Finite Group Databasebeta

← C2×#13077665 #15618524

Subgroups — C2×#13077665 #15618524

Order 2816.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13077665C2116yesmaximal, direct product factor
3C2×#10622451C211yesmaximal, characteristic, complemented
4C2×#10622741C211yesmaximal, characteristic, complemented
5C2×#10622319C211yesmaximal, characteristic, complemented
6C2×#10622724C211yesmaximal, characteristic, complemented
7C2×#10622343C211yesmaximal, characteristic, complemented
8C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
9C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
10C2×#10622322C211yesmaximal, characteristic, complemented
11C2×#10622453C211yesmaximal, characteristic, complemented
12C2×#10622742C211yesmaximal, characteristic, complemented
13C2×#10622340C211yesmaximal, characteristic, complemented
14C2×#10622339C211yesmaximal, characteristic, complemented
15C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C23×C8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992C411yescharacteristic
23C2×#66990C411yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic, complemented
28C22×#4313C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×#4313C2211yescharacteristic, complemented
31C22×C8×D11C2211yescharacteristic, complemented
32#10623078C418yes—
33#10623078C2218yes—
34C2×#66949C411yescharacteristic
35C2×#66947C411yescharacteristic
36C2×#66937C411yescharacteristic
37C2×#66936C411yescharacteristic
38C2×#66935C411yescharacteristic
39C2×#66931C411yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×#66925C2211yescharacteristic
42C11×#435C2218yescomplemented
43C2×C11×C4⋊C8C2211yescharacteristic, complemented
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic, complemented
46C2×C11×#97C2211yescharacteristic, complemented
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
49#10622742C2218yescomplemented
50#10622741C2218yescomplemented
51#10622724C2218yescomplemented
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×(C2×D11)⋊C8C2218yescomplemented
59C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
61C2×#66879C2211yescharacteristic, complemented
62C2×Dic11⋊C8C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65D4×C11⋊C8C2218yescomplemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67C2×C4×C11⋊C8C2211yescharacteristic, complemented
68#10622453C2218yescomplemented
69#10622451C2218yescomplemented
70#10622343C2218yescomplemented
71#10622340C2218yescomplemented
72#10622339C2218yescomplemented
73(C22⋊D11)⋊C8C2218yescomplemented
74#10622322C2218yescomplemented
75#10622319C2218yescomplemented
76C24×D11C2×C411yescharacteristic
77C22×D4×C11C2×C411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11C2×C411yescharacteristic
81C22×C22⋊D11C2×C411yescharacteristic
82C22×C22⋊D11C2×C411yescharacteristic
83C22×C22⋊D11C2×C411yescharacteristic
84C23×Dic11C2×C411yescharacteristic
85C2×#4339—42no—
86C2×#4339—42no—
87C2×#4339C2×C414yes—
88C2×#4339C2314yes—
89C22×D44C2×C411yescharacteristic
90C22×D44C2×C411yescharacteristic
91C22×C4×D11—42no—
92C22×C4×D11—42no—
93C22×C4×D11C2×C411yescharacteristic
94C22×C4×D11C2×C411yescharacteristic
95C22×C4×D11C2×C414yes—
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2314yes—
100C22×Dic22C2×C411yescharacteristic
101C2×C11×M16—42no—
102C2×C11×M16C2314yescomplemented
