Finite Group Databasebeta

← C2×#13073533 #14925540

Subgroups — C2×#13073533 #14925540

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×#66940C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
5#13073533C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622607C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic
10C2×#10622570C211yesmaximal, characteristic
11C2×#10622260C211yesmaximal, characteristic, complemented
12C2×#10622585C211yesmaximal, characteristic, complemented
13C2×#10622589C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66949—28no—
49C2×#66949C2218yescomplemented
50C2×#66940—28no—
51C2×#66940C2218yescomplemented
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yes—
54C2×#66931—28no—
55C2×#66931C2218yescomplemented
56C11×#396C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622607C2218yescomplemented
63#10622589C2218yescomplemented
64#10622585C2218yescomplemented
65#10622570C2218yes—
66#10622570C2218yes—
67#10622561C2218yescomplemented
68#10622555C2218yescomplemented
69#10622280C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11Q818yescomplemented
82C22×C22⋊D11C2314yes—
83C23×Dic11—24no—
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11C2314yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×C4×D11—24no—
95C22×C4×D11—24no—
96C22×C4×D11—24no—
97C22×C4×D11C2314yes—
98C22×Dic22—24no—
99C22×Dic22—24no—
100C22×Dic22D418yescomplemented
101C22×Dic22C2314yes—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4—42no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—42no—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×C4⋊Dic11—24no—
129C2×C4⋊Dic11—42no—
130C2×C4⋊Dic11C2314yes—
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⋊C4—24no—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11—24no—
151C2×C4×Dic11—24no—
152C2×C4×Dic11D418yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156#66949—232no—
157#66940—232no—
158(C22⋊D11)⋊C4—232no—
159#66931—232no—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2538—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11C2×Q814yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11C2×Q814yes—
181C23×D11C2412yes—
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×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11C2×D414yes—
199C22×C4×C11C2×D414yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C2×C22⋊D11—232no—
207C2×C22⋊D11—28no—
208C2×C22⋊D11—28no—
209C2×C22⋊D11C2×Q8116yescomplemented
210C22×Dic11—28no—
211C22×Dic11—28no—
212C22×Dic11—28no—
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×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—416no—
228C22×Dic11C2×D414yes—
229C22×Dic11C2×D414yes—
230C22×Dic11C2×D414yes—
231C22×Dic11C2×D414yes—
232C22×Dic11C2×Q814yes—
233C22×Dic11#4114yes—
234C22×Dic11#4114yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—28no—
245C2×C4×D11—416no—
246C2×Dic22—232no—
247C2×Dic22—28no—
248C2×Dic22—28no—
249C2×Dic22C2×D4116yescomplemented
250C11×C4⋊C4—28no—
251C11×C4⋊C4—28no—
252C11×C4⋊C4—44no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—44no—
256C22⋊Dic11—28no—
257C22⋊Dic11—44no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263C4⋊Dic11—28no—
264C4⋊Dic11—44no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274C4×Dic11—28no—
275C4×Dic11—28no—
276C4×Dic11C2×D4116yes—
277C22×C22⋊Q8—111no—
278C22×C22⋊Q8—111no—
279C22×C4×Q8—111no—
280C22×C4×D4—111no—
281#2538—1116no—
282C2×#396—111no—
283C2×#396—111no—
284C2×#396—111no—
285C2×#396D1111yescharacteristic, complemented
286C2×#390—111no—
287C2×#390—111no—
288C2×#389—111no—
289C2×#389—111no—
290C2×#384—111no—
291C2×#380—111no—
292C2×#380—111no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
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×C11C22×D412yes—
307C23×C11C22×D412yes—
308C23×C11C22×Q814yes—
309C23×C11C22×Q812yes—
310C23×C11C2×#4112yes—
311C23×C11C2×#4112yes—
312C23×C11H(5,𝔽2)12yes—
313C23×C112−1+412yes—
314C23×C11C2511yescharacteristic
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—28no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11C22×Q814yes—
329C2×C4×C11—28no—
330C2×C4×C11—28no—
