Finite Group Databasebeta

← C2×#13077357 #15617680

Subgroups — C2×#13077357 #15617680

Order 2816.

2850 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C211yesmaximal, characteristic, complemented
2C22×#66954C211yesmaximal, characteristic, complemented
3C2×#10623079C211yesmaximal, characteristic
4#13077357C2116yesmaximal, direct product factor
5C2×#10622741C211yesmaximal, characteristic, complemented
6C2×#10622342C211yesmaximal, characteristic, complemented
7C2×#10622319C211yesmaximal, characteristic, complemented
8C2×#10622624C211yesmaximal, characteristic, complemented
9C2×#10622449C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
11C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
12C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
13C2×#10622340C211yesmaximal, characteristic, complemented
14C2×#10622340C211yesmaximal, characteristic, complemented
15C2×#10622320C211yesmaximal, 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
28C2×#66960—28no—
29C2×#66960C2218yescomplemented
30C2×#66954—28no—
31C2×#66954C2218yescomplemented
32C22×#4313C2211yescharacteristic
33C22×#4313C2211yescharacteristic
34C22×#4313C2211yescharacteristic
35C22×#4313C2211yescharacteristic
36C22×C8×D11C2211yescharacteristic
37C22×C8×D11C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic
40#10623079C418yes—
41#10623079C2218yes—
42C2×#66948C411yescharacteristic
43C2×#66941C411yescharacteristic
44C2×#66938C411yescharacteristic
45C2×#66938C411yescharacteristic
46C2×#66937C411yescharacteristic
47C2×#66937C411yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×C42×D11C2211yescharacteristic
50C11×#435C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×#97C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic
57#10622741C2218yescomplemented
58C8×C22⋊D11C2218yescomplemented
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66C2×C8×Dic11C2211yescharacteristic
67#10622624C2218yescomplemented
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69C2×#66867C2211yescharacteristic
70#10622449C2218yescomplemented
71D11×C4⋊C8C2218yescomplemented
72#10622342C2218yescomplemented
73#10622340C2218yescomplemented
74#10622340C2218yescomplemented
75(C22⋊D11)⋊C8C2218yescomplemented
76#10622320C2218yescomplemented
77#10622319C2218yescomplemented
78C22×D4×C11C2×C411yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11C2×C411yescharacteristic
82C22×C22⋊D11C2×C411yescharacteristic
83C22×C22⋊D11C2×C411yescharacteristic
84C22×C22⋊D11C2×C411yescharacteristic
85C22×C22⋊D11C2×C411yescharacteristic
86C22×C22⋊D11C2×C411yescharacteristic
87C2×#4339—24no—
88C2×#4339—24no—
89C2×#4339—24no—
90C2×#4339—24no—
91C2×#4339C2×C414yes—
92C2×#4339C2×C414yes—
93C2×#4339C2314yes—
94C2×#4339C2314yes—
95C22×D44C2×C411yescharacteristic
96C22×D44C2×C411yescharacteristic
97C22×D44C2×C411yescharacteristic
98C22×C4×D11C2×C411yescharacteristic
99C22×C4×D11C2×C411yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2311yescharacteristic
103C22×Dic22C2×C411yescharacteristic
