Finite Group Databasebeta

← C2×#13073626 #14923816

Subgroups — C2×#13073626 #14923816

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×#66950C211yesmaximal, characteristic
2C22×#66949C211yesmaximal, characteristic
3#13073626C2116yesmaximal, direct product factor
4C2×#10622597C211yesmaximal, characteristic, complemented
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622592C211yesmaximal, characteristic, complemented
7C2×#10622592C211yesmaximal, characteristic, complemented
8C2×#10622542C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622602C211yesmaximal, characteristic
12C2×#10622602C211yesmaximal, characteristic
13C2×#10622280C211yesmaximal, characteristic
14C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
15C2×D11×#95C211yesmaximal, characteristic
16C2×C11×#389C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66950—28no—
41C2×#66950C2218yes—
42C2×#66949—28no—
43C2×#66949C2218yes—
44C11×#389C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622602C2218yes—
58#10622602C2218yes—
59#10622597C2218yescomplemented
60#10622596C2218yescomplemented
61#10622592C2218yescomplemented
62#10622592C2218yescomplemented
63C4×(C2×D11)⋊C4C2218yes—
64#10622542C2218yescomplemented
65#10622280C2218yes—
66D11×#95C2218yes—
67#10622260C2218yescomplemented
68#10622259C2218yescomplemented
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×C4×D11—24no—
85C22×C4×D11—24no—
86C22×C4×D11—24no—
87C22×C4×D11—24no—
88C22×C4×D11—42no—
89C22×C4×D11—42no—
90C22×C4×D11—42no—
91C22×C4×D11—42no—
92C22×C4×D11Q818yescomplemented
93C22×C4×D11C2314yes—
94C22×C4×D11C2314yes—
95C22×C4×D11C2314yes—
96C22×Dic22—24no—
97C22×Dic22—24no—
98C22×Dic22—24no—
99C22×Dic22—24no—
100C22×Dic22—42no—
101C22×Dic22—42no—
102C22×Dic22C2314yes—
103C22×Dic22C2314yes—
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4—24no—
107C2×C11×C4⋊C4—42no—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C42×C11—42no—
113C2×C42×C11C2314yes—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4D418yes—
117C2×(C2×D11)⋊C4Q818yescomplemented
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×C4⋊Dic11—24no—
123C2×C4⋊Dic11—24no—
124C2×C4⋊Dic11C2314yes—
125C2×C4⋊Dic11C2314yes—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—24no—
128C2×Dic11⋊C4—24no—
129C2×Dic11⋊C4—42no—
130C2×Dic11⋊C4—42no—
131C2×Dic11⋊C4—42no—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×C4×Dic11—42no—
139C2×C4×Dic11C2314yes—
140#66950—232no—
141#66949—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×C11C2411yescharacteristic
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
160C23×D11C2×D414yes—
161C23×D11C2×Q814yes—
162C23×D11C2×Q814yes—
163C23×D11C2412yes—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
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—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11C2×D414yes—
182C22×C4×C11C2×Q814yes—
183C22×C4×C11C2×Q814yes—
184C22×C4×C11#4114yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
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×Dic11C2×D414yes—
210C22×Dic11C2×Q814yes—
211C22×Dic11C2×Q814yes—
212C22×Dic11#4114yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C2×C4×D11—28no—
221C2×C4×D11—28no—
222C2×C4×D11—28no—
223C2×C4×D11—28no—
224C2×C4×D11—416no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11—416no—
230C2×C4×D11—416no—
231C2×C4×D11C2×Q8116yescomplemented
232C2×Dic22—28no—
233C2×Dic22—28no—
234C2×Dic22—28no—
235C2×Dic22—28no—
236C2×Dic22—44no—
237C2×Dic22—44no—
238C2×Dic22—416no—
239C2×Dic22—416no—
240C11×C4⋊C4—28no—
241C11×C4⋊C4—28no—
242C11×C4⋊C4—28no—
243C11×C4⋊C4—44no—
244C42×C11—44no—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—28no—
247(C2×D11)⋊C4C2×D4116yes—
248(C2×D11)⋊C4C2×Q8116yescomplemented
249C4⋊Dic11—28no—
250C4⋊Dic11—28no—
251Dic11⋊C4—28no—
252Dic11⋊C4—28no—
253Dic11⋊C4—28no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256Dic11⋊C4—44no—
257C4×Dic11—44no—
258C22×C22⋊Q8—111no—
259C22×C22⋊Q8—111no—
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×#389D1111yescharacteristic, complemented
269C2×#385—111no—