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—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—44no—
348C2×C4×C11—44no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
351C2×C4×C11C22×D414yes—
352C2×C4×C11C22×D414yes—
353C22⋊D11—232no—
354C2×Dic11—28no—
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—22no—
368C2×Dic11—22no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—416no—
374C2×Dic11#121116yes—
375C2×Dic11C22⋊Q8116yescomplemented
376C2×Dic11C22×D414yes—
377C2×Dic11C22×D414yes—
378C2×Dic11C22×D414yes—
379C2×Dic11C22×D414yes—
380C2×Dic11C22×Q814yes—
381C2×Dic11C2×#4114yes—
382C2×Dic11C2×#4114yes—
383C4×D11—416no—
384Dic22—232no—
385C23×Q8—111no—
386C23×D4—111no—
387C24×C4—111no—
388C24×C4—111no—
389C2×C22⋊Q8—118no—
390C2×C22⋊Q8—118no—
391C2×C22⋊Q8—228no—
392C2×C22⋊Q8—228no—
393C2×C4×Q8—118no—
394C2×C4×Q8—228no—
395C2×C4×D4—118no—
396C2×C4×D4—228no—
397C22×C4⋊C4—111no—
398C22×C4⋊C4—111no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4C2×D1111yescharacteristic
409C22×C4⋊C4C2×D1111yescharacteristic
410C22×C4⋊C4C2×D1111yescharacteristic
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#396—118no—
425#396—118no—
426#396—118no—
427#396C2×D1118yescomplemented
428#390—118no—
429#390—118no—
430#389—118no—
431#389—118no—
432#384—118no—
433#380—118no—
434#380—118no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95C2×D1111yescharacteristic
439C22×C11—24no—
440C22×C11—24no—
441C22×C11—24no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—416no—
447C22×C11C2×#12114yes—
448C22×C11C2×C22⋊Q814yes—
449C22×C11#53714yes—
450C22×C11D4×Q814yes—
451C22×C11#55014yes—
452C22×C11#55414yes—
453C22×C11#55614yes—
454C22×C11C23×D411yescharacteristic
455C22×C11C23×D411yescharacteristic
456C22×C11C23×Q811yescharacteristic
457C22×C11C22×#4111yescharacteristic
458C22×C11C22×#4111yescharacteristic
459C22×C11C2×H(5,𝔽2)11yescharacteristic
460C22×C11C2×2−1+411yescharacteristic
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—416no—
469C4×C11—24no—
470C4×C11—24no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475Dic11—24no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480Dic11C2×#12118yes—
481Dic11C2×C22⋊Q818yescomplemented
482C25—111no—
483C25C22×D1111yescharacteristic
484C22×Q8—118no—
485C22×Q8—114no—
486C22×Q8—224no—
487C22×Q8—224no—
488C22×D4—118no—
489C22×D4—114no—
490C22×D4—224no—
491C22×D4—224no—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—114no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—114no—
501C23×C4—224no—
502C23×C4—224no—
503C23×C4—224no—
504C23×C4—224no—
505C23×C4—224no—
506C23×C4—224no—
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C23×C4C22×D1111yescharacteristic
513C22⋊Q8—2232no—
514C22⋊Q8—2232no—
515C4×Q8—2232no—
516C4×D4—2232no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4—114no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—224no—
532C2×C4⋊C4—224no—
533C2×C4⋊C4—224no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—224no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—442no—
542C2×C4⋊C4C22×D1114yes—
543C2×C4⋊C4C22×D1114yes—
544C2×C4⋊C4C22×D1114yes—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4C22×D1114yes—
563C2×C22⋊C4C22×D1114yes—
564C2×C22⋊C4C22×D1114yes—
565C2×C42—118no—
566C2×C42—114no—
567C2×C42—114no—
568C2×C42—114no—
569C2×C42—224no—
570C2×C42—224no—
571#95—114no—
572#95—114no—
573#95—114no—
574#95C22×D1114yes—
575C2×C11—44no—
576C2×C11#253818yescomplemented
577C2×C11C22×#12111yescharacteristic
578C2×C11C22×C22⋊Q811yescharacteristic
579C2×C11C2×#53711yescharacteristic
580C2×C11C2×D4×Q811yescharacteristic
581C2×C11C2×#55011yescharacteristic
582C2×C11C2×#55411yescharacteristic
583C2×C11C2×#55611yescharacteristic
584D11—44no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—114no—
592C24—112no—
593C24—222no—
594C24—222no—
595C24—222no—
596C24—222no—
597C24—222no—
598C24—222no—
599C24Q8×D1114yes—
600C24C23×D1112yes—
601C24C23×D1111yescharacteristic
602C2×Q8—1116no—
603C2×Q8—228no—
604C2×Q8—2232no—
605C2×Q8—228no—
606C2×D4—1116no—
607C2×D4—228no—
608C2×D4—2232no—
609C2×D4—228no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—114no—
627C22×C4—114no—
628C22×C4—114no—
629C22×C4—114no—
630C22×C4—114no—