104C22×Dic22C2×C411yescharacteristic
105C2×C11×M16—24no—
106C2×C11×M16C2314yes—
107C22×C8×C11—24no—
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2314yes—
112C22×C8×C11C2311yescharacteristic
113C4×D4×C11C2×C414yes—
114C4×D4×C11C2314yes—
115C2×C11×C4⋊C4C2×C411yescharacteristic
116C2×C11×C22⋊C4C2×C411yescharacteristic
117C2×C11×C22⋊C4C2×C411yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C22⋊Dic11C2×C411yescharacteristic
120C2×C22⋊Dic11C2×C411yescharacteristic
121#66993C2×C418yes—
122#66991C2×C418yes—
123C4×C22⋊D11C2×C414yes—
124C4×C22⋊D11C2×C414yes—
125C4×C22⋊D11C2314yes—
126C4×C22⋊D11C2314yes—
127C2×(C2×D11)⋊C4C2×C411yescharacteristic
128C2×(C2×D11)⋊C4C2×C411yescharacteristic
129C2×(C2×D11)⋊C4C2×C411yescharacteristic
130C2×(C2×D11)⋊C4C2×C411yescharacteristic
131C2×C4⋊Dic11C2×C411yescharacteristic
132C2×Dic11⋊C4C2×C411yescharacteristic
133C2×Dic11⋊C4C2×C411yescharacteristic
134C2×C4×Dic11C2×C411yescharacteristic
135C2×C4×Dic11C2×C411yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×#4318—24no—
138C2×#4318C2314yes—
139C22×C11⋊C8—24no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2314yes—
144C22×C11⋊C8C2311yescharacteristic
145#66960—232no—
146#66954—232no—
147C2×#4313—24no—
148C2×#4313—24no—
149C2×#4313—24no—
150C2×#4313D418yescomplemented
151C2×#4313C2314yes—
152C2×#4313C2314yes—
153C2×#4313C2314yes—
154C2×#4313C2314yes—
155C2×C8×D11—24no—
156C2×C8×D11—24no—
157C2×C8×D11—24no—
158C2×C8×D11—24no—
159C2×C8×D11C2314yes—
160C2×C8×D11C2314yes—
161C2×C8×D11C2314yes—
162C2×C8×D11C2314yes—
163#66948C2×C418yes—
164#66941C2×C418yes—
165#66938C2×C418yes—
166#66938C2×C418yes—
167#66937C2×C418yes—
168#66937C2×C418yes—
169C4×D44C2×C414yes—
170C4×D44C2314yes—
171C42×D11C2×C414yes—
172C42×D11C2314yes—
173C11×C4⋊C8C2314yes—
174C11×C22⋊C8C2314yes—
175C11×C22⋊C8C2314yes—
176C11×#97C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182(C2×D11)⋊C8C2314yes—
183Dic11⋊C8C2314yes—
184Dic11⋊C8C2314yes—
185C8×Dic11C2314yes—
186C8×Dic11C2314yes—
187C4⋊(C11⋊C8)C2314yes—
188#66867C2314yes—
189C2×#2935—111nomaximal, Sylow
190C24×C11C22×C411yescharacteristic
191C24×C11C22×C411yescharacteristic
192C23×D11C22×C411yescharacteristic
193C23×D11C22×C411yescharacteristic
194C23×D11C22×C411yescharacteristic
195C2×D4×C11—42no—
196C2×D4×C11C22×C414yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11C22×C414yes—
217C2×C22⋊D11C22×C414yes—
218C2×C22⋊D11C22×C414yes—
219C2×C22⋊D11C22×C414yes—
220C2×C22⋊D11C22×C414yes—
221C2×C22⋊D11C22×C414yes—
222C22×Dic11C22×C411yescharacteristic
223C22×Dic11C22×C411yescharacteristic
224C22×Dic11C22×C411yescharacteristic
225C22×Dic11C22×C411yescharacteristic
226C22×Dic11C22×C411yescharacteristic
227#4339—216no—
228#4339—216no—
229#4339—28no—
230#4339—28no—
231#4339—28no—
232#4339—28no—
233C2×D44—24no—
234C2×D44—24no—
235C2×D44—42no—
236C2×D44C22×C414yes—
237C2×D44C22×C414yes—
238C2×D44C22×C414yes—
239C2×C4×D11—24no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—42no—
245C2×C4×D11C22×C414yes—
