Finite Group Databasebeta

← C2×C11×#3343 #14638428

Subgroups — C2×C11×#3343 #14638428

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic, complemented
2C2×C11×#547C211yesmaximal, characteristic
3C11×#3343C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#484C211yesmaximal, characteristic, complemented
6C2×C11×#482C211yesmaximal, characteristic, complemented
7C2×C11×#483C211yesmaximal, characteristic, complemented
8C2×C11×#480C211yesmaximal, characteristic, complemented
9C2×C11×#477C211yesmaximal, characteristic, complemented
10C2×C11×#478C211yesmaximal, 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×#41—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C11×#552—24no—
22C11×#552C2218yescomplemented
23C11×#547—24no—
24C11×#547C2218yes—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#126—21no—
27C2×C11×#125—21no—
28C2×C11×#125C2211yescharacteristic
29C2×C11×#123—21no—
30C2×C11×#123—21no—
31C2×C11×#123—21no—
32C2×C11×C22⋊Q8—21no—
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C2×C11×#121C2211yescharacteristic
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2211yescharacteristic
40C2×C11×#117—21no—
41C2×C11×#117C2211yescharacteristic
42C22×C11×C4⋊C4C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C11×#501C2218yescomplemented
46C11×#484C2218yescomplemented
47C11×#483C2218yescomplemented
48C11×#482C2218yescomplemented
49C11×#480C2218yescomplemented
50C11×#478C2218yescomplemented
51C11×#477C2218yescomplemented
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
77C2×C11×#41—28no—
78C2×C11×#41—48no—
79C22×Q8×C11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C2×C11×SD16—24no—
92C2×C11×SD16C2314yes—
93C2×C11×M16—24no—
94C2×C11×M16C2314yes—
95C22×C8×C11—24no—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2314yes—
100C22×C8×C11C2311yescharacteristic
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8C2314yes—
103C11×#126—28no—
104C11×#125—28no—
105C11×#125—22no—
106C11×#125C2314yes—
107C11×#123—28no—
108C11×#123—28no—
109C11×#123—28no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—28no—
113C11×C22⋊Q8C2314yes—
114C11×C22⋊Q8C2314yes—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121C2314yes—
118C11×#121C2314yes—
119C4×Q8×C11—22no—
120C4×Q8×C11C2314yes—
121C4×D4×C11—22no—
122C4×D4×C11D414yes—
123C4×D4×C11C2314yes—
124C4×D4×C11C2314yes—
125C11×#117—22no—
126C11×#117—28no—
127C11×#117C2314yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—22no—
133C2×C11×C4⋊C4—22no—
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⋊C4—21no—
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⋊C4C2314yes—
147C2×C11×C4⋊C4C2314yes—
148C2×C11×C4⋊C4C2314yes—
149C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
156C2×C11×C22⋊C4D411yescharacteristic
157C2×C11×C22⋊C4D411yescharacteristic
158C2×C42×C11—21no—
159C2×C42×C11—21no—
160C2×C42×C11C2311yescharacteristic
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#107C2314yes—
164C11×#107C2314yes—
165C11×#107C2314yes—
166C11×#107C2314yes—
167C11×#106C2314yes—
168C11×#106C2314yes—
169C11×#106C2314yes—
170C11×C4⋊C8C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173C11×#103C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×#102C2314yes—
177C11×C22⋊C8C2314yes—
178C11×C22⋊C8C2314yes—
179C11×#97C2314yes—
180C2×#3343C1111yesmaximal, characteristic, direct product factor, Sylow
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C24×C11C2×D411yescharacteristic
184C11×#41—432no—
185C2×Q8×C11—21no—
186C2×Q8×C11—24no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—44no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C2×D4×C11C2×D414yes—
200C2×D4×C11C2412yes—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