631C22×C4—114no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—114no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—228no—
641C22×C4—228no—
642C22×C4—228no—
643C22×C4—228no—
644C22×C4—228no—
645C22×C4—228no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—4416no—
661C22×C4—4416no—
662C22×C4D4×D1114yes—
663C22×C4D4×D1114yes—
664C22×C4C23×D1112yes—
665C22×C4C23×D1112yes—
666C22×C4C23×D1112yes—
667C22×C4C23×D1112yes—
668C22×C4C23×D1112yes—
669C22×C4C23×D1112yes—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—44no—
673C4⋊C4—228no—
674C4⋊C4—228no—
675C4⋊C4—228no—
676C4⋊C4—228no—
677C4⋊C4—228no—
678C4⋊C4—228no—
679C4⋊C4—228no—
680C4⋊C4—228no—
681C4⋊C4—228no—
682C4⋊C4—228no—
683C4⋊C4—444no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—44no—
687C22⋊C4—228no—
688C22⋊C4—228no—
689C22⋊C4—228no—
690C22⋊C4—228no—
691C22⋊C4—444no—
692C22⋊C4—444no—
693C22⋊C4—444no—
694C42—1116no—
695C42—228no—
696C42—228no—
697C11C2×#253811yescharacteristic, complemented, Sylow
698C23—28no—
699C23—28no—
700C23—28no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—114no—
712C23—228no—
713C23—228no—
714C23—228no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—444no—
722C23—444no—
723C23—444no—
724C23—444no—
725C23C2×D4×D1112yes—
726C23C2×D4×D1112yes—
727C23#6703712yes—
728C23C2×Q8×D1114yes—
729C23C2×Q8×D1112yes—
730C23#41×D1112yes—
731C23#41×D1112yes—
732C23#6704312yes—
733C23C24×D1111yescharacteristic
734Q8—2232no—
735D4—2232no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—1116no—
759C2×C4—1116no—
760C2×C4—114no—
761C2×C4—114no—
762C2×C4—114no—
763C2×C4—114no—
764C2×C4—114no—
765C2×C4—114no—
766C2×C4—114no—
767C2×C4—228no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—4416no—
783C2×C4—4416no—
784C2×C4—444no—
785C2×C4—444no—
786C2×C4—444no—
787C2×C4—444no—
788C2×C4C2×D4×D1114yes—
789C2×C4C2×D4×D1114yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—416no—
796C22—42no—
797C22—42no—
798C22—224no—
799C22—224no—
800C22—224no—
801C22—442no—
802C22—442no—
803C22—4416no—
804C22—442no—
805C22—442no—
806C22#1062312814yes—
807C22#1062313014yes—
808C22D11×#12114yes—
809C22D11×C22⋊Q814yes—
810C22#1062316314yes—
811C22#1062316714yes—
812C22#1062323314yes—
813C22C22×D4×D1111yescharacteristic
814C22C22×D4×D1111yescharacteristic
815C22C2×#6703711yescharacteristic
816C22C22×Q8×D1111yescharacteristic
817C22C2×#41×D1111yescharacteristic
818C22C2×#41×D1111yescharacteristic
819C22C2×#6704311yescharacteristic
820C4—24no—
821C4—24no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—118no—
827C4—118no—
828C4—224no—
829C4—442no—
830C4—442no—
831C4—442no—
832C4—442no—
833C2—44no—
834C2—444no—
835C2#1307353318yesdirect product factor
836C2C2×D11×#12111yescharacteristic
837C2C2×D11×C22⋊Q811yescharacteristic
838C2C2×#1062312811yescharacteristic
839C2C2×#1062316311yescharacteristic
840C2C2×#1062313011yescharacteristic
841C2C2×#1062316711yescharacteristic
842C2C2×#1062323311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2538
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. C22×#66931C2semidirect
3. C22×#66940C2semidirect
5. #13073533C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622607C2semidirect
11. C2×#10622260C2semidirect
12. C2×#10622585C2semidirect
13. C2×#10622589C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#396C2semidirect
49. C2×#66949C22semidirect
51. C2×#66940C22semidirect
55. C2×#66931C22semidirect
56. C11×#396C22semidirect
61. #10622607C22semidirect
62. #10622607C22semidirect
63. #10622589C22semidirect
64. #10622585C22semidirect
67. #10622561C22semidirect
68. #10622555C22semidirect
69. #10622280C22semidirect
70. #10622260C22semidirect
81. C22×C22⋊D11Q8semidirect
100. C22×Dic22D4semidirect
209. C2×C22⋊D11C2×Q8semidirect
249. C2×Dic22C2×D4semidirect
285. C2×#396D11semidirect
375. C2×Dic11C22⋊Q8semidirect
427. #396C2×D11semidirect
481. Dic11C2×C22⋊Q8semidirect
576. C2×C11#2538semidirect
697. C11C2×#2538semidirect
835. C2#13073533direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669312
C22×#669402
C22×(C22⋊D11)⋊C42
#130735332
C2×#106225612
C2×#106226072
C2×#106225702
C2×#106222602
C2×#106225852
C2×#106225892
C2×#106222802
C2×#106225552
C2×C11×#3962
C2×#253811