Finite Group Databasebeta

← C2×C11×#3198 #14637935

Subgroups — C2×C11×#3198 #14637935

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic, complemented
3C11×#3198C2116yesmaximal, direct product factor
4C2×C11×#481C211yesmaximal, characteristic, complemented
5C2×C11×#485C211yesmaximal, characteristic, complemented
6C2×C11×#482C211yesmaximal, characteristic, complemented
7C2×C11×#480C211yesmaximal, characteristic, complemented
8C2×C11×#469C211yesmaximal, characteristic, complemented
9C2×C11×#468C211yesmaximal, characteristic, complemented
10C2×C11×#466C211yesmaximal, characteristic, complemented
11C2×C11×#465C211yesmaximal, characteristic, complemented
12C2×C11×#449C211yesmaximal, characteristic, complemented
13C2×C11×#449C211yesmaximal, characteristic, complemented
14C2×C11×#450C211yesmaximal, characteristic, complemented
15C2×C11×#447C211yesmaximal, characteristic, complemented
16C2×C11×#408C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic, complemented
19C23×D4×C11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×D8C2211yescharacteristic
23C22×C11×D8C2211yescharacteristic
24C22×C11×M16C2211yescharacteristic, complemented
25C23×C8×C11C2211yescharacteristic, complemented
26C11×#537—24no—
27C11×#537C2218yescomplemented
28C11×#535—24no—
29C11×#535C2218yescomplemented
30C2×C11×#127—21no—
31C2×C11×#124—21no—
32C2×C11×C22⋊Q8—21no—
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic, complemented
35C2×C11×#121—21no—
36C2×C11×#121—21no—
37C2×C11×#121—21no—
38C2×C11×#121C2211yescharacteristic
39C2×C11×#121C2211yescharacteristic
40C2×C11×#121C2211yescharacteristic
41C2×C11×#121C2211yescharacteristic
42C2×C11×#121C2211yescharacteristic
43C2×C11×#121C2211yescharacteristic, complemented
44C2×C11×#120—21no—
45C2×C11×#120—21no—
46C2×C11×#117C2211yescharacteristic
47C22×C11×C4⋊C4C2211yescharacteristic, complemented
48C11×#485C2218yescomplemented
49C11×#482C2218yescomplemented
50C11×#481C2218yescomplemented
51C11×#480C2218yescomplemented
52C11×#469C2218yescomplemented
53C11×#468C2218yescomplemented
54C11×#466C2218yescomplemented
55C11×#465C2218yescomplemented
56C11×#450C2218yescomplemented
57C11×#449C2218yescomplemented
58C11×#449C2218yescomplemented
59C11×#447C2218yescomplemented
60C2×C11×#107C2211yescharacteristic, complemented
61C2×C11×#107C2211yescharacteristic, complemented
62C2×C11×#106C2211yescharacteristic, complemented
63C2×C11×#106C2211yescharacteristic, complemented
64C2×C11×#103C2211yescharacteristic, complemented
65C2×C11×#103C2211yescharacteristic, complemented
66C2×C11×#102C2211yescharacteristic
67C2×C11×#102C2211yescharacteristic
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70C2×C11×#102C2211yescharacteristic, complemented
71C2×C11×#102C2211yescharacteristic, complemented
72C11×#408C2218yescomplemented
73C2×C11×C22⋊C8C2211yescharacteristic
74C2×C11×C22⋊C8C2211yescharacteristic
75C2×C11×C22⋊C8C2211yescharacteristic, complemented
76C2×C11×C22⋊C8C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41—42no—
82C2×C11×#41—42no—
83C2×C11×#41D414yes—
84C2×C11×#41C2314yes—
85C2×C11×#41C2314yescomplemented
86C22×Q8×C11D411yescharacteristic
87C22×Q8×C11C2311yescharacteristic
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11—22no—
97C22×D4×C11—42no—
98C22×D4×C11—42no—
99C22×D4×C11D411yescharacteristic
100C22×D4×C11D411yescharacteristic
101C22×D4×C11D411yescharacteristic
102C22×D4×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2314yes—
106C23×C4×C11—21no—
107C23×C4×C11—21no—
