Finite Group Databasebeta

← C2×#13077663 #15618522

Subgroups — C2×#13077663 #15618522

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#13077663C2116yesmaximal, direct product factor
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622342C211yesmaximal, characteristic, complemented
5C2×#10622341C211yesmaximal, characteristic, complemented
6C2×#10622319C211yesmaximal, characteristic, complemented
7C2×#10622740C211yesmaximal, characteristic, complemented
8C2×#10622447C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
10C2×#10622322C211yesmaximal, characteristic, complemented
11C2×#10622453C211yesmaximal, characteristic, complemented
12C2×#10622723C211yesmaximal, characteristic, complemented
13C2×#10622340C211yesmaximal, characteristic, complemented
14C2×#10622739C211yesmaximal, characteristic, complemented
15C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992C411yescharacteristic
23C2×#66990C411yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C22×#4313C2211yescharacteristic, complemented
29C22×C8×D11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
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#10622740C2218yescomplemented
50#10622739C2218yescomplemented
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, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
61C2×#66879C2211yescharacteristic, complemented
62C2×Dic11⋊C8C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65#10622625C2218yescomplemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67C2×C4×C11⋊C8C2211yescharacteristic, complemented
68#10622453C2218yescomplemented
69#10622447C2218yescomplemented
70#10622342C2218yescomplemented
71#10622341C2218yescomplemented
72#10622340C2218yescomplemented
73D11×C22⋊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×M16C2314yes—
103C22×C8×C11—42no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2314yescomplemented
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
135C2×#4318—42no—
136C2×#4318—42no—
137C2×#4318C2314yes—
138C2×#4318C2314yescomplemented
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C2×#4313—42no—
144C2×#4313C2314yescomplemented
145C2×C8×D11—42no—
146C2×C8×D11—42no—
147C2×C8×D11—42no—
148C2×C8×D11C2314yes—
149C2×C8×D11C2314yes—
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—42no—
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—24no—
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—
279#4318—44no—
280#4318—44no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4313—44no—
290C8×D11—44no—
291C8×D11—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—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—28no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11—416no—
330C22×D11#13114yes—
331C22×D11C23×C412yes—
332C22×D11C23×C412yes—
333C22×D11C23×C412yes—
334D4×C11—44no—
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—28no—
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
396C23×C8—111no—
397C23×C8—111no—
398C23×C8—111no—
399C23×C8C2×D1111yescharacteristic, complemented
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—111no—
441C2×C22⋊C8—111no—
442C2×C22⋊C8—118no—
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—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11#51812yes—
458C22×C11C2×#13112yes—
459C22×C11#56812yes—
460C22×C11C24×C411yescharacteristic
461C2×D11—22no—
462C2×D11—28no—
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×D11C2×#13114yes—
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×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×D1114yescomplemented
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—42no—
592C2×C11—42no—
593C2×C11#297614yescomplemented
594C2×C11C2×#51811yescharacteristic
595C2×C11C22×#13111yescharacteristic
596C2×C11C2×#56811yescharacteristic
597D11—24no—
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—42no—
615C2×D4—114no—
616C2×D4—114no—
617C2×D4—114no—
618C2×D4—114no—
619C2×D4—114no—
620C2×D4—114no—
621C2×D4—224no—
622C2×D4—224no—
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—22no—
718C23—114no—
719C23—112no—
720C23—112no—
721C23—112no—
722C23—228no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—444no—
732C23—444no—
733C23—4416no—
734C23C22×C4×D1112yes—
735C23C22×C4×D1112yes—
736C23C22×C4×D1111yescharacteristic
737Q8—444no—
738D4—44no—
739D4—228no—
740D4—228no—
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—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—114no—
802C22—228no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—222no—
808C22—222no—
809C22—222no—
810C22—222no—
811C22—4416no—
812C22—444no—
813C22—444no—
814C22#1062307612yes—
815C22#1062327612yes—
816C22D11×#13112yes—
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—42no—
831C2—42no—
832C2—224no—
833C2—442no—
834C2—442no—
835C2#1307766314yesdirect product factor
836C2C2×#1062307611yescharacteristic
837C2C2×D11×#13111yescharacteristic
838C2C2×#1062327611yescharacteristic
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. #13077663C2direct (N × H)
3. C2×#10622625C2semidirect
4. C2×#10622342C2semidirect
5. C2×#10622341C2semidirect
6. C2×#10622319C2semidirect
7. C2×#10622740C2semidirect
8. C2×#10622447C2semidirect
9. C2×C8×C22⋊D11C2semidirect
10. C2×#10622322C2semidirect
11. C2×#10622453C2semidirect
12. C2×#10622723C2semidirect
13. C2×#10622340C2semidirect
14. C2×#10622739C2semidirect
15. C2×D11×C22⋊C8C2semidirect
16. C2×C11×#435C2semidirect
20. C23×C8×C11C22semidirect
27. C22×#4318C22semidirect
28. 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. #10622740C22semidirect
50. #10622739C22semidirect
51. #10622723C22semidirect
52. C8×C22⋊D11C22semidirect
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. #10622625C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. C2×C4×C11⋊C8C22semidirect
68. #10622453C22semidirect
69. #10622447C22semidirect
70. #10622342C22semidirect
71. #10622341C22semidirect
72. #10622340C22semidirect
73. D11×C22⋊C8C22semidirect
74. #10622322C22semidirect
75. #10622319C22semidirect
108. C22×C8×C11C23semidirect
138. C2×#4318C23semidirect
144. 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
399. C23×C8C2×D11semidirect
420. #435C2×D11semidirect
428. C2×C4⋊C8C2×D11semidirect
444. C2×C22⋊C8C2×D11semidirect
446. C2×#97C2×D11semidirect
534. C22×C8C22×D11semidirect
574. C4⋊C8C22×D11semidirect
586. C22⋊C8C22×D11semidirect
588. #97C22×D11semidirect
593. C2×C11#2976semidirect
711. C11C2×#2976semidirect
835. C2#13077663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230782
#130776632
C2×#106226252
C2×#106223422
C2×#106223412
C2×#106223192
C2×#106227402
C2×#106224472
C2×C8×C22⋊D112
C2×#106223222
C2×#106224532
C2×#106227232
C2×#106223402
C2×#106227392
C2×D11×C22⋊C82
C2×C11×#4352
C2×#297611