Finite Group Databasebeta

← C2×C11×#3317 #14638331

Subgroups — C2×C11×#3317 #14638331

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic, complemented
2C2×C11×#550C211yesmaximal, characteristic
3C11×#3317C2116yesmaximal, direct product factor
4C2×C11×#490C211yesmaximal, characteristic, complemented
5C2×C11×#481C211yesmaximal, characteristic, complemented
6C2×C11×#482C211yesmaximal, characteristic, complemented
7C2×C11×#479C211yesmaximal, characteristic, complemented
8C2×C11×#468C211yesmaximal, characteristic, complemented
9C2×C11×#465C211yesmaximal, characteristic, complemented
10C2×C11×#460C211yesmaximal, characteristic, complemented
11C2×C11×#452C211yesmaximal, characteristic, complemented
12C2×C11×#452C211yesmaximal, characteristic, complemented
13C2×C11×#441C211yesmaximal, characteristic, complemented
14C2×C11×#435C211yesmaximal, characteristic, complemented
15C2×C11×#417C211yesmaximal, characteristic, complemented
16C2×C11×#416C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×M16C2211yescharacteristic
23C23×C8×C11C2211yescharacteristic
24C11×#552—24no—
25C11×#552C2218yescomplemented
26C11×#550—24no—
27C11×#550C2218yes—
28C2×C11×#127—21no—
29C2×C11×#127C2211yescharacteristic
30C2×C11×#126—21no—
31C2×C11×#125—21no—
32C2×C11×#125C2211yescharacteristic
33C2×C11×#123—21no—
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C11×C22⋊Q8C2211yescharacteristic
36C2×C11×#121—21no—
37C2×C11×#121—21no—
38C2×C11×#121C2211yescharacteristic
39C2×C11×#121C2211yescharacteristic
40C2×C4×Q8×C11C2211yescharacteristic
41C2×C4×Q8×C11C2211yescharacteristic
42C2×C4×D4×C11—21no—
43C2×C4×D4×C11C2211yescharacteristic
44C2×C11×#117—21no—
45C2×C11×#117C2211yescharacteristic
46C22×C11×C4⋊C4C2211yescharacteristic
47C11×#490C2218yescomplemented
48C11×#482C2218yescomplemented
49C11×#481C2218yescomplemented
50C11×#479C2218yescomplemented
51C11×#468C2218yescomplemented
52C11×#465C2218yescomplemented
53C11×#460C2218yescomplemented
54C11×#452C2218yescomplemented
55C11×#452C2218yescomplemented
56C11×#441C2218yescomplemented
57C11×#435C2218yescomplemented
58C2×C11×#107C2211yescharacteristic
59C2×C11×#106C2211yescharacteristic
60C2×C11×#106C2211yescharacteristic
61C2×C11×C4⋊C8C2211yescharacteristic
62C11×#417C2218yescomplemented
63C11×#416C2218yescomplemented
64C2×C11×#103C2211yescharacteristic
65C2×C11×#103C2211yescharacteristic
66C2×C11×#103C2211yescharacteristic
67C2×C11×#103C2211yescharacteristic
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70C2×C11×#102C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2211yescharacteristic
73C2×C11×#102C2211yescharacteristic
74C2×C11×C22⋊C8C2211yescharacteristic
75C2×C11×C22⋊C8C2211yescharacteristic
76C2×C11×#97C2211yescharacteristic
77C2×C11×#41—22no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C2×C11×#41C2314yes—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11D411yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11—21no—
98C23×C4×C11—21no—
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C2×C11×Q16—24no—
102C2×C11×Q16C2314yes—
103C2×C11×SD16—42no—
104C2×C11×SD16—42no—
105C2×C11×SD16C2314yes—
106C2×C11×SD16C2314yes—
107C2×C11×M16—42no—
108C2×C11×M16C2314yes—
109C22×C8×C11—42no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2314yes—
115C11×#127—28no—
116C11×#127—22no—
117C11×#127C2314yes—
