Finite Group Databasebeta

← C2×#13077688 #15618552

Subgroups — C2×#13077688 #15618552

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2#13077688C2116yesmaximal, direct product factor
3C2×#10622741C211yesmaximal, characteristic, complemented
4C2×#10622342C211yesmaximal, characteristic, complemented
5C2×#10622319C211yesmaximal, characteristic, complemented
6C2×#10622624C211yesmaximal, characteristic, complemented
7C2×#10622449C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
9C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
10C2×#10622318C211yesmaximal, characteristic, complemented
11C2×#10622446C211yesmaximal, characteristic, complemented
12C2×#10622742C211yesmaximal, characteristic, complemented
13C2×#10622723C211yesmaximal, characteristic, complemented
14C2×#10622340C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66993C411yescharacteristic
23C2×#66991C411yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32#10623079C418yes—
33#10623079C2218yes—
34C2×#66948C411yescharacteristic
35C2×#66941C411yescharacteristic
36C2×#66938C411yescharacteristic
37C2×#66938C411yescharacteristic
38C2×#66937C411yescharacteristic
39C2×#66937C411yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×C42×D11C2211yescharacteristic
42C11×#435C2218yescomplemented
43C2×C11×C4⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×#97C2211yescharacteristic
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49#10622742C2218yescomplemented
50#10622741C2218yescomplemented
51#10622723C2218yescomplemented
52C8×C22⋊D11C2218yescomplemented
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622624C2218yescomplemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67C2×#66867C2211yescharacteristic
68#10622449C2218yescomplemented
69#10622446C2218yescomplemented
70#10622342C2218yescomplemented
71#10622340C2218yescomplemented
72#10622340C2218yescomplemented
73(C22⋊D11)⋊C8C2218yescomplemented
74#10622319C2218yescomplemented
75#10622318C2218yescomplemented
76C22×D4×C11C2×C411yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11C2×C411yescharacteristic
80C22×C22⋊D11C2×C411yescharacteristic
81C22×C22⋊D11C2×C411yescharacteristic
82C22×C22⋊D11C2×C411yescharacteristic
83C22×C22⋊D11C2×C411yescharacteristic
84C22×C22⋊D11C2×C411yescharacteristic
85C2×#4339—42no—
86C2×#4339—42no—
87C2×#4339—42no—
88C2×#4339—42no—
89C2×#4339C2×C414yes—
90C2×#4339C2×C414yes—
91C2×#4339C2314yes—
92C2×#4339C2314yes—
93C22×D44C2×C411yescharacteristic
94C22×D44C2×C411yescharacteristic
95C22×D44C2×C411yescharacteristic
96C22×C4×D11C2×C411yescharacteristic
97C22×C4×D11C2×C411yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×Dic22C2×C411yescharacteristic
102C22×Dic22C2×C411yescharacteristic
103C2×C11×M16—42no—
104C2×C11×M16C2314yes—
105C22×C8×C11—42no—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2314yes—
111C4×D4×C11C2×C414yes—
112C4×D4×C11C2314yes—
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11C2×C411yescharacteristic
118C2×C22⋊Dic11C2×C411yescharacteristic
119#66993C2×C418yes—
120#66991C2×C418yes—
121C4×C22⋊D11C2×C414yes—
122C4×C22⋊D11C2×C414yes—
123C4×C22⋊D11C2314yes—
124C4×C22⋊D11C2314yes—
125C2×(C2×D11)⋊C4C2×C411yescharacteristic
126C2×(C2×D11)⋊C4C2×C411yescharacteristic
127C2×(C2×D11)⋊C4C2×C411yescharacteristic
128C2×(C2×D11)⋊C4C2×C411yescharacteristic
