Finite Group Databasebeta

← C2×C11×#3346 #14638431

Subgroups — C2×C11×#3346 #14638431

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#553C211yesmaximal, characteristic
3C11×#3346C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#484C211yesmaximal, characteristic, complemented
6C2×C11×#481C211yesmaximal, characteristic, complemented
7C2×C11×#485C211yesmaximal, characteristic, complemented
8C2×C11×#480C211yesmaximal, characteristic, complemented
9C2×C11×#479C211yesmaximal, characteristic, complemented
10C2×C11×#474C211yesmaximal, characteristic, complemented
11C2×C11×#468C211yesmaximal, characteristic, complemented
12C2×C11×#465C211yesmaximal, characteristic, complemented
13C2×C11×#440C211yesmaximal, characteristic, complemented
14C2×C11×#435C211yesmaximal, characteristic, complemented
15C2×C11×#428C211yesmaximal, characteristic, complemented
16C22×C11×#107C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#554—24no—
21C11×#554C2218yescomplemented
22C11×#553—24no—
23C11×#553C2218yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#126—21no—
26C2×C11×#125—21no—
27C2×C11×#125C2211yescharacteristic
28C2×C11×#123—21no—
29C2×C11×C22⋊Q8—21no—
30C2×C11×C22⋊Q8—21no—
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×#121—21no—
34C2×C11×#121C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×D4×C11—21no—
38C2×C4×D4×C11—21no—
39C2×C4×D4×C11C2211yescharacteristic
40C2×C4×D4×C11C2211yescharacteristic
41C2×C11×#117C2211yescharacteristic
42C22×C11×C4⋊C4C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C11×#501C2218yescomplemented
46C11×#485C2218yescomplemented
47C11×#484C2218yescomplemented
48C11×#481C2218yescomplemented
49C11×#480C2218yescomplemented
50C11×#479C2218yescomplemented
51C11×#474C2218yescomplemented
52C11×#468C2218yescomplemented
53C11×#465C2218yescomplemented
54C11×#440C2218yescomplemented
55C11×#435C2218yescomplemented
56C11×#428C2218yescomplemented
57C2×C11×#107C2211yescharacteristic
58C2×C11×#107C2211yescharacteristic
59C2×C11×#107C2211yescharacteristic
60C2×C11×#107C2211yescharacteristic
61C2×C11×#107C2211yescharacteristic
62C2×C11×#107C2211yescharacteristic
63C2×C11×#107C2218yescomplemented
64C2×C11×#106C2211yescharacteristic
65C2×C11×#106C2211yescharacteristic
66C2×C11×#106C2211yescharacteristic
67C2×C11×C4⋊C8C2211yescharacteristic
68C2×C11×#103C2211yescharacteristic
69C2×C11×#103C2211yescharacteristic
70C2×C11×#103C2211yescharacteristic
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×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11D411yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C2×C11×SD16—24no—
90C2×C11×SD16C2314yes—
91C2×C11×M16—24no—
92C2×C11×M16C2314yes—
93C22×C8×C11—24no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2314yes—
98C22×C8×C11C2311yescharacteristic
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8C2314yes—
101C11×#126—28no—
102C11×#125—28no—
103C11×#125—22no—
104C11×#125C2314yes—
105C11×#123—28no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—28no—
109C11×C22⋊Q8—28no—
110C11×C22⋊Q8C2314yes—
111C11×C22⋊Q8C2314yes—
112C11×#121—28no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121C2314yes—
116C11×#121C2314yes—
117C4×Q8×C11—22no—
118C4×Q8×C11C2314yes—
119C4×D4×C11—28no—
120C4×D4×C11—28no—
121C4×D4×C11—22no—
122C4×D4×C11D414yes—
123C4×D4×C11C2314yes—
124C4×D4×C11C2314yes—
125C11×#117—22no—
126C11×#117C2314yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—22no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—22no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4D411yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2314yes—
146C2×C11×C4⋊C4C2314yes—
147C2×C11×C4⋊C4C2314yes—
148C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
155C2×C11×C22⋊C4D411yescharacteristic
