Finite Group Databasebeta

← C2×C11×#3347 #14638432

Subgroups — C2×C11×#3347 #14638432

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic, complemented
2C2×C11×#553C211yesmaximal, characteristic, complemented
3C11×#3347C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#482C211yesmaximal, characteristic, complemented
6C2×C11×#482C211yesmaximal, characteristic, complemented
7C2×C11×#482C211yesmaximal, characteristic, complemented
8C2×C11×#480C211yesmaximal, characteristic, complemented
9C2×C11×#478C211yesmaximal, characteristic, complemented
10C2×C11×#474C211yesmaximal, characteristic, complemented
11C2×C11×#469C211yesmaximal, characteristic, complemented
12C2×C11×#466C211yesmaximal, characteristic, complemented
13C2×C11×#442C211yesmaximal, characteristic, complemented
14C2×C11×#435C211yesmaximal, characteristic, complemented
15C2×C11×#428C211yesmaximal, characteristic, complemented
16C2×C11×#427C211yesmaximal, characteristic, complemented
17C22×C11×D8C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#555—24no—
21C11×#555C2218yescomplemented
22C11×#553—24no—
23C11×#553C2218yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#126—21no—
26C2×C11×#125C2211yescharacteristic
27C2×C11×#124—21no—
28C2×C11×#124—21no—
29C2×C11×#123—21no—
30C2×C11×#121—21no—
31C2×C11×#121—21no—
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C2×C4×D4×C11—21no—
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2211yescharacteristic
40C2×C11×#117—21no—
41C2×C11×#117C2211yescharacteristic
42C2×C11×#117C2211yescharacteristic
43C2×C11×#117C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C11×#501C2218yescomplemented
46C11×#482C2218yescomplemented
47C11×#482C2218yescomplemented
48C11×#482C2218yescomplemented
49C11×#480C2218yescomplemented
50C11×#478C2218yescomplemented
51C11×#474C2218yescomplemented
52C11×#469C2218yescomplemented
53C11×#466C2218yescomplemented
54C11×#442C2218yescomplemented
55C11×#435C2218yescomplemented
56C11×#428C2218yescomplemented
57C11×#427C2218yescomplemented
58C2×C11×#107C2211yescharacteristic
59C2×C11×#107C2211yescharacteristic
60C2×C11×#107C2211yescharacteristic
61C2×C11×#107C2211yescharacteristic
62C2×C11×#107C2211yescharacteristic
63C2×C11×#106C2211yescharacteristic
64C2×C11×#106C2211yescharacteristic
65C2×C11×#106C2211yescharacteristic
66C2×C11×#106C2211yescharacteristic
67C2×C11×C4⋊C8C2211yescharacteristic
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
77C22×Q8×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C2×C11×D8—24no—
91C2×C11×D8C2314yes—
92C2×C11×M16—24no—
93C2×C11×M16C2314yes—
94C22×C8×C11—24no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2314yes—
99C22×C8×C11C2311yescharacteristic
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8C2314yes—
102C11×#126—28no—
103C11×#125—22no—
104C11×#125C2314yes—
105C11×#124—28no—
106C11×#124—28no—
107C11×#123—28no—
108C11×#121—28no—
109C11×#121—28no—
110C11×#121—22no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121C2314yes—
115C11×#121C2314yes—
116C11×#121C2314yes—
117C11×#121C2314yes—
118C4×D4×C11—28no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11D414yes—
122C4×D4×C11C2314yes—
123C4×D4×C11C2314yes—
124C4×D4×C11C2314yes—
125C11×#117—22no—
126C11×#117—22no—
127C11×#117—22no—
128C11×#117—28no—
129C11×#117C2314yes—
130C11×#117C2314yes—
131C11×#117C2314yes—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—22no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2314yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—21no—
149C2×C11×C22⋊C4—21no—
150C2×C11×C22⋊C4—21no—
151C2×C11×C22⋊C4—21no—
152C2×C11×C22⋊C4—21no—
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4D411yescharacteristic
155C2×C11×C22⋊C4D411yescharacteristic
156C2×C42×C11—21no—
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#107C2314yes—
164C11×#107C2314yes—
165C11×#106C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×#106C2314yes—
