Finite Group Databasebeta

← C2×C11×#3388 #14638555

Subgroups — C2×C11×#3388 #14638555

Order 2816.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic, complemented
2C2×C11×#554C211yesmaximal, characteristic
3C11×#3388C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#501C211yesmaximal, characteristic, complemented
6C2×C11×#499C211yesmaximal, characteristic, complemented
7C2×C11×#479C211yesmaximal, characteristic, complemented
8C2×C11×#479C211yesmaximal, characteristic, complemented
9C2×C11×#475C211yesmaximal, characteristic, complemented
10C2×C11×#478C211yesmaximal, characteristic
11C2×C11×#478C211yesmaximal, characteristic
12C2×C11×#476C211yesmaximal, characteristic
13C2×C11×#446C211yesmaximal, characteristic, complemented
14C2×C11×#440C211yesmaximal, characteristic
15C2×C11×#440C211yesmaximal, characteristic
16C2×C4×C11×SD16C211yesmaximal, characteristic
17C22×C11×SD16C2211yescharacteristic
18C11×#557—24no—
19C11×#557C2218yescomplemented
20C11×#554—24no—
21C11×#554C2218yes—
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125—21no—
26C2×C11×#125—21no—
27C2×C11×#125C2211yescharacteristic
28C2×C11×#125C2211yescharacteristic
29C2×C11×#125C2211yescharacteristic
30C2×C11×#125C2211yescharacteristic
31C2×C11×C22⋊Q8—21no—
32C2×C11×C22⋊Q8—21no—
33C2×C11×C22⋊Q8—21no—
34C2×C4×Q8×C11—21no—
35C2×C4×Q8×C11C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×Q8×C11C2211yescharacteristic
39C2×C4×D4×C11C2211yescharacteristic
40C2×C4×D4×C11C2211yescharacteristic
41C2×C4×D4×C11C2211yescharacteristic
42C22×C11×C4⋊C4—21no—
43C11×#501C2218yescomplemented
44C11×#501C2218yescomplemented
45C11×#499C2218yescomplemented
46C11×#479C2218yescomplemented
47C11×#479C2218yescomplemented
48C11×#478C2218yes—
49C11×#478C2218yes—
50C11×#476C2218yes—
51C11×#475C2218yescomplemented
52C11×#446C2218yescomplemented
53C11×#440C2218yes—
54C11×#440C2218yes—
55C4×C11×SD16C2218yes—
56C2×C11×#107C2211yescharacteristic
57C2×C11×#107C2211yescharacteristic
58C2×C11×#107C2211yescharacteristic
59C2×C11×#107C2211yescharacteristic
60C2×C11×#106C2211yescharacteristic
61C2×C11×#106C2211yescharacteristic
62C2×C11×#106C2211yescharacteristic
63C2×C11×#106C2211yescharacteristic
64C2×C11×#106C2211yescharacteristic
65C2×C11×C4⋊C8C2211yescharacteristic
66C2×C11×C4⋊C8C2211yescharacteristic
67C2×C11×C4⋊C8C2211yescharacteristic
68C2×C11×#103C2211yescharacteristic
69C2×C11×#103C2211yescharacteristic
70C2×C11×#103C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2211yescharacteristic
73C2×C11×#102C2211yescharacteristic
74C2×C11×#97C2211yescharacteristic
75C2×C11×#97C2211yescharacteristic
76C2×C4×C8×C11C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11D411yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C2×C11×SD16Q818yescomplemented
86C2×C11×SD16C2314yes—
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C4⋊Q8—28no—
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8—22no—
94C11×C4⋊Q8C2314yes—
95C11×C4⋊Q8C2314yes—
96C11×#125—28no—
97C11×#125—28no—
98C11×#125—22no—
99C11×#125—22no—
100C11×#125—22no—
101C11×#125—22no—
102C11×#125C2314yes—
103C11×#125C2314yes—
104C11×#125C2314yes—
105C11×#125C2314yes—
106C11×C22⋊Q8—28no—
107C11×C22⋊Q8—28no—
108C11×C22⋊Q8—28no—
109C4×Q8×C11—28no—
110C4×Q8×C11—22no—
111C4×Q8×C11—22no—
112C4×Q8×C11—22no—
113C4×Q8×C11D414yes—
114C4×Q8×C11C2314yes—
115C4×Q8×C11C2314yes—
116C4×Q8×C11C2314yes—
117C4×Q8×C11C2314yes—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11C2314yes—
122C4×D4×C11C2314yes—
123C4×D4×C11C2314yes—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—28no—
138C2×C11×C4⋊C4D411yescharacteristic
139C2×C11×C4⋊C4D411yescharacteristic