156C2×C11×C22⋊C4D411yescharacteristic
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#107C2314yes—
164C11×#107C2314yes—
165C11×#107C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×#106C2314yes—
169C11×C4⋊C8C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173C11×#102C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177C11×C22⋊C8C2314yes—
178C11×#97C2314yes—
179C2×#3346C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—82no—
188C2×Q8×C11C2412yes—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—44no—
196C2×D4×C11—82no—
197C2×D4×C11C2×D414yes—
198C2×D4×C11C2412yes—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—82no—
215C22×C4×C11—82no—
216C22×C4×C11—82no—
217C22×C4×C11—82no—
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2411yescharacteristic
227C11×SD16—28no—
228C11×M16—28no—
229C2×C8×C11—28no—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11#4114yes—
234C2×C8×C11C2412yes—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C2×D414yes—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
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×C11C2×D412yes—
271C42×C11C2412yes—
272C2×#554C2×C1111yescharacteristic, complemented
273C2×#553C2×C1111yescharacteristic
274#3346C2×C11116yesdirect product factor
275C2×#501C2×C1111yescharacteristic, complemented
276C2×#484C2×C1111yescharacteristic, complemented
277C2×#481C2×C1111yescharacteristic, complemented
278C2×#485C2×C1111yescharacteristic, complemented
279C2×#480C2×C1111yescharacteristic, complemented
280C2×#479C2×C1111yescharacteristic, complemented
281C2×#474C2×C1111yescharacteristic, complemented
282C2×#468C2×C1111yescharacteristic, complemented
283C2×#465C2×C1111yescharacteristic, complemented
284C2×#440C2×C1111yescharacteristic, complemented
285C2×#435C2×C1111yescharacteristic, complemented
286C2×#428C2×C1111yescharacteristic, complemented
287C22×#107C2×C1111yescharacteristic, complemented
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11#13714yes—
298C23×C11C22×D412yes—
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—42no—
304Q8×C11—84no—
305D4×C11—28no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—48no—
309D4×C11—42no—
310D4×C11—84no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—84no—
336C2×C4×C11—84no—
337C2×C4×C11—84no—
338C2×C4×C11—84no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C2×#4112yes—
345C2×C4×C112−1+412yes—
346C2×C4×C11C2511yescharacteristic
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—22no—
350C8×C11C2×#4114yes—
351C22×SD16C22×C1111yescharacteristic
352C22×M16C22×C1111yescharacteristic
353C23×C8C22×C1111yescharacteristic
354#554—24no—
355#554C22×C1118yescomplemented
356#553—24no—
357#553C22×C1118yes—
358C2×C4⋊Q8C22×C1111yescharacteristic
359C2×#126—21no—
360C2×#125—21no—
361C2×#125C22×C1111yescharacteristic
362C2×#123—21no—
363C2×C22⋊Q8—21no—
364C2×C22⋊Q8—21no—
365C2×C22⋊Q8C22×C1111yescharacteristic
366C2×C22⋊Q8C22×C1111yescharacteristic
367C2×#121—21no—
368C2×#121C22×C1111yescharacteristic
369C2×#121C22×C1111yescharacteristic
370C2×C4×Q8C22×C1111yescharacteristic
371C2×C4×D4—21no—
372C2×C4×D4—21no—
373C2×C4×D4C22×C1111yescharacteristic
374C2×C4×D4C22×C1111yescharacteristic
375C2×#117C22×C1111yescharacteristic
376C22×C4⋊C4C22×C1111yescharacteristic
377C22×C4⋊C4C22×C1111yescharacteristic
378C22×C4⋊C4C22×C1111yescharacteristic
379#501C22×C1118yescomplemented
380#485C22×C1118yescomplemented
381#484C22×C1118yescomplemented
382#481C22×C1118yescomplemented
383#480C22×C1118yescomplemented
384#479C22×C1118yescomplemented
385#474C22×C1118yescomplemented
386#468C22×C1118yescomplemented
387#465C22×C1118yescomplemented
388#440C22×C1118yescomplemented
389#435C22×C1118yescomplemented
390#428C22×C1118yescomplemented
391C2×#107C22×C1111yescharacteristic