169C11×C4⋊C8C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177C11×C22⋊C8C2314yes—
178C11×#97C2314yes—
179C2×#3347C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11—21no—
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C24×C11C2×D411yescharacteristic
184C2×Q8×C11—24no—
185C2×Q8×C11—82no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—42no—
197C2×D4×C11—44no—
198C2×D4×C11—82no—
199C2×D4×C11—82no—
200C2×D4×C11—82no—
201C2×D4×C11C2×D414yes—
202C2×D4×C11C2412yes—
203C2×D4×C11C2412yes—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—24no—
216C22×C4×C11—24no—
217C22×C4×C11—44no—
218C22×C4×C11—82no—
219C22×C4×C11—82no—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2411yescharacteristic
229C11×D8—28no—
230C11×M16—28no—
231C2×C8×C11—28no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11#4114yes—
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C2×C8×C11C2412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2×D414yes—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C4⋊C4C2412yes—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4C2×D414yes—
267C11×C22⋊C4C2×D414yes—
268C42×C11—24no—
269C42×C11—24no—
270C42×C11—24no—
271C42×C11C2×D412yes—
272C42×C11C2412yes—
273C2×#555C2×C1111yescharacteristic, complemented
274C2×#553C2×C1111yescharacteristic, complemented
275#3347C2×C11116yesdirect product factor
276C2×#501C2×C1111yescharacteristic, complemented
277C2×#482C2×C1111yescharacteristic, complemented
278C2×#482C2×C1111yescharacteristic, complemented
279C2×#482C2×C1111yescharacteristic, complemented
280C2×#480C2×C1111yescharacteristic, complemented
281C2×#478C2×C1111yescharacteristic, complemented
282C2×#474C2×C1111yescharacteristic, complemented
283C2×#469C2×C1111yescharacteristic, complemented
284C2×#466C2×C1111yescharacteristic, complemented
285C2×#442C2×C1111yescharacteristic, complemented
286C2×#435C2×C1111yescharacteristic, complemented
287C2×#428C2×C1111yescharacteristic, complemented
288C2×#427C2×C1111yescharacteristic, complemented
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11C22×D412yes—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306Q8×C11—84no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—44no—
312D4×C11—48no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—84no—
316D4×C11—84no—
317D4×C11—84no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—48no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—84no—
342C2×C4×C11—84no—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4112yes—
349C2×C4×C112−1+412yes—
350C2×C4×C11C2511yescharacteristic
351C8×C11—22no—
352C8×C11—22no—
353C8×C11—22no—
354C8×C11C2×#4114yes—
355C22×D8C22×C1111yescharacteristic
356C22×M16C22×C1111yescharacteristic
357C23×C8C22×C1111yescharacteristic
358#555—24no—
359#555C22×C1118yescomplemented
360#553—24no—
361#553C22×C1118yescomplemented
362C2×C4⋊Q8C22×C1111yescharacteristic
363C2×#126—21no—
364C2×#125C22×C1111yescharacteristic
365C2×#124—21no—
366C2×#124—21no—
367C2×#123—21no—
368C2×#121—21no—
369C2×#121—21no—
370C2×#121C22×C1111yescharacteristic
371C2×#121C22×C1111yescharacteristic
372C2×#121C22×C1111yescharacteristic
373C2×#121C22×C1111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4C22×C1111yescharacteristic
376C2×C4×D4C22×C1111yescharacteristic
377C2×C4×D4C22×C1111yescharacteristic
378C2×#117—21no—
379C2×#117C22×C1111yescharacteristic
380C2×#117C22×C1111yescharacteristic
381C2×#117C22×C1111yescharacteristic
382C22×C4⋊C4C22×C1111yescharacteristic
383#501C22×C1118yescomplemented
384#482C22×C1118yescomplemented
385#482C22×C1118yescomplemented
386#482C22×C1118yescomplemented
387#480C22×C1118yescomplemented
388#478C22×C1118yescomplemented
389#474C22×C1118yescomplemented
390#469C22×C1118yescomplemented
391#466C22×C1118yescomplemented
392#442C22×C1118yescomplemented
393#435C22×C1118yescomplemented
