Finite Group Databasebeta

← C11×#23017 #14600210

Subgroups — C11×#23017 #14600210

Order 2816.

864 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
1C11×#3035C211yesmaximal, characteristic
2C2×C11×#444C211yesmaximal, characteristic, complemented
3C2×C11×#443C211yesmaximal, characteristic, complemented
4C11×#2935C211yesmaximal, characteristic, complemented
5C11×#2906C211yesmaximal, characteristic, complemented
6C11×#1963C211yesmaximal, characteristic, complemented
7C11×#1950C211yesmaximal, characteristic, complemented
8C11×#1938C211yesmaximal, characteristic, complemented
9C11×#1937C211yesmaximal, characteristic, complemented
10C11×#1876C211yesmaximal, characteristic, complemented
11C11×#1876C211yesmaximal, characteristic, complemented
12C11×#1866C211yesmaximal, characteristic, complemented
13C11×#1866C211yesmaximal, characteristic, complemented
14C11×#1768C211yesmaximal, characteristic, complemented
15C11×#1759C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic
20C2×C11×#131C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C4×C11×#41C2211yescharacteristic
24C11×#464C411yescharacteristic, complemented
25C11×#464C411yescharacteristic, complemented
26C11×#463C411yescharacteristic, complemented
27C11×#463C411yescharacteristic, complemented
28C11×#462C411yescharacteristic, complemented
29C11×#461C411yescharacteristic, complemented
30C11×#460C411yescharacteristic, complemented
31C11×#459C411yescharacteristic, complemented
32C11×#444—24no—
33C11×#443—24no—
34C11×#436—21no—
35C11×#435—21no—
36C11×#435—21no—
37C8×D4×C11—21no—
38C2×C11×#108C2211yescharacteristic
39C2×C11×#108C2211yescharacteristic
40C11×#424—21no—
41C11×#424—21no—
42C11×#424C2211yescharacteristic
43C11×#424C2211yescharacteristic
44C11×#423—21no—
45C11×#423C2211yescharacteristic
46C2×C11×C4⋊C8—21no—
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C2×C11×#104C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic
54C2×C11×#104C2211yescharacteristic
55C11×#416C2211yescharacteristic
56C11×#416C2211yescharacteristic
57C11×#408C2211yescharacteristic
58C11×#408C2211yescharacteristic
59C4×C11×M16C2211yescharacteristic
60C2×C11×#97C2211yescharacteristic
61C2×C4×C8×C11C2211yescharacteristic
62C11×#376C2211yescharacteristic
63C11×#341C2211yescharacteristic
64C11×#341C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#336C2211yescharacteristic
68C11×#336C2211yescharacteristic
69C2×C11×#41C2311yescharacteristic
70C2×C11×#41C2311yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C11×#135—22no—
73C11×#135—22no—
74C11×#135—22no—
75C11×#135—22no—
76C2×C11×Q16C2×C411yescharacteristic
77C2×C11×Q16C2×C411yescharacteristic
78C2×C11×SD16C2×C411yescharacteristic
79C2×C11×SD16C2×C411yescharacteristic
80C2×C11×SD16C2×C411yescharacteristic
81C2×C11×SD16C2×C411yescharacteristic
82C2×C11×D8C2×C411yescharacteristic
83C2×C11×D8C2×C411yescharacteristic
84C11×#131—22no—
85C11×#131—22no—
86C11×#131—22no—
87C11×#131—22no—
88C11×#131—41no—
89C11×#131—41no—
90C11×#131—41no—
91C11×#131—41no—
92C2×C11×M16—21no—
93C2×C11×M16—21no—
94C2×C11×M16—21no—
95C2×C11×M16—21no—
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C2×C11×M16C2311yescharacteristic
99C2×C11×M16C2311yescharacteristic
100C22×C8×C11—21no—
101C22×C8×C11—21no—
102C22×C8×C11—21no—
103C22×C8×C11—21no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×C4⋊Q8C2×C411yescharacteristic
109C11×#127C2×C411yescharacteristic
110C11×#124C2×C411yescharacteristic
111C11×#124C2×C411yescharacteristic
112C11×#121—21no—
113C11×#121—21no—
114C4×Q8×C11C2×C411yescharacteristic
115C4×Q8×C11C2×C411yescharacteristic
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11C2×C411yescharacteristic
121C4×D4×C11C2×C411yescharacteristic
122C11×#117—21no—