246C2×C4×D11C22×C412yes—
247C2×C4×D11C22×C412yes—
248C2×C4×D11C22×C414yes—
249C2×C4×D11C22×C412yes—
250C2×C4×D11C2×D414yes—
251C2×C4×D11#4114yes—
252C2×C4×D11C2412yes—
253C2×C4×D11C2412yes—
254C2×C4×D11C2412yes—
255C2×Dic22—24no—
256C2×Dic22—24no—
257C2×Dic22C22×C414yes—
258C2×Dic22C22×C414yes—
259C11×M16—28no—
260C2×C8×C11—28no—
261C2×C8×C11—22no—
262C2×C8×C11—22no—
263C2×C8×C11—22no—
264C2×C8×C11C2×D414yes—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4C22×C414yes—
270C11×C22⋊C4C22×C414yes—
271C11×C22⋊C4C22×C414yes—
272C42×C11C22×C412yes—
273C42×C11C2412yes—
274C22⋊Dic11C22×C414yes—
275C22⋊Dic11C22×C414yes—
276(C2×D11)⋊C4C22×C414yes—
277(C2×D11)⋊C4C22×C414yes—
278(C2×D11)⋊C4C22×C414yes—
279(C2×D11)⋊C4C22×C414yes—
280C4⋊Dic11C22×C414yes—
281Dic11⋊C4C22×C414yes—
282Dic11⋊C4C22×C414yes—
283C4×Dic11C22×C412yes—
284C4×Dic11C22×C414yes—
285C4×Dic11C22×C414yes—
286C4×Dic11C2412yes—
287#4318—28no—
288C2×C11⋊C8—28no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2×D414yes—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297#4313—28no—
298#4313—28no—
299#4313—28no—
300#4313C2×D4116yescomplemented
301C8×D11—28no—
302C8×D11—28no—
303C8×D11—28no—
304C8×D11—28no—
305C22×#131—111no—
306C22×#131—111no—
307C2×#532—111no—
308#2935—1116no—
309C2×#436—111no—
310C2×#436—111no—
311C2×#435—111no—
312C2×#435—111no—
313C2×#435—111no—
314C2×#435D1111yescharacteristic, complemented
315C2×C8×D4—111no—
316C2×C8×D4—111no—
317C22×C4⋊C8—111no—
318C2×#408—111no—
319C2×#408—111no—
320C2×C4×M16—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11C23×C412yes—
328C23×C11C23×C412yes—
329C23×C11C23×C411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11C4×D414yes—
339C22×D11C23×C412yes—
340C22×D11C23×C412yes—
341C22×D11C23×C412yes—
342D4×C11—44no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—24no—
348C2×C4×C11—24no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11C23×C412yes—
354C2×C4×C11C23×C412yes—
355C2×C4×C11C23×C412yes—
356C2×C4×C11C23×C412yes—
357C2×C4×C11C23×C411yescharacteristic
358C2×C4×C11C22×D412yes—
359C2×C4×C11C2×#4112yes—
360C2×C4×C11C2511yescharacteristic
361C22⋊D11—28no—
362C22⋊D11—28no—
363C22⋊D11—28no—
364C22⋊D11—28no—
365C22⋊D11—28no—
366C22⋊D11—28no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11C4×D414yes—
371C2×Dic11#13114yescomplemented
372C2×Dic11C23×C412yes—
373C2×Dic11C23×C412yes—
374C2×Dic11C23×C412yes—
375C2×Dic11C23×C412yes—
376C2×Dic11C23×C412yes—
377D44—28no—
378D44—28no—
379D44—44no—
380C4×D11—24no—
381C4×D11—24no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—28no—
387C4×D11—44no—
388C4×D11C4×D418yes—
389C4×D11C22×D414yes—
390C4×D11C2×#4114yes—
391Dic22—28no—
392Dic22—28no—
393C8×C11—22no—
394C8×C11—22no—
395C8×C11—22no—
396C8×C11C22×D414yes—
397C11⋊C8—22no—
398C11⋊C8—22no—
399C11⋊C8—22no—
400C11⋊C8C22×D414yes—
401C22×#41—111no—
402C22×#41—111no—
403C2×#131—118no—
404C2×#131—118no—
405C2×#131—228no—
406C2×#131—228no—
407C22×M16—111no—
408C22×M16—111no—
409C22×M16—111no—
