42no—
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2314yes—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156#66947—232no—
157C4⋊C4×D11—232no—
158#66937—232no—
159#66936—232no—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2618—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
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×D11C2×D414yes—
188C23×D11C2×D414yes—
189C23×D11#4114yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
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×C11C2×D414yes—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11—416no—
224C22×Dic11—22no—
225C22×Dic11—22no—
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×Dic11C2×D414yes—
241C22×Dic11C2×D414yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×D44—28no—
249C2×D44—28no—
250C2×D44—28no—
251C2×D44—416no—
252C2×C4×D11—232no—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—28no—
256C2×C4×D11—416no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—416no—
262C2×C4×D11C2×D4116yes—
263C2×C4×D11C2×D4116yescomplemented
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C4⋊C4—44no—
267C11×C22⋊C4—28no—
268C11×C22⋊C4—28no—
269C11×C22⋊C4—44no—
270C22⋊Dic11—28no—
271C22⋊Dic11—44no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279C4⋊Dic11—28no—
280C4⋊Dic11—28no—
281C4⋊Dic11—44no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—28no—
286Dic11⋊C4—28no—
287C22×#123—111no—
288C22×#123—111no—
289C22×#121—111no—
290C23×C4⋊C4—111no—
291#2618—1116no—
292C2×#398—111no—
293C2×#398—111no—
294C2×#396—111no—
295C2×#396—111no—
296C2×#396—111no—
297C2×#396D1111yescharacteristic, complemented
298C2×#394—111no—
299C2×#394—111no—
300C2×#386—111no—
301C2×#386—111no—
302C2×#380—111no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11C22×D412yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4112yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C112−1+412yes—
323C23×C112−1+412yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11#121116yes—
350C22×D11C22×D414yes—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
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—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11C22×D414yes—
376C2×C4×C11C22×D414yes—
377C22⋊D11—416no—
378C22⋊D11—416no—
379C2×Dic11—28no—
380C2×Dic11—28no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
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—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11C22×D414yes—
402C2×Dic11C22×D414yes—
403D44—416no—
404C4×D11—232no—
405C4×D11—416no—
406C4×D11—416no—
407C23×D4—111no—
408C23×D4—111no—
409C23×D4—111no—
410C24×C4—111no—
411C24×C4—111no—
412C24×C4—111no—
413C2×#123—118no—
414C2×#123—118no—
415C2×#123—228no—
416C2×#123—228no—
417C2×#121—118no—
418C2×#121—228no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—118no—
428C22×C4⋊C4—228no—
429C22×C4⋊C4C2×D1111yescharacteristic
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C4⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C22⋊C4C2×D1111yescharacteristic
444#398—118no—
445#398—118no—
446#396—118no—
447#396—118no—
448#396—118no—
449#396C2×D1118yescomplemented
450#394—118no—
451#394—118no—
452#386—118no—
453#386—118no—
454#380—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95C2×D1111yescharacteristic
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—88no—
469C22×C11C2×#12114yes—
470C22×C11#53414yes—
471C22×C11#53614yes—
472C22×C11#53714yes—
473C22×C11#53714yes—
474C22×C11#53914yes—
475C22×C11#53914yes—
476C22×C11C23×D411yescharacteristic
477C22×C11C23×D411yescharacteristic
478C22×C11C22×#4111yescharacteristic
479C22×C11C2×H(5,𝔽2)11yescharacteristic
480C22×C11C2×H(5,𝔽2)11yescharacteristic
481C22×C11C2×2−1+411yescharacteristic
482C22×C11C2×2−1+411yescharacteristic
483C2×D11—232no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—88no—
498C2×D11C2×#12118yes—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C22×D4—114no—
515C22×D4—114no—
516C22×D4—114no—
517C22×D4—224no—
518C22×D4—224no—
519C22×D4—224no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—442no—
525C22×D4—442no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—118no—
529C23×C4—114no—
530C23×C4—118no—
531C23×C4—114no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—114no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—442no—
541C23×C4—442no—
542C23×C4—442no—
543C23×C4—442no—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#123—2232no—
551#123—2232no—
552#121—2232no—
553C2×C4⋊C4—24no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—42no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—2232no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4—224no—
572C2×C4⋊C4—442no—
573C2×C4⋊C4C22×D1114yes—