123C11×#117C2311yescharacteristic
124C2×C42×C11—21no—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C11×#108—22no—
129C11×#108—22no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8—21no—
134C11×C4⋊C8—21no—
135C11×C4⋊C8—21no—
136C11×C4⋊C8C2×C411yescharacteristic
137C11×C4⋊C8C2×C411yescharacteristic
138C11×C4⋊C8C2×C411yescharacteristic
139C11×C4⋊C8C2×C411yescharacteristic
140C11×C4⋊C8D411yescharacteristic
141C11×C4⋊C8D411yescharacteristic
142C11×C4⋊C8D411yescharacteristic
143C11×C4⋊C8D411yescharacteristic
144C11×#104—22no—
145C11×#104—22no—
146C11×#104—22no—
147C11×#104—41no—
148C11×#104—41no—
149C11×#104D414yescomplemented
150C11×#103C2×C411yescharacteristic
151C11×#103C2×C411yescharacteristic
152C11×#103C2×C411yescharacteristic
153C11×#103C2×C411yescharacteristic
154C11×#102C2×C411yescharacteristic
155C11×#102C2×C411yescharacteristic
156C11×#102C2×C411yescharacteristic
157C11×#102C2×C411yescharacteristic
158C11×C22⋊C8—21no—
159C11×C22⋊C8—21no—
160C11×C22⋊C8—21no—
161C11×C22⋊C8—21no—
162C11×#97—22no—
163C11×#97—21no—
164C4×C8×C11—22no—
165C4×C8×C11—21no—
166C11×#95—21no—
167C11×#95—21no—
168#23017C1111yesmaximal, characteristic, direct product factor, Sylow
169C11×#41—21no—
170C11×#41—21no—
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C11×#41—21no—
176C11×#41—21no—
177C11×#41—21no—
178C11×#41—21no—
179C11×#41C2×D412yes—
180C11×#41#4112yes—
181C2×Q8×C11C22×C411yescharacteristic
182C2×Q8×C11C22×C411yescharacteristic
183C2×Q8×C11C22×C411yescharacteristic
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11C22×C411yescharacteristic
190C2×D4×C11C22×C411yescharacteristic
191C2×D4×C11C22×C411yescharacteristic
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11#4111yescharacteristic
200C22×C4×C11#4111yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C11×Q16—22no—
203C11×Q16—22no—
204C11×SD16—22no—
205C11×SD16—22no—
206C11×SD16—22no—
207C11×SD16—22no—
208C11×D8—22no—
209C11×D8—22no—
210C11×M16—21no—
211C11×M16—21no—
212C11×M16—21no—
213C11×M16—21no—
214C11×M16—21no—
215C11×M16—21no—
216C11×M16—21no—
217C11×M16—42no—
218C11×M16—42no—
219C11×M16—42no—
220C11×M16—42no—
221C11×M16C2×D412yes—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—42no—
235C2×C8×C11—42no—
236C2×C8×C11—42no—
237C2×C8×C11—42no—
238C2×C8×C11C22×C411yescharacteristic
239C2×C8×C11C22×C411yescharacteristic
240C2×C8×C11C22×C411yescharacteristic
241C2×C8×C11C22×C411yescharacteristic
242C2×C8×C11C2×D411yescharacteristic
243C2×C8×C11C2×D411yescharacteristic
244C2×C8×C11C2×D411yescharacteristic
245C2×C8×C11C2×D411yescharacteristic
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C22×C411yescharacteristic
251C11×C4⋊C4C22×C411yescharacteristic
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—21no—
264C42×C11—21no—
265C42×C11C22×C411yescharacteristic
266C42×C11C22×C411yescharacteristic
267C42×C11C2×D412yes—
268C42×C11C2×D411yescharacteristic
269C42×C11C2×D411yescharacteristic
270#3035C2×C1111yescharacteristic
271C2×#444C2×C1111yescharacteristic, complemented
272C2×#443C2×C1111yescharacteristic, complemented
273#2935C2×C1111yescharacteristic, complemented
274#2906C2×C1111yescharacteristic, complemented
275#1963C2×C1111yescharacteristic, complemented
276#1950C2×C1111yescharacteristic, complemented
277#1938C2×C1111yescharacteristic, complemented
278#1937C2×C1111yescharacteristic, complemented
279#1876C2×C1111yescharacteristic, complemented
280#1876C2×C1111yescharacteristic, complemented
281#1866C2×C1111yescharacteristic, complemented
282#1866C2×C1111yescharacteristic, complemented
283#1768C2×C1111yescharacteristic, complemented
284#1759C2×C1111yescharacteristic, complemented
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11C2×#4111yescharacteristic
289Q8×C11—21no—
290Q8×C11—21no—