410C22×M16—111no—
411C22×M16—111no—
412C22×M16C2×D1111yescharacteristic
413C23×C8—111no—
414C23×C8—111no—
415C23×C8—111no—
416C23×C8—111no—
417C23×C8—111no—
418C23×C8C2×D1111yescharacteristic
419#532—118no—
420#532—118no—
421C2×C4⋊Q8—111no—
422C2×#127—111no—
423C2×#124—111no—
424C2×#124—111no—
425C2×#121—111no—
426C2×#121—111no—
427C2×#121—111no—
428C2×#121—111no—
429C2×C4×D4—111no—
430C2×C4×D4—111no—
431C2×C4×D4—111no—
432C2×C4×D4C2×D1111yescharacteristic
433C22×C42—111no—
434#436—118no—
435#436—118no—
436#435—118no—
437#435—118no—
438#435—118no—
439#435C2×D1118yescomplemented
440C8×D4—118no—
441C8×D4—118no—
442C2×C4⋊C8—111no—
443C2×C4⋊C8—111no—
444C2×C4⋊C8—111no—
445C2×C4⋊C8—118no—
446C2×C4⋊C8C2×D1111yescharacteristic
447#408—118no—
448#408—118no—
449C2×C22⋊C8—111no—
450C2×C22⋊C8—111no—
451C2×C22⋊C8—111no—
452C2×C22⋊C8—111no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×C22⋊C8C2×D1111yescharacteristic
456C2×C22⋊C8C2×D1111yescharacteristic
457C4×M16—118no—
458C2×#97—111no—
459C2×#97C2×D1111yescharacteristic
460C2×C4×C8—111no—
461C2×C4×C8—111no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—44no—
469C22×C11—44no—
470C22×C11C2×C4×D412yes—
471C22×C11C2×#13112yes—
472C22×C11#56812yes—
473C22×C11C24×C411yescharacteristic
474C2×D11—28no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—44no—
484C2×D11—44no—
485C2×D11C2×C4×D414yes—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—22no—
489C4×C11—22no—
490C4×C11C2×C4×D412yes—
491C4×C11C23×D411yescharacteristic
492C4×C11C22×#4111yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—22no—
496Dic11C2×C4×D414yes—
497Dic11C2×#13114yescomplemented
498C2×#41—114no—
499C2×#41—114no—
500C2×#41—114no—
501C2×#41—114no—
502C2×#41—224no—
503C2×#41—224no—
504C2×#41—224no—
505C2×#41—224no—
506C22×Q8—111no—
507C22×Q8—111no—
508C22×D4—111no—
509C22×D4—111no—
510C22×D4—111no—
511C22×D4—111no—
512C22×D4—111no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—111no—
516C22×D4—111no—
517C22×D4C4×D1111yescharacteristic
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525#131—2232no—
526#131—2232no—
527C2×M16—24no—
528C2×M16—114no—
529C2×M16—118no—
530C2×M16—114no—
531C2×M16—114no—
532C2×M16—114no—
533C2×M16—114no—
534C2×M16—224no—
535C2×M16—224no—
536C2×M16—224no—
537C2×M16—224no—
538C2×M16C22×D1114yes—
539C22×C8—24no—
540C22×C8—111no—
541C22×C8—114no—
542C22×C8—111no—
543C22×C8—111no—
544C22×C8—111no—
545C22×C8—114no—
546C22×C8—114no—
547C22×C8—114no—
548C22×C8—114no—
549C22×C8—224no—
550C22×C8—224no—
551C22×C8—224no—
552C22×C8—224no—
553C22×C8—224no—
554C22×C8C22×D1114yes—
555C22×C8C22×D1111yescharacteristic
556C22×C8C22×D1111yescharacteristic
557C22×C8C22×D1111yescharacteristic
558C22×C8C22×D1111yescharacteristic
559C4⋊Q8—118no—
560#127—118no—
561#124—118no—
562#124—118no—
563#121—118no—
564#121—118no—
565#121—118no—
566#121—118no—
567C4×D4—114no—
568C4×D4—114no—
569C4×D4—114no—
570C4×D4—114no—
571C4×D4—114no—
572C4×D4—114no—
573C4×D4C4×D1114yes—