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C2×C11×SD16—42no—
112C2×C11×SD16—42no—
113C2×C11×SD16C2314yes—
114C2×C11×SD16C2314yes—
115C2×C11×D8—42no—
116C2×C11×D8—42no—
117C2×C11×D8C2314yes—
118C2×C11×D8C2314yes—
119C2×C11×M16—42no—
120C2×C11×M16C2314yescomplemented
121C22×C8×C11—42no—
122C22×C8×C11C2311yescharacteristic
123C22×C8×C11C2311yescharacteristic
124C22×C8×C11C2311yescharacteristic
125C22×C8×C11C2311yescharacteristic
126C22×C8×C11C2314yescomplemented
127C11×#127—28no—
128C11×#124—28no—
129C11×C22⋊Q8—28no—
130C11×C22⋊Q8—22no—
131C11×C22⋊Q8—22no—
132C11×C22⋊Q8C2314yes—
133C11×C22⋊Q8C2314yescomplemented
134C11×#121—28no—
135C11×#121—28no—
136C11×#121—28no—
137C11×#121—22no—
138C11×#121—22no—
139C11×#121—22no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—22no—
143C11×#121C2314yes—
144C11×#121C2314yes—
145C11×#121C2314yes—
146C11×#121C2314yes—
147C11×#121C2314yes—
148C11×#121C2314yescomplemented
149C11×#120—28no—
150C11×#120—28no—
151C11×#117—22no—
152C11×#117C2314yes—
153C2×C11×C4⋊C4—21no—
154C2×C11×C4⋊C4—22no—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2314yescomplemented
162C2×C11×C22⋊C4—21no—
163C2×C11×C22⋊C4—21no—
164C2×C11×C22⋊C4—21no—
165C2×C11×C22⋊C4—21no—
166C2×C11×C22⋊C4—21no—
167C2×C11×C22⋊C4—21no—
168C2×C11×C22⋊C4—21no—
169C2×C11×C22⋊C4—21no—
170C2×C11×C22⋊C4—21no—
171C2×C42×C11—21no—
172C11×#107C2314yescomplemented
173C11×#107C2314yescomplemented
174C11×#106C2314yescomplemented
175C11×#106C2314yescomplemented
176C11×#103C2314yescomplemented
177C11×#103C2314yescomplemented
178C11×#102C2314yes—
179C11×#102C2314yes—
180C11×#102C2314yes—
181C11×#102C2314yes—
182C11×#102C2314yescomplemented
183C11×#102C2314yescomplemented
184C11×C22⋊C8C2314yes—
185C11×C22⋊C8C2314yes—
186C11×C22⋊C8C2314yescomplemented
187C11×C22⋊C8C2314yescomplemented
188C2×#3198C1111yesmaximal, characteristic, direct product factor, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—24no—
193C24×C11—44no—
194C24×C11—82no—
195C24×C11—82no—
196C24×C11C2×D411yescharacteristic
197C24×C11C2×D411yescharacteristic
198C24×C11C2×D411yescharacteristic
199C11×#41—48no—
200C11×#41—44no—
201C11×#41—44no—
202C11×#41—44no—
203C11×#41—44no—
204C11×#41—48no—
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11—42no—
209C2×Q8×C11C2×D414yes—
210C2×Q8×C11C2412yes—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—24no—
214C2×D4×C11—24no—
215C2×D4×C11—24no—
216C2×D4×C11—24no—
217C2×D4×C11—24no—
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—24no—
222C2×D4×C11—22no—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—44no—
229C2×D4×C11—44no—
230C2×D4×C11—42no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11—44no—
234C2×D4×C11—48no—
235C2×D4×C11—44no—
236C2×D4×C11—82no—
237C2×D4×C11—82no—
238C2×D4×C11—82no—
239C2×D4×C11—82no—
240C2×D4×C11—82no—
241C2×D4×C11—82no—
242C2×D4×C11C2×D414yes—
243C2×D4×C11C2×D414yes—
244C2×D4×C11C2×D414yes—
245C2×D4×C11C2412yes—
246C2×D4×C11C2412yes—
247C2×D4×C11C2412yes—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—24no—
260C22×C4×C11—24no—
261C22×C4×C11—44no—
262C22×C4×C11—82no—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C11×SD16—44no—
274C11×SD16—44no—
275C11×D8—44no—
276C11×D8—44no—
277C11×M16—44no—
278C2×C8×C11—22no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11—22no—
282C2×C8×C11—44no—
283C2×C8×C11C2412yes—
284C2×C8×C11C2412yes—
285C2×C8×C11C2412yes—
286C2×C8×C11C2412yes—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—24no—
290C11×C4⋊C4—24no—
