Finite Group Databasebeta

← C2×C11×#3344 #14638429

Subgroups — C2×C11×#3344 #14638429

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#552C211yesmaximal, characteristic
3C11×#3344C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#484C211yesmaximal, characteristic, complemented
6C2×C11×#485C211yesmaximal, characteristic, complemented
7C2×C11×#483C211yesmaximal, characteristic, complemented
8C2×C11×#483C211yesmaximal, characteristic, complemented
9C2×C11×#479C211yesmaximal, characteristic, complemented
10C2×C11×#475C211yesmaximal, characteristic, complemented
11C2×C11×#470C211yesmaximal, characteristic, complemented
12C2×C11×#467C211yesmaximal, characteristic, complemented
13C2×C11×#441C211yesmaximal, characteristic, complemented
14C2×C11×#435C211yesmaximal, characteristic
15C2×C11×#428C211yesmaximal, characteristic, complemented
16C22×C11×#106C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#554—24no—
21C11×#554C2218yes—
22C11×#552—24no—
23C11×#552C2218yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#126—21no—
26C2×C11×#125—21no—
27C2×C11×#125—21no—
28C2×C11×#125C2211yescharacteristic
29C2×C11×#123—21no—
30C2×C11×C22⋊Q8—21no—
31C2×C11×C22⋊Q8—21no—
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C11×C22⋊Q8C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×D4×C11—21no—
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×#485C2218yescomplemented
47C11×#484C2218yescomplemented
48C11×#483C2218yescomplemented
49C11×#483C2218yescomplemented
50C11×#479C2218yescomplemented
51C11×#475C2218yescomplemented
52C11×#470C2218yescomplemented
53C11×#467C2218yescomplemented
54C11×#441C2218yescomplemented
55C11×#435C2218yes—
56C11×#428C2218yescomplemented
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×#106C2211yescharacteristic
66C2×C11×#106C2218yescomplemented
67C2×C11×C4⋊C8C2211yescharacteristic
68C2×C11×#103C2211yescharacteristic
69C2×C11×#103C2211yescharacteristic
70C2×C11×#103C2211yescharacteristic
71C2×C11×#103C2211yescharacteristic
72C2×C11×#103C2211yescharacteristic
73C2×C11×#103C2211yescharacteristic
74C2×C11×C22⋊C8C2211yescharacteristic
75C2×C11×C22⋊C8C2211yescharacteristic
76C2×C11×#97C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11D411yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C2×C11×Q16—24no—
87C2×C11×Q16C2314yes—
88C2×C11×M16—24no—
89C2×C11×M16C2314yes—
90C22×C8×C11—24no—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2314yes—
95C22×C8×C11C2311yescharacteristic
96C11×C4⋊Q8—22no—
97C11×C4⋊Q8C2314yes—
98C11×#126—28no—
99C11×#125—28no—
100C11×#125—28no—
101C11×#125—22no—
102C11×#125C2314yes—
103C11×#123—28no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—28no—
109C11×C22⋊Q8—28no—
110C11×C22⋊Q8C2314yes—
111C11×C22⋊Q8C2314yes—
112C11×C22⋊Q8C2314yes—
113C11×C22⋊Q8C2314yes—
114C4×Q8×C11—22no—
115C4×Q8×C11—22no—
116C4×Q8×C11C2314yes—
117C4×Q8×C11C2314yes—
118C4×D4×C11—28no—
119C4×D4×C11D414yes—
120C4×D4×C11C2314yes—
121C11×#117—22no—
122C11×#117—28no—
123C11×#117C2314yes—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊C4—22no—
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—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⋊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×#106C2314yes—
164C11×#106C2314yes—
165C11×#106C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×#106C2314yes—
169C11×C4⋊C8C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173C11×#103C2314yes—
174C11×#103C2314yes—
175C11×#103C2314yes—
176C11×C22⋊C8C2314yes—
177C11×C22⋊C8C2314yes—