118C11×#126—28no—
119C11×#125—28no—
120C11×#125—22no—
121C11×#125C2314yes—
122C11×#123—28no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8C2314yes—
126C11×C22⋊Q8C2314yes—
127C11×#121—22no—
128C11×#121—22no—
129C11×#121—28no—
130C11×#121—28no—
131C11×#121C2314yes—
132C11×#121C2314yes—
133C4×Q8×C11—22no—
134C4×Q8×C11—22no—
135C4×Q8×C11C2314yes—
136C4×Q8×C11C2314yes—
137C4×D4×C11—28no—
138C4×D4×C11D414yes—
139C4×D4×C11C2314yes—
140C11×#117—22no—
141C11×#117—28no—
142C11×#117C2314yes—
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4—22no—
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4—21no—
147C2×C11×C4⋊C4—21no—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4D411yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2314yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4—21no—
162C2×C11×C22⋊C4D411yescharacteristic
163C2×C11×C22⋊C4D411yescharacteristic
164C2×C42×C11—21no—
165C2×C42×C11—21no—
166C2×C42×C11—21no—
167C2×C42×C11C2311yescharacteristic
168C11×#107C2314yes—
169C11×#106C2314yes—
170C11×#106C2314yes—
171C11×C4⋊C8C2314yes—
172C11×#103C2314yes—
173C11×#103C2314yes—
174C11×#103C2314yes—
175C11×#103C2314yes—
176C11×#102C2314yes—
177C11×#102C2314yes—
178C11×#102C2314yes—
179C11×#102C2314yes—
180C11×#102C2314yes—
181C11×#102C2314yes—
182C11×C22⋊C8C2314yes—
183C11×C22⋊C8C2314yes—
184C11×#97C2314yes—
185C2×#3317C1111yesmaximal, characteristic, direct product factor, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C24×C11C2×D411yescharacteristic
190C11×#41—28no—
191C11×#41—28no—
192C11×#41—44no—
193C11×#41—44no—
194C11×#41—48no—
195C11×#41—48no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11#4114yes—
202C2×Q8×C11C2412yes—
203C2×Q8×C11C2412yes—
204C2×D4×C11—24no—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—24no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—24no—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—42no—
217C2×D4×C11—44no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—82no—
221C2×D4×C11—82no—
222C2×D4×C11—82no—
223C2×D4×C11C2×D414yes—
224C2×D4×C11C2412yes—
225C2×D4×C11C2412yes—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—24no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C11×Q16—28no—
252C11×SD16—44no—
253C11×SD16—44no—
254C11×M16—44no—
255C2×C8×C11—22no—
256C2×C8×C11—22no—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11—44no—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C2×C8×C11C2412yes—
263C2×C8×C11C2412yes—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2×D414yes—
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2412yes—
278C11×C4⋊C4C2412yes—
279C11×C4⋊C4C2412yes—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4C2×D414yes—
286C11×C22⋊C4C2×D414yes—
287C42×C11—24no—
288C42×C11—24no—
289C42×C11—24no—
290C42×C11C2×D412yes—
291C42×C11C2412yes—
292C2×#552C2×C1111yescharacteristic, complemented
293C2×#550C2×C1111yescharacteristic
294#3317C2×C11116yesdirect product factor
295C2×#490C2×C1111yescharacteristic, complemented
296C2×#481C2×C1111yescharacteristic, complemented
297C2×#482C2×C1111yescharacteristic, complemented
298C2×#479C2×C1111yescharacteristic, complemented
299C2×#468C2×C1111yescharacteristic, complemented
300C2×#465C2×C1111yescharacteristic, complemented
301C2×#460C2×C1111yescharacteristic, complemented