129C2×C4⋊Dic11C2×C411yescharacteristic
130C2×Dic11⋊C4C2×C411yescharacteristic
131C2×Dic11⋊C4C2×C411yescharacteristic
132C2×C4×Dic11C2×C411yescharacteristic
133C2×C4×Dic11C2×C411yescharacteristic
134C2×C4×Dic11C2311yescharacteristic
135C2×#4318—42no—
136C2×#4318C2314yes—
137C22×C11⋊C8—42no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2314yes—
143C2×#4313—42no—
144C2×#4313—42no—
145C2×#4313C2314yes—
146C2×#4313C2314yes—
147C2×C8×D11—42no—
148C2×C8×D11—42no—
149C2×C8×D11C2314yes—
150C2×C8×D11C2314yes—
151#66948C2×C418yes—
152#66941C2×C418yes—
153#66938C2×C418yes—
154#66938C2×C418yes—
155#66937C2×C418yes—
156#66937C2×C418yes—
157C4×D44C2×C414yes—
158C4×D44C2314yes—
159C42×D11C2×C414yes—
160C42×D11C2314yes—
161C11×C4⋊C8C2314yes—
162C11×C22⋊C8C2314yes—
163C11×C22⋊C8C2314yes—
164C11×#97C2314yes—
165C22⋊(C11⋊C8)C2314yes—
166C22⋊(C11⋊C8)C2314yes—
167(C2×D11)⋊C8C2314yes—
168(C2×D11)⋊C8C2314yes—
169(C2×D11)⋊C8C2314yes—
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yes—
173(C2×D11)⋊C8C2314yes—
174(C2×D11)⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177C8×Dic11C2314yes—
178C8×Dic11C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180#66867C2314yes—
181C2×#2981—111nomaximal, Sylow
182C24×C11C22×C411yescharacteristic
183C24×C11C22×C411yescharacteristic
184C23×D11C22×C411yescharacteristic
185C23×D11C22×C411yescharacteristic
186C23×D11C22×C411yescharacteristic
187C2×D4×C11—42no—
188C2×D4×C11C22×C414yes—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11C22×C414yes—
209C2×C22⋊D11C22×C414yes—
210C2×C22⋊D11C22×C414yes—
211C2×C22⋊D11C22×C414yes—
212C2×C22⋊D11C22×C414yes—
213C2×C22⋊D11C22×C414yes—
214C22×Dic11C22×C411yescharacteristic
215C22×Dic11C22×C411yescharacteristic
216C22×Dic11C22×C411yescharacteristic
217C22×Dic11C22×C411yescharacteristic
218C22×Dic11C22×C411yescharacteristic
219#4339—48no—
220#4339—48no—
221#4339—44no—
222#4339—44no—
223#4339—44no—
224#4339—44no—
225C2×D44—42no—
226C2×D44—42no—
227C2×D44—42no—
228C2×D44C22×C414yes—
229C2×D44C22×C414yes—
230C2×D44C22×C414yes—
231C2×C4×D11—24no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—42no—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C22×C414yes—
241C2×C4×D11C22×C412yes—
242C2×C4×D11C22×C412yes—
243C2×C4×D11C22×C414yes—
244C2×C4×D11C2412yes—
245C2×C4×D11C2412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—42no—
248C2×Dic22—42no—
249C2×Dic22C22×C414yes—
250C2×Dic22C22×C414yes—
251C11×M16—44no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11—22no—
256C2×C8×C11—44no—
257C2×C8×C11C2412yes—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4C22×C414yes—
262C11×C22⋊C4C22×C414yes—
263C11×C22⋊C4C22×C414yes—
264C42×C11C22×C412yes—
265C42×C11C2412yes—
266C22⋊Dic11C22×C414yes—
267C22⋊Dic11C22×C414yes—
268(C2×D11)⋊C4C22×C414yes—
269(C2×D11)⋊C4C22×C414yes—
270(C2×D11)⋊C4C22×C414yes—
271(C2×D11)⋊C4C22×C414yes—
272C4⋊Dic11C22×C414yes—
273Dic11⋊C4C22×C414yes—
274Dic11⋊C4C22×C414yes—
275C4×Dic11C22×C412yes—
276C4×Dic11C22×C414yes—
277C4×Dic11C22×C414yes—
278C4×Dic11C2412yes—
279#4318—44no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—44no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4313—44no—
290#4313—44no—
291C8×D11—44no—
292C8×D11—44no—
293C2×#532—111no—
294#2981—1116no—
295C2×#436—111no—
296C2×#436—111no—