178C11×#97C2314yes—
179C2×#3344C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11C2×D411yescharacteristic
181C24×C11C2×D411yescharacteristic
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—82no—
190C2×Q8×C11C2412yes—
191C2×Q8×C11C2412yes—
192C2×D4×C11—24no—
193C2×D4×C11C2×D414yes—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—24no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—44no—
210C22×C4×C11—82no—
211C22×C4×C11—82no—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C11×Q16—28no—
222C11×M16—28no—
223C2×C8×C11—28no—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11#4114yes—
228C2×C8×C11C2412yes—
229C2×C8×C11C2412yes—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
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⋊C4C2×D414yes—
263C11×C22⋊C4C2×D414yes—
264C42×C11—24no—
265C42×C11—24no—
266C42×C11—24no—
267C42×C11C2×D412yes—
268C42×C11C2412yes—
269C2×#554C2×C1111yescharacteristic
270C2×#552C2×C1111yescharacteristic
271#3344C2×C11116yesdirect product factor
272C2×#501C2×C1111yescharacteristic, complemented
273C2×#484C2×C1111yescharacteristic, complemented
274C2×#485C2×C1111yescharacteristic, complemented
275C2×#483C2×C1111yescharacteristic, complemented
276C2×#483C2×C1111yescharacteristic, complemented
277C2×#479C2×C1111yescharacteristic, complemented
278C2×#475C2×C1111yescharacteristic, complemented
279C2×#470C2×C1111yescharacteristic, complemented
280C2×#467C2×C1111yescharacteristic, complemented
281C2×#441C2×C1111yescharacteristic, complemented
282C2×#435C2×C1111yescharacteristic
283C2×#428C2×C1111yescharacteristic, complemented
284C22×#106C2×C1111yescharacteristic, complemented
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11#13714yes—
291C23×C11C22×D412yes—
292C23×C11C22×D412yes—
293C23×C11C22×D411yescharacteristic
294Q8×C11—22no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—42no—
299Q8×C11—42no—
300Q8×C11—84no—
301D4×C11—28no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—48no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—84no—
330C2×C4×C11—84no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4112yes—
337C2×C4×C112−1+412yes—
338C2×C4×C11C2511yescharacteristic
339C8×C11—22no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11C2×#4114yes—
343C22×Q16C22×C1111yescharacteristic
344C22×M16C22×C1111yescharacteristic
345C23×C8C22×C1111yescharacteristic
346#554—24no—
347#554C22×C1118yes—
348#552—24no—
349#552C22×C1118yes—
350C2×C4⋊Q8C22×C1111yescharacteristic
351C2×#126—21no—
352C2×#125—21no—
353C2×#125—21no—
354C2×#125C22×C1111yescharacteristic
355C2×#123—21no—
356C2×C22⋊Q8—21no—
357C2×C22⋊Q8—21no—
358C2×C22⋊Q8C22×C1111yescharacteristic
359C2×C22⋊Q8C22×C1111yescharacteristic
360C2×C22⋊Q8C22×C1111yescharacteristic
361C2×C22⋊Q8C22×C1111yescharacteristic
362C2×C4×Q8C22×C1111yescharacteristic
363C2×C4×Q8C22×C1111yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C22×C1111yescharacteristic
366C2×#117—21no—
367C2×#117C22×C1111yescharacteristic
368C22×C4⋊C4C22×C1111yescharacteristic
369C22×C4⋊C4C22×C1111yescharacteristic
370C22×C4⋊C4C22×C1111yescharacteristic
371#501C22×C1118yescomplemented
372#485C22×C1118yescomplemented
373#484C22×C1118yescomplemented
374#483C22×C1118yescomplemented
375#483C22×C1118yescomplemented
376#479C22×C1118yescomplemented
377#475C22×C1118yescomplemented
378#470C22×C1118yescomplemented
379#467C22×C1118yescomplemented
380#441C22×C1118yescomplemented
381#435C22×C1118yes—
382#428C22×C1118yescomplemented
383C2×#107C22×C1111yescharacteristic
