Finite Group Databasebeta

← C2×#13073624 #14923812

Subgroups — C2×#13073624 #14923812

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2#13073624C2116yesmaximal, direct product factor
3C2×#10622593C211yesmaximal, characteristic, complemented
4C2×#10622596C211yesmaximal, characteristic, complemented
5C2×#10622592C211yesmaximal, characteristic, complemented
6C2×#10622842C211yesmaximal, characteristic, complemented
7C2×#10622843C211yesmaximal, characteristic, complemented
8C2×#10622587C211yesmaximal, characteristic, complemented
9C2×#10622585C211yesmaximal, characteristic, complemented
10C2×#10622585C211yesmaximal, characteristic, complemented
11C2×#10622823C211yesmaximal, characteristic
12C2×#10622559C211yesmaximal, characteristic
13C2×#10622555C211yesmaximal, characteristic
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic
15C22×C11⋊#95C211yesmaximal, characteristic
16C22×C11×C22⋊Q8C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C2×C11×C22⋊Q8—28no—
23C2×C11×C22⋊Q8C2218yes—
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66931—28no—
43C2×#66931C2218yes—
44#10622843C2218yescomplemented
45#10622842C2218yescomplemented
46#10622823C2218yes—
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2218yes—
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622596C2218yescomplemented
61#10622593C2218yescomplemented
62#10622592C2218yescomplemented
63#10622587C2218yescomplemented
64#10622585C2218yescomplemented
65#10622585C2218yescomplemented
66#10622559C2218yes—
67#10622555C2218yes—
68C22⋊C4×Dic11C2218yes—
69C25×C11C2311yescharacteristic
70C22×Q8×C11—24no—
71C22×Q8×C11—24no—
72C22×Q8×C11—42no—
73C22×Q8×C11C2314yes—
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—42no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11—42no—
87C23×Dic11—42no—
88C23×Dic11—42no—
89C23×Dic11Q818yescomplemented
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2314yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2314yes—
100C22×Dic22—24no—
101C22×Dic22—24no—
102C22×Dic22—42no—
103C22×Dic22C2314yes—
104C11×C22⋊Q8—232no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4—24no—
107C2×C11×C4⋊C4—24no—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4D418yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11Q818yescomplemented
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C4⋊Dic11—24no—
120C2×C4⋊Dic11C2314yes—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4—24no—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—42no—
126C2×Dic11⋊C4—42no—
127C2×Dic11⋊C4—42no—
128C2×Dic11⋊C4—42no—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×C4×Dic11—42no—
138C2×C4×Dic11—42no—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141#66931—232no—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C2×#2549—111nomaximal, Sylow
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11C2×D414yes—
160C24×C11C2×Q814yes—
161C24×C11C2×Q814yes—
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C2×Q8×C11—28no—
165C2×Q8×C11—28no—
166C2×Q8×C11—44no—
167C2×Q8×C11—416no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—28no—
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—28no—
185C22×C4×C11—44no—
186C22×C4×C11—416no—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11#4114yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×Dic11—28no—
197C22×Dic11—22no—
198C22×Dic11—28no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
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—416no—
218C22×Dic11—44no—
219C22×Dic11—44no—
220C22×Dic11—44no—
221C22×Dic11—416no—
222C22×Dic11C2×Q814yes—
223C22×Dic11C2×Q814yes—
224C22×Dic11C2×Q814yes—
225C22×Dic11C2×Q814yes—
226C22×Dic11C2×Q8116yescomplemented
227C22×Dic11#4114yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C2×Dic22—28no—
237C2×Dic22—28no—
238C2×Dic22—44no—
239C2×Dic22—416no—
240C11×C4⋊C4—28no—
241C11×C4⋊C4—28no—
242C11×C4⋊C4—28no—
243C11×C22⋊C4—28no—
244C11×C22⋊C4C2×D4116yes—
245C22⋊Dic11—28no—
246C22⋊Dic11C2×Q8116yescomplemented
247C4⋊Dic11—28no—
248Dic11⋊C4—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—28no—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256C4×Dic11—44no—
257C4×Dic11—44no—
258C22×C22⋊Q8—111no—
259C22×C22⋊Q8D1111yescharacteristic