291C11×C4⋊C4—24no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2412yes—
296C11×C4⋊C4C2412yes—
297C11×C4⋊C4C2412yes—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—24no—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—24no—
305C11×C22⋊C4—24no—
306C11×C22⋊C4—24no—
307C42×C11—24no—
308C2×#537C2×C1111yescharacteristic, complemented
309C2×#535C2×C1111yescharacteristic, complemented
310#3198C2×C11116yesdirect product factor
311C2×#481C2×C1111yescharacteristic, complemented
312C2×#485C2×C1111yescharacteristic, complemented
313C2×#482C2×C1111yescharacteristic, complemented
314C2×#480C2×C1111yescharacteristic, complemented
315C2×#469C2×C1111yescharacteristic, complemented
316C2×#468C2×C1111yescharacteristic, complemented
317C2×#466C2×C1111yescharacteristic, complemented
318C2×#465C2×C1111yescharacteristic, complemented
319C2×#449C2×C1111yescharacteristic, complemented
320C2×#449C2×C1111yescharacteristic, complemented
321C2×#450C2×C1111yescharacteristic, complemented
322C2×#447C2×C1111yescharacteristic, complemented
323C2×#408C2×C1111yescharacteristic, complemented
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—48no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11—42no—
346C23×C11—84no—
347C23×C11—84no—
348C23×C11—816no—
349C23×C11C22×D412yes—
350C23×C11C22×D412yes—
351C23×C11C22×D412yes—
352C23×C11C22×D411yescharacteristic
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—44no—
356Q8×C11—42no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—44no—
364D4×C11—44no—
365D4×C11—44no—
366D4×C11—48no—
367D4×C11—48no—
368D4×C11—42no—
369D4×C11—42no—
370D4×C11—42no—
371D4×C11—84no—
372D4×C11—84no—
373D4×C11—84no—
374D4×C11—84no—
375D4×C11—84no—
376D4×C11—84no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—24no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—48no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—42no—
399C2×C4×C11—42no—
400C2×C4×C11—84no—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11H(5,𝔽2)12yes—
406C2×C4×C11H(5,𝔽2)12yes—
407C2×C4×C11C2511yescharacteristic
408C8×C11—22no—
409C8×C11—22no—
410C8×C11—22no—
411C8×C11—22no—
412C22×#41C22×C1111yescharacteristic
413C22×#41C22×C1111yescharacteristic, complemented
414C23×D4C22×C1111yescharacteristic
415C22×SD16C22×C1111yescharacteristic
416C22×SD16C22×C1111yescharacteristic
417C22×D8C22×C1111yescharacteristic
418C22×D8C22×C1111yescharacteristic
419C22×M16C22×C1111yescharacteristic, complemented
420C23×C8C22×C1111yescharacteristic, complemented
421#537—24no—
422#537C22×C1118yescomplemented
423#535—24no—
424#535C22×C1118yescomplemented
425C2×#127—21no—
426C2×#124—21no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8C22×C1111yescharacteristic
429C2×C22⋊Q8C22×C1111yescharacteristic, complemented
430C2×#121—21no—
431C2×#121—21no—
432C2×#121—21no—
433C2×#121C22×C1111yescharacteristic
434C2×#121C22×C1111yescharacteristic
435C2×#121C22×C1111yescharacteristic
436C2×#121C22×C1111yescharacteristic
437C2×#121C22×C1111yescharacteristic
438C2×#121C22×C1111yescharacteristic, complemented
439C2×#120—21no—
440C2×#120—21no—
441C2×#117C22×C1111yescharacteristic
442C22×C4⋊C4C22×C1111yescharacteristic, complemented
443#485C22×C1118yescomplemented
444#482C22×C1118yescomplemented
445#481C22×C1118yescomplemented
446#480C22×C1118yescomplemented
447#469C22×C1118yescomplemented
448#468C22×C1118yescomplemented
449#466C22×C1118yescomplemented
450#465C22×C1118yescomplemented
451#450C22×C1118yescomplemented
452#449C22×C1118yescomplemented