297C2×#435—111no—
298C2×#435—111no—
299C2×#435—111no—
300C2×#435D1111yescharacteristic, complemented
301C2×C8×D4—111no—
302C2×C8×D4—111no—
303C2×#432—111no—
304C2×#431—111no—
305C2×#408—111no—
306C2×#408—111no—
307C2×#408—111no—
308C2×#408—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11C23×C412yes—
316C23×C11C23×C412yes—
317C23×C11C23×C411yescharacteristic
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11C23×C412yes—
328C22×D11C23×C412yes—
329C22×D11C23×C412yes—
330D4×C11—44no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11C23×C412yes—
342C2×C4×C11C23×C412yes—
343C2×C4×C11C23×C412yes—
344C2×C4×C11C23×C412yes—
345C2×C4×C11C23×C411yescharacteristic
346C2×C4×C11H(5,𝔽2)12yes—
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11C2511yescharacteristic
349C22⋊D11—28no—
350C22⋊D11—28no—
351C22⋊D11—44no—
352C22⋊D11—44no—
353C22⋊D11—44no—
354C22⋊D11—44no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11#13114yes—
360C2×Dic11C23×C412yes—
361C2×Dic11C23×C412yes—
362C2×Dic11C23×C412yes—
363C2×Dic11C23×C412yes—
364C2×Dic11C23×C412yes—
365D44—44no—
366D44—44no—
367D44—44no—
368C4×D11—24no—
369C4×D11—24no—
370C4×D11—24no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—28no—
378C4×D11—44no—
379Dic22—44no—
380Dic22—44no—
381C8×C11—22no—
382C8×C11—22no—
383C8×C11—22no—
384C8×C11—22no—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C22×#41—111no—
390C22×#41—111no—
391C22×M16—111no—
392C22×M16—111no—
393C22×M16—111no—
394C22×M16C2×D1111yescharacteristic
395C23×C8—111no—
396C23×C8—111no—
397C23×C8—111no—
398C23×C8C2×D1111yescharacteristic
399#532—118no—
400#532—118no—
401C2×C4⋊Q8—111no—
402C2×#127—111no—
403C2×#124—111no—
404C2×#124—111no—
405C2×#121—111no—
406C2×#121—111no—
407C2×#121—111no—
408C2×#121—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411C2×C4×D4—111no—
412C2×C4×D4C2×D1111yescharacteristic
413C22×C42—111no—
414#436—118no—
415#436—118no—
416#435—118no—
417#435—118no—
418#435—118no—
419#435C2×D1118yescomplemented
420C8×D4—118no—
421C8×D4—118no—
422#432—118no—
423#431—118no—
424C2×C4⋊C8—111no—
425C2×C4⋊C8—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8C2×D1111yescharacteristic
428#408—118no—
429#408—118no—
430#408—118no—
431#408—118no—
432C2×C22⋊C8—111no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×C22⋊C8—111no—
437C2×C22⋊C8—111no—
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×C22⋊C8C2×D1111yescharacteristic
443C2×C22⋊C8C2×D1111yescharacteristic
444C2×#97—111no—
445C2×#97C2×D1111yescharacteristic
446C2×C4×C8—111no—
447C2×C4×C8—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11#51812yes—
457C22×C11C2×#13112yes—
458C22×C11#56812yes—
459C22×C11C24×C411yescharacteristic
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—44no—
470C2×D11—44no—
471C2×D11—44no—
472C4×C11—22no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11#51812yes—
477C4×C11C2×H(5,𝔽2)11yescharacteristic
478C4×C11C2×H(5,𝔽2)11yescharacteristic
479Dic11—22no—
480Dic11—22no—
481Dic11—22no—
482Dic11—22no—
483Dic11C2×#13114yes—
484C2×#41—114no—
485C2×#41—114no—
486C2×#41—114no—
487C2×#41—114no—
488C2×#41—442no—
489C2×#41—442no—
490C2×#41—442no—
491C2×#41—442no—
492C22×Q8—111no—
493C22×Q8—111no—
494C22×D4—111no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—111no—
499C22×D4—111no—
