Finite Group Databasebeta

← C2×#13077662 #15618521

Subgroups — C2×#13077662 #15618521

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×#10623055C211yesmaximal, characteristic
2#13077662C2116yesmaximal, direct product factor
3C2×#10622301C211yesmaximal, characteristic, complemented
4C2×#10622451C211yesmaximal, characteristic, complemented
5C2×#10622319C211yesmaximal, characteristic, complemented
6C2×#10622319C211yesmaximal, characteristic, complemented
7C2×#10622449C211yesmaximal, characteristic, complemented
8C2×#10622449C211yesmaximal, characteristic, complemented
9C2×C8×D44C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic, complemented
11C2×#10622613C211yesmaximal, characteristic, complemented
12C2×#10622340C211yesmaximal, characteristic, complemented
13C2×#10622340C211yesmaximal, characteristic, complemented
14C2×#10622339C211yesmaximal, characteristic, complemented
15C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#433C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×#4313C2211yescharacteristic, complemented
23C22×#4313C2211yescharacteristic, complemented
24C22×C8×D11C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic, complemented
27C22×C8×D11C2211yescharacteristic, complemented
28#10623055C418yes—
29#10623055C2218yes—
30C2×#66950C411yescharacteristic
31C2×#66950C411yescharacteristic
32C2×#66948C411yescharacteristic
33C2×#66948C411yescharacteristic
34C2×#66939C411yescharacteristic
35C2×#66939C411yescharacteristic
36C2×#66935C411yescharacteristic
37C2×#66935C411yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C11×#433C2218yescomplemented
43C2×C11×C4⋊C8C2211yescharacteristic, complemented
44C2×C11×C4⋊C8C2211yescharacteristic, complemented
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×#97C2211yescharacteristic, complemented
48C2×C4×C8×C11C2211yescharacteristic, complemented
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×(C2×D11)⋊C8C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
57C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
58C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
59#10622613C2218yescomplemented
60C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
62C2×#66867C2211yescharacteristic, complemented
63C2×C4×C11⋊C8C2211yescharacteristic, complemented
64#10622451C2218yescomplemented
65#10622449C2218yescomplemented
66#10622449C2218yescomplemented
67#10622447C2218yescomplemented
68#10622340C2218yescomplemented
69#10622340C2218yescomplemented
70#10622339C2218yescomplemented
71D11×C22⋊C8C2218yescomplemented
72#10622319C2218yescomplemented
73#10622319C2218yescomplemented
74#10622301C2218yescomplemented
75C8×D44C2218yescomplemented
76C24×D11C2×C411yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11C2×C411yescharacteristic
79C22×C22⋊D11C2×C411yescharacteristic
80C23×Dic11C2×C411yescharacteristic
81C2×#4339—42no—
82C2×#4339—42no—
83C2×#4339C2×C414yes—
84C2×#4339C2314yes—
85C22×D44C2×C411yescharacteristic
86C22×D44C2×C411yescharacteristic
87C22×D44C2×C411yescharacteristic
88C22×D44C2×C411yescharacteristic
89C22×D44C2×C411yescharacteristic
90C22×C4×D11—42no—
91C22×C4×D11—42no—
92C22×C4×D11C2×C411yescharacteristic
93C22×C4×D11C2×C411yescharacteristic
94C22×C4×D11C2×C414yes—
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2314yes—
100C22×Dic22C2×C411yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#117C2×C414yes—
106C11×#117C2314yes—
107C2×C11×C4⋊C4C2×C411yescharacteristic
108C2×C11×C4⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×(C2×D11)⋊C4C2×C411yescharacteristic
114C2×(C2×D11)⋊C4C2×C411yescharacteristic
115C2×(C2×D11)⋊C4C2×C411yescharacteristic
116C2×(C2×D11)⋊C4C2×C411yescharacteristic
117C2×(C2×D11)⋊C4C2×C411yescharacteristic
118C2×(C2×D11)⋊C4C2×C411yescharacteristic
119C2×(C2×D11)⋊C4C2×C411yescharacteristic
120C2×(C2×D11)⋊C4C2×C411yescharacteristic
121C2×C4⋊Dic11C2×C411yescharacteristic
122C2×C4⋊Dic11C2×C411yescharacteristic
123C2×C4⋊Dic11C2×C411yescharacteristic
124C2×C4⋊Dic11C2×C411yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C2×#4313—42no—
130C2×#4313—42no—
