Finite Group Databasebeta

← C2×#13072020 #14922469

Subgroups — C2×#13072020 #14922469

Order 2816.

3570 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C22×#66947C211yesmaximal, characteristic
3C22×#66925C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072020C2116yesmaximal, direct product factor
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622593C211yesmaximal, characteristic, complemented
8C2×#10622289C211yesmaximal, characteristic, complemented
9C2×#10622607C211yesmaximal, characteristic, complemented
10C2×#10622585C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622603C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622277C211yesmaximal, characteristic, complemented
16C2×C11×#389C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66947—28no—
45C2×#66947—28no—
46C2×#66947C2218yes—
47C2×#66947C2218yes—
48C2×C4⋊C4×D11—28no—
49C2×C4⋊C4×D11C2218yescomplemented
50C2×#66925—28no—
51C2×#66925C2218yescomplemented
52C11×#389C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622603C2218yescomplemented
63#10622602C2218yescomplemented
64#10622593C2218yescomplemented
65#10622585C2218yescomplemented
66#10622553C2218yescomplemented
67#10622289C2218yescomplemented
68#10622278C2218yes—
69#10622277C2218yescomplemented
70#10622270C2218yescomplemented
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44C2314yes—
90C22×C4×D11—24no—
91C22×C4×D11—24no—
92C22×C4×D11—24no—
93C22×C4×D11—24no—
94C22×C4×D11—24no—
95C22×C4×D11—24no—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11D418yes—
99C22×C4×D11C2314yes—
100C22×C4×D11C2314yes—
101C22×C4×D11C2314yes—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C42×C11—24no—
111C2×C42×C11C2314yes—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4D418yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×C4⋊Dic11—24no—
131C2×C4⋊Dic11C2314yes—
132C2×Dic11⋊C4—24no—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2314yes—
148#66947—232no—
149#66947—232no—
150C4⋊C4×D11—232no—
151#66925—232no—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C2×#2413—111nomaximal, Sylow
161C24×C11C2411yescharacteristic
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11C2×D414yes—
174C23×D11C2×D414yes—
175C23×D11#4114yes—
176C23×D11C2412yes—
177C23×D11C2412yes—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
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×C11C2×D414yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11#4114yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11C2×D414yes—
222C22×Dic11C2×D414yes—
223C22×Dic11#4114yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C2×D44—28no—
231C2×D44—28no—
232C2×D44—28no—
233C2×D44—416no—
234C2×C4×D11—232no—
235C2×C4×D11—28no—
236C2×C4×D11—232no—
237C2×C4×D11—28no—
238C2×C4×D11—28no—
239C2×C4×D11—28no—
240C2×C4×D11—28no—
241C2×C4×D11—28no—
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—416no—
245C2×C4×D11C2×D4116yes—
246C11×C4⋊C4—28no—
247C11×C4⋊C4—28no—
248C11×C4⋊C4—28no—
249C11×C4⋊C4—28no—
250C42×C11—28no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—28no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4C2×D4116yes—
260C4⋊Dic11—28no—
261Dic11⋊C4—28no—
262Dic11⋊C4—28no—
263Dic11⋊C4—28no—
264Dic11⋊C4—28no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268C4×Dic11—28no—
269C22×#123—111no—
270C22×#123—111no—
271C22×#117—111no—
272C23×C4⋊C4—111no—
273#2413—1116no—
274C2×#398—111no—
275C2×#398—111no—
276C2×#396—111no—
277C2×#396—111no—
278C2×#389—111no—
279C2×#389D1111yescharacteristic, complemented
280C2×#388—111no—
281C2×#388—111no—
282C2×#386—111no—
283C2×#385—111no—
284C2×#381—111no—
285C23×C11C22×D412yes—
286C23×C11C22×D412yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C112−1+412yes—
291C23×C112−1+412yes—
292C23×C11C2511yescharacteristic
293C22×D11—28no—
294C22×D11—28no—
295C22×D11—28no—
296C22×D11—28no—
297C22×D11—28no—
298C22×D11—28no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—44no—
311C22×D11—44no—
312C22×D11—44no—
313C22×D11—44no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—44no—
317C22×D11#121116yes—
318C22×D11C22×D414yes—
319C22×D11C22×D414yes—