260#2549—1116no—
261C2×#398—111no—
262C2×#398—111no—
263C2×#395—111no—
264C2×#395—111no—
265C2×#391—111no—
266C2×#391—111no—
267C2×#389—111no—
268C2×#389—111no—
269C2×#385—111no—
270C2×#385—111no—
271C2×#380—111no—
272C2×C4×C22⋊C4—111no—
273C22×#95—111no—
274C23×C11—28no—
275C23×C11—28no—
276C23×C11—28no—
277C23×C11—28no—
278C23×C11—28no—
279C23×C11—28no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11C4⋊Q8116yes—
285C23×C11C22×D414yes—
286C23×C11C22×D412yes—
287C23×C11C22×Q814yes—
288C23×C11C22×Q814yes—
289C23×C11C22×Q812yes—
290C23×C11C22×Q812yes—
291C23×C11C2×#4112yes—
292C23×C11C2×#4112yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11H(5,𝔽2)12yes—
295C23×C11C2511yescharacteristic
296Q8×C11—416no—
297C2×C4×C11—28no—
298C2×C4×C11—28no—
299C2×C4×C11—28no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—416no—
316C2×C4×C11—44no—
317C2×C4×C11—44no—
318C2×C4×C11—44no—
319C2×C4×C11C22×D414yes—
320C2×C4×C11C22×D414yes—
321C2×C4×C11C2×#4114yes—
322C2×Dic11—28no—
323C2×Dic11—28no—
324C2×Dic11—28no—
325C2×Dic11—28no—
326C2×Dic11—28no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—416no—
347C2×Dic11—416no—
348C2×Dic11—44no—
349C2×Dic11—44no—
350C2×Dic11—44no—
351C2×Dic11C22×Q814yes—
352C2×Dic11C22×Q814yes—
353C2×Dic11C22×Q814yes—
354C2×Dic11C22×Q814yes—
355C2×Dic11C2×#4114yes—
356Dic22—416no—
357C23×Q8—111no—
358C23×Q8C2×D1111yescharacteristic
359C24×C4—111no—
360C24×C4—111no—
361C24×C4C2×D1111yescharacteristic
362C2×C22⋊Q8—28no—
363C2×C22⋊Q8—118no—
364C2×C22⋊Q8—228no—
365C2×C22⋊Q8C2×D1118yes—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4C2×D1111yescharacteristic
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C4⋊C4C2×D1111yescharacteristic
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4C2×D1111yescharacteristic
381C22×C22⋊C4C2×D1111yescharacteristic
382C22×C42—111no—
383C22×C42—111no—
384#398—118no—
385#398—118no—
386#395—118no—
387#395—118no—
388#391—118no—
389#391—118no—
390#389—118no—
391#389—118no—
392#385—118no—
393#385—118no—
394#380—118no—
395C4×C22⋊C4—118no—
396C2×#95—111no—
397C2×#95—111no—
398C2×#95—111no—
399C2×#95—111no—
400C2×#95—111no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—118no—
407C2×#95—111no—
408C2×#95—111no—
409C22×C11—24no—
410C22×C11—24no—
411C22×C11—24no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—232no—
416C22×C11C2×C4⋊Q818yes—
417C22×C11C2×C4⋊Q814yes—
418C22×C11#53314yes—
419C22×C11#54314yes—
420C22×C11#54614yes—
421C22×C11#54614yes—
422C22×C11#55414yes—
423C22×C11#55414yes—
424C22×C11C23×D411yescharacteristic
425C22×C11C23×Q811yescharacteristic
426C22×C11C23×Q811yescharacteristic
427C22×C11C22×#4111yescharacteristic
428C22×C11C22×#4111yescharacteristic
429C22×C11C2×H(5,𝔽2)11yescharacteristic
430C22×C11C2×H(5,𝔽2)11yescharacteristic
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—24no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437Dic11—24no—
438Dic11—24no—
439Dic11—24no—
440Dic11—24no—
441Dic11—24no—
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445C25C22×D1111yescharacteristic
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8—114no—
450C22×Q8—224no—
451C22×Q8—224no—
452C22×Q8—442no—
453C22×Q8C22×D1114yes—
454C23×C4—24no—
455C23×C4—24no—
456C23×C4—42no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—118no—
463C23×C4—114no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—114no—
468C23×C4—224no—
469C23×C4—224no—
470C23×C4—442no—
471C23×C4—442no—
472C23×C4—442no—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1114yes—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C22⋊Q8—232no—
481C22⋊Q8—2232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—442no—
500C2×C4⋊C4—442no—
501C2×C4⋊C4—442no—
502C2×C4⋊C4—442no—
503C2×C4⋊C4C22×D1114yes—
504C2×C4⋊C4C22×D1114yes—
505C2×C4⋊C4C22×D1114yes—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4C22⋊D1118yes—
512C2×C22⋊C4C22×D1114yes—
513C2×C22⋊C4C22×D1114yes—
514C2×C42—114no—
515C2×C42—114no—
516C2×C42—442no—
517C2×C42—442no—
518#95—114no—
519#95—114no—
520#95—114no—
521#95—114no—
522#95—114no—
523#95—114no—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530C2×C11—28no—
531C2×C11#254918yescomplemented
532C2×C11C22×C4⋊Q811yescharacteristic
533C2×C11C2×#53311yescharacteristic