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—21no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—44no—
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×SD16—28no—
230C11×M16—28no—
231C2×C8×C11—28no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11#4114yescomplemented
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C2×C8×C11C2412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2×D414yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4C2×D414yes—
269C11×C22⋊C4C2×D414yes—
270C42×C11—24no—
271C42×C11—24no—
272C42×C11C2×D412yes—
273C42×C11C2412yes—
274C2×#552C2×C1111yescharacteristic, complemented
275C2×#547C2×C1111yescharacteristic
276#3343C2×C11116yesdirect product factor
277C2×#501C2×C1111yescharacteristic, complemented
278C2×#484C2×C1111yescharacteristic, complemented
279C2×#482C2×C1111yescharacteristic, complemented
280C2×#483C2×C1111yescharacteristic, complemented
281C2×#480C2×C1111yescharacteristic, complemented
282C2×#477C2×C1111yescharacteristic, complemented
283C2×#478C2×C1111yescharacteristic, complemented
284C2×#468C2×C1111yescharacteristic, complemented
285C2×#465C2×C1111yescharacteristic, complemented
286C2×#440C2×C1111yescharacteristic, complemented
287C2×#435C2×C1111yescharacteristic, complemented
288C2×#428C2×C1111yescharacteristic, complemented
289C22×#107C2×C1111yescharacteristic, complemented
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11AGL(1,ℤ/8)14yes—
300C23×C11C22×D412yes—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—48no—
306Q8×C11—42no—
307D4×C11—28no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—48no—
311D4×C11—48no—
312D4×C11—42no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
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—22no—
329C2×C4×C11—22no—
330C2×C4×C11—48no—
331C2×C4×C11—48no—
332C2×C4×C11—42no—
333C2×C4×C11—48no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—48no—
340C2×C4×C11—42no—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C112−1+412yes—
348C2×C4×C11C2511yescharacteristic
349C8×C11—22no—
350C8×C11—22no—
351C8×C11—22no—
352C8×C11C2×#4114yescomplemented
353C22×#41—21no—
354C22×SD16C22×C1111yescharacteristic
355C22×M16C22×C1111yescharacteristic
356C23×C8C22×C1111yescharacteristic
357#552—24no—
358#552C22×C1118yescomplemented
359#547—24no—
360#547C22×C1118yes—
361C2×C4⋊Q8C22×C1111yescharacteristic
362C2×#126—21no—
363C2×#125—21no—
364C2×#125C22×C1111yescharacteristic
365C2×#123—21no—
366C2×#123—21no—
367C2×#123—21no—
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8C22×C1111yescharacteristic
370C2×C22⋊Q8C22×C1111yescharacteristic
371C2×#121C22×C1111yescharacteristic
372C2×#121C22×C1111yescharacteristic
373C2×C4×Q8C22×C1111yescharacteristic
374C2×C4×D4C22×C1111yescharacteristic
375C2×C4×D4C22×C1111yescharacteristic
376C2×#117—21no—
377C2×#117C22×C1111yescharacteristic
378C22×C4⋊C4C22×C1111yescharacteristic
379C22×C4⋊C4C22×C1111yescharacteristic
380C22×C4⋊C4C22×C1111yescharacteristic
381#501C22×C1118yescomplemented
382#484C22×C1118yescomplemented
383#483C22×C1118yescomplemented
384#482C22×C1118yescomplemented
385#480C22×C1118yescomplemented
386#478C22×C1118yescomplemented
387#477C22×C1118yescomplemented
388#468C22×C1118yescomplemented
389#465C22×C1118yescomplemented
390#440C22×C1118yescomplemented
391#435C22×C1118yescomplemented
392#428C22×C1118yescomplemented
393C2×#107C22×C1111yescharacteristic
394C2×#107C22×C1111yescharacteristic
395C2×#107C22×C1111yescharacteristic
396C2×#107C22×C1111yescharacteristic
397C2×#107C22×C1111yescharacteristic
398C2×#107C22×C1111yescharacteristic
399C2×#107C22×C1118yescomplemented
400C2×#106C22×C1111yescharacteristic
401C2×#106C22×C1111yescharacteristic
402C2×#106C22×C1111yescharacteristic
403C2×C4⋊C8C22×C1111yescharacteristic
