Finite Group Databasebeta

← C2×#13077770 #15618869

Subgroups — C2×#13077770 #15618869

Order 2816.

1982 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623059C211yesmaximal, characteristic
2#13077770C2116yesmaximal, direct product factor
3C2×#10622314C211yesmaximal, characteristic, complemented
4C2×C8×Dic22C211yesmaximal, characteristic, complemented
5C2×#10622342C211yesmaximal, characteristic, complemented
6C2×#10622341C211yesmaximal, characteristic, complemented
7C2×#10622319C211yesmaximal, characteristic, complemented
8C2×C8×D44C211yesmaximal, characteristic, complemented
9C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
10C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
11C2×#10622453C211yesmaximal, characteristic, complemented
12C2×#10622446C211yesmaximal, characteristic, complemented
13C2×#10622612C211yesmaximal, characteristic, complemented
14C2×#10622452C211yesmaximal, characteristic, complemented
15C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#433C211yesmaximal, characteristic, complemented
17C2×C11×#117C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26#10623059C418yes—
27#10623059C2218yes—
28C2×#66951C411yescharacteristic
29C2×#66949C411yescharacteristic
30C2×#66947C411yescharacteristic
31C2×#66942C411yescharacteristic
32C2×#66938C411yescharacteristic
33C2×#66937C411yescharacteristic
34C2×#66936C411yescharacteristic
35C2×#66932C411yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×#66925C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#433C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×C4⋊C8C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×#97C2211yescharacteristic
46C2×C4×C8×C11C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×#66879C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×Dic11⋊C8C2211yescharacteristic
54C2×Dic11⋊C8C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×C8×Dic11C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622612C2218yescomplemented
60C2×C4⋊(C11⋊C8)C2211yescharacteristic
61C2×C4⋊(C11⋊C8)C2211yescharacteristic
62C2×C4⋊(C11⋊C8)C2211yescharacteristic
63C2×C4⋊(C11⋊C8)C2211yescharacteristic
64#10622453C2218yescomplemented
65#10622452C2218yescomplemented
66#10622446C2218yescomplemented
67D11×C4⋊C8C2218yescomplemented
68#10622342C2218yescomplemented
69#10622341C2218yescomplemented
70(C22⋊D11)⋊C8C2218yescomplemented
71(C22⋊D11)⋊C8C2218yescomplemented
72#10622319C2218yescomplemented
73#10622314C2218yescomplemented
74C8×D44C2218yescomplemented
75C8×Dic22C2218yescomplemented
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11C2×C411yescharacteristic
78C22×C22⋊D11C2×C411yescharacteristic
79C22×D44C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×Dic22C2×C411yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#117C2×C414yes—
90C11×#117C2314yes—
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11C2×C411yescharacteristic
98C2×C22⋊Dic11C2×C411yescharacteristic
99C4×C22⋊D11C2×C414yes—
100C4×C22⋊D11C2×C414yes—
101C4×C22⋊D11C2314yes—
102C4×C22⋊D11C2314yes—
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109C2×C4⋊Dic11C2×C411yescharacteristic
110C2×C4⋊Dic11C2×C411yescharacteristic