500C22×D4—111no—
501C22×D4—111no—
502C22×D4—111no—
503C22×D4C4×D1111yescharacteristic
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—111no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C2×M16—42no—
512C2×M16—114no—
513C2×M16—114no—
514C2×M16—114no—
515C2×M16—442no—
516C2×M16—442no—
517C2×M16—442no—
518C2×M16C22×D1114yes—
519C22×C8—42no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—114no—
525C22×C8—114no—
526C22×C8—114no—
527C22×C8—442no—
528C22×C8—442no—
529C22×C8—442no—
530C22×C8C22×D1111yescharacteristic
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1111yescharacteristic
534C22×C8C22×D1114yes—
535C4⋊Q8—118no—
536#127—118no—
537#124—118no—
538#124—118no—
539#121—118no—
540#121—118no—
541#121—118no—
542#121—118no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—114no—
549C4×D4C4×D1114yes—
550C4×D4C22×D1114yes—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4C4×D1111yescharacteristic
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
557C2×C22⋊C4—111no—
558C2×C22⋊C4—111no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4C4×D1111yescharacteristic
562C2×C22⋊C4C4×D1111yescharacteristic
563C2×C42—111no—
564C2×C42—111no—
565C2×C42—111no—
566C2×C42—114no—
567C2×C42—114no—
568C2×C42C22×D1111yescharacteristic
569C4⋊C8—114no—
570C4⋊C8—114no—
571C4⋊C8—114no—
572C4⋊C8C22×D1114yes—
573C22⋊C8—114no—
574C22⋊C8—114no—
575C22⋊C8—114no—
576C22⋊C8—114no—
577C22⋊C8—114no—
578C22⋊C8—114no—
579C22⋊C8—114no—
580C22⋊C8—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583C22⋊C8C22×D1114yes—
584C22⋊C8C22×D1114yes—
585#97—114no—
586#97C22×D1114yes—
587C4×C8—114no—
588C4×C8—114no—
589C2×C11—42no—
590C2×C11—42no—
591C2×C11#298114yescomplemented
592C2×C11C2×#51811yescharacteristic
593C2×C11C22×#13111yescharacteristic
594C2×C11C2×#56811yescharacteristic
595D11—42no—
596D11—42no—
597D11—42no—
598C24—111no—
599C24—111no—
600C24—111no—
601C24C2×C4×D1111yescharacteristic
602C24C2×C4×D1111yescharacteristic
603#41—448no—
604#41—448no—
605#41—444no—
606#41—444no—
607#41—444no—
608#41—444no—
609C2×Q8—114no—
610C2×Q8—114no—
611C2×Q8—442no—
612C2×Q8—442no—
613C2×D4—42no—
614C2×D4—114no—
615C2×D4—114no—
616C2×D4—114no—
617C2×D4—114no—
618C2×D4—114no—
619C2×D4—114no—
620C2×D4—114no—
621C2×D4—114no—
622C2×D4—114no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—442no—
626C2×D4—442no—
627C2×D4—442no—
628C2×D4—442no—
629C2×D4—442no—
630C2×D4—442no—
631C2×D4—442no—
632C2×D4C2×C4×D1114yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—114no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—114no—
650C22×C4—224no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—442no—
658C22×C4C2×C4×D1111yescharacteristic
659C22×C4C2×C4×D1111yescharacteristic
660C22×C4C2×C4×D1111yescharacteristic
661C22×C4C2×C4×D1111yescharacteristic
662C22×C4C2×C4×D1112yes—
663C22×C4C2×C4×D1112yes—
664C22×C4C23×D1112yes—
665C22×C4C23×D1112yes—
666C22×C4C23×D1111yescharacteristic
667M16—44no—
668M16—444no—
669M16—444no—
670M16—444no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—44no—
676C2×C8—112no—
677C2×C8—112no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—222no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8—444no—
685C2×C8—444no—
686C2×C8—444no—
687C2×C8C23×D1112yes—
688C2×C8C23×D1112yes—
689C2×C8C23×D1112yes—