320C22×D11C2×#4114yes—
321C2×C4×C11—28no—
322C2×C4×C11—28no—
323C2×C4×C11—28no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11C22×D414yes—
347C2×C4×C11C22×D414yes—
348C2×C4×C11C2×#4114yes—
349C2×Dic11—28no—
350C2×Dic11—28no—
351C2×Dic11—28no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—44no—
368C2×Dic11—44no—
369C2×Dic11—44no—
370C2×Dic11C22×D414yes—
371C2×Dic11C22×D414yes—
372C2×Dic11C2×#4114yes—
373D44—416no—
374C4×D11—232no—
375C4×D11—232no—
376C4×D11—416no—
377C23×D4—111no—
378C24×C4—111no—
379C24×C4—111no—
380C24×C4—111no—
381C2×#123—118no—
382C2×#123—118no—
383C2×#123—228no—
384C2×#123—228no—
385C2×#117—118no—
386C2×#117—228no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—111no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4—111no—
395C22×C4⋊C4—118no—
396C22×C4⋊C4—228no—
397C22×C4⋊C4C2×D1111yescharacteristic
398C22×C4⋊C4C2×D1111yescharacteristic
399C22×C4⋊C4C2×D1111yescharacteristic
400C22×C4⋊C4C2×D1111yescharacteristic
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C22⋊C4—111no—
404C22×C22⋊C4—111no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C42—111no—
411C22×C42C2×D1111yescharacteristic
412#398—118no—
413#398—118no—
414#396—118no—
415#396—118no—
416#389—118no—
417#389C2×D1118yescomplemented
418#388—118no—
419#388—118no—
420#386—118no—
421#385—118no—
422#381—118no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95—111no—
428C2×#95—111no—
429C2×#95C2×D1111yescharacteristic
430C2×#95C2×D1111yescharacteristic
431C22×C11C2×#12114yes—
432C22×C11#52514yes—
433C22×C11#53614yes—
434C22×C11#54714yes—
435C22×C11#54714yes—
436C22×C11#55214yes—
437C22×C11#55214yes—
438C22×C11C23×D411yescharacteristic
439C22×C11C23×D411yescharacteristic
440C22×C11C22×#4111yescharacteristic
441C22×C11C22×#4111yescharacteristic
442C22×C11C22×#4111yescharacteristic
443C22×C11C2×2−1+411yescharacteristic
444C22×C11C2×2−1+411yescharacteristic
445C2×D11—24no—
446C2×D11—232no—
447C2×D11—24no—
448C2×D11—24no—
449C2×D11—24no—
450C2×D11—24no—
451C2×D11—24no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—88no—
460C2×D11C2×#12118yes—
461C4×C11—24no—
462C4×C11—24no—
463C4×C11—24no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468Dic11—24no—
469Dic11—24no—
470Dic11—24no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C25—111no—
475C25—111no—
476C22×D4—114no—
477C22×D4—224no—
478C22×D4—224no—
479C22×D4—224no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—118no—
484C23×C4—114no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—114no—
489C23×C4—114no—
490C23×C4—224no—
491C23×C4—224no—
492C23×C4—224no—
493C23×C4—224no—
494C23×C4—224no—
495C23×C4—224no—
496C23×C4—224no—
497C23×C4—224no—
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C23×C4C22×D1111yescharacteristic
505#123—2232no—
506#123—2232no—
507#117—2232no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—114no—
520C2×C4⋊C4—2232no—
521C2×C4⋊C4—224no—
522C2×C4⋊C4—224no—
523C2×C4⋊C4—224no—
524C2×C4⋊C4—224no—
525C2×C4⋊C4—224no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4—224no—
529C2×C4⋊C4C22×D1114yes—
530C2×C4⋊C4C22×D1114yes—
531C2×C4⋊C4C22×D1114yes—
532C2×C4⋊C4C22×D1114yes—
533C2×C22⋊C4—118no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—224no—
544C2×C22⋊C4—224no—
545C2×C22⋊C4—224no—
546C2×C22⋊C4—224no—
547C2×C22⋊C4—224no—
548C2×C22⋊C4—224no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C42—24no—
552C2×C42—114no—
553C2×C42—224no—
554C2×C42C22×D1114yes—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95C22×D1114yes—
562#95C22×D1114yes—
563C2×C11#241318yescomplemented
564C2×C11C22×#12111yescharacteristic
565C2×C11C2×#52511yescharacteristic
566C2×C11C2×#53611yescharacteristic
567C2×C11C2×#54711yescharacteristic
568C2×C11C2×#54711yescharacteristic
569C2×C11C2×#55211yescharacteristic
570C2×C11C2×#55211yescharacteristic
571D11—28no—
572D11—82no—
573C24—114no—
574C24—114no—
575C24—114no—
576C24—112no—
577C24—112no—
578C24—222no—
579C24—222no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24—222no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—222no—
588C24—222no—
589C24C23×D1111yescharacteristic
590C2×D4—228no—