111C2×Dic11⋊C4C2×C411yescharacteristic
112C2×Dic11⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×Dic11⋊C4C2×C411yescharacteristic
116C2×Dic11⋊C4C2×C411yescharacteristic
117C2×C4×Dic11C2×C411yescharacteristic
118C2×C4×Dic11C2×C411yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2311yescharacteristic
121C2×#4318—42no—
122C2×#4318C2314yes—
123C22×C11⋊C8—42no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2314yes—
129C2×#4313—42no—
130C2×#4313C2314yes—
131C2×C8×D11—42no—
132C2×C8×D11—42no—
133C2×C8×D11—42no—
134C2×C8×D11C2314yes—
135C2×C8×D11C2314yes—
136C2×C8×D11C2314yes—
137#66951C2×C418yes—
138#66949C2×C418yes—
139#66947C2×C418yes—
140#66942C2×C418yes—
141#66938C2×C418yes—
142#66937C2×C418yes—
143#66936C2×C418yes—
144#66932C2×C418yes—
145C4×D44C2×C414yes—
146C4×D44C2314yes—
147#66925C2×C414yes—
148#66925C2314yes—
149C42×D11C2×C414yes—
150C42×D11C2314yes—
151C4×Dic22C2×C414yes—
152C4×Dic22C2314yes—
153C11×C4⋊C8C2314yes—
154C11×C4⋊C8C2314yes—
155C11×C22⋊C8C2314yes—
156C11×C22⋊C8C2314yes—
157C11×#97C2314yes—
158C4×C8×C11C2314yes—
159(C2×D11)⋊C8C2314yes—
160(C2×D11)⋊C8C2314yes—
161(C2×D11)⋊C8C2314yes—
162(C2×D11)⋊C8C2314yes—
163#66879C2314yes—
164Dic11⋊C8C2314yes—
165Dic11⋊C8C2314yes—
166Dic11⋊C8C2314yes—
167Dic11⋊C8C2314yes—
168C8×Dic11C2314yes—
169C8×Dic11C2314yes—
170C8×Dic11C2314yes—
171C4⋊(C11⋊C8)C2314yes—
172C4⋊(C11⋊C8)C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C2×#2994—111nomaximal, Sylow
176C24×C11C22×C411yescharacteristic
177C23×D11C22×C411yescharacteristic
178C23×D11C22×C411yescharacteristic
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—24no—
190C2×C22⋊D11—24no—
191C2×C22⋊D11C22×C414yes—
192C2×C22⋊D11C22×C414yes—
193C22×Dic11C22×C411yescharacteristic
194C22×Dic11C22×C411yescharacteristic
195C22×Dic11C22×C411yescharacteristic
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C2×D44—24no—
200C2×D44C22×C414yes—
201C2×C4×D11—24no—
202C2×C4×D11—24no—
203C2×C4×D11—22no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11C22×C412yes—
208C2×C4×D11C22×C414yes—
209C2×C4×D11C22×C414yes—
210C2×C4×D11C22×C412yes—
211C2×C4×D11C2412yes—
212C2×C4×D11C2412yes—
213C2×Dic22—24no—
214C2×Dic22C22×C414yes—
215C2×C8×C11—22no—
216C2×C8×C11—22no—
217C2×C8×C11—22no—
218C2×C8×C11—22no—
219C2×C8×C11C2412yes—
220C2×C8×C11C2412yes—
221C2×C8×C11C2412yes—
222C2×C8×C11C2412yes—
223C11×C4⋊C4C22×C414yes—
224C11×C4⋊C4C22×C414yes—
225C11×C22⋊C4C22×C414yes—
226C11×C22⋊C4C22×C414yes—
227C42×C11C22×C412yes—
228C42×C11C22×C412yes—
229C42×C11C2412yes—
230C42×C11C2412yes—
231C22⋊Dic11C22×C414yes—
232C22⋊Dic11C22×C414yes—
233(C2×D11)⋊C4C22×C414yes—
234(C2×D11)⋊C4C22×C414yes—
235(C2×D11)⋊C4C22×C414yes—
236(C2×D11)⋊C4C22×C414yes—
237(C2×D11)⋊C4C22×C414yes—
238(C2×D11)⋊C4C22×C414yes—
239C4⋊Dic11C22×C414yes—
240C4⋊Dic11C22×C414yes—
241Dic11⋊C4C22×C414yes—
242Dic11⋊C4C22×C414yes—
243Dic11⋊C4C22×C414yes—
244Dic11⋊C4C22×C414yes—
245Dic11⋊C4C22×C414yes—
246Dic11⋊C4C22×C414yes—
247C4×Dic11C22×C412yes—
248C4×Dic11C22×C412yes—
249C4×Dic11C22×C414yes—
250C4×Dic11C22×C414yes—
251C4×Dic11C2412yes—
252C4×Dic11C2412yes—
253#4318—44no—