534C2×C11C2×#54311yescharacteristic
535C2×C11C2×#54611yescharacteristic
536C2×C11C2×#54611yescharacteristic
537C2×C11C2×#55411yescharacteristic
538C2×C11C2×#55411yescharacteristic
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24Q8×D1114yes—
544C24Q8×D1114yes—
545C24C2×C22⋊D1114yes—
546C24C23×D1112yes—
547C24C23×D1111yescharacteristic
548C2×Q8—28no—
549C2×Q8—28no—
550C2×Q8—44no—
551C2×Q8—416no—
552C2×Q8—228no—
553C2×Q8—228no—
554C2×Q8—444no—
555C2×Q8—4416no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—44no—
574C22×C4—416no—
575C22×C4—114no—
576C22×C4—114no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—114no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—1116no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—228no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—228no—
610C22×C4—4416no—
611C22×C4—444no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4—4416no—
615C22×C4#434114yes—
616C22×C4C2×C22⋊D1114yes—
617C22×C4C2×C22⋊D1114yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1112yes—
620C22×C4C23×D1112yes—
621C22×C4C23×D1112yes—
622C22×C4C23×D1112yes—
623C22×C4C23×D1112yes—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—228no—
628C4⋊C4—228no—
629C4⋊C4—228no—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—444no—
633C4⋊C4—444no—
634C4⋊C4—444no—
635C4⋊C4—444no—
636C22⋊C4—28no—
637C22⋊C4—1116no—
638C22⋊C4—228no—
639C22⋊C4C2×C22⋊D11116yes—
640C42—444no—
641C42—444no—
642C11C2×#254911yescharacteristic, complemented, Sylow
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23#66997116yes—
654C23C2×#434112yes—
655C23#6703712yes—
656C23C2×Q8×D1114yes—
657C23C2×Q8×D1114yes—
658C23C2×Q8×D1112yes—
659C23C2×Q8×D1112yes—
660C23#41×D1112yes—
661C23#6704212yes—
662C23C22×C22⋊D1114yes—
663C23C22×C22⋊D1112yes—
664C23C24×D1111yescharacteristic
665Q8—416no—
666Q8—4416no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—114no—
690C2×C4—114no—
691C2×C4—114no—
692C2×C4—114no—
693C2×C4—114no—
694C2×C4—228no—
695C2×C4—228no—
696C2×C4—228no—
697C2×C4—228no—
698C2×C4—228no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—4416no—
719C2×C4—4416no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4—444no—
723C2×C4C2×#434114yes—
724C2×C4C22×C22⋊D1114yes—
725C2×C4C22×C22⋊D1114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—232no—
733C22#1062315314yes—
734C22#1062316514yes—
735C22#1062316614yes—
736C22#1062316714yes—
737C22#1062333714yes—
738C22C2×#6699718yes—
739C22C2×#6699714yes—
740C22#1062336014yes—
741C22C22×#434111yescharacteristic
742C22C2×#6703711yescharacteristic
743C22C22×Q8×D1111yescharacteristic
744C22C22×Q8×D1111yescharacteristic
745C22C2×#41×D1111yescharacteristic
746C22C2×#6704211yescharacteristic
747C22C23×C22⋊D1111yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—224no—
755C4—224no—
756C4—224no—
757C4—224no—
758C4—224no—
759C4—442no—
760C4—442no—
761C4—442no—
762C2—28no—
763C2#1307362418yesdirect product factor
764C2C22×#6699711yescharacteristic
765C2C2×#1062315311yescharacteristic
766C2C2×#1062316511yescharacteristic
767C2C2×#1062336011yescharacteristic
768C2C2×#1062333711yescharacteristic
769C2C2×#1062316711yescharacteristic
770C2C2×#1062316611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2549
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13073624C2direct (N × H)
3. C2×#10622593C2semidirect
4. C2×#10622596C2semidirect
5. C2×#10622592C2semidirect
6. C2×#10622842C2semidirect
7. C2×#10622843C2semidirect
8. C2×#10622587C2semidirect
9. C2×#10622585C2semidirect
10. C2×#10622585C2semidirect
44. #10622843C22semidirect
45. #10622842C22semidirect
60. #10622596C22semidirect
61. #10622593C22semidirect
62. #10622592C22semidirect
63. #10622587C22semidirect
64. #10622585C22semidirect
65. #10622585C22semidirect
89. C23×Dic11Q8semidirect
116. C2×C22⋊Dic11Q8semidirect
226. C22×Dic11C2×Q8semidirect
246. C22⋊Dic11C2×Q8semidirect
531. C2×C11#2549semidirect
642. C11C2×#2549semidirect
763. C2#13073624direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
#130736242
C2×#106225932
C2×#106225962
C2×#106225922
C2×#106228422
C2×#106228432
C2×#106225872
C2×#106225852
C2×#106228232
C2×#106225592
C2×#106225552
C2×C22⋊C4×Dic112
C22×C11⋊#952
C22×C11×C22⋊Q82
C2×#254911