591C2×D4—228no—
592C2×D4—228no—
593C2×D4—4416no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—114no—
613C22×C4—114no—
614C22×C4—114no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—1116no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—228no—
623C22×C4—228no—
624C22×C4—228no—
625C22×C4—2232no—
626C22×C4—228no—
627C22×C4—2232no—
628C22×C4—228no—
629C22×C4—228no—
630C22×C4—228no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—228no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—4416no—
648C22×C4#433914yes—
649C22×C4D4×D1114yes—
650C22×C4D4×D1114yes—
651C22×C4C23×D1112yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—228no—
663C4⋊C4—228no—
664C4⋊C4—228no—
665C4⋊C4—228no—
666C4⋊C4—228no—
667C4⋊C4—228no—
668C4⋊C4—228no—
669C4⋊C4—228no—
670C22⋊C4—1116no—
671C22⋊C4—228no—
672C22⋊C4—228no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—228no—
676C22⋊C4—228no—
677C22⋊C4—228no—
678C22⋊C4—228no—
679C42—28no—
680C42—228no—
681C11C2×#241311yescharacteristic, complemented, Sylow
682C23—1116no—
683C23—114no—
684C23—114no—
685C23—114no—
686C23—228no—
687C23—228no—
688C23—228no—
689C23—228no—
690C23—228no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—228no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—222no—
703C23—444no—
704C23—444no—
705C23—444no—
706C23—444no—
707C23—444no—
708C23—444no—
709C23—444no—
710C23C2×#433912yes—
711C23C2×D4×D1112yes—
712C23C2×D4×D1112yes—
713C23#6704012yes—
714C23#6704012yes—
715C23#41×D1112yes—
716C23#41×D1112yes—
717C23C24×D1111yescharacteristic
718D4—4416no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—114no—
745C2×C4—114no—
746C2×C4—114no—
747C2×C4—2232no—
748C2×C4—2232no—
749C2×C4—228no—
750C2×C4—228no—
751C2×C4—228no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—4416no—
768C2×C4—444no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4C2×#433914yes—
772C2×C4C2×D4×D1114yes—
773C2×C4C2×D4×D1114yes—
774C22—118no—
775C22—224no—
776C22—224no—
777C22—224no—
778C22—224no—
779C22—2232no—
780C22—224no—
781C22—224no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—888no—
790C22#1062303814yes—
791C22#1062307814yes—
792C22#1062311214yes—
793C22D11×#12114yes—
794C22#1062316214yes—
795C22#1062322414yes—
796C22#1062325514yes—
797C22C22×#433911yescharacteristic
798C22C22×D4×D1111yescharacteristic
799C22C22×D4×D1111yescharacteristic
800C22C2×#6704011yescharacteristic
801C22C2×#6704011yescharacteristic
802C22C2×#41×D1111yescharacteristic
803C22C2×#41×D1111yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—224no—
812C4—224no—
813C4—224no—
814C4—442no—
815C4—442no—
816C4—442no—
817C2—228no—
818C2—882no—
819C2#1307202018yesdirect product factor
820C2C2×D11×#12111yescharacteristic
821C2C2×#1062307811yescharacteristic
822C2C2×#1062325511yescharacteristic
823C2C2×#1062303811yescharacteristic
824C2C2×#1062316211yescharacteristic
825C2C2×#1062322411yescharacteristic
826C2C2×#1062311211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11C2×#2413
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C22×#66925C2semidirect
4. C22×C4⋊C4×D11C2semidirect
5. #13072020C2direct (N × H)
6. C2×#10622270C2semidirect
7. C2×#10622593C2semidirect
8. C2×#10622289C2semidirect
9. C2×#10622607C2semidirect
10. C2×#10622585C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622603C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622277C2semidirect
16. C2×C11×#389C2semidirect
49. C2×C4⋊C4×D11C22semidirect
51. C2×#66925C22semidirect
52. C11×#389C22semidirect
61. #10622607C22semidirect
62. #10622603C22semidirect
63. #10622602C22semidirect
64. #10622593C22semidirect
65. #10622585C22semidirect
66. #10622553C22semidirect
67. #10622289C22semidirect
69. #10622277C22semidirect
70. #10622270C22semidirect
279. C2×#389D11semidirect
417. #389C2×D11semidirect
563. C2×C11#2413semidirect
681. C11C2×#2413semidirect
819. C2#13072020direct (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×#669252
C22×C4⋊C4×D112
#130720202
C2×#106222702
C2×#106225932
C2×#106222892
C2×#106226072
C2×#106225852
C2×#106225532
C2×#106226032
C2×#106222782
C2×#106226022
C2×#106222772
C2×C11×#3892
C2×#241311