394#428C22×C1118yescomplemented
395#427C22×C1118yescomplemented
396C2×#107C22×C1111yescharacteristic
397C2×#107C22×C1111yescharacteristic
398C2×#107C22×C1111yescharacteristic
399C2×#107C22×C1111yescharacteristic
400C2×#107C22×C1111yescharacteristic
401C2×#106C22×C1111yescharacteristic
402C2×#106C22×C1111yescharacteristic
403C2×#106C22×C1111yescharacteristic
404C2×#106C22×C1111yescharacteristic
405C2×C4⋊C8C22×C1111yescharacteristic
406C2×#102C22×C1111yescharacteristic
407C2×#102C22×C1111yescharacteristic
408C2×#102C22×C1111yescharacteristic
409C2×#102C22×C1111yescharacteristic
410C2×#102C22×C1111yescharacteristic
411C2×#102C22×C1111yescharacteristic
412C2×C22⋊C8C22×C1111yescharacteristic
413C2×C22⋊C8C22×C1111yescharacteristic
414C2×#97C22×C1111yescharacteristic
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—44no—
422C22×C11—44no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—84no—
430C22×C11—84no—
431C22×C11#54712yes—
432C22×C11#57512yes—
433C22×C11#57612yes—
434C22×C11C23×D411yescharacteristic
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11#54712yes—
446C4×C11C22×#4111yescharacteristic
447C4×C11C2×2−1+411yescharacteristic
448C22×Q8—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4D4×C1111yescharacteristic
454C22×D4C23×C1111yescharacteristic
455C22×D4C23×C1111yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4C23×C1111yescharacteristic
460C23×C4C23×C1111yescharacteristic
461C2×D8—24no—
462C2×D8C23×C1114yes—
463C2×M16—24no—
464C2×M16C23×C1114yes—
465C22×C8—24no—
466C22×C8C23×C1111yescharacteristic
467C22×C8C23×C1114yes—
468C22×C8C23×C1111yescharacteristic
469C22×C8C23×C1111yescharacteristic
470C22×C8C23×C1111yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C23×C1114yes—
473#126—28no—
474#125—22no—
475#125C23×C1114yes—
476#124—28no—
477#124—28no—
478#123—28no—
479#121—28no—
480#121—28no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121C23×C1114yes—
486#121C23×C1114yes—
487#121C23×C1114yes—
488#121C23×C1114yes—
489C4×D4—28no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4D4×C1114yes—
493C4×D4C23×C1114yes—
494C4×D4C23×C1114yes—
495C4×D4C23×C1114yes—
496#117—22no—
497#117—22no—
498#117—22no—
499#117—28no—
500#117C23×C1114yes—
501#117C23×C1114yes—
502#117C23×C1114yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4D4×C1111yescharacteristic
509C2×C4⋊C4C23×C1111yescharacteristic
510C2×C4⋊C4C23×C1111yescharacteristic
511C2×C4⋊C4C23×C1114yes—
512C2×C4⋊C4C23×C1111yescharacteristic
513C2×C4⋊C4C23×C1111yescharacteristic
514C2×C4⋊C4C23×C1111yescharacteristic
515C2×C4⋊C4C23×C1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4D4×C1111yescharacteristic
526C2×C22⋊C4D4×C1111yescharacteristic
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42C23×C1111yescharacteristic
531#107C23×C1114yes—
532#107C23×C1114yes—
533#107C23×C1114yes—
534#107C23×C1114yes—
535#107C23×C1114yes—
536#106C23×C1114yes—
537#106C23×C1114yes—
538#106C23×C1114yes—
539#106C23×C1114yes—
540C4⋊C8C23×C1114yes—
541#102C23×C1114yes—
542#102C23×C1114yes—
543#102C23×C1114yes—
544#102C23×C1114yes—
545#102C23×C1114yes—
546#102C23×C1114yes—
547C22⋊C8C23×C1114yes—
548C22⋊C8C23×C1114yes—
549#97C23×C1114yes—
550C2×C11—42no—
551C2×C11—42no—
552C2×C11—82no—
553C2×C11—82no—
554C2×C11#334714yesdirect product factor
555C2×C11C2×#54711yescharacteristic
556C2×C11C2×#57511yescharacteristic
557C2×C11C2×#57611yescharacteristic
558C24—21no—
559C24—21no—
560C24C2×D4×C1111yescharacteristic
561C24C2×D4×C1111yescharacteristic
562C2×Q8—24no—
563C2×Q8—82no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4C2×D4×C1114yes—
580C2×D4C24×C1112yes—
581C2×D4C24×C1112yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4C2×D4×C1111yescharacteristic
599C22×C4C2×D4×C1111yescharacteristic
600C22×C4C2×D4×C1111yescharacteristic
601C22×C4C2×D4×C1111yescharacteristic
602C22×C4C2×D4×C1112yes—
603C22×C4C2×D4×C1112yes—