254C2×C11⋊C8—22no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8—22no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—44no—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2412yes—
261C2×C11⋊C8C2412yes—
262C2×C11⋊C8C2412yes—
263#4313—44no—
264C8×D11—44no—
265C8×D11—44no—
266C8×D11—44no—
267C2×#529—111no—
268#2994—1116no—
269C2×#446—111no—
270C2×C8×Q8—111no—
271C2×#436—111no—
272C2×#435—111no—
273C2×#435—111no—
274C2×C8×D4—111no—
275C2×C8×D4—111no—
276C2×C8×D4—111no—
277C2×#433—111no—
278C2×#433D1111yescharacteristic, complemented
279C2×#431—111no—
280C2×#424—111no—
281C2×#424—111no—
282C22×C4⋊C8—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11C23×C412yes—
287C23×C11C23×C411yescharacteristic
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11#13114yes—
294C22×D11C23×C412yes—
295C22×D11C23×C412yes—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C23×C412yes—
309C2×C4×C11C23×C411yescharacteristic
310C2×C4×C11H(5,𝔽2)12yes—
311C2×C4×C112−1+412yes—
312C2×C4×C11C2511yescharacteristic
313C22⋊D11—28no—
314C22⋊D11—28no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11#13114yes—
321C2×Dic11C23×C412yes—
322C2×Dic11C23×C412yes—
323C2×Dic11C23×C412yes—
324C2×Dic11C23×C412yes—
325C2×Dic11C23×C412yes—
326C2×Dic11C23×C412yes—
327D44—28no—
328C4×D11—28no—
329C4×D11—24no—
330C4×D11—24no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—28no—
336Dic22—28no—
337C8×C11—22no—
338C8×C11—22no—
339C8×C11—22no—
340C8×C11—22no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C11⋊C8—22no—
344C11⋊C8—22no—
345C22×M16—111no—
346C22×M16—111no—
347C23×C8—111no—
348C23×C8—111no—
349C23×C8—111no—
350C23×C8—111no—
351#529—118no—
352#529—118no—
353C2×#126—111no—
354C2×#126—111no—
355C2×#125—111no—
356C2×#124—111no—
357C2×#123—111no—
358C2×#123—111no—
359C2×C22⋊Q8—111no—
360C2×#121—111no—
361C2×C4×Q8—111no—
362C2×C4×D4—111no—
363C2×C4×D4—111no—
364C2×C4×D4—111no—
365C2×#117—111no—
366C2×#117C2×D1111yescharacteristic
367C22×C42—111no—
368#446—118no—
369C8×Q8—118no—
370#436—118no—
371#435—118no—
372#435—118no—
373C8×D4—118no—
374C8×D4—118no—
375C8×D4—118no—
376#433—118no—
377#433C2×D1118yescomplemented
378#431—118no—
379#424—118no—
380#424—118no—
381C2×C4⋊C8—111no—
382C2×C4⋊C8—111no—
383C2×C4⋊C8—111no—
384C2×C4⋊C8—111no—
385C2×C4⋊C8—111no—
386C2×C4⋊C8—111no—
387C2×C4⋊C8—111no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—118no—
390C2×C4⋊C8C2×D1111yescharacteristic
391C2×C4⋊C8C2×D1111yescharacteristic
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8C2×D1111yescharacteristic
397C2×C22⋊C8C2×D1111yescharacteristic
398C2×#97—111no—
399C2×#97C2×D1111yescharacteristic
400C2×C4×C8—111no—
401C2×C4×C8—111no—
402C2×C4×C8—111no—
403C2×C4×C8C2×D1111yescharacteristic
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—44no—
408C22×C11#52012yes—
409C22×C11C2×#13112yes—
410C22×C11C2×#13112yes—
411C22×C11C24×C411yescharacteristic
412C2×D11—22no—
413C2×D11—28no—
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—44no—
419C2×D11C2×#13114yes—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11#52012yes—
426C4×C11C2×H(5,𝔽2)11yescharacteristic
427C4×C11C2×2−1+411yescharacteristic
428Dic11—22no—
429Dic11—22no—