404C2×#103C22×C1111yescharacteristic
405C2×#103C22×C1111yescharacteristic
406C2×#103C22×C1111yescharacteristic
407C2×#102C22×C1111yescharacteristic
408C2×#102C22×C1111yescharacteristic
409C2×#102C22×C1111yescharacteristic
410C2×C22⋊C8C22×C1111yescharacteristic
411C2×C22⋊C8C22×C1111yescharacteristic
412C2×#97C22×C1111yescharacteristic
413C22×C11—28no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—44no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—84no—
424C22×C11#54712yes—
425C22×C11C2×AGL(1,ℤ/8)14yes—
426C22×C11C2×AGL(1,ℤ/8)12yes—
427C22×C11#57812yes—
428C22×C11C23×D411yescharacteristic
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11#54712yes—
441C4×C11C22×#4111yescharacteristic
442C4×C11C2×2−1+411yescharacteristic
443C2×#41—28no—
444C2×#41—48no—
445C22×Q8—21no—
446C22×Q8C23×C1111yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4D4×C1111yescharacteristic
450C22×D4C23×C1111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C23×C1111yescharacteristic
456C23×C4C23×C1111yescharacteristic
457C2×SD16—24no—
458C2×SD16C23×C1114yes—
459C2×M16—24no—
460C2×M16C23×C1114yes—
461C22×C8—24no—
462C22×C8C23×C1111yescharacteristic
463C22×C8C23×C1114yes—
464C22×C8C23×C1111yescharacteristic
465C22×C8C23×C1111yescharacteristic
466C22×C8C23×C1111yescharacteristic
467C4⋊Q8—22no—
468C4⋊Q8C23×C1114yes—
469#126—28no—
470#125—28no—
471#125—22no—
472#125C23×C1114yes—
473#123—28no—
474#123—28no—
475#123—28no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—28no—
479C22⋊Q8C23×C1114yes—
480C22⋊Q8C23×C1114yes—
481#121—22no—
482#121—22no—
483#121C23×C1114yes—
484#121C23×C1114yes—
485C4×Q8—22no—
486C4×Q8C23×C1114yes—
487C4×D4—22no—
488C4×D4D4×C1114yes—
489C4×D4C23×C1114yes—
490C4×D4C23×C1114yes—
491#117—22no—
492#117—28no—
493#117C23×C1114yes—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C1111yescharacteristic
507C2×C4⋊C4C23×C1111yescharacteristic
508C2×C4⋊C4C23×C1111yescharacteristic
509C2×C4⋊C4C23×C1111yescharacteristic
510C2×C4⋊C4C23×C1111yescharacteristic
511C2×C4⋊C4C23×C1111yescharacteristic
512C2×C4⋊C4C23×C1114yes—
513C2×C4⋊C4C23×C1114yes—
514C2×C4⋊C4C23×C1114yes—
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⋊C4D4×C1111yescharacteristic
523C2×C22⋊C4D4×C1111yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42C23×C1111yescharacteristic
527#107C23×C1114yes—
528#107C23×C1114yes—
529#107C23×C1114yes—
530#107C23×C1114yes—
531#107C23×C1114yes—
532#107C23×C1114yes—
533#106C23×C1114yes—
534#106C23×C1114yes—
535#106C23×C1114yes—
536C4⋊C8C23×C1114yes—
537#103C23×C1114yes—
538#103C23×C1114yes—
539#103C23×C1114yes—
540#102C23×C1114yes—
541#102C23×C1114yes—
542#102C23×C1114yes—
543C22⋊C8C23×C1114yes—
544C22⋊C8C23×C1114yes—
545#97C23×C1114yes—
546C2×C11—24no—
547C2×C11—42no—
548C2×C11—82no—
549C2×C11#334314yesdirect product factor
550C2×C11C2×#54711yescharacteristic
551C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
552C2×C11C2×#57811yescharacteristic
553C24—21no—
554C24C2×D4×C1111yescharacteristic
555C24C2×D4×C1111yescharacteristic
556#41—432no—
557C2×Q8—21no—
558C2×Q8—24no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—44no—
562C2×Q8C24×C1112yes—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4C2×D4×C1114yes—
572C2×D4C24×C1112yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4C2×D4×C1111yescharacteristic
593C22×C4C2×D4×C1111yescharacteristic
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1112yes—
597C22×C4C2×D4×C1112yes—
598C22×C4C24×C1112yes—
599C22×C4C24×C1112yes—
600C22×C4C24×C1111yescharacteristic
601SD16—28no—
602M16—28no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—28no—
607C2×C8C11×#4114yescomplemented
608C2×C8C24×C1112yes—
609C2×C8C24×C1112yes—
610C2×C8C24×C1112yes—