604C22×C4C24×C1112yes—
605C22×C4C24×C1112yes—
606C22×C4C24×C1111yescharacteristic
607D8—28no—
608M16—28no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8C11×#4114yes—
614C2×C8C24×C1112yes—
615C2×C8C24×C1112yes—
616C2×C8C24×C1112yes—
617C2×C8C24×C1112yes—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4C2×D4×C1114yes—
629C4⋊C4C24×C1112yes—
630C4⋊C4C24×C1112yes—
631C4⋊C4C24×C1112yes—
632C4⋊C4C24×C1112yes—
633C4⋊C4C24×C1112yes—
634C4⋊C4C24×C1112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4C2×D4×C1114yes—
645C22⋊C4C2×D4×C1114yes—
646C42—24no—
647C42—24no—
648C42—24no—
649C42C2×D4×C1112yes—
650C42C24×C1112yes—
651C11C2×#334711yescharacteristic, direct product factor, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C22×D4×C1112yes—
667C23C22×D4×C1112yes—
668C23C22×D4×C1111yescharacteristic
669Q8—84no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—48no—
676D4—42no—
677D4—42no—
678D4—84no—
679D4—84no—
680D4—84no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4C22×D4×C1112yes—
707C2×C4C22×D4×C1112yes—
708C2×C4C22×D4×C1112yes—
709C2×C4C22×D4×C1112yes—
710C2×C4C22×D4×C1111yescharacteristic
711C2×C4C2×C11×#4112yes—
712C2×C4C11×2−1+412yes—
713C2×C4C25×C1111yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×C11×#4114yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—84no—
733C22—84no—
734C22C11×#54712yes—
735C22C11×#57512yes—
736C22C11×#57612yes—
737C22C23×D4×C1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4C11×#54712yes—
749C4C22×C11×#4111yescharacteristic
750C4C2×C11×2−1+411yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—82no—
755C2C11×#334714yesdirect product factor
756C2C2×C11×#54711yescharacteristic
757C2C2×C11×#57511yescharacteristic
758C2C2×C11×#57611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
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×#555C2semidirect
2. C2×C11×#553C2semidirect
3. C11×#3347C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#482C2semidirect
6. C2×C11×#482C2semidirect
7. C2×C11×#482C2semidirect
8. C2×C11×#480C2semidirect
9. C2×C11×#478C2semidirect
10. C2×C11×#474C2semidirect
11. C2×C11×#469C2semidirect
12. C2×C11×#466C2semidirect
13. C2×C11×#442C2semidirect
14. C2×C11×#435C2semidirect
15. C2×C11×#428C2semidirect
16. C2×C11×#427C2semidirect
21. C11×#555C22semidirect
23. C11×#553C22semidirect
45. C11×#501C22semidirect
46. C11×#482C22semidirect
47. C11×#482C22semidirect
48. C11×#482C22semidirect
49. C11×#480C22semidirect
50. C11×#478C22semidirect
51. C11×#474C22semidirect
52. C11×#469C22semidirect
53. C11×#466C22semidirect
54. C11×#442C22semidirect
55. C11×#435C22semidirect
56. C11×#428C22semidirect
57. C11×#427C22semidirect
179. C2×#3347C11direct (N × H)
273. C2×#555C2×C11semidirect
274. C2×#553C2×C11semidirect
275. #3347C2×C11direct (N × H)
276. C2×#501C2×C11semidirect
277. C2×#482C2×C11semidirect
278. C2×#482C2×C11semidirect
279. C2×#482C2×C11semidirect
280. C2×#480C2×C11semidirect
281. C2×#478C2×C11semidirect
282. C2×#474C2×C11semidirect
283. C2×#469C2×C11semidirect
284. C2×#466C2×C11semidirect
285. C2×#442C2×C11semidirect
286. C2×#435C2×C11semidirect
287. C2×#428C2×C11semidirect
288. C2×#427C2×C11semidirect
359. #555C22×C11semidirect
361. #553C22×C11semidirect
383. #501C22×C11semidirect
384. #482C22×C11semidirect
385. #482C22×C11semidirect
386. #482C22×C11semidirect
387. #480C22×C11semidirect
388. #478C22×C11semidirect
389. #474C22×C11semidirect
390. #469C22×C11semidirect
391. #466C22×C11semidirect
392. #442C22×C11semidirect
393. #435C22×C11semidirect
394. #428C22×C11semidirect
395. #427C22×C11semidirect
554. C2×C11#3347direct (N × H)
651. C11C2×#3347direct (N × H)
755. C2C11×#3347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#5532
C11×#33472
C2×C11×#5012
C2×C11×#4822
C2×C11×#4802
C2×C11×#4782
C2×C11×#4742
C2×C11×#4692
C2×C11×#4662
C2×C11×#4422
C2×C11×#4352
C2×C11×#4282
C2×C11×#4272
C2×#334711