302C2×#452C2×C1111yescharacteristic, complemented
303C2×#452C2×C1111yescharacteristic, complemented
304C2×#441C2×C1111yescharacteristic, complemented
305C2×#435C2×C1111yescharacteristic, complemented
306C2×#417C2×C1111yescharacteristic, complemented
307C2×#416C2×C1111yescharacteristic, complemented
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11C22×D412yes—
323C23×C11C22×D412yes—
324C23×C11C22×D411yescharacteristic
325Q8×C11—24no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—42no—
330Q8×C11C2×#4114yes—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—44no—
336D4×C11—48no—
337D4×C11—48no—
338D4×C11—48no—
339D4×C11—42no—
340D4×C11—42no—
341D4×C11—84no—
342D4×C11—84no—
343D4×C11—84no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—48no—
362C2×C4×C11—48no—
363C2×C4×C11—48no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C2×#4112yes—
375C2×C4×C11H(5,𝔽2)12yes—
376C2×C4×C11C2511yescharacteristic
377C8×C11—22no—
378C8×C11—22no—
379C8×C11—22no—
380C8×C11—22no—
381C22×#41C22×C1111yescharacteristic
382C22×#41C22×C1111yescharacteristic
383C22×Q16C22×C1111yescharacteristic
384C22×SD16C22×C1111yescharacteristic
385C22×SD16C22×C1111yescharacteristic
386C22×M16C22×C1111yescharacteristic
387C23×C8C22×C1111yescharacteristic
388#552—24no—
389#552C22×C1118yescomplemented
390#550—24no—
391#550C22×C1118yes—
392C2×#127—21no—
393C2×#127C22×C1111yescharacteristic
394C2×#126—21no—
395C2×#125—21no—
396C2×#125C22×C1111yescharacteristic
397C2×#123—21no—
398C2×C22⋊Q8C22×C1111yescharacteristic
399C2×C22⋊Q8C22×C1111yescharacteristic
400C2×#121—21no—
401C2×#121—21no—
402C2×#121C22×C1111yescharacteristic
403C2×#121C22×C1111yescharacteristic
404C2×C4×Q8C22×C1111yescharacteristic
405C2×C4×Q8C22×C1111yescharacteristic
406C2×C4×D4—21no—
407C2×C4×D4C22×C1111yescharacteristic
408C2×#117—21no—
409C2×#117C22×C1111yescharacteristic
410C22×C4⋊C4C22×C1111yescharacteristic
411#490C22×C1118yescomplemented
412#482C22×C1118yescomplemented
413#481C22×C1118yescomplemented
414#479C22×C1118yescomplemented
415#468C22×C1118yescomplemented
416#465C22×C1118yescomplemented
417#460C22×C1118yescomplemented
418#452C22×C1118yescomplemented
419#452C22×C1118yescomplemented
420#441C22×C1118yescomplemented
421#435C22×C1118yescomplemented
422C2×#107C22×C1111yescharacteristic
423C2×#106C22×C1111yescharacteristic
424C2×#106C22×C1111yescharacteristic
425C2×C4⋊C8C22×C1111yescharacteristic
426#417C22×C1118yescomplemented
427#416C22×C1118yescomplemented
428C2×#103C22×C1111yescharacteristic
429C2×#103C22×C1111yescharacteristic
430C2×#103C22×C1111yescharacteristic
431C2×#103C22×C1111yescharacteristic
432C2×#102C22×C1111yescharacteristic
433C2×#102C22×C1111yescharacteristic
434C2×#102C22×C1111yescharacteristic
435C2×#102C22×C1111yescharacteristic
436C2×#102C22×C1111yescharacteristic
437C2×#102C22×C1111yescharacteristic
438C2×C22⋊C8C22×C1111yescharacteristic
439C2×C22⋊C8C22×C1111yescharacteristic
440C2×#97C22×C1111yescharacteristic
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—44no—
448C22×C11—44no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—84no—
456C22×C11—84no—
457C22×C11#54612yes—
458C22×C11#57512yes—
459C22×C11#57712yes—
460C22×C11C23×D411yescharacteristic
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—24no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#54612yes—