140C2×C11×C4⋊C4D411yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—21no—
149C2×C11×C22⋊C4—21no—
150C2×C42×C11—21no—
151C2×C42×C11—21no—
152C2×C42×C11—21no—
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C11×#107C2314yes—
157C11×#107C2314yes—
158C11×#107C2314yes—
159C11×#107C2314yes—
160C11×#106C2314yes—
161C11×#106C2314yes—
162C11×#106C2314yes—
163C11×#106C2314yes—
164C11×#106C2314yes—
165C11×C4⋊C8C2314yes—
166C11×C4⋊C8C2314yes—
167C11×C4⋊C8C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×#97C2314yes—
175C11×#97C2314yes—
176C4×C8×C11C2314yes—
177C2×#3388C1111yesmaximal, characteristic, direct product factor, Sylow
178C24×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—24no—
181C2×Q8×C11—24no—
182C2×Q8×C11—22no—
183C2×Q8×C11—42no—
184C2×Q8×C11—44no—
185C2×Q8×C11—82no—
186C2×Q8×C11C2×D414yes—
187C2×Q8×C11C2×Q814yes—
188C2×Q8×C11C2412yes—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11C2×Q814yes—
192C2×D4×C11C2412yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—44no—
204C22×C4×C11—82no—
205C22×C4×C11—82no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C11×SD16C2×Q8116yescomplemented
214C2×C8×C11—22no—
215C2×C8×C11—22no—
216C2×C8×C11—22no—
217C2×C8×C11C2×Q814yes—
218C2×C8×C11C2412yes—
219C2×C8×C11C2412yes—
220C2×C8×C11C2412yes—
221C2×C8×C11C2412yes—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4C2×D414yes—
242C11×C4⋊C4C2×D414yes—
243C11×C4⋊C4C2×D414yes—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C11×C4⋊C4C2412yes—
249C11×C4⋊C4C2412yes—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C42×C11—24no—
254C42×C11—24no—
255C42×C11—24no—
256C42×C11C2×D412yes—
257C42×C11C2×D412yes—
258C42×C11C2×D412yes—
259C42×C11C2412yes—
260C42×C11C2412yes—
261C42×C11C2412yes—
262C2×#557C2×C1111yescharacteristic, complemented
263C2×#554C2×C1111yescharacteristic
264#3388C2×C11116yesdirect product factor
265C2×#501C2×C1111yescharacteristic, complemented
266C2×#501C2×C1111yescharacteristic, complemented
267C2×#499C2×C1111yescharacteristic, complemented
268C2×#479C2×C1111yescharacteristic, complemented
269C2×#479C2×C1111yescharacteristic, complemented
270C2×#475C2×C1111yescharacteristic, complemented
271C2×#478C2×C1111yescharacteristic
272C2×#478C2×C1111yescharacteristic
273C2×#476C2×C1111yescharacteristic
274C2×#446C2×C1111yescharacteristic, complemented
275C2×#440C2×C1111yescharacteristic
276C2×#440C2×C1111yescharacteristic
277C2×C4×SD16C2×C1111yescharacteristic
278C23×C11—24no—
279C23×C11—22no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11C22×D411yescharacteristic
283Q8×C11—24no—
284Q8×C11—22no—
285Q8×C11—44no—
286Q8×C11—48no—
287Q8×C11—84no—
288Q8×C11C22×Q814yes—
289D4×C11—24no—
290D4×C11—22no—
291D4×C11C22×Q814yes—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—48no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—84no—
314C2×C4×C11—84no—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×Q812yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C8×C11—22no—
326C8×C11—22no—
327C8×C11—22no—
328C8×C11C22×Q814yes—
329C22×SD16C22×C1111yescharacteristic
330#557—24no—
331#557C22×C1118yescomplemented
332#554—24no—
333#554C22×C1118yes—
334C2×C4⋊Q8—21no—
335C2×C4⋊Q8C22×C1111yescharacteristic
336C2×C4⋊Q8C22×C1111yescharacteristic
337C2×#125—21no—
338C2×#125—21no—
339C2×#125C22×C1111yescharacteristic
340C2×#125C22×C1111yescharacteristic
341C2×#125C22×C1111yescharacteristic
342C2×#125C22×C1111yescharacteristic
343C2×C22⋊Q8—21no—
344C2×C22⋊Q8—21no—
345C2×C22⋊Q8—21no—
346C2×C4×Q8—21no—
347C2×C4×Q8C22×C1111yescharacteristic
348C2×C4×Q8C22×C1111yescharacteristic
349C2×C4×Q8C22×C1111yescharacteristic
350C2×C4×Q8C22×C1111yescharacteristic