103C22×C8×C11—42no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2314yes—
109C4×D4×C11C2×C414yes—
110C4×D4×C11C2314yes—
111C2×C11×C4⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4C2×C411yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11C2×C411yescharacteristic
116C2×C22⋊Dic11C2×C411yescharacteristic
117#66992C2×C418yes—
118#66990C2×C418yes—
119C4×C22⋊D11C2×C414yes—
120C4×C22⋊D11C2×C414yes—
121C4×C22⋊D11C2314yes—
122C4×C22⋊D11C2314yes—
123C2×(C2×D11)⋊C4C2×C411yescharacteristic
124C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×Dic11⋊C4C2×C411yescharacteristic
133C2×Dic11⋊C4C2×C411yescharacteristic
134C2×C4×Dic11C2311yescharacteristic
135C22×C11⋊C8—42no—
136C22×C11⋊C8—42no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2314yes—
142C22×C11⋊C8C2314yescomplemented
143C2×#4313—42no—
144C2×#4313—42no—
145C2×#4313—42no—
146C2×#4313C2314yes—
147C2×#4313C2314yes—
148C2×#4313C2314yescomplemented
149C2×C8×D11—42no—
150C2×C8×D11C2314yescomplemented
151#66949C2×C418yes—
152#66947C2×C418yes—
153#66937C2×C418yes—
154#66936C2×C418yes—
155#66935C2×C418yes—
156#66931C2×C418yes—
157C4×D44C2×C414yes—
158C4×D44C2314yes—
159#66925C2×C414yes—
160#66925C2314yes—
161C11×C4⋊C8C2314yescomplemented
162C11×C22⋊C8C2314yes—
163C11×C22⋊C8C2314yescomplemented
164C11×#97C2314yescomplemented
165C22⋊(C11⋊C8)C2314yes—
166C22⋊(C11⋊C8)C2314yescomplemented
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)⋊C8C2314yescomplemented
174(C2×D11)⋊C8C2314yescomplemented
175#66879C2314yescomplemented
176Dic11⋊C8C2314yescomplemented
177Dic11⋊C8C2314yescomplemented
178C8×Dic11C2314yescomplemented
179C4⋊(C11⋊C8)C2314yescomplemented
180C4×C11⋊C8C2314yescomplemented
181C2×#2976—111nomaximal, Sylow
182C24×C11C22×C411yescharacteristic
183C24×C11C22×C411yescharacteristic
184C23×D11—24no—
185C23×D11—42no—
186C23×D11—42no—
187C23×D11C22×C411yescharacteristic
188C23×D11C22×C411yescharacteristic
189C23×D11C22×C411yescharacteristic
190C23×D11C22×C414yes—
191C2×D4×C11—24no—
192C2×D4×C11C22×C414yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2411yescharacteristic
206C2×C22⋊D11—24no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11C22×C414yes—
211C2×C22⋊D11C22×C414yes—
212C2×C22⋊D11C22×C414yes—
213C2×C22⋊D11C22×C414yes—
214C22×Dic11—42no—
215C22×Dic11C22×C411yescharacteristic
216C22×Dic11C22×C411yescharacteristic
217C22×Dic11C22×C411yescharacteristic
218C22×Dic11C22×C411yescharacteristic
219C22×Dic11C22×C411yescharacteristic
220C22×Dic11C22×C414yes—
221#4339—48no—
222#4339—44no—
223#4339—44no—
224C2×D44—42no—
225C2×D44—42no—
226C2×D44C22×C414yes—
227C2×D44C22×C414yes—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—48no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C22×C412yes—
241C2×C4×D11C22×C412yes—
242C2×C4×D11C22×C414yes—
243C2×C4×D11C22×C414yes—
244C2×C4×D11C2412yes—
245C2×C4×D11C2412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—42no—
248C2×Dic22C22×C414yes—
249C11×M16—44no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11—44no—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C2×C8×C11C2412yes—
258C2×C8×C11C2412yes—
259C11×C4⋊C4C22×C414yes—
260C11×C22⋊C4C22×C414yes—
261C11×C22⋊C4C22×C414yes—
262C42×C11C22×C412yes—
263C42×C11C2412yes—
264C22⋊Dic11C22×C414yes—
265C22⋊Dic11C22×C414yes—
266(C2×D11)⋊C4C22×C414yes—
267(C2×D11)⋊C4C22×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—