453#449C22×C1118yescomplemented
454#447C22×C1118yescomplemented
455C2×#107C22×C1111yescharacteristic, complemented
456C2×#107C22×C1111yescharacteristic, complemented
457C2×#106C22×C1111yescharacteristic, complemented
458C2×#106C22×C1111yescharacteristic, complemented
459C2×#103C22×C1111yescharacteristic, complemented
460C2×#103C22×C1111yescharacteristic, complemented
461C2×#102C22×C1111yescharacteristic
462C2×#102C22×C1111yescharacteristic
463C2×#102C22×C1111yescharacteristic
464C2×#102C22×C1111yescharacteristic
465C2×#102C22×C1111yescharacteristic, complemented
466C2×#102C22×C1111yescharacteristic, complemented
467#408C22×C1118yescomplemented
468C2×C22⋊C8C22×C1111yescharacteristic
469C2×C22⋊C8C22×C1111yescharacteristic
470C2×C22⋊C8C22×C1111yescharacteristic, complemented
471C2×C22⋊C8C22×C1111yescharacteristic, complemented
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—44no—
482C22×C11—44no—
483C22×C11—44no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—816no—
494C22×C11—84no—
495C22×C11—84no—
496C22×C11—84no—
497C22×C11#53412yes—
498C22×C11#57612yes—
499C22×C11#57712yes—
500C22×C11C23×D411yescharacteristic
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11#53412yes—
510C4×C11C2×H(5,𝔽2)11yescharacteristic
511C4×C11C2×H(5,𝔽2)11yescharacteristic
512C25—21no—
513C2×#41—22no—
514C2×#41—42no—
515C2×#41—42no—
516C2×#41—42no—
517C2×#41—42no—
518C2×#41D4×C1114yes—
519C2×#41C23×C1114yes—
520C2×#41C23×C1114yescomplemented
521C22×Q8D4×C1111yescharacteristic
522C22×Q8C23×C1111yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—22no—
532C22×D4—42no—
533C22×D4—42no—
534C22×D4D4×C1111yescharacteristic
535C22×D4D4×C1111yescharacteristic
536C22×D4D4×C1111yescharacteristic
537C22×D4C23×C1111yescharacteristic
538C22×D4C23×C1111yescharacteristic
539C22×D4C23×C1111yescharacteristic
540C22×D4C23×C1114yes—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C23×C1111yescharacteristic
544C23×C4C23×C1111yescharacteristic
545C23×C4C23×C1111yescharacteristic
546C2×SD16—42no—
547C2×SD16—42no—
548C2×SD16C23×C1114yes—
549C2×SD16C23×C1114yes—
550C2×D8—42no—
551C2×D8—42no—
552C2×D8C23×C1114yes—
553C2×D8C23×C1114yes—
554C2×M16—42no—
555C2×M16C23×C1114yescomplemented
556C22×C8—42no—
557C22×C8C23×C1111yescharacteristic
558C22×C8C23×C1111yescharacteristic
559C22×C8C23×C1111yescharacteristic
560C22×C8C23×C1111yescharacteristic
561C22×C8C23×C1114yescomplemented
562#127—28no—
563#124—28no—
564C22⋊Q8—28no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8C23×C1114yes—
568C22⋊Q8C23×C1114yescomplemented
569#121—28no—
570#121—28no—
571#121—28no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121C23×C1114yes—
579#121C23×C1114yes—
580#121C23×C1114yes—
581#121C23×C1114yes—
582#121C23×C1114yes—
583#121C23×C1114yescomplemented
584#120—28no—
585#120—28no—
586#117—22no—
587#117C23×C1114yes—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4C23×C1111yescharacteristic
593C2×C4⋊C4C23×C1111yescharacteristic
594C2×C4⋊C4C23×C1111yescharacteristic
595C2×C4⋊C4C23×C1111yescharacteristic
596C2×C4⋊C4C23×C1114yescomplemented
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C42—21no—
607#107C23×C1114yescomplemented
608#107C23×C1114yescomplemented
609#106C23×C1114yescomplemented
610#106C23×C1114yescomplemented
611#103C23×C1114yescomplemented
612#103C23×C1114yescomplemented
613#102C23×C1114yes—
614#102C23×C1114yes—
615#102C23×C1114yes—
616#102C23×C1114yes—
617#102C23×C1114yescomplemented
618#102C23×C1114yescomplemented
619C22⋊C8C23×C1114yes—