392C2×#107C22×C1111yescharacteristic
393C2×#107C22×C1111yescharacteristic
394C2×#107C22×C1111yescharacteristic
395C2×#107C22×C1111yescharacteristic
396C2×#107C22×C1111yescharacteristic
397C2×#107C22×C1118yescomplemented
398C2×#106C22×C1111yescharacteristic
399C2×#106C22×C1111yescharacteristic
400C2×#106C22×C1111yescharacteristic
401C2×C4⋊C8C22×C1111yescharacteristic
402C2×#103C22×C1111yescharacteristic
403C2×#103C22×C1111yescharacteristic
404C2×#103C22×C1111yescharacteristic
405C2×#102C22×C1111yescharacteristic
406C2×#102C22×C1111yescharacteristic
407C2×#102C22×C1111yescharacteristic
408C2×C22⋊C8C22×C1111yescharacteristic
409C2×C22⋊C8C22×C1111yescharacteristic
410C2×#97C22×C1111yescharacteristic
411C22×C11—28no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—44no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—84no—
422C22×C11#54712yes—
423C22×C11C2×#13714yes—
424C22×C11C2×#13712yes—
425C22×C11#57612yes—
426C22×C11C23×D411yescharacteristic
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11#54712yes—
439C4×C11C22×#4111yescharacteristic
440C4×C11C2×2−1+411yescharacteristic
441C22×Q8—21no—
442C22×Q8C23×C1111yescharacteristic
443C22×D4—21no—
444C22×D4—21no—
445C22×D4D4×C1111yescharacteristic
446C22×D4C23×C1111yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—21no—
451C23×C4C23×C1111yescharacteristic
452C23×C4C23×C1111yescharacteristic
453C2×SD16—24no—
454C2×SD16C23×C1114yes—
455C2×M16—24no—
456C2×M16C23×C1114yes—
457C22×C8—24no—
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1114yes—
460C22×C8C23×C1111yescharacteristic
461C22×C8C23×C1111yescharacteristic
462C22×C8C23×C1111yescharacteristic
463C4⋊Q8—22no—
464C4⋊Q8C23×C1114yes—
465#126—28no—
466#125—28no—
467#125—22no—
468#125C23×C1114yes—
469#123—28no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474C22⋊Q8C23×C1114yes—
475C22⋊Q8C23×C1114yes—
476#121—28no—
477#121—22no—
478#121—22no—
479#121C23×C1114yes—
480#121C23×C1114yes—
481C4×Q8—22no—
482C4×Q8C23×C1114yes—
483C4×D4—28no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4D4×C1114yes—
487C4×D4C23×C1114yes—
488C4×D4C23×C1114yes—
489#117—22no—
490#117C23×C1114yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4D4×C1111yescharacteristic
504C2×C4⋊C4C23×C1111yescharacteristic
505C2×C4⋊C4C23×C1111yescharacteristic
506C2×C4⋊C4C23×C1111yescharacteristic
507C2×C4⋊C4C23×C1111yescharacteristic
508C2×C4⋊C4C23×C1111yescharacteristic
509C2×C4⋊C4C23×C1114yes—
510C2×C4⋊C4C23×C1114yes—
511C2×C4⋊C4C23×C1114yes—
512C2×C4⋊C4C23×C1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C1111yescharacteristic
520C2×C22⋊C4D4×C1111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C1111yescharacteristic
524#107C23×C1114yes—
525#107C23×C1114yes—
526#107C23×C1114yes—
527#107C23×C1114yes—
528#107C23×C1114yes—
529#107C23×C1114yes—
530#106C23×C1114yes—
531#106C23×C1114yes—
532#106C23×C1114yes—
533C4⋊C8C23×C1114yes—
534#103C23×C1114yes—
535#103C23×C1114yes—
536#103C23×C1114yes—
537#102C23×C1114yes—
538#102C23×C1114yes—
539#102C23×C1114yes—
540C22⋊C8C23×C1114yes—
541C22⋊C8C23×C1114yes—
542#97C23×C1114yes—
543C2×C11—24no—
544C2×C11—42no—
545C2×C11—82no—
546C2×C11#334614yesdirect product factor
547C2×C11C2×#54711yescharacteristic
548C2×C11C22×#13711yescharacteristic
549C2×C11C2×#57611yescharacteristic
550C24—21no—
551C24C2×D4×C1111yescharacteristic
552C24C2×D4×C1111yescharacteristic
553C2×Q8—21no—
554C2×Q8—24no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—82no—
558C2×Q8C24×C1112yes—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—21no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—44no—
566C2×D4—82no—
567C2×D4C2×D4×C1114yes—
568C2×D4C24×C1112yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C2×D4×C1111yescharacteristic
590C22×C4C2×D4×C1111yescharacteristic