574C4×D4C22×D1114yes—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4C4×D1111yescharacteristic
579C2×C22⋊C4—111no—
580C2×C22⋊C4—111no—
581C2×C22⋊C4—111no—
582C2×C22⋊C4—111no—
583C2×C22⋊C4—111no—
584C2×C22⋊C4—111no—
585C2×C22⋊C4C4×D1111yescharacteristic
586C2×C22⋊C4C4×D1111yescharacteristic
587C2×C42—111no—
588C2×C42—111no—
589C2×C42—111no—
590C2×C42—114no—
591C2×C42—114no—
592C2×C42C22×D1111yescharacteristic
593C4⋊C8—114no—
594C4⋊C8—114no—
595C4⋊C8—114no—
596C4⋊C8C22×D1114yes—
597C22⋊C8—114no—
598C22⋊C8—114no—
599C22⋊C8—114no—
600C22⋊C8—114no—
601C22⋊C8—114no—
602C22⋊C8—114no—
603C22⋊C8C22×D1114yes—
604C22⋊C8C22×D1114yes—
605#97—114no—
606#97C22×D1114yes—
607C4×C8—114no—
608C4×C8—114no—
609C2×C11—42no—
610C2×C11—42no—
611C2×C11#293514yescomplemented
612C2×C11C22×C4×D411yescharacteristic
613C2×C11C22×#13111yescharacteristic
614C2×C11C2×#56811yescharacteristic
615D11—24no—
616D11—42no—
617D11—42no—
618C24—111no—
619C24—111no—
620C24—111no—
621C24C2×C4×D1111yescharacteristic
622C24C2×C4×D1111yescharacteristic
623#41—228no—
624#41—228no—
625#41—2216no—
626#41—2216no—
627#41—228no—
628#41—228no—
629C2×Q8—114no—
630C2×Q8—114no—
631C2×Q8—224no—
632C2×Q8—224no—
633C2×D4—42no—
634C2×D4—114no—
635C2×D4—114no—
636C2×D4—114no—
637C2×D4—114no—
638C2×D4—114no—
639C2×D4—114no—
640C2×D4—114no—
641C2×D4—114no—
642C2×D4—114no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—442no—
652C2×D4C2×C4×D1114yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—112no—
660C22×C4—114no—
661C22×C4—114no—
662C22×C4—112no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—114no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—114no—
672C22×C4—224no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—442no—
678C22×C4C2×C4×D1111yescharacteristic
679C22×C4C2×C4×D1111yescharacteristic
680C22×C4C2×C4×D1111yescharacteristic
681C22×C4C2×C4×D1111yescharacteristic
682C22×C4C2×C4×D1112yes—
683C22×C4C2×C4×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1111yescharacteristic
687M16—28no—
688M16—1116no—
689M16—228no—
690M16—228no—
691M16—228no—
692M16—228no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—28no—
697C2×C8—114no—
698C2×C8—112no—
699C2×C8—112no—
700C2×C8—112no—
701C2×C8—112no—
702C2×C8—228no—
703C2×C8—228no—
704C2×C8—228no—
705C2×C8—228no—
706C2×C8—222no—
707C2×C8—222no—
708C2×C8—222no—
709C2×C8—228no—
710C2×C8D4×D1114yes—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C2×C8C23×D1112yes—
714C2×C8C23×D1112yes—
715C4⋊C4—114no—
716C4⋊C4—114no—
717C4⋊C4—114no—
718C4⋊C4C2×C4×D1114yes—
719C22⋊C4—114no—
720C22⋊C4—114no—
721C22⋊C4—114no—
722C22⋊C4—114no—
723C22⋊C4—114no—
724C22⋊C4—114no—
725C22⋊C4C2×C4×D1114yes—
726C22⋊C4C2×C4×D1114yes—
727C42—112no—
728C42—114no—
729C42—114no—
730C42—112no—
731C42C2×C4×D1112yes—
732C42C23×D1112yes—
733C11C2×#293511yescharacteristic, complemented, Sylow
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—114no—
741C23—112no—
742C23—112no—
743C23—112no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23C22×C4×D1112yes—