131C2×#4313—42no—
132C2×#4313—42no—
133C2×#4313C2314yes—
134C2×#4313C2314yes—
135C2×#4313C2314yescomplemented
136C2×#4313C2314yescomplemented
137C2×C8×D11—42no—
138C2×C8×D11—42no—
139C2×C8×D11—42no—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142C2×C8×D11C2314yes—
143C2×C8×D11C2314yescomplemented
144C2×C8×D11C2314yescomplemented
145#66950C2×C418yes—
146#66950C2×C418yes—
147#66948C2×C418yes—
148#66948C2×C418yes—
149#66939C2×C418yes—
150#66939C2×C418yes—
151#66935C2×C418yes—
152#66935C2×C418yes—
153C4×D44C2×C414yes—
154C4×D44C2×C414yes—
155C4×D44C2×C414yes—
156C4×D44C2×C414yes—
157C4×D44C2314yes—
158C4×D44C2314yes—
159C4×D44C2314yes—
160C4×D44C2314yes—
161C11×C4⋊C8C2314yescomplemented
162C11×C4⋊C8C2314yescomplemented
163C11×C22⋊C8C2314yes—
164C11×C22⋊C8C2314yes—
165C11×#97C2314yescomplemented
166C4×C8×C11C2314yescomplemented
167C22⋊(C11⋊C8)C2314yes—
168C22⋊(C11⋊C8)C2314yes—
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(C2×D11)⋊C8C2314yescomplemented
176(C2×D11)⋊C8C2314yescomplemented
177C4⋊(C11⋊C8)C2314yescomplemented
178C4⋊(C11⋊C8)C2314yescomplemented
179#66867C2314yescomplemented
180C4×C11⋊C8C2314yescomplemented
181C2×#2976—111nomaximal, Sylow
182C24×C11C22×C411yescharacteristic
183C23×D11—24no—
184C23×D11—42no—
185C23×D11—42no—
186C23×D11C22×C411yescharacteristic
187C23×D11C22×C411yescharacteristic
188C23×D11C22×C411yescharacteristic
189C23×D11C22×C411yescharacteristic
190C23×D11C22×C414yes—
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×C411yescharacteristic
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11C22×C414yes—
204C2×C22⋊D11C22×C414yes—
205C22×Dic11—42no—
206C22×Dic11C22×C411yescharacteristic
207C22×Dic11C22×C411yescharacteristic
208C22×Dic11C22×C411yescharacteristic
209C22×Dic11C22×C411yescharacteristic
210C22×Dic11C22×C414yes—
211#4339—48no—
212#4339—44no—
213#4339—44no—
214C2×D44—24no—
215C2×D44—24no—
216C2×D44—42no—
217C2×D44—42no—
218C2×D44—42no—
219C2×D44C22×C414yes—
220C2×D44C22×C414yes—
221C2×D44C22×C414yes—
222C2×D44C22×C414yes—
223C2×D44C22×C414yes—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—48no—
235C2×C4×D11—44no—
236C2×C4×D11—44no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C22×C412yes—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C22×C412yes—
241C2×C4×D11C22×C414yes—
242C2×C4×D11C22×C414yes—
243C2×C4×D11C2412yes—
244C2×C4×D11C2412yes—
245C2×C4×D11C2412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—42no—
248C2×Dic22C22×C414yes—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C11×C4⋊C4C22×C414yes—
258C11×C4⋊C4C22×C414yes—
259C11×C22⋊C4C22×C414yes—
260C11×C22⋊C4C22×C414yes—
261C42×C11C22×C412yes—
262C42×C11C22×C412yes—
263C42×C11C2412yes—
264C42×C11C2412yes—
265(C2×D11)⋊C4C22×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—
272(C2×D11)⋊C4C22×C414yes—
273C4⋊Dic11C22×C414yes—
274C4⋊Dic11C22×C414yes—
275C4⋊Dic11C22×C414yes—
276C4⋊Dic11C22×C414yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8C2412yes—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284C2×C11⋊C8C2412yes—
285#4313—44no—
286#4313—44no—
287#4313—44no—
288#4313—44no—
289C8×D11—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×#435—111no—
301C2×C8×D4—111no—
302C2×C8×D4—111no—
303C2×#433—111no—
304C2×#433D1111yescharacteristic, complemented
305C2×#408—111no—
306C2×#408—111no—
307C2×#407—111no—
308C22×C22⋊C8—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11C23×C412yes—
313C23×C11C23×C411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—28no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—416no—
329C22×D11#13114yes—
330C22×D11C23×C412yes—
331C22×D11C23×C412yes—
332C22×D11C23×C412yes—
333C22×D11C23×C412yes—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11C23×C412yes—
343C2×C4×C11C23×C412yes—
344C2×C4×C11C23×C412yes—
345C2×C4×C11C23×C412yes—
346C2×C4×C11C23×C412yes—
347C2×C4×C11C23×C411yescharacteristic
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11H(5,𝔽2)12yes—
350C2×C4×C11C2511yescharacteristic
351C22⋊D11—44no—
352C22⋊D11—44no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—44no—