472C4×C11C22×#4111yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—24no—
478C2×#41—42no—
479C2×#41—42no—
480C2×#41C23×C1114yes—
481C2×#41C23×C1114yes—
482C22×Q8C23×C1111yescharacteristic
483C22×Q8C23×C1111yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4D4×C1111yescharacteristic
491C22×D4C23×C1111yescharacteristic
492C22×D4C23×C1111yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C1111yescharacteristic
497C23×C4C23×C1111yescharacteristic
498C2×Q16—24no—
499C2×Q16C23×C1114yes—
500C2×SD16—42no—
501C2×SD16—42no—
502C2×SD16C23×C1114yes—
503C2×SD16C23×C1114yes—
504C2×M16—42no—
505C2×M16C23×C1114yes—
506C22×C8—42no—
507C22×C8C23×C1111yescharacteristic
508C22×C8C23×C1111yescharacteristic
509C22×C8C23×C1111yescharacteristic
510C22×C8C23×C1111yescharacteristic
511C22×C8C23×C1114yes—
512#127—28no—
513#127—22no—
514#127C23×C1114yes—
515#126—28no—
516#125—28no—
517#125—22no—
518#125C23×C1114yes—
519#123—28no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8C23×C1114yes—
523C22⋊Q8C23×C1114yes—
524#121—22no—
525#121—22no—
526#121—28no—
527#121—28no—
528#121C23×C1114yes—
529#121C23×C1114yes—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8C23×C1114yes—
533C4×Q8C23×C1114yes—
534C4×D4—28no—
535C4×D4D4×C1114yes—
536C4×D4C23×C1114yes—
537#117—22no—
538#117—28no—
539#117C23×C1114yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4D4×C1111yescharacteristic
549C2×C4⋊C4C23×C1111yescharacteristic
550C2×C4⋊C4C23×C1111yescharacteristic
551C2×C4⋊C4C23×C1114yes—
552C2×C4⋊C4C23×C1111yescharacteristic
553C2×C4⋊C4C23×C1111yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C1111yescharacteristic
560C2×C22⋊C4D4×C1111yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C1111yescharacteristic
565#107C23×C1114yes—
566#106C23×C1114yes—
567#106C23×C1114yes—
568C4⋊C8C23×C1114yes—
569#103C23×C1114yes—
570#103C23×C1114yes—
571#103C23×C1114yes—
572#103C23×C1114yes—
573#102C23×C1114yes—
574#102C23×C1114yes—
575#102C23×C1114yes—
576#102C23×C1114yes—
577#102C23×C1114yes—
578#102C23×C1114yes—
579C22⋊C8C23×C1114yes—
580C22⋊C8C23×C1114yes—
581#97C23×C1114yes—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11—82no—
585C2×C11—82no—
586C2×C11#331714yesdirect product factor
587C2×C11C2×#54611yescharacteristic
588C2×C11C2×#57511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590C24—21no—
591C24—21no—
592C24C2×D4×C1111yescharacteristic
593C24C2×D4×C1111yescharacteristic
594#41—28no—
595#41—28no—
596#41—44no—
597#41—44no—
598#41—48no—
599#41—48no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8C11×#4114yes—
606C2×Q8C24×C1112yes—
607C2×Q8C24×C1112yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—82no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4C2×D4×C1114yes—
628C2×D4C24×C1112yes—
629C2×D4C24×C1112yes—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4C2×D4×C1111yescharacteristic
647C22×C4C2×D4×C1111yescharacteristic
648C22×C4C2×D4×C1111yescharacteristic
649C22×C4C2×D4×C1111yescharacteristic
650C22×C4C2×D4×C1112yes—
651C22×C4C2×D4×C1112yes—
652C22×C4C24×C1112yes—
653C22×C4C24×C1112yes—
654C22×C4C24×C1111yescharacteristic
655Q16—28no—
656SD16—44no—
657SD16—44no—
658M16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8C24×C1112yes—
665C2×C8C24×C1112yes—
666C2×C8C24×C1112yes—
667C2×C8C24×C1112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4C2×D4×C1114yes—