611C2×C8C24×C1112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4C2×D4×C1114yes—
628C4⋊C4C24×C1112yes—
629C4⋊C4C24×C1112yes—
630C4⋊C4C24×C1112yes—
631C4⋊C4C24×C1112yes—
632C4⋊C4C24×C1112yes—
633C4⋊C4C24×C1112yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4C2×D4×C1114yes—
641C22⋊C4C2×D4×C1114yes—
642C42—24no—
643C42—24no—
644C42C2×D4×C1112yes—
645C42C24×C1112yes—
646C11C2×#334311yescharacteristic, direct product factor, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C11×AGL(1,ℤ/8)14yes—
657C23C22×D4×C1112yes—
658C23C22×D4×C1112yes—
659C23C22×D4×C1111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—48no—
663Q8—42no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—42no—
690C2×C4—48no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4C22×D4×C1112yes—
699C2×C4C22×D4×C1112yes—
700C2×C4C22×D4×C1112yes—
701C2×C4C22×D4×C1112yes—
702C2×C4C22×D4×C1111yescharacteristic
703C2×C4C2×C11×#4112yes—
704C2×C4C11×2−1+412yes—
705C2×C4C25×C1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×C11×#4114yescomplemented
710C22—22no—
711C22—22no—
712C22—28no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22C11×#54712yes—
722C22C2×C11×AGL(1,ℤ/8)14yes—
723C22C2×C11×AGL(1,ℤ/8)12yes—
724C22C11×#57812yes—
725C22C23×D4×C1111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4C11×#54712yes—
738C4C22×C11×#4111yescharacteristic
739C4C2×C11×2−1+411yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2C11×#334314yesdirect product factor
744C2C2×C11×#54711yescharacteristic
745C2C22×C11×AGL(1,ℤ/8)11yescharacteristic
746C2C2×C11×#57811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#547C2
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×#3343C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#484C2semidirect
6. C2×C11×#482C2semidirect
7. C2×C11×#483C2semidirect
8. C2×C11×#480C2semidirect
9. C2×C11×#477C2semidirect
10. C2×C11×#478C2semidirect
11. C2×C11×#468C2semidirect
12. C2×C11×#465C2semidirect
13. C2×C11×#440C2semidirect
14. C2×C11×#435C2semidirect
15. C2×C11×#428C2semidirect
16. C22×C11×#107C2semidirect
22. C11×#552C22semidirect
45. C11×#501C22semidirect
46. C11×#484C22semidirect
47. C11×#483C22semidirect
48. C11×#482C22semidirect
49. C11×#480C22semidirect
50. C11×#478C22semidirect
51. C11×#477C22semidirect
52. C11×#468C22semidirect
53. C11×#465C22semidirect
54. C11×#440C22semidirect
55. C11×#435C22semidirect
56. C11×#428C22semidirect
63. C2×C11×#107C22semidirect
180. C2×#3343C11direct (N × H)
235. C2×C8×C11#41semidirect
274. C2×#552C2×C11semidirect
276. #3343C2×C11direct (N × H)
277. C2×#501C2×C11semidirect
278. C2×#484C2×C11semidirect
279. C2×#482C2×C11semidirect
280. C2×#483C2×C11semidirect
281. C2×#480C2×C11semidirect
282. C2×#477C2×C11semidirect
283. C2×#478C2×C11semidirect
284. C2×#468C2×C11semidirect
285. C2×#465C2×C11semidirect
286. C2×#440C2×C11semidirect
287. C2×#435C2×C11semidirect
288. C2×#428C2×C11semidirect
289. C22×#107C2×C11semidirect
352. C8×C11C2×#41semidirect
358. #552C22×C11semidirect
381. #501C22×C11semidirect
382. #484C22×C11semidirect
383. #483C22×C11semidirect
384. #482C22×C11semidirect
385. #480C22×C11semidirect
386. #478C22×C11semidirect
387. #477C22×C11semidirect
388. #468C22×C11semidirect
389. #465C22×C11semidirect
390. #440C22×C11semidirect
391. #435C22×C11semidirect
392. #428C22×C11semidirect
399. C2×#107C22×C11semidirect
549. C2×C11#3343direct (N × H)
607. C2×C8C11×#41semidirect
646. C11C2×#3343direct (N × H)
709. C8C2×C11×#41semidirect
743. C2C11×#3343direct (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×#5472
C11×#33432
C2×C11×#5012
C2×C11×#4842
C2×C11×#4822
C2×C11×#4832
C2×C11×#4802
C2×C11×#4772
C2×C11×#4782
C2×C11×#4682
C2×C11×#4652
C2×C11×#4402
C2×C11×#4352
C2×C11×#4282
C22×C11×#1072
C2×#334311