384C2×#107C22×C1111yescharacteristic
385C2×#107C22×C1111yescharacteristic
386C2×#106C22×C1111yescharacteristic
387C2×#106C22×C1111yescharacteristic
388C2×#106C22×C1111yescharacteristic
389C2×#106C22×C1111yescharacteristic
390C2×#106C22×C1111yescharacteristic
391C2×#106C22×C1111yescharacteristic
392C2×#106C22×C1118yescomplemented
393C2×C4⋊C8C22×C1111yescharacteristic
394C2×#103C22×C1111yescharacteristic
395C2×#103C22×C1111yescharacteristic
396C2×#103C22×C1111yescharacteristic
397C2×#103C22×C1111yescharacteristic
398C2×#103C22×C1111yescharacteristic
399C2×#103C22×C1111yescharacteristic
400C2×C22⋊C8C22×C1111yescharacteristic
401C2×C22⋊C8C22×C1111yescharacteristic
402C2×#97C22×C1111yescharacteristic
403C22×C11—28no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—44no—
410C22×C11#54712yes—
411C22×C11C2×#13714yes—
412C22×C11C2×#13712yes—
413C22×C11#57712yes—
414C22×C11C23×D411yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11#54712yes—
428C4×C11C22×#4111yescharacteristic
429C4×C11C2×2−1+411yescharacteristic
430C22×Q8—21no—
431C22×Q8C23×C1111yescharacteristic
432C22×Q8C23×C1111yescharacteristic
433C22×D4D4×C1111yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4C23×C1111yescharacteristic
438C23×C4C23×C1111yescharacteristic
439C2×Q16—24no—
440C2×Q16C23×C1114yes—
441C2×M16—24no—
442C2×M16C23×C1114yes—
443C22×C8—24no—
444C22×C8C23×C1111yescharacteristic
445C22×C8C23×C1114yes—
446C22×C8C23×C1111yescharacteristic
447C22×C8C23×C1111yescharacteristic
448C22×C8C23×C1111yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8C23×C1114yes—
451#126—28no—
452#125—28no—
453#125—28no—
454#125—22no—
455#125C23×C1114yes—
456#123—28no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8C23×C1114yes—
464C22⋊Q8C23×C1114yes—
465C22⋊Q8C23×C1114yes—
466C22⋊Q8C23×C1114yes—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8C23×C1114yes—
470C4×Q8C23×C1114yes—
471C4×D4—28no—
472C4×D4D4×C1114yes—
473C4×D4C23×C1114yes—
474#117—22no—
475#117—28no—
476#117C23×C1114yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C1111yescharacteristic
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C4⋊C4C23×C1111yescharacteristic
498C2×C4⋊C4C23×C1114yes—
499C2×C4⋊C4C23×C1114yes—
500C2×C4⋊C4C23×C1114yes—
501C2×C4⋊C4C23×C1111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4D4×C1111yescharacteristic
508C2×C22⋊C4D4×C1111yescharacteristic
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42C23×C1111yescharacteristic
513#107C23×C1114yes—
514#107C23×C1114yes—
515#107C23×C1114yes—
516#106C23×C1114yes—
517#106C23×C1114yes—
518#106C23×C1114yes—
519#106C23×C1114yes—
520#106C23×C1114yes—
521#106C23×C1114yes—
522C4⋊C8C23×C1114yes—
523#103C23×C1114yes—
524#103C23×C1114yes—
525#103C23×C1114yes—
526#103C23×C1114yes—
527#103C23×C1114yes—
528#103C23×C1114yes—
529C22⋊C8C23×C1114yes—
530C22⋊C8C23×C1114yes—
531#97C23×C1114yes—
532C2×C11—24no—
533C2×C11—42no—
534C2×C11#334414yesdirect product factor
535C2×C11C2×#54711yescharacteristic
536C2×C11C22×#13711yescharacteristic
537C2×C11C2×#57711yescharacteristic
538C24C2×D4×C1111yescharacteristic
539C24C2×D4×C1111yescharacteristic
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—82no—
548C2×Q8C24×C1112yes—
549C2×Q8C24×C1112yes—
550C2×D4—24no—
551C2×D4C2×D4×C1114yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C2×D4×C1111yescharacteristic
573C22×C4C2×D4×C1111yescharacteristic
574C22×C4C2×D4×C1112yes—
575C22×C4C2×D4×C1112yes—
576C22×C4C24×C1112yes—
577C22×C4C24×C1112yes—
578C22×C4C24×C1111yescharacteristic