291Q8×C11—21no—
292Q8×C11—21no—
293Q8×C11—21no—
294Q8×C11C4×D412yes—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—21no—
298D4×C11—21no—
299D4×C11—21no—
300D4×C11—21no—
301D4×C11—21no—
302D4×C11—42no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—81no—
308D4×C11C4×D412yes—
309C2×C4×C11—21no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—42no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—81no—
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C23×C411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C112−1+411yescharacteristic
340C8×C11—21no—
341C8×C11—21no—
342C8×C11—21no—
343C8×C11—21no—
344C8×C11—21no—
345C8×C11—21no—
346C8×C11—21no—
347C8×C11—21no—
348C8×C11—22no—
349C8×C11—41no—
350C8×C11—41no—
351C8×C11—41no—
352C2×#135C22×C1111yescharacteristic
353C2×#135C22×C1111yescharacteristic
354C2×#131C22×C1111yescharacteristic
355C2×#131C22×C1111yescharacteristic
356C2×#131C22×C1111yescharacteristic
357C2×#131C22×C1111yescharacteristic
358#532C22×C1111yescharacteristic
359C4×#41C22×C1111yescharacteristic
360#464C4×C1111yescharacteristic, complemented
361#464C4×C1111yescharacteristic, complemented
362#463C4×C1111yescharacteristic, complemented
363#463C4×C1111yescharacteristic, complemented
364#462C4×C1111yescharacteristic, complemented
365#461C4×C1111yescharacteristic, complemented
366#460C4×C1111yescharacteristic, complemented
367#459C4×C1111yescharacteristic, complemented
368#444—24no—
369#443—24no—
370#436—21no—
371#435—21no—
372#435—21no—
373C8×D4—21no—
374C2×#108C22×C1111yescharacteristic
375C2×#108C22×C1111yescharacteristic
376#424—21no—
377#424—21no—
378#424C22×C1111yescharacteristic
379#424C22×C1111yescharacteristic
380#423—21no—
381#423C22×C1111yescharacteristic
382C2×C4⋊C8—21no—
383C2×C4⋊C8C22×C1111yescharacteristic
384C2×C4⋊C8C22×C1111yescharacteristic
385C2×#104C22×C1111yescharacteristic
386C2×#104C22×C1111yescharacteristic
387C2×#104C22×C1111yescharacteristic
388C2×#104C22×C1111yescharacteristic
389C2×#104C22×C1111yescharacteristic
390C2×#104C22×C1111yescharacteristic
391#416C22×C1111yescharacteristic
392#416C22×C1111yescharacteristic
393#408C22×C1111yescharacteristic
394#408C22×C1111yescharacteristic
395C4×M16C22×C1111yescharacteristic
396C2×#97C22×C1111yescharacteristic
397C2×C4×C8C22×C1111yescharacteristic
398#376C22×C1111yescharacteristic
399#341C22×C1111yescharacteristic
400#341C22×C1111yescharacteristic
401#339C22×C1111yescharacteristic
402#339C22×C1111yescharacteristic
403#336C22×C1111yescharacteristic
404#336C22×C1111yescharacteristic
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—22no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11C2×C4×D411yescharacteristic
417C22×C11#54711yescharacteristic
418C22×C11#55311yescharacteristic
419C4×C11—22no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—81no—
430C4×C11C2×C4×D411yescharacteristic
431C4×C11#52011yescharacteristic
432C4×C11D4211yescharacteristic
433C4×C11#54811yescharacteristic
434C2×#41C23×C1111yescharacteristic
435C2×#41C23×C1111yescharacteristic
436C2×#41C23×C1111yescharacteristic
437#135—22no—
438#135—22no—
439#135—22no—
440#135—22no—
441C2×Q16C2×C4×C1111yescharacteristic
442C2×Q16C2×C4×C1111yescharacteristic
443C2×SD16C2×C4×C1111yescharacteristic
444C2×SD16C2×C4×C1111yescharacteristic
445C2×SD16C2×C4×C1111yescharacteristic
446C2×SD16C2×C4×C1111yescharacteristic
447C2×D8C2×C4×C1111yescharacteristic
448C2×D8C2×C4×C1111yescharacteristic
449#131—22no—
450#131—22no—
451#131—22no—
452#131—22no—
453#131—41no—
454#131—41no—
455#131—41no—
456#131—41no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16C23×C1111yescharacteristic
462C2×M16C23×C1111yescharacteristic
463C2×M16C23×C1111yescharacteristic
464C2×M16C23×C1111yescharacteristic