690C2×C8C23×D1112yes—
691C4⋊C4—114no—
692C4⋊C4—114no—
693C4⋊C4—114no—
694C4⋊C4C2×C4×D1114yes—
695C22⋊C4—114no—
696C22⋊C4—114no—
697C22⋊C4—114no—
698C22⋊C4—114no—
699C22⋊C4—114no—
700C22⋊C4—114no—
701C22⋊C4C2×C4×D1114yes—
702C22⋊C4C2×C4×D1114yes—
703C42—112no—
704C42—114no—
705C42—114no—
706C42—112no—
707C42C2×C4×D1112yes—
708C42C23×D1112yes—
709C11C2×#298111yescharacteristic, complemented, Sylow
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—112no—
717C23—112no—
718C23—112no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23C22×C4×D1112yes—
729C23C22×C4×D1112yes—
730C23C22×C4×D1111yescharacteristic
731Q8—444no—
732Q8—444no—
733D4—44no—
734D4—228no—
735D4—228no—
736D4—444no—
737D4—444no—
738D4—444no—
739D4—444no—
740D4—444no—
741D4—444no—
742D4—444no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—114no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—228no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—444no—
774C2×C4C22×C4×D1112yes—
775C2×C4C22×C4×D1112yes—
776C2×C4C22×C4×D1112yes—
777C2×C4C22×C4×D1112yes—
778C2×C4C22×C4×D1111yescharacteristic
779C2×C4#6703712yes—
780C2×C4#6704212yes—
781C2×C4C24×D1111yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—222no—
787C8—222no—
788C8—222no—
789C8—222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—222no—
799C22—222no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—444no—
808C22—444no—
809C22—444no—
810C22#1062307612yes—
811C22#1062327612yes—
812C22D11×#13112yes—
813C22C23×C4×D1111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—114no—
819C4—222no—
820C4—222no—
821C4—222no—
822C4—222no—
823C4#1062307612yes—
824C4C2×#6703711yescharacteristic
825C4C2×#6704211yescharacteristic
826C2—42no—
827C2—42no—
828C2—442no—
829C2—442no—
830C2—442no—
831C2#1307768814yesdirect product factor
832C2C2×#1062307611yescharacteristic
833C2C2×D11×#13111yescharacteristic
834C2C2×#1062327611yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C23×C4
prime radicalC2×#10623079C2
cosocleC2×C4×C11C25
hypercenterC2×#435D11
hypocenterC11C2×#2981
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #13077688C2direct (N × H)
3. C2×#10622741C2semidirect
4. C2×#10622342C2semidirect
5. C2×#10622319C2semidirect
6. C2×#10622624C2semidirect
7. C2×#10622449C2semidirect
8. C2×C8×C22⋊D11C2semidirect
9. C2×(C22⋊D11)⋊C8C2semidirect
10. C2×#10622318C2semidirect
11. C2×#10622446C2semidirect
12. C2×#10622742C2semidirect
13. C2×#10622723C2semidirect
14. C2×#10622340C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#435C2semidirect
42. C11×#435C22semidirect
49. #10622742C22semidirect
50. #10622741C22semidirect
51. #10622723C22semidirect
52. C8×C22⋊D11C22semidirect
65. #10622624C22semidirect
68. #10622449C22semidirect
69. #10622446C22semidirect
70. #10622342C22semidirect
71. #10622340C22semidirect
72. #10622340C22semidirect
73. (C22⋊D11)⋊C8C22semidirect
74. #10622319C22semidirect
75. #10622318C22semidirect
300. C2×#435D11semidirect
419. #435C2×D11semidirect
591. C2×C11#2981semidirect
709. C11C2×#2981semidirect
831. C2#13077688direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
#130776882
C2×#106227412
C2×#106223422
C2×#106223192
C2×#106226242
C2×#106224492
C2×C8×C22⋊D112
C2×(C22⋊D11)⋊C82
C2×#106223182
C2×#106224462
C2×#106227422
C2×#106227232
C2×#106223402
C2×C11×#4352
C2×#298111