270C2×#385—111no—
271C2×#380—111no—
272C2×C4×C22⋊C4—111no—
273C22×#95—111no—
274C23×C11C22×D412yes—
275C23×C11C22×Q812yes—
276C23×C11C22×Q812yes—
277C23×C11C2×#4112yes—
278C23×C11C2×#4112yes—
279C23×C11H(5,𝔽2)12yes—
280C23×C11H(5,𝔽2)12yes—
281C23×C11C2511yescharacteristic
282C22×D11—28no—
283C22×D11—28no—
284C22×D11—28no—
285C22×D11—28no—
286C22×D11—28no—
287C22×D11—28no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11C4⋊Q8116yes—
293C22×D11C22×D414yes—
294C22×D11C22×Q814yes—
295C22×D11C22×Q814yes—
296C2×C4×C11—28no—
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—22no—
316C2×C4×C11—22no—
317C2×C4×C11—44no—
318C2×C4×C11—44no—
319C2×C4×C11—44no—
320C2×C4×C11C22×D414yes—
321C2×C4×C11C22×Q814yes—
322C2×C4×C11C22×Q814yes—
323C2×C4×C11C2×#4114yes—
324C2×Dic11—28no—
325C2×Dic11—28no—
326C2×Dic11—28no—
327C2×Dic11—28no—
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—44no—
346C2×Dic11—44no—
347C2×Dic11—44no—
348C2×Dic11C22×D414yes—
349C2×Dic11C22×Q814yes—
350C2×Dic11C22×Q814yes—
351C2×Dic11C2×#4114yes—
352C4×D11—416no—
353C4×D11—416no—
354C4×D11—416no—
355Dic22—416no—
356Dic22—416no—
357C23×Q8—111no—
358C23×Q8—111no—
359C24×C4—111no—
360C24×C4—111no—
361C24×C4—111no—
362C2×C22⋊Q8—118no—
363C2×C22⋊Q8—118no—
364C2×C22⋊Q8—228no—
365C2×C22⋊Q8—228no—
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⋊C4C2×D1111yescharacteristic
375C22×C4⋊C4C2×D1111yescharacteristic
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C4⋊C4C2×D1111yescharacteristic
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C42—111no—
383C22×C42C2×D1111yescharacteristic
384#398—118no—
385#398—118no—
386#395—118no—
387#395—118no—
388#391—118no—
389#391—118no—
390#389—118no—
391#389C2×D1118yescomplemented
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×#95C2×D1111yescharacteristic
408C2×#95C2×D1111yescharacteristic
409C22×C11C2×C4⋊Q814yes—
410C22×C11#53314yes—
411C22×C11#54314yes—
412C22×C11#54614yes—
413C22×C11#54614yes—
414C22×C11#55414yes—
415C22×C11#55414yes—
416C22×C11C23×D411yescharacteristic
417C22×C11C23×Q811yescharacteristic
418C22×C11C23×Q811yescharacteristic
419C22×C11C22×#4111yescharacteristic
420C22×C11C22×#4111yescharacteristic
421C22×C11C2×H(5,𝔽2)11yescharacteristic
422C22×C11C2×H(5,𝔽2)11yescharacteristic
423C2×D11—24no—
424C2×D11—24no—
425C2×D11—24no—
426C2×D11—24no—
427C2×D11—24no—
428C2×D11—24no—
429C2×D11—232no—
430C2×D11C2×C4⋊Q818yes—
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—24no—
434C4×C11—24no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438Dic11—24no—
439Dic11—24no—
440Dic11—24no—
441Dic11—24no—
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445C25—111no—
446C22×Q8—114no—
447C22×Q8—114no—
448C22×Q8—224no—
449C22×Q8—224no—
450C22×Q8—224no—
451C22×Q8—224no—
452C22×Q8—442no—
453C22×Q8—442no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—118no—
459C23×C4—114no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—114no—
464C23×C4—114no—
465C23×C4—224no—
466C23×C4—224no—
467C23×C4—224no—
468C23×C4—224no—
469C23×C4—442no—
470C23×C4—442no—
471C23×C4—442no—
472C23×C4—442no—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C22⋊Q8—2232no—
481C22⋊Q8—2232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—42no—
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⋊C4C22×D1114yes—
503C2×C4⋊C4C22×D1114yes—
504C2×C4⋊C4C22×D1114yes—
505C2×C4⋊C4C22×D1114yes—
506C2×C22⋊C4—118no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C42—42no—
515C2×C42—114no—
516C2×C42—442no—
517C2×C42C22×D1114yes—
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#95C22×D1114yes—
529#95C22×D1114yes—
530C2×C11#254918yescomplemented
531C2×C11C22×C4⋊Q811yescharacteristic
532C2×C11C2×#53311yescharacteristic
533C2×C11C2×#54311yescharacteristic
534C2×C11C2×#54611yescharacteristic
535C2×C11C2×#54611yescharacteristic
536C2×C11C2×#55411yescharacteristic
537C2×C11C2×#55411yescharacteristic
538D11—28no—
539C24—114no—
540C24—114no—
541C24—114no—
542C24—112no—
543C24—222no—
544C24—222no—
545C24—222no—
546C24—222no—
547C24C23×D1111yescharacteristic
548C2×Q8—228no—
549C2×Q8—228no—