591C22×C4C2×D4×C1111yescharacteristic
592C22×C4C2×D4×C1112yes—
593C22×C4C2×D4×C1112yes—
594C22×C4C24×C1112yes—
595C22×C4C24×C1112yes—
596C22×C4C24×C1111yescharacteristic
597SD16—28no—
598M16—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—28no—
603C2×C8C11×#4114yes—
604C2×C8C24×C1112yes—
605C2×C8C24×C1112yes—
606C2×C8C24×C1112yes—
607C2×C8C24×C1112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C1114yes—
624C4⋊C4C24×C1112yes—
625C4⋊C4C24×C1112yes—
626C4⋊C4C24×C1112yes—
627C4⋊C4C24×C1112yes—
628C4⋊C4C24×C1112yes—
629C4⋊C4C24×C1112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4C2×D4×C1114yes—
637C22⋊C4C2×D4×C1114yes—
638C42—24no—
639C42—24no—
640C42C2×D4×C1112yes—
641C42C24×C1112yes—
642C11C2×#334611yescharacteristic, direct product factor, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C11×#13714yes—
653C23C22×D4×C1112yes—
654C23C22×D4×C1112yes—
655C23C22×D4×C1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4C22×D4×C1112yes—
695C2×C4C22×D4×C1112yes—
696C2×C4C22×D4×C1112yes—
697C2×C4C22×D4×C1112yes—
698C2×C4C22×D4×C1111yescharacteristic
699C2×C4C2×C11×#4112yes—
700C2×C4C11×2−1+412yes—
701C2×C4C25×C1111yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×C11×#4114yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22C11×#54712yes—
718C22C2×C11×#13714yes—
719C22C2×C11×#13712yes—
720C22C11×#57612yes—
721C22C23×D4×C1111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4C11×#54712yes—
734C4C22×C11×#4111yescharacteristic
735C4C2×C11×2−1+411yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2C11×#334614yesdirect product factor
740C2C2×C11×#54711yescharacteristic
741C2C22×C11×#13711yescharacteristic
742C2C2×C11×#57611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#553C2
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×#554C2semidirect
3. C11×#3346C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#484C2semidirect
6. C2×C11×#481C2semidirect
7. C2×C11×#485C2semidirect
8. C2×C11×#480C2semidirect
9. C2×C11×#479C2semidirect
10. C2×C11×#474C2semidirect
11. C2×C11×#468C2semidirect
12. C2×C11×#465C2semidirect
13. C2×C11×#440C2semidirect
14. C2×C11×#435C2semidirect
15. C2×C11×#428C2semidirect
16. C22×C11×#107C2semidirect
21. C11×#554C22semidirect
45. C11×#501C22semidirect
46. C11×#485C22semidirect
47. C11×#484C22semidirect
48. C11×#481C22semidirect
49. C11×#480C22semidirect
50. C11×#479C22semidirect
51. C11×#474C22semidirect
52. C11×#468C22semidirect
53. C11×#465C22semidirect
54. C11×#440C22semidirect
55. C11×#435C22semidirect
56. C11×#428C22semidirect
63. C2×C11×#107C22semidirect
179. C2×#3346C11direct (N × H)
272. C2×#554C2×C11semidirect
274. #3346C2×C11direct (N × H)
275. C2×#501C2×C11semidirect
276. C2×#484C2×C11semidirect
277. C2×#481C2×C11semidirect
278. C2×#485C2×C11semidirect
279. C2×#480C2×C11semidirect
280. C2×#479C2×C11semidirect
281. C2×#474C2×C11semidirect
282. C2×#468C2×C11semidirect
283. C2×#465C2×C11semidirect
284. C2×#440C2×C11semidirect
285. C2×#435C2×C11semidirect
286. C2×#428C2×C11semidirect
287. C22×#107C2×C11semidirect
355. #554C22×C11semidirect
379. #501C22×C11semidirect
380. #485C22×C11semidirect
381. #484C22×C11semidirect
382. #481C22×C11semidirect
383. #480C22×C11semidirect
384. #479C22×C11semidirect
385. #474C22×C11semidirect
386. #468C22×C11semidirect
387. #465C22×C11semidirect
388. #440C22×C11semidirect
389. #435C22×C11semidirect
390. #428C22×C11semidirect
397. C2×#107C22×C11semidirect
546. C2×C11#3346direct (N × H)
642. C11C2×#3346direct (N × H)
739. C2C11×#3346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#5532
C11×#33462
C2×C11×#5012
C2×C11×#4842
C2×C11×#4812
C2×C11×#4852
C2×C11×#4802
C2×C11×#4792
C2×C11×#4742
C2×C11×#4682
C2×C11×#4652
C2×C11×#4402
C2×C11×#4352
C2×C11×#4282
C22×C11×#1072
C2×#334611