358C2×Dic11C23×C412yes—
359C2×Dic11C23×C412yes—
360C2×Dic11C23×C412yes—
361C2×Dic11C23×C412yes—
362D44—28no—
363D44—28no—
364D44—44no—
365D44—44no—
366D44—44no—
367C4×D11—24no—
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—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×M16—111no—
396C23×C8—111no—
397C23×C8—111no—
398C23×C8—111no—
399C23×C8—111no—
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×D4—111no—
414C2×#117C2×D1111yescharacteristic
415#436—118no—
416#436—118no—
417#435—118no—
418#435—118no—
419#435—118no—
420#435—118no—
421C8×D4—118no—
422C8×D4—118no—
423#433—118no—
424#433C2×D1118yescomplemented
425C2×C4⋊C8—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8C2×D1111yescharacteristic, complemented
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
445C2×#97—111no—
446C2×#97C2×D1111yescharacteristic, complemented
447C2×C4×C8—111no—
448C2×C4×C8C2×D1111yescharacteristic, complemented
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—44no—
453C22×C11#51812yes—
454C22×C11C2×#13112yes—
455C22×C11#56812yes—
456C22×C11C24×C411yescharacteristic
457C2×D11—22no—
458C2×D11—28no—
459C2×D11—22no—
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—416no—
470C2×D11—44no—
471C2×D11—44no—
472C2×D11—44no—
473C2×D11C2×#13114yes—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—22no—
479C4×C11#51812yes—
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
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×D4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—114no—
507C23×C4—114no—
508C23×C4—442no—
509C23×C4—442no—
510C23×C4C22×D1111yescharacteristic
511C2×M16—114no—
512C2×M16—114no—
513C2×M16—114no—
514C2×M16—114no—
515C2×M16—442no—
516C2×M16—442no—
517C2×M16—442no—
518C2×M16—442no—
519C22×C8—111no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—114no—
524C22×C8—114no—
525C22×C8—114no—
526C22×C8—114no—
527C22×C8—442no—
528C22×C8—442no—
529C22×C8—442no—
530C22×C8—442no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1111yescharacteristic
534C22×C8C22×D1111yescharacteristic
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×D4—114no—
550C4×D4—114no—
551#117C4×D1114yes—
552#117C22×D1114yes—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4C4×D1111yescharacteristic
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×C42C22×D1111yescharacteristic
570C2×C42C22×D1111yescharacteristic
571C4⋊C8—114no—
572C4⋊C8—114no—
573C4⋊C8C22×D1114yescomplemented
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×D1114yes—
587#97—114no—
588#97C22×D1114yescomplemented
589C4×C8—114no—
590C4×C8C22×D1114yescomplemented
591C2×C11—42no—
592C2×C11#297614yescomplemented
593C2×C11C2×#51811yescharacteristic
594C2×C11C22×#13111yescharacteristic
595C2×C11C2×#56811yescharacteristic
596D11—24no—
597D11—42no—
598D11—42no—
599D11—42no—
600C24—111no—
601C24—111no—
602C24—111no—
603C24—111no—
604C24—114no—
605C24—224no—
606C24—442no—
607C24—442no—
608C24C2×C4×D1111yescharacteristic
609#41—448no—
610#41—444no—
611#41—444no—
612C2×Q8—114no—
613C2×Q8—442no—
614C2×D4—114no—
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×D4—442no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—114no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—114no—
644C22×C4—114no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—448no—
654C22×C4—444no—
655C22×C4—444no—
656C22×C4—442no—
657C22×C4—442no—
658C22×C4—442no—
659C22×C4C2×C4×D1111yescharacteristic
660C22×C4C2×C4×D1111yescharacteristic
661C22×C4C2×C4×D1111yescharacteristic
662C22×C4C2×C4×D1111yescharacteristic
663C22×C4C2×C4×D1111yescharacteristic
664C22×C4C2×C4×D1112yes—
665C22×C4C23×D1112yes—
666C22×C4C23×D1111yescharacteristic
667M16—444no—
668M16—444no—
669M16—444no—
670M16—444no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—112no—
676C2×C8—112no—
677C2×C8—112no—
678C2×C8—112no—
679C2×C8—222no—
680C2×C8—222no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—444no—
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⋊C4C2×C4×D1114yes—
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—