275Dic11⋊C4C22×C414yes—
276Dic11⋊C4C22×C414yes—
277C4×Dic11C22×C412yes—
278C4×Dic11C2412yes—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—44no—
284C2×C11⋊C8—44no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4313—44no—
290#4313—44no—
291#4313—44no—
292C8×D11—44no—
293C2×#525—111no—
294#2976—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×#433—111no—
304C2×#433—111no—
305C2×#408—111no—
306C2×#408—111no—
307C2×#407—111no—
308C22×C22⋊C8—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11#13114yes—
315C23×C11C23×C412yes—
316C23×C11C23×C412yes—
317C23×C11C23×C411yescharacteristic
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—28no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—416no—
331C22×D11C23×C412yes—
332C22×D11C23×C412yes—
333C22×D11C23×C412yes—
334D4×C11—28no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11C23×C412yes—
346C2×C4×C11C23×C412yes—
347C2×C4×C11C23×C412yes—
348C2×C4×C11C23×C412yes—
349C2×C4×C11C23×C411yescharacteristic
350C2×C4×C11H(5,𝔽2)12yes—
351C2×C4×C11H(5,𝔽2)12yes—
352C2×C4×C11C2511yescharacteristic
353C22⋊D11—28no—
354C22⋊D11—44no—
355C22⋊D11—44no—
356C22⋊D11—44no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—44no—
363C2×Dic11C23×C412yes—
364C2×Dic11C23×C412yes—
365C2×Dic11C23×C412yes—
366C2×Dic11C23×C412yes—
367C2×Dic11C23×C412yes—
368D44—44no—
369D44—44no—
370C4×D11—24no—
371C4×D11—24no—
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—44no—
380C4×D11—44no—
381Dic22—44no—
382C8×C11—22no—
383C8×C11—22no—
384C8×C11—22no—
385C8×C11—22no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C24×C4—111no—
392C22×M16—111no—
393C22×M16—111no—
394C22×M16—111no—
395C22×M16C2×D1111yescharacteristic, complemented
396C23×C8—111no—
397C23×C8—111no—
398C23×C8—111no—
399C23×C8C2×D1111yescharacteristic
400#525—118no—
401#525—118no—
402C2×#123—111no—
403C2×#123—111no—
404C2×C22⋊Q8—111no—
405C2×C22⋊Q8—111no—
406C2×#121—111no—
407C2×#121—111no—
408C2×#120—111no—
409C2×#120—111no—
410C2×C4×D4—111no—
411C2×C4×D4—111no—
412C2×C4×D4—111no—
413C2×C4×D4C2×D1111yescharacteristic
414C2×#117—111no—
415#436—118no—
416#436—118no—
417#435—118no—
418#435—118no—
419#435—118no—
420#435C2×D1118yescomplemented
421C8×D4—118no—
422C8×D4—118no—
423#433—118no—
424#433—118no—
425C2×C4⋊C8—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8—111no—
428C2×C4⋊C8C2×D1111yescharacteristic, complemented
429#408—118no—
430#408—118no—
431#407—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—118no—
441C2×C22⋊C8—111no—
442C2×C22⋊C8—111no—
443C2×C22⋊C8C2×D1111yescharacteristic
444C2×C22⋊C8C2×D1111yescharacteristic, complemented
445C2×#97—111no—
446C2×#97C2×D1111yescharacteristic, complemented
447C2×C4×C8—111no—
448C2×C4×C8—111no—
449C22×C11—22no—
450C22×C11—28no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—44no—
456C22×C11#51812yes—
457C22×C11C2×#13114yes—
458C22×C11C2×#13112yes—
459C22×C11#56812yes—
460C22×C11C24×C411yescharacteristic
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—22no—
470C2×D11—416no—
471C2×D11—44no—
472C2×D11—44no—
473C2×D11—44no—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11#51812yes—
479C4×C11C2×H(5,𝔽2)11yescharacteristic
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481Dic11—22no—
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—22no—
486C25—111no—
487C2×#41—114no—
488C2×#41—114no—
489C2×#41—442no—