351C2×C4×D4C22×C1111yescharacteristic
352C2×C4×D4C22×C1111yescharacteristic
353C2×C4×D4C22×C1111yescharacteristic
354C22×C4⋊C4—21no—
355#501C22×C1118yescomplemented
356#501C22×C1118yescomplemented
357#499C22×C1118yescomplemented
358#479C22×C1118yescomplemented
359#479C22×C1118yescomplemented
360#478C22×C1118yes—
361#478C22×C1118yes—
362#476C22×C1118yes—
363#475C22×C1118yescomplemented
364#446C22×C1118yescomplemented
365#440C22×C1118yes—
366#440C22×C1118yes—
367C4×SD16C22×C1118yes—
368C2×#107C22×C1111yescharacteristic
369C2×#107C22×C1111yescharacteristic
370C2×#107C22×C1111yescharacteristic
371C2×#107C22×C1111yescharacteristic
372C2×#106C22×C1111yescharacteristic
373C2×#106C22×C1111yescharacteristic
374C2×#106C22×C1111yescharacteristic
375C2×#106C22×C1111yescharacteristic
376C2×#106C22×C1111yescharacteristic
377C2×C4⋊C8C22×C1111yescharacteristic
378C2×C4⋊C8C22×C1111yescharacteristic
379C2×C4⋊C8C22×C1111yescharacteristic
380C2×#103C22×C1111yescharacteristic
381C2×#103C22×C1111yescharacteristic
382C2×#103C22×C1111yescharacteristic
383C2×#102C22×C1111yescharacteristic
384C2×#102C22×C1111yescharacteristic
385C2×#102C22×C1111yescharacteristic
386C2×#97C22×C1111yescharacteristic
387C2×#97C22×C1111yescharacteristic
388C2×C4×C8C22×C1111yescharacteristic
389C22×C11—24no—
390C22×C11—48no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11D4×Q812yes—
394C22×C11#57512yes—
395C22×C11#57712yes—
396C22×C11C23×D411yescharacteristic
397C4×C11—24no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—22no—
403C4×C11—22no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—42no—
410C4×C11D4×Q812yes—
411C4×C11C23×Q811yescharacteristic
412C4×C11C2×2−1+411yescharacteristic
413C22×Q8—21no—
414C22×Q8—21no—
415C22×Q8D4×C1111yescharacteristic
416C22×Q8C23×C1111yescharacteristic
417C22×D4C23×C1111yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C2×SD16Q8×C1118yescomplemented
422C2×SD16C23×C1114yes—
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426C22×C8C23×C1111yescharacteristic
427C4⋊Q8—28no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8C23×C1114yes—
431C4⋊Q8C23×C1114yes—
432#125—28no—
433#125—28no—
434#125—22no—
435#125—22no—
436#125—22no—
437#125—22no—
438#125C23×C1114yes—
439#125C23×C1114yes—
440#125C23×C1114yes—
441#125C23×C1114yes—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C4×Q8—28no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8D4×C1114yes—
450C4×Q8C23×C1114yes—
451C4×Q8C23×C1114yes—
452C4×Q8C23×C1114yes—
453C4×Q8C23×C1114yes—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4C23×C1114yes—
458C4×D4C23×C1114yes—
459C4×D4C23×C1114yes—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—28no—
474C2×C4⋊C4D4×C1111yescharacteristic
475C2×C4⋊C4D4×C1111yescharacteristic
476C2×C4⋊C4D4×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C4⋊C4C23×C1111yescharacteristic
482C2×C4⋊C4C23×C1111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42C23×C1111yescharacteristic
490C2×C42C23×C1111yescharacteristic
491C2×C42C23×C1111yescharacteristic
492#107C23×C1114yes—
493#107C23×C1114yes—
494#107C23×C1114yes—
495#107C23×C1114yes—
496#106C23×C1114yes—
497#106C23×C1114yes—
498#106C23×C1114yes—
499#106C23×C1114yes—
500#106C23×C1114yes—
501C4⋊C8C23×C1114yes—
502C4⋊C8C23×C1114yes—
503C4⋊C8C23×C1114yes—
504#103C23×C1114yes—
505#103C23×C1114yes—
506#103C23×C1114yes—
507#102C23×C1114yes—
508#102C23×C1114yes—
509#102C23×C1114yes—
510#97C23×C1114yes—
511#97C23×C1114yes—
512C4×C8C23×C1114yes—
513C2×C11—44no—
514C2×C11#338814yesdirect product factor
515C2×C11C2×D4×Q811yescharacteristic
516C2×C11C2×#57511yescharacteristic
517C2×C11C2×#57711yescharacteristic