430Dic11—22no—
431Dic11—22no—
432Dic11—22no—
433Dic11C2×#13114yes—
434C22×Q8—111no—
435C22×D4—111no—
436C22×D4—111no—
437C22×D4—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4C22×D1111yescharacteristic
443C2×M16—114no—
444C2×M16—114no—
445C2×M16—442no—
446C2×M16—442no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—114no—
452C22×C8—114no—
453C22×C8—114no—
454C22×C8—114no—
455C22×C8—442no—
456C22×C8—442no—
457C22×C8—442no—
458C22×C8—442no—
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463#126—118no—
464#126—118no—
465#125—118no—
466#124—118no—
467#123—118no—
468#123—118no—
469C22⋊Q8—118no—
470#121—118no—
471C4×Q8—114no—
472C4×Q8—114no—
473C4×D4—114no—
474C4×D4—114no—
475C4×D4—114no—
476C4×D4—114no—
477C4×D4—114no—
478C4×D4—114no—
479#117—114no—
480#117—114no—
481#117C4×D1114yes—
482#117C22×D1114yes—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4C4×D1111yescharacteristic
492C2×C4⋊C4C4×D1111yescharacteristic
493C2×C22⋊C4—111no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—111no—
497C2×C22⋊C4—111no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—111no—
501C2×C22⋊C4C4×D1111yescharacteristic
502C2×C22⋊C4C4×D1111yescharacteristic
503C2×C42—111no—
504C2×C42—111no—
505C2×C42—111no—
506C2×C42—111no—
507C2×C42—114no—
508C2×C42—114no—
509C2×C42C22×D1111yescharacteristic
510C2×C42C22×D1111yescharacteristic
511C4⋊C8—114no—
512C4⋊C8—114no—
513C4⋊C8—114no—
514C4⋊C8—114no—
515C4⋊C8—114no—
516C4⋊C8—114no—
517C4⋊C8—114no—
518C4⋊C8—114no—
519C4⋊C8C22×D1114yes—
520C4⋊C8C22×D1114yes—
521C22⋊C8—114no—
522C22⋊C8—114no—
523C22⋊C8—114no—
524C22⋊C8—114no—
525C22⋊C8C22×D1114yes—
526C22⋊C8C22×D1114yes—
527#97—114no—
528#97C22×D1114yes—
529C4×C8—114no—
530C4×C8—114no—
531C4×C8—114no—
532C4×C8C22×D1114yes—
533C2×C11—42no—
534C2×C11#299414yescomplemented
535C2×C11C2×#52011yescharacteristic
536C2×C11C22×#13111yescharacteristic
537C2×C11C22×#13111yescharacteristic
538D11—24no—
539D11—42no—
540C24—111no—
541C24—111no—
542C24C2×C4×D1111yescharacteristic
543C2×Q8—114no—
544C2×Q8—224no—
545C2×D4—114no—
546C2×D4—114no—
547C2×D4—114no—
548C2×D4—224no—
549C2×D4—224no—
550C2×D4—224no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—112no—
560C22×C4—114no—
561C22×C4—114no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—224no—
566C22×C4—224no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×C4×D1111yescharacteristic
576C22×C4C2×C4×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1111yescharacteristic
579M16—444no—
580M16—444no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—112no—
586C2×C8—112no—
587C2×C8—112no—
588C2×C8—112no—
589C2×C8—222no—
590C2×C8—222no—
591C2×C8—222no—
592C2×C8—222no—
593C2×C8—444no—
594C2×C8—444no—
595C2×C8—444no—
596C2×C8—444no—
597C2×C8C23×D1112yes—
598C2×C8C23×D1112yes—
599C2×C8C23×D1112yes—
600C2×C8C23×D1112yes—
601C4⋊C4—114no—
602C4⋊C4—114no—
603C4⋊C4—114no—
604C4⋊C4—114no—
605C4⋊C4—114no—
606C4⋊C4—114no—
607C4⋊C4—114no—
608C4⋊C4—114no—
609C4⋊C4C2×C4×D1114yes—
610C4⋊C4C2×C4×D1114yes—
611C22⋊C4—114no—
612C22⋊C4—114no—
613C22⋊C4—114no—
614C22⋊C4—114no—
615C22⋊C4—114no—
616C22⋊C4—114no—
617C22⋊C4—114no—
618C22⋊C4—114no—