490C2×#41—442no—
491C22×Q8—111no—
492C22×D4—111no—
493C22×D4—111no—
494C22×D4—111no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4C4×D1111yescharacteristic
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—114no—
506C23×C4—114no—
507C23×C4—442no—
508C23×C4—442no—
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×D1114yescomplemented
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—
535#123—118no—
536#123—118no—
537C22⋊Q8—118no—
538C22⋊Q8—118no—
539#121—118no—
540#121—118no—
541#120—118no—
542#120—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—
551#117—114no—
552#117—114no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4C4×D1111yescharacteristic
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—111no—
563C2×C22⋊C4—111no—
564C2×C22⋊C4—111no—
565C2×C22⋊C4—111no—
566C2×C22⋊C4—111no—
567C2×C22⋊C4C4×D1111yescharacteristic
568C2×C22⋊C4C4×D1111yescharacteristic
569C2×C42—111no—
570C2×C42C22×D1111yescharacteristic
571C4⋊C8—114no—
572C4⋊C8—114no—
573C4⋊C8—114no—
574C4⋊C8C22×D1114yescomplemented
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⋊C8—114no—
584C22⋊C8—114no—
585C22⋊C8C22×D1114yes—
586C22⋊C8C22×D1114yescomplemented
587#97—114no—
588#97C22×D1114yescomplemented
589C4×C8—114no—
590C4×C8—114no—
591C2×C11—24no—
592C2×C11—42no—
593C2×C11#297614yescomplemented
594C2×C11C2×#51811yescharacteristic
595C2×C11C22×#13111yescharacteristic
596C2×C11C2×#56811yescharacteristic
597D11—42no—
598D11—42no—
599D11—42no—
600C24—111no—
601C24—111no—
602C24—111no—
603C24—114no—
604C24—224no—
605C24—442no—
606C24—442no—
607C24C2×C4×D1111yescharacteristic
608C24C2×C4×D1111yescharacteristic
609#41—448no—
610#41—444no—
611#41—444no—
612C2×Q8—114no—
613C2×Q8—442no—
614C2×D4—24no—
615C2×D4—114no—
616C2×D4—114no—
617C2×D4—114no—
618C2×D4—114no—
619C2×D4—114no—
620C2×D4—114no—
621C2×D4—224no—
622C2×D4—442no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—442no—
626C2×D4—442no—
627C2×D4C2×C4×D1114yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—114no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—114no—
645C22×C4—114no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—448no—
653C22×C4—444no—
654C22×C4—444no—
655C22×C4—442no—
656C22×C4—442no—
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⋊C4—114no—
695C4⋊C4—114no—
696C4⋊C4C2×C4×D1114yes—
697C22⋊C4—114no—
698C22⋊C4—114no—
699C22⋊C4—114no—
700C22⋊C4—114no—
701C22⋊C4—114no—
702C22⋊C4—114no—
703C22⋊C4—114no—
704C22⋊C4—114no—
705C22⋊C4C2×C4×D1114yes—
706C22⋊C4C2×C4×D1114yes—
707C42—112no—
708C42—112no—
709C42C2×C4×D1112yes—
710C42C23×D1112yes—
711C11C2×#297611yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—112no—
718C23—112no—
719C23—112no—
720C23—222no—
721C23—228no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—444no—
731C23—444no—
732C23—4416no—
733C23#6696014yes—
734C23C22×C4×D1112yes—
735C23C22×C4×D1112yes—
736C23C22×C4×D1111yescharacteristic
737Q8—444no—
738D4—28no—
739D4—228no—
740D4—444no—
741D4—444no—
742D4—444no—
743D4—444no—
744D4—444no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—112no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—444no—
775C2×C4—444no—
776C2×C4—444no—
777C2×C4C22×C4×D1112yes—
778C2×C4C22×C4×D1112yes—
779C2×C4C22×C4×D1112yes—
780C2×C4C22×C4×D1112yes—
781C2×C4C22×C4×D1111yescharacteristic
782C2×C4#6703712yes—
783C2×C4#6704212yes—