620C22⋊C8C23×C1114yes—
621C22⋊C8C23×C1114yescomplemented
622C22⋊C8C23×C1114yescomplemented
623C2×C11—42no—
624C2×C11—42no—
625C2×C11—42no—
626C2×C11—82no—
627C2×C11—82no—
628C2×C11—82no—
629C2×C11#319814yesdirect product factor
630C2×C11C2×#53411yescharacteristic
631C2×C11C2×#57611yescharacteristic
632C2×C11C2×#57711yescharacteristic
633C24—21no—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24C2×D4×C1111yescharacteristic
641C24C2×D4×C1111yescharacteristic
642C24C2×D4×C1111yescharacteristic
643#41—48no—
644#41—44no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—48no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—42no—
653C2×Q8C2×D4×C1114yes—
654C2×Q8C24×C1112yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—48no—
679C2×D4—44no—
680C2×D4—82no—
681C2×D4—82no—
682C2×D4—82no—
683C2×D4—82no—
684C2×D4—82no—
685C2×D4—82no—
686C2×D4C2×D4×C1114yes—
687C2×D4C2×D4×C1114yes—
688C2×D4C2×D4×C1114yes—
689C2×D4C24×C1112yes—
690C2×D4C24×C1112yes—
691C2×D4C24×C1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—44no—
706C22×C4—82no—
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1111yescharacteristic
709C22×C4C2×D4×C1111yescharacteristic
710C22×C4C2×D4×C1112yes—
711C22×C4C2×D4×C1112yes—
712C22×C4C2×D4×C1112yes—
713C22×C4C24×C1112yes—
714C22×C4C24×C1112yes—
715C22×C4C24×C1112yes—
716C22×C4C24×C1111yescharacteristic
717SD16—44no—
718SD16—44no—
719D8—44no—
720D8—44no—
721M16—44no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—44no—
727C2×C8C24×C1112yes—
728C2×C8C24×C1112yes—
729C2×C8C24×C1112yes—
730C2×C8C24×C1112yes—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4C24×C1112yes—
739C4⋊C4C24×C1112yes—
740C4⋊C4C24×C1112yes—
741C4⋊C4C24×C1112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C42—24no—
752C11C2×#319811yescharacteristic, direct product factor, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—48no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—84no—
776C23—84no—
777C23—816no—
778C23C22×D4×C1112yes—
779C23C22×D4×C1112yes—
780C23C22×D4×C1112yes—
781C23C22×D4×C1111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—44no—
793D4—44no—
794D4—44no—
795D4—48no—
796D4—48no—
797D4—42no—
798D4—42no—
799D4—42no—
800D4—84no—
801D4—84no—
802D4—84no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—48no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—84no—
830C2×C4C22×D4×C1112yes—
831C2×C4C22×D4×C1112yes—
832C2×C4C22×D4×C1112yes—
833C2×C4C22×D4×C1111yescharacteristic
834C2×C4C11×H(5,𝔽2)12yes—
835C2×C4C11×H(5,𝔽2)12yes—
836C2×C4C25×C1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—816no—
863C22—84no—
864C22—84no—
865C22—84no—
866C22C11×#53412yes—
867C22C11×#57612yes—
868C22C11×#57712yes—
869C22C23×D4×C1111yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4C11×#53412yes—
879C4C2×C11×H(5,𝔽2)11yescharacteristic
880C4C2×C11×H(5,𝔽2)11yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—82no—
886C2—82no—
887C2C11×#319814yesdirect product factor
888C2C2×C11×#53411yescharacteristic
889C2C2×C11×#57611yescharacteristic
890C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#537C2semidirect
2. C2×C11×#535C2semidirect
3. C11×#3198C2direct (N × H)
4. C2×C11×#481C2semidirect
5. C2×C11×#485C2semidirect
6. C2×C11×#482C2semidirect
7. C2×C11×#480C2semidirect
8. C2×C11×#469C2semidirect
9. C2×C11×#468C2semidirect
10. C2×C11×#466C2semidirect
11. C2×C11×#465C2semidirect
12. C2×C11×#449C2semidirect
13. C2×C11×#449C2semidirect
14. C2×C11×#450C2semidirect
15. C2×C11×#447C2semidirect