574C2×C4⋊C4C22×D1114yes—
575C2×C4⋊C4C22×D1114yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4—442no—
597C2×C22⋊C4C22×D1114yes—
598C2×C22⋊C4C22×D1114yes—
599C2×C22⋊C4C22×D1114yes—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95C22×D1114yes—
606C2×C11—82no—
607C2×C11#261818yescomplemented
608C2×C11C22×#12111yescharacteristic
609C2×C11C2×#53411yescharacteristic
610C2×C11C2×#53611yescharacteristic
611C2×C11C2×#53711yescharacteristic
612C2×C11C2×#53711yescharacteristic
613C2×C11C2×#53911yescharacteristic
614C2×C11C2×#53911yescharacteristic
615D11—28no—
616D11—82no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—114no—
625C24—114no—
626C24—114no—
627C24—112no—
628C24—112no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—228no—
643C2×D4—228no—
644C2×D4—228no—
645C2×D4—228no—
646C2×D4—228no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—4416no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—4416no—
653C2×D4—4416no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—1116no—
675C22×C4—1116no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—228no—
681C22×C4—2232no—
682C22×C4—228no—
683C22×C4—228no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—4416no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4—444no—
705C22×C4—4416no—
706C22×C4D4×D1114yes—
707C22×C4D4×D1114yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—44no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—228no—
721C4⋊C4—228no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—444no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—44no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C11C2×#261811yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—1116no—
753C23—114no—
754C23—114no—
755C23—114no—
756C23—228no—
757C23—228no—
758C23—228no—
759C23—228no—
760C23—228no—
761C23—228no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23C2×D4×D1112yes—
781C23C2×D4×D1112yes—
782C23#6703712yes—
783C23#6704012yes—
784C23#41×D1112yes—
785C23#6704212yes—
786C23#6704312yes—
787C23C24×D1111yescharacteristic
788D4—4416no—
789D4—4416no—
790D4—4416no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—2232no—
816C2×C4—228no—
817C2×C4—228no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—4416no—
835C2×C4—4416no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4C2×D4×D1114yes—
841C2×C4C2×D4×D1114yes—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—88no—
850C22—118no—
851C22—224no—
852C22—224no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—2232no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—888no—
866C22D11×#12114yes—
867C22#1062313614yes—
868C22#1062313914yes—
869C22#1062315914yes—
870C22#1062316014yes—
871C22#1062316914yes—
872C22#1062323814yes—
873C22C22×D4×D1111yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C2×#6703711yescharacteristic
876C22C2×#6704011yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#6704211yescharacteristic
879C22C2×#6704311yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—224no—
887C4—224no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—82no—
893C2—228no—
894C2—882no—
895C2#1307436318yesdirect product factor
896C2C2×D11×#12111yescharacteristic
897C2C2×#1062313611yescharacteristic
898C2C2×#1062315911yescharacteristic
899C2C2×#1062313911yescharacteristic
900C2C2×#1062316011yescharacteristic
901C2C2×#1062323811yescharacteristic
902C2C2×#1062316911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#396D11
hypocenterC11C2×#2618
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66936C2semidirect
4. C22×C4⋊C4×D11C2semidirect
5. #13074363C2direct (N × H)
6. C2×#10622270C2semidirect
7. C2×#10622597C2semidirect
8. C2×#10622561C2semidirect
9. C2×#10622607C2semidirect
10. C2×#10622607C2semidirect
11. C2×#10622574C2semidirect
12. C2×#10622572C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622600C2semidirect
16. C2×C11×#396C2semidirect
47. C2×#66947C22semidirect
49. C2×C4⋊C4×D11C22semidirect
53. C2×#66936C22semidirect
54. C11×#396C22semidirect
61. #10622607C22semidirect
62. #10622607C22semidirect
63. #10622600C22semidirect
64. #10622597C22semidirect
65. #10622574C22semidirect
66. #10622572C22semidirect
67. #10622569C22semidirect
68. #10622561C22semidirect
69. #10622278C22semidirect
70. #10622270C22semidirect
106. C22×C4×D11D4semidirect
263. C2×C4×D11C2×D4semidirect
297. C2×#396D11semidirect
449. #396C2×D11semidirect
607. C2×C11#2618semidirect
737. C11C2×#2618semidirect
895. C2#13074363direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669362
C22×#669372
C22×C4⋊C4×D112
#130743632
C2×#106222702
C2×#106225972
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225722
C2×#106222782
C2×#106225692
C2×#106226002
C2×C11×#3962
C2×#261811