784C2×C4C24×D1111yescharacteristic
785C8—22no—
786C8—22no—
787C8—22no—
788C8—22no—
789C8—222no—
790C8—222no—
791C8—222no—
792C8—222no—
793C22—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—222no—
808C22—222no—
809C22—4416no—
810C22—444no—
811C22—444no—
812C22—444no—
813C22#1062307612yes—
814C22C2×#6696014yes—
815C22C2×#6696012yes—
816C22#1062328112yes—
817C22C23×C4×D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—222no—
823C4—222no—
824C4—222no—
825C4—222no—
826C4—222no—
827C4#1062307612yes—
828C4C2×#6703711yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—24no—
831C2—42no—
832C2—442no—
833C2—442no—
834C2—442no—
835C2#1307766514yesdirect product factor
836C2C2×#1062307611yescharacteristic
837C2C22×#6696011yescharacteristic
838C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C23×C4
prime radicalC2×#10623078C2
cosocleC2×C4×C11C25
hypercenterC2×#435D11
hypocenterC11C2×#2976
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #13077665C2direct (N × H)
3. C2×#10622451C2semidirect
4. C2×#10622741C2semidirect
5. C2×#10622319C2semidirect
6. C2×#10622724C2semidirect
7. C2×#10622343C2semidirect
8. C2×D4×C11⋊C8C2semidirect
9. C2×(C22⋊D11)⋊C8C2semidirect
10. C2×#10622322C2semidirect
11. C2×#10622453C2semidirect
12. C2×#10622742C2semidirect
13. C2×#10622340C2semidirect
14. C2×#10622339C2semidirect
15. C22×(C2×D11)⋊C8C2semidirect
16. C2×C11×#435C2semidirect
19. C22×C11×M16C22semidirect
27. C23×C11⋊C8C22semidirect
30. C22×#4313C22semidirect
31. C22×C8×D11C22semidirect
42. C11×#435C22semidirect
43. C2×C11×C4⋊C8C22semidirect
45. C2×C11×C22⋊C8C22semidirect
46. C2×C11×#97C22semidirect
48. C2×C22⋊(C11⋊C8)C22semidirect
49. #10622742C22semidirect
50. #10622741C22semidirect
51. #10622724C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. C2×(C2×D11)⋊C8C22semidirect
60. C2×(C2×D11)⋊C8C22semidirect
61. C2×#66879C22semidirect
62. C2×Dic11⋊C8C22semidirect
63. C2×Dic11⋊C8C22semidirect
64. C2×C8×Dic11C22semidirect
65. D4×C11⋊C8C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. C2×C4×C11⋊C8C22semidirect
68. #10622453C22semidirect
69. #10622451C22semidirect
70. #10622343C22semidirect
71. #10622340C22semidirect
72. #10622339C22semidirect
73. (C22⋊D11)⋊C8C22semidirect
74. #10622322C22semidirect
75. #10622319C22semidirect
102. C2×C11×M16C23semidirect
142. C22×C11⋊C8C23semidirect
148. C2×#4313C23semidirect
150. C2×C8×D11C23semidirect
161. C11×C4⋊C8C23semidirect
163. C11×C22⋊C8C23semidirect
164. C11×#97C23semidirect
166. C22⋊(C11⋊C8)C23semidirect
173. (C2×D11)⋊C8C23semidirect
174. (C2×D11)⋊C8C23semidirect
175. #66879C23semidirect
176. Dic11⋊C8C23semidirect
177. Dic11⋊C8C23semidirect
178. C8×Dic11C23semidirect
179. C4⋊(C11⋊C8)C23semidirect
180. C4×C11⋊C8C23semidirect
300. C2×#435D11semidirect
395. C22×M16C2×D11semidirect
420. #435C2×D11semidirect
428. C2×C4⋊C8C2×D11semidirect
444. C2×C22⋊C8C2×D11semidirect
446. C2×#97C2×D11semidirect
518. C2×M16C22×D11semidirect
574. C4⋊C8C22×D11semidirect
586. C22⋊C8C22×D11semidirect
588. #97C22×D11semidirect
593. C2×C11#2976semidirect
711. C11C2×#2976semidirect
835. C2#13077665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230782
#130776652
C2×#106224512
C2×#106227412
C2×#106223192
C2×#106227242
C2×#106223432
C2×D4×C11⋊C82
C2×(C22⋊D11)⋊C82
C2×#106223222
C2×#106224532
C2×#106227422
C2×#106223402
C2×#106223392
C22×(C2×D11)⋊C82
C2×C11×#4352
C2×#297611