16. C2×C11×#408C2semidirect
18. C22×C11×#41C22semidirect
24. C22×C11×M16C22semidirect
25. C23×C8×C11C22semidirect
27. C11×#537C22semidirect
29. C11×#535C22semidirect
34. C2×C11×C22⋊Q8C22semidirect
43. C2×C11×#121C22semidirect
47. C22×C11×C4⋊C4C22semidirect
48. C11×#485C22semidirect
49. C11×#482C22semidirect
50. C11×#481C22semidirect
51. C11×#480C22semidirect
52. C11×#469C22semidirect
53. C11×#468C22semidirect
54. C11×#466C22semidirect
55. C11×#465C22semidirect
56. C11×#450C22semidirect
57. C11×#449C22semidirect
58. C11×#449C22semidirect
59. C11×#447C22semidirect
60. C2×C11×#107C22semidirect
61. C2×C11×#107C22semidirect
62. C2×C11×#106C22semidirect
63. C2×C11×#106C22semidirect
64. C2×C11×#103C22semidirect
65. C2×C11×#103C22semidirect
70. C2×C11×#102C22semidirect
71. C2×C11×#102C22semidirect
72. C11×#408C22semidirect
75. C2×C11×C22⋊C8C22semidirect
76. C2×C11×C22⋊C8C22semidirect
85. C2×C11×#41C23semidirect
120. C2×C11×M16C23semidirect
126. C22×C8×C11C23semidirect
133. C11×C22⋊Q8C23semidirect
148. C11×#121C23semidirect
161. C2×C11×C4⋊C4C23semidirect
172. C11×#107C23semidirect
173. C11×#107C23semidirect
174. C11×#106C23semidirect
175. C11×#106C23semidirect
176. C11×#103C23semidirect
177. C11×#103C23semidirect
182. C11×#102C23semidirect
183. C11×#102C23semidirect
186. C11×C22⋊C8C23semidirect
187. C11×C22⋊C8C23semidirect
188. C2×#3198C11direct (N × H)
308. C2×#537C2×C11semidirect
309. C2×#535C2×C11semidirect
310. #3198C2×C11direct (N × H)
311. C2×#481C2×C11semidirect
312. C2×#485C2×C11semidirect
313. C2×#482C2×C11semidirect
314. C2×#480C2×C11semidirect
315. C2×#469C2×C11semidirect
316. C2×#468C2×C11semidirect
317. C2×#466C2×C11semidirect
318. C2×#465C2×C11semidirect
319. C2×#449C2×C11semidirect
320. C2×#449C2×C11semidirect
321. C2×#450C2×C11semidirect
322. C2×#447C2×C11semidirect
323. C2×#408C2×C11semidirect
413. C22×#41C22×C11semidirect
419. C22×M16C22×C11semidirect
420. C23×C8C22×C11semidirect
422. #537C22×C11semidirect
424. #535C22×C11semidirect
429. C2×C22⋊Q8C22×C11semidirect
438. C2×#121C22×C11semidirect
442. C22×C4⋊C4C22×C11semidirect
443. #485C22×C11semidirect
444. #482C22×C11semidirect
445. #481C22×C11semidirect
446. #480C22×C11semidirect
447. #469C22×C11semidirect
448. #468C22×C11semidirect
449. #466C22×C11semidirect
450. #465C22×C11semidirect
451. #450C22×C11semidirect
452. #449C22×C11semidirect
453. #449C22×C11semidirect
454. #447C22×C11semidirect
455. C2×#107C22×C11semidirect
456. C2×#107C22×C11semidirect
457. C2×#106C22×C11semidirect
458. C2×#106C22×C11semidirect
459. C2×#103C22×C11semidirect
460. C2×#103C22×C11semidirect
465. C2×#102C22×C11semidirect
466. C2×#102C22×C11semidirect
467. #408C22×C11semidirect
470. C2×C22⋊C8C22×C11semidirect
471. C2×C22⋊C8C22×C11semidirect
520. C2×#41C23×C11semidirect
555. C2×M16C23×C11semidirect
561. C22×C8C23×C11semidirect
568. C22⋊Q8C23×C11semidirect
583. #121C23×C11semidirect
596. C2×C4⋊C4C23×C11semidirect
607. #107C23×C11semidirect
608. #107C23×C11semidirect
609. #106C23×C11semidirect
610. #106C23×C11semidirect
611. #103C23×C11semidirect
612. #103C23×C11semidirect
617. #102C23×C11semidirect
618. #102C23×C11semidirect
621. C22⋊C8C23×C11semidirect
622. C22⋊C8C23×C11semidirect
629. C2×C11#3198direct (N × H)
752. C11C2×#3198direct (N × H)
887. C2C11×#3198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#5352
C11×#31982
C2×C11×#4812
C2×C11×#4852
C2×C11×#4822
C2×C11×#4802
C2×C11×#4692
C2×C11×#4682
C2×C11×#4662
C2×C11×#4652
C2×C11×#4492
C2×C11×#4502
C2×C11×#4472
C2×C11×#4082
C2×#319811