753C23C22×C4×D1112yes—
754C23C22×C4×D1111yescharacteristic
755Q8—228no—
756Q8—228no—
757D4—44no—
758D4—228no—
759D4—228no—
760D4—228no—
761D4—228no—
762D4—228no—
763D4—228no—
764D4—228no—
765D4—228no—
766D4—444no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—114no—
778C2×C4—114no—
779C2×C4—112no—
780C2×C4—112no—
781C2×C4—118no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—112no—
785C2×C4—112no—
786C2×C4—112no—
787C2×C4—228no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—224no—
792C2×C4—224no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—444no—
798C2×C4C22×C4×D1112yes—
799C2×C4C22×C4×D1112yes—
800C2×C4C22×C4×D1112yes—
801C2×C4C22×C4×D1112yes—
802C2×C4C22×C4×D1111yescharacteristic
803C2×C4C2×D4×D1112yes—
804C2×C4#41×D1112yes—
805C2×C4C24×D1111yescharacteristic
806C8—22no—
807C8—22no—
808C8—22no—
809C8—114no—
810C8—222no—
811C8—222no—
812C8—222no—
813C8C2×D4×D1114yes—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—114no—
823C22—228no—
824C22—222no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—444no—
833C22—444no—
834C22C4×D4×D1112yes—
835C22#1062327612yes—
836C22D11×#13112yes—
837C22C23×C4×D1111yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—114no—
843C4—114no—
844C4—222no—
845C4—222no—
846C4—222no—
847C4C4×D4×D1112yes—
848C4C22×D4×D1111yescharacteristic
849C4C2×#41×D1111yescharacteristic
850C2—42no—
851C2—42no—
852C2—224no—
853C2—442no—
854C2—442no—
855C2#1307735714yesdirect product factor
856C2C2×C4×D4×D1111yescharacteristic
857C2C2×D11×#13111yescharacteristic
858C2C2×#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×#2935
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#66960C2semidirect
2. C22×#66954C2semidirect
4. #13077357C2direct (N × H)
5. C2×#10622741C2semidirect
6. C2×#10622342C2semidirect
7. C2×#10622319C2semidirect
8. C2×#10622624C2semidirect
9. C2×#10622449C2semidirect
10. C2×C8×C22⋊D11C2semidirect
11. C2×(C22⋊D11)⋊C8C2semidirect
12. C2×D11×C4⋊C8C2semidirect
13. C2×#10622340C2semidirect
14. C2×#10622340C2semidirect
15. C2×#10622320C2semidirect
16. C2×C11×#435C2semidirect
29. C2×#66960C22semidirect
31. C2×#66954C22semidirect
50. C11×#435C22semidirect
57. #10622741C22semidirect
58. C8×C22⋊D11C22semidirect
67. #10622624C22semidirect
70. #10622449C22semidirect
71. D11×C4⋊C8C22semidirect
72. #10622342C22semidirect
73. #10622340C22semidirect
74. #10622340C22semidirect
75. (C22⋊D11)⋊C8C22semidirect
76. #10622320C22semidirect
77. #10622319C22semidirect
150. C2×#4313D4semidirect
300. #4313C2×D4semidirect
314. C2×#435D11semidirect
371. C2×Dic11#131semidirect
439. #435C2×D11semidirect
497. Dic11C2×#131semidirect
611. C2×C11#2935semidirect
733. C11C2×#2935semidirect
855. C2#13077357direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669602
C22×#669542
C2×#106230792
#130773572
C2×#106227412
C2×#106223422
C2×#106223192
C2×#106226242
C2×#106224492
C2×C8×C22⋊D112
C2×(C22⋊D11)⋊C82
C2×D11×C4⋊C82
C2×#106223402
C2×#106223202
C2×C11×#4352
C2×#293511