707C42C2×C4×D1112yes—
708C42C2×C4×D1112yes—
709C42C23×D1112yes—
710C42C23×D1112yes—
711C11C2×#297611yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—22no—
715C23—114no—
716C23—112no—
717C23—112no—
718C23—112no—
719C23—112no—
720C23—228no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—444no—
733C23—444no—
734C23—4416no—
735C23C22×C4×D1112yes—
736C23C22×C4×D1111yescharacteristic
737Q8—444no—
738D4—228no—
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—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—112no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—444no—
774C2×C4—444no—
775C2×C4—444no—
776C2×C4C22×C4×D1112yes—
777C2×C4C22×C4×D1112yes—
778C2×C4C22×C4×D1112yes—
779C2×C4C22×C4×D1112yes—
780C2×C4C22×C4×D1112yes—
781C2×C4C22×C4×D1111yescharacteristic
782C2×C4#6704212yes—
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—44no—
797C22—114no—
798C22—228no—
799C22—222no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—222no—
808C22—222no—
809C22—222no—
810C22—4416no—
811C22—444no—
812C22—444no—
813C22—444no—
814C22#1062305212yes—
815C22D11×#13112yes—
816C22#1062328112yes—
817C22C23×C4×D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—222no—
824C4—222no—
825C4—222no—
826C4—222no—
827C4#1062305212yes—
828C4C2×#6704211yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—42no—
831C2—224no—
832C2—442no—
833C2—442no—
834C2—442no—
835C2#1307766214yesdirect product factor
836C2C2×#1062305211yescharacteristic
837C2C2×D11×#13111yescharacteristic
838C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#433C2
socleC23×C11C23×C4
prime radicalC2×#10623055C2
cosocleC2×C4×C11C25
hypercenterC2×#433D11
hypocenterC11C2×#2976
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13077662C2direct (N × H)
3. C2×#10622301C2semidirect
4. C2×#10622451C2semidirect
5. C2×#10622319C2semidirect
6. C2×#10622319C2semidirect
7. C2×#10622449C2semidirect
8. C2×#10622449C2semidirect
9. C2×C8×D44C2semidirect
10. C2×#10622447C2semidirect
11. C2×#10622613C2semidirect
12. C2×#10622340C2semidirect
13. C2×#10622340C2semidirect
14. C2×#10622339C2semidirect
15. C2×D11×C22⋊C8C2semidirect
16. C2×C11×#433C2semidirect
22. C22×#4313C22semidirect
23. C22×#4313C22semidirect
26. C22×C8×D11C22semidirect
27. C22×C8×D11C22semidirect
42. C11×#433C22semidirect
43. C2×C11×C4⋊C8C22semidirect
44. C2×C11×C4⋊C8C22semidirect
47. C2×C11×#97C22semidirect
48. C2×C4×C8×C11C22semidirect
55. C2×(C2×D11)⋊C8C22semidirect
56. C2×(C2×D11)⋊C8C22semidirect
57. C2×(C2×D11)⋊C8C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. #10622613C22semidirect
60. C2×C4⋊(C11⋊C8)C22semidirect
61. C2×C4⋊(C11⋊C8)C22semidirect
62. C2×#66867C22semidirect
63. C2×C4×C11⋊C8C22semidirect
64. #10622451C22semidirect
65. #10622449C22semidirect
66. #10622449C22semidirect
67. #10622447C22semidirect
68. #10622340C22semidirect
69. #10622340C22semidirect
70. #10622339C22semidirect
71. D11×C22⋊C8C22semidirect
72. #10622319C22semidirect
73. #10622319C22semidirect
74. #10622301C22semidirect
75. C8×D44C22semidirect
135. C2×#4313C23semidirect
136. C2×#4313C23semidirect
143. C2×C8×D11C23semidirect
144. C2×C8×D11C23semidirect
161. C11×C4⋊C8C23semidirect
162. C11×C4⋊C8C23semidirect
165. C11×#97C23semidirect
166. C4×C8×C11C23semidirect
173. (C2×D11)⋊C8C23semidirect
174. (C2×D11)⋊C8C23semidirect
175. (C2×D11)⋊C8C23semidirect
176. (C2×D11)⋊C8C23semidirect
177. C4⋊(C11⋊C8)C23semidirect
178. C4⋊(C11⋊C8)C23semidirect
179. #66867C23semidirect
180. C4×C11⋊C8C23semidirect
304. C2×#433D11semidirect
424. #433C2×D11semidirect
427. C2×C4⋊C8C2×D11semidirect
428. C2×C4⋊C8C2×D11semidirect
446. C2×#97C2×D11semidirect
448. C2×C4×C8C2×D11semidirect
573. C4⋊C8C22×D11semidirect
574. C4⋊C8C22×D11semidirect
588. #97C22×D11semidirect
590. C4×C8C22×D11semidirect
592. C2×C11#2976semidirect
711. C11C2×#2976semidirect
835. C2#13077662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230552
#130776622
C2×#106223012
C2×#106224512
C2×#106223192
C2×#106224492
C2×C8×D442
C2×#106224472
C2×#106226132
C2×#106223402
C2×#106223392
C2×D11×C22⋊C82
C2×C11×#4332
C2×#297611