680C4⋊C4C24×C1112yes—
681C4⋊C4C24×C1112yes—
682C4⋊C4C24×C1112yes—
683C4⋊C4C24×C1112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4C2×D4×C1114yes—
690C22⋊C4C2×D4×C1114yes—
691C42—24no—
692C42—24no—
693C42—24no—
694C42C2×D4×C1112yes—
695C42C24×C1112yes—
696C11C2×#331711yescharacteristic, direct product factor, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C22×D4×C1112yes—
712C23C22×D4×C1112yes—
713C23C22×D4×C1111yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8C2×C11×#4114yes—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—42no—
729D4—42no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4C22×D4×C1112yes—
759C2×C4C22×D4×C1112yes—
760C2×C4C22×D4×C1112yes—
761C2×C4C22×D4×C1112yes—
762C2×C4C22×D4×C1111yescharacteristic
763C2×C4C2×C11×#4112yes—
764C2×C4C11×H(5,𝔽2)12yes—
765C2×C4C25×C1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22C11×#54612yes—
787C22C11×#57512yes—
788C22C11×#57712yes—
789C22C23×D4×C1111yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4C11×#54612yes—
801C4C22×C11×#4111yescharacteristic
802C4C2×C11×H(5,𝔽2)11yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2C11×#331714yesdirect product factor
808C2C2×C11×#54611yescharacteristic
809C2C2×C11×#57511yescharacteristic
810C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#550C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#552C2semidirect
3. C11×#3317C2direct (N × H)
4. C2×C11×#490C2semidirect
5. C2×C11×#481C2semidirect
6. C2×C11×#482C2semidirect
7. C2×C11×#479C2semidirect
8. C2×C11×#468C2semidirect
9. C2×C11×#465C2semidirect
10. C2×C11×#460C2semidirect
11. C2×C11×#452C2semidirect
12. C2×C11×#452C2semidirect
13. C2×C11×#441C2semidirect
14. C2×C11×#435C2semidirect
15. C2×C11×#417C2semidirect
16. C2×C11×#416C2semidirect
25. C11×#552C22semidirect
47. C11×#490C22semidirect
48. C11×#482C22semidirect
49. C11×#481C22semidirect
50. C11×#479C22semidirect
51. C11×#468C22semidirect
52. C11×#465C22semidirect
53. C11×#460C22semidirect
54. C11×#452C22semidirect
55. C11×#452C22semidirect
56. C11×#441C22semidirect
57. C11×#435C22semidirect
62. C11×#417C22semidirect
63. C11×#416C22semidirect
185. C2×#3317C11direct (N × H)
292. C2×#552C2×C11semidirect
294. #3317C2×C11direct (N × H)
295. C2×#490C2×C11semidirect
296. C2×#481C2×C11semidirect
297. C2×#482C2×C11semidirect
298. C2×#479C2×C11semidirect
299. C2×#468C2×C11semidirect
300. C2×#465C2×C11semidirect
301. C2×#460C2×C11semidirect
302. C2×#452C2×C11semidirect
303. C2×#452C2×C11semidirect
304. C2×#441C2×C11semidirect
305. C2×#435C2×C11semidirect
306. C2×#417C2×C11semidirect
307. C2×#416C2×C11semidirect
389. #552C22×C11semidirect
411. #490C22×C11semidirect
412. #482C22×C11semidirect
413. #481C22×C11semidirect
414. #479C22×C11semidirect
415. #468C22×C11semidirect
416. #465C22×C11semidirect
417. #460C22×C11semidirect
418. #452C22×C11semidirect
419. #452C22×C11semidirect
420. #441C22×C11semidirect
421. #435C22×C11semidirect
426. #417C22×C11semidirect
427. #416C22×C11semidirect
586. C2×C11#3317direct (N × H)
696. C11C2×#3317direct (N × H)
807. C2C11×#3317direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#5502
C11×#33172
C2×C11×#4902
C2×C11×#4812
C2×C11×#4822
C2×C11×#4792
C2×C11×#4682
C2×C11×#4652
C2×C11×#4602
C2×C11×#4522
C2×C11×#4412
C2×C11×#4352
C2×C11×#4172
C2×C11×#4162
C2×#331711