619C22⋊C4C2×C4×D1114yes—
620C22⋊C4C2×C4×D1114yes—
621C42—112no—
622C42—114no—
623C42—114no—
624C42—112no—
625C42—112no—
626C42—112no—
627C42C2×C4×D1112yes—
628C42C2×C4×D1112yes—
629C42C23×D1112yes—
630C42C23×D1112yes—
631C11C2×#299411yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—114no—
636C23—112no—
637C23—112no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23C22×C4×D1112yes—
644C23C22×C4×D1111yescharacteristic
645Q8—228no—
646D4—228no—
647D4—228no—
648D4—228no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—114no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—112no—
662C2×C4—112no—
663C2×C4—112no—
664C2×C4—228no—
665C2×C4—228no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—224no—
672C2×C4—224no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4C22×C4×D1112yes—
678C2×C4C22×C4×D1112yes—
679C2×C4C22×C4×D1112yes—
680C2×C4C22×C4×D1112yes—
681C2×C4C22×C4×D1112yes—
682C2×C4C22×C4×D1111yescharacteristic
683C2×C4#6704212yes—
684C2×C4#6704312yes—
685C2×C4C24×D1111yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—222no—
691C8—222no—
692C8—222no—
693C8—222no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—114no—
699C22—228no—
700C22—222no—
701C22—222no—
702C22—222no—
703C22—222no—
704C22—222no—
705C22—444no—
706C22#1062305412yes—
707C22D11×#13112yes—
708C22D11×#13112yes—
709C22C23×C4×D1111yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—114no—
716C4—222no—
717C4—222no—
718C4—222no—
719C4—222no—
720C4—222no—
721C4#1062305412yes—
722C4C2×#6704211yescharacteristic
723C4C2×#6704311yescharacteristic
724C2—42no—
725C2—224no—
726C2—442no—
727C2#1307777014yesdirect product factor
728C2C2×#1062305411yescharacteristic
729C2C2×D11×#13111yescharacteristic
730C2C2×D11×#13111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#433C2
socleC23×C11C23×C4
prime radicalC2×#66937C4
cosocleC2×C4×C11C25
hypercenterC2×#433D11
hypocenterC11C2×#2994
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13077770C2direct (N × H)
3. C2×#10622314C2semidirect
4. C2×C8×Dic22C2semidirect
5. C2×#10622342C2semidirect
6. C2×#10622341C2semidirect
7. C2×#10622319C2semidirect
8. C2×C8×D44C2semidirect
9. C2×(C22⋊D11)⋊C8C2semidirect
10. C2×(C22⋊D11)⋊C8C2semidirect
11. C2×#10622453C2semidirect
12. C2×#10622446C2semidirect
13. C2×#10622612C2semidirect
14. C2×#10622452C2semidirect
15. C2×D11×C4⋊C8C2semidirect
16. C2×C11×#433C2semidirect
40. C11×#433C22semidirect
59. #10622612C22semidirect
64. #10622453C22semidirect
65. #10622452C22semidirect
66. #10622446C22semidirect
67. D11×C4⋊C8C22semidirect
68. #10622342C22semidirect
69. #10622341C22semidirect
70. (C22⋊D11)⋊C8C22semidirect
71. (C22⋊D11)⋊C8C22semidirect
72. #10622319C22semidirect
73. #10622314C22semidirect
74. C8×D44C22semidirect
75. C8×Dic22C22semidirect
278. C2×#433D11semidirect
377. #433C2×D11semidirect
534. C2×C11#2994semidirect
631. C11C2×#2994semidirect
727. C2#13077770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230592
#130777702
C2×#106223142
C2×C8×Dic222
C2×#106223422
C2×#106223412
C2×#106223192
C2×C8×D442
C2×(C22⋊D11)⋊C82
C2×#106224532
C2×#106224462
C2×#106226122
C2×#106224522
C2×D11×C4⋊C82
C2×C11×#4332
C2×#299411