550C2×Q8—228no—
551C2×Q8—228no—
552C2×Q8—444no—
553C2×Q8—444no—
554C2×Q8—4416no—
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—22no—
572C22×C4—22no—
573C22×C4—114no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—114no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—1116no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—228no—
586C22×C4—228no—
587C22×C4—228no—
588C22×C4—222no—
589C22×C4—222no—
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—228no—
606C22×C4—4416no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—444no—
610C22×C4—444no—
611C22×C4—4416no—
612C22×C4—4416no—
613C22×C4#433914yes—
614C22×C4D4×D1114yes—
615C22×C4Q8×D1114yes—
616C22×C4Q8×D1114yes—
617C22×C4C23×D1112yes—
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—44no—
628C4⋊C4—228no—
629C4⋊C4—228no—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—228no—
633C4⋊C4—444no—
634C4⋊C4—444no—
635C4⋊C4—444no—
636C22⋊C4—1116no—
637C22⋊C4—1116no—
638C22⋊C4—228no—
639C22⋊C4—228no—
640C42—44no—
641C42—444no—
642C11C2×#254911yescharacteristic, complemented, Sylow
643C23—1116no—
644C23—114no—
645C23—114no—
646C23—114no—
647C23—228no—
648C23—228no—
649C23—228no—
650C23—228no—
651C23—228no—
652C23—222no—
653C23—222no—
654C23—222no—
655C23—222no—
656C23—228no—
657C23C2×#433912yes—
658C23C2×D4×D1112yes—
659C23#6703712yes—
660C23C2×Q8×D1112yes—
661C23C2×Q8×D1112yes—
662C23#41×D1112yes—
663C23#6704212yes—
664C23C24×D1111yescharacteristic
665Q8—4416no—
666Q8—4416no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
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—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—114no—
692C2×C4—114no—
693C2×C4—114no—
694C2×C4—114no—
695C2×C4—228no—
696C2×C4—228no—
697C2×C4—228no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—228no—
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—4416no—
717C2×C4—4416no—
718C2×C4—4416no—
719C2×C4—444no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4C2×#433914yes—
723C2×C4C2×D4×D1114yes—
724C2×C4C2×Q8×D1114yes—
725C2×C4C2×Q8×D1114yes—
726C22—118no—
727C22—224no—
728C22—224no—
729C22—224no—
730C22—224no—
731C22—224no—
732C22—224no—
733C22—2232no—
734C22#1062304214yes—
735C22#1062308114yes—
736C22#1062310914yes—
737C22#1062314114yes—
738C22#1062316514yes—
739C22#1062322114yes—
740C22D11×C4⋊Q814yes—
741C22C22×#433911yescharacteristic
742C22C22×D4×D1111yescharacteristic
743C22C2×#6703711yescharacteristic
744C22C22×Q8×D1111yescharacteristic
745C22C22×Q8×D1111yescharacteristic
746C22C2×#41×D1111yescharacteristic
747C22C2×#6704211yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—224no—
756C4—224no—
757C4—224no—
758C4—224no—
759C4—442no—
760C4—442no—
761C4—442no—
762C2—228no—
763C2#1307362618yesdirect product factor
764C2C2×D11×C4⋊Q811yescharacteristic
765C2C2×#1062310911yescharacteristic
766C2C2×#1062316511yescharacteristic
767C2C2×#1062314111yescharacteristic
768C2C2×#1062308111yescharacteristic
769C2C2×#1062304211yescharacteristic
770C2C2×#1062322111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11C2×#2549
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #13073626C2direct (N × H)
4. C2×#10622597C2semidirect
5. C2×#10622596C2semidirect
6. C2×#10622592C2semidirect
7. C2×#10622592C2semidirect
8. C2×#10622542C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622260C2semidirect
16. C2×C11×#389C2semidirect
44. C11×#389C22semidirect
59. #10622597C22semidirect
60. #10622596C22semidirect
61. #10622592C22semidirect
62. #10622592C22semidirect
64. #10622542C22semidirect
67. #10622260C22semidirect
68. #10622259C22semidirect
92. C22×C4×D11Q8semidirect
117. C2×(C2×D11)⋊C4Q8semidirect
231. C2×C4×D11C2×Q8semidirect
248. (C2×D11)⋊C4C2×Q8semidirect
268. C2×#389D11semidirect
391. #389C2×D11semidirect
530. C2×C11#2549semidirect
642. C11C2×#2549semidirect
763. C2#13073626direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669492
#130736262
C2×#106225972
C2×#106225962
C2×#106225922
C2×#106225422
C2×#106222592
C2×#106222602
C2×#106226022
C2×#106222802
C2×C4×(C2×D11)⋊C42
C2×D11×#952
C2×C11×#3892
C2×#254911