579Q16—28no—
580M16—28no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—28no—
585C2×C8C11×#4114yes—
586C2×C8C24×C1112yes—
587C2×C8C24×C1112yes—
588C2×C8C24×C1112yes—
589C2×C8C24×C1112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4C2×D4×C1114yes—
609C4⋊C4C24×C1112yes—
610C4⋊C4C24×C1112yes—
611C4⋊C4C24×C1112yes—
612C4⋊C4C24×C1112yes—
613C4⋊C4C24×C1112yes—
614C4⋊C4C24×C1112yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4C2×D4×C1114yes—
621C22⋊C4C2×D4×C1114yes—
622C42—24no—
623C42—24no—
624C42—24no—
625C42C2×D4×C1112yes—
626C42C24×C1112yes—
627C11C2×#334411yescharacteristic, direct product factor, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23C11×#13714yes—
634C23C22×D4×C1112yes—
635C23C22×D4×C1112yes—
636C23C22×D4×C1111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—84no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—48no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—84no—
674C2×C4C22×D4×C1112yes—
675C2×C4C22×D4×C1112yes—
676C2×C4C22×D4×C1112yes—
677C2×C4C22×D4×C1112yes—
678C2×C4C22×D4×C1111yescharacteristic
679C2×C4C2×C11×#4112yes—
680C2×C4C11×2−1+412yes—
681C2×C4C25×C1111yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×C11×#4114yes—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22C11×#54712yes—
694C22C2×C11×#13714yes—
695C22C2×C11×#13712yes—
696C22C11×#57712yes—
697C22C23×D4×C1111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4C11×#54712yes—
711C4C22×C11×#4111yescharacteristic
712C4C2×C11×2−1+411yescharacteristic
713C2—24no—
714C2—42no—
715C2C11×#334414yesdirect product factor
716C2C2×C11×#54711yescharacteristic
717C2C22×C11×#13711yescharacteristic
718C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×D4×C11D4
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
3. C11×#3344C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#484C2semidirect
6. C2×C11×#485C2semidirect
7. C2×C11×#483C2semidirect
8. C2×C11×#483C2semidirect
9. C2×C11×#479C2semidirect
10. C2×C11×#475C2semidirect
11. C2×C11×#470C2semidirect
12. C2×C11×#467C2semidirect
13. C2×C11×#441C2semidirect
15. C2×C11×#428C2semidirect
16. C22×C11×#106C2semidirect
45. C11×#501C22semidirect
46. C11×#485C22semidirect
47. C11×#484C22semidirect
48. C11×#483C22semidirect
49. C11×#483C22semidirect
50. C11×#479C22semidirect
51. C11×#475C22semidirect
52. C11×#470C22semidirect
53. C11×#467C22semidirect
54. C11×#441C22semidirect
56. C11×#428C22semidirect
66. C2×C11×#106C22semidirect
179. C2×#3344C11direct (N × H)
271. #3344C2×C11direct (N × H)
272. C2×#501C2×C11semidirect
273. C2×#484C2×C11semidirect
274. C2×#485C2×C11semidirect
275. C2×#483C2×C11semidirect
276. C2×#483C2×C11semidirect
277. C2×#479C2×C11semidirect
278. C2×#475C2×C11semidirect
279. C2×#470C2×C11semidirect
280. C2×#467C2×C11semidirect
281. C2×#441C2×C11semidirect
283. C2×#428C2×C11semidirect
284. C22×#106C2×C11semidirect
371. #501C22×C11semidirect
372. #485C22×C11semidirect
373. #484C22×C11semidirect
374. #483C22×C11semidirect
375. #483C22×C11semidirect
376. #479C22×C11semidirect
377. #475C22×C11semidirect
378. #470C22×C11semidirect
379. #467C22×C11semidirect
380. #441C22×C11semidirect
382. #428C22×C11semidirect
392. C2×#106C22×C11semidirect
534. C2×C11#3344direct (N × H)
627. C11C2×#3344direct (N × H)
715. C2C11×#3344direct (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×#5522
C11×#33442
C2×C11×#5012
C2×C11×#4842
C2×C11×#4852
C2×C11×#4832
C2×C11×#4792
C2×C11×#4752
C2×C11×#4702
C2×C11×#4672
C2×C11×#4412
C2×C11×#4352
C2×C11×#4282
C22×C11×#1062
C2×#334411