518C24—21no—
519C2×Q8—21no—
520C2×Q8—24no—
521C2×Q8—24no—
522C2×Q8—22no—
523C2×Q8—42no—
524C2×Q8—44no—
525C2×Q8—82no—
526C2×Q8C2×D4×C1114yes—
527C2×Q8C2×Q8×C1114yes—
528C2×Q8C24×C1112yes—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4C2×Q8×C1114yes—
532C2×D4C24×C1112yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—44no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C24×C1111yescharacteristic
553SD16C2×Q8×C11116yescomplemented
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8C2×Q8×C1114yes—
558C2×C8C24×C1112yes—
559C2×C8C24×C1112yes—
560C2×C8C24×C1112yes—
561C2×C8C24×C1112yes—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×D4×C1114yes—
582C4⋊C4C2×D4×C1114yes—
583C4⋊C4C2×D4×C1114yes—
584C4⋊C4C24×C1112yes—
585C4⋊C4C24×C1112yes—
586C4⋊C4C24×C1112yes—
587C4⋊C4C24×C1112yes—
588C4⋊C4C24×C1112yes—
589C4⋊C4C24×C1112yes—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C42—24no—
594C42—24no—
595C42—24no—
596C42C2×D4×C1112yes—
597C42C2×D4×C1112yes—
598C42C2×D4×C1112yes—
599C42C24×C1112yes—
600C42C24×C1112yes—
601C42C24×C1112yes—
602C11C2×#338811yescharacteristic, direct product factor, Sylow
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C22×D4×C1111yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—44no—
611Q8—48no—
612Q8—84no—
613Q8C22×Q8×C1114yes—
614D4—24no—
615D4—22no—
616D4C22×Q8×C1114yes—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—48no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4C22×D4×C1112yes—
641C2×C4C22×D4×C1112yes—
642C2×C4C22×D4×C1112yes—
643C2×C4C22×D4×C1112yes—
644C2×C4C22×D4×C1112yes—
645C2×C4C22×D4×C1112yes—
646C2×C4C22×D4×C1111yescharacteristic
647C2×C4C22×Q8×C1112yes—
648C2×C4C11×2−1+412yes—
649C2×C4C25×C1111yescharacteristic
650C8—22no—
651C8—22no—
652C8—22no—
653C8C22×Q8×C1114yes—
654C22—24no—
655C22—42no—
656C22—42no—
657C22—48no—
658C22D4×Q8×C1112yes—
659C22C11×#57512yes—
660C22C11×#57712yes—
661C22C23×D4×C1111yescharacteristic
662C4—24no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4D4×Q8×C1112yes—
676C4C23×Q8×C1111yescharacteristic
677C4C2×C11×2−1+411yescharacteristic
678C2—44no—
679C2C11×#338814yesdirect product factor
680C2C2×D4×Q8×C1111yescharacteristic
681C2C2×C11×#57511yescharacteristic
682C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#557C2semidirect
3. C11×#3388C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#501C2semidirect
6. C2×C11×#499C2semidirect
7. C2×C11×#479C2semidirect
8. C2×C11×#479C2semidirect
9. C2×C11×#475C2semidirect
13. C2×C11×#446C2semidirect
19. C11×#557C22semidirect
43. C11×#501C22semidirect
44. C11×#501C22semidirect
45. C11×#499C22semidirect
46. C11×#479C22semidirect
47. C11×#479C22semidirect
51. C11×#475C22semidirect
52. C11×#446C22semidirect
85. C2×C11×SD16Q8semidirect
177. C2×#3388C11direct (N × H)
213. C11×SD16C2×Q8semidirect
262. C2×#557C2×C11semidirect
264. #3388C2×C11direct (N × H)
265. C2×#501C2×C11semidirect
266. C2×#501C2×C11semidirect
267. C2×#499C2×C11semidirect
268. C2×#479C2×C11semidirect
269. C2×#479C2×C11semidirect
270. C2×#475C2×C11semidirect
274. C2×#446C2×C11semidirect
331. #557C22×C11semidirect
355. #501C22×C11semidirect
356. #501C22×C11semidirect
357. #499C22×C11semidirect
358. #479C22×C11semidirect
359. #479C22×C11semidirect
363. #475C22×C11semidirect
364. #446C22×C11semidirect
421. C2×SD16Q8×C11semidirect
514. C2×C11#3388direct (N × H)
553. SD16C2×Q8×C11semidirect
602. C11C2×#3388direct (N × H)
679. C2C11×#3388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#5542
C11×#33882
C2×C11×#5012
C2×C11×#4992
C2×C11×#4792
C2×C11×#4752
C2×C11×#4782
C2×C11×#4762
C2×C11×#4462
C2×C11×#4402
C2×C4×C11×SD162
C2×#338811