465C22×C8—21no—
466C22×C8—21no—
467C22×C8—21no—
468C22×C8—21no—
469C22×C8C23×C1111yescharacteristic
470C22×C8C23×C1111yescharacteristic
471C22×C8C23×C1111yescharacteristic
472C22×C8C23×C1111yescharacteristic
473C4⋊Q8C2×C4×C1111yescharacteristic
474#127C2×C4×C1111yescharacteristic
475#124C2×C4×C1111yescharacteristic
476#124C2×C4×C1111yescharacteristic
477#121—21no—
478#121—21no—
479C4×Q8C2×C4×C1111yescharacteristic
480C4×Q8C2×C4×C1111yescharacteristic
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4C2×C4×C1111yescharacteristic
486C4×D4C2×C4×C1111yescharacteristic
487#117—21no—
488#117C23×C1111yescharacteristic
489C2×C42—21no—
490C2×C42C23×C1111yescharacteristic
491C2×C42C23×C1111yescharacteristic
492C2×C42C23×C1111yescharacteristic
493#108—22no—
494#108—22no—
495C4⋊C8—21no—
496C4⋊C8—21no—
497C4⋊C8—21no—
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8C2×C4×C1111yescharacteristic
502C4⋊C8C2×C4×C1111yescharacteristic
503C4⋊C8C2×C4×C1111yescharacteristic
504C4⋊C8C2×C4×C1111yescharacteristic
505C4⋊C8D4×C1111yescharacteristic
506C4⋊C8D4×C1111yescharacteristic
507C4⋊C8D4×C1111yescharacteristic
508C4⋊C8D4×C1111yescharacteristic
509#104—22no—
510#104—22no—
511#104—22no—
512#104—41no—
513#104—41no—
514#104D4×C1114yescomplemented
515#103C2×C4×C1111yescharacteristic
516#103C2×C4×C1111yescharacteristic
517#103C2×C4×C1111yescharacteristic
518#103C2×C4×C1111yescharacteristic
519#102C2×C4×C1111yescharacteristic
520#102C2×C4×C1111yescharacteristic
521#102C2×C4×C1111yescharacteristic
522#102C2×C4×C1111yescharacteristic
523C22⋊C8—21no—
524C22⋊C8—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527#97—22no—
528#97—21no—
529C4×C8—22no—
530C4×C8—21no—
531#95—21no—
532#95—21no—
533C2×C11—21no—
534C2×C11—21no—
535C2×C11—42no—
536C2×C11—81no—
537C2×C11—81no—
538C2×C11#236111yescharacteristic
539C2×C11#295511yescharacteristic
540C2×C11#295711yescharacteristic
541#41—21no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41C2×D4×C1112yes—
552#41C11×#4112yes—
553C2×Q8C22×C4×C1111yescharacteristic
554C2×Q8C22×C4×C1111yescharacteristic
555C2×Q8C22×C4×C1111yescharacteristic
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C22×C4×C1111yescharacteristic
562C2×D4C22×C4×C1111yescharacteristic
563C2×D4C22×C4×C1111yescharacteristic
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4C11×#4111yescharacteristic
572C22×C4C11×#4111yescharacteristic
573C22×C4C24×C1111yescharacteristic
574Q16—22no—
575Q16—22no—
576SD16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580D8—22no—
581D8—22no—
582M16—21no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—21no—
589M16—42no—
590M16—42no—
591M16—42no—
592M16—42no—
593M16C2×D4×C1112yes—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—42no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—42no—
610C2×C8C22×C4×C1111yescharacteristic
611C2×C8C22×C4×C1111yescharacteristic
612C2×C8C22×C4×C1111yescharacteristic
613C2×C8C22×C4×C1111yescharacteristic
614C2×C8C2×D4×C1111yescharacteristic
615C2×C8C2×D4×C1111yescharacteristic
616C2×C8C2×D4×C1111yescharacteristic
617C2×C8C2×D4×C1111yescharacteristic
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4C22×C4×C1111yescharacteristic
623C4⋊C4C22×C4×C1111yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42C22×C4×C1111yescharacteristic
638C42C22×C4×C1111yescharacteristic
639C42C2×D4×C1112yes—
640C42C2×D4×C1111yescharacteristic
641C42C2×D4×C1111yescharacteristic
642C11#2301711yescharacteristic, direct product factor, Sylow
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×C11×#4111yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8C4×D4×C1112yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4C4×D4×C1112yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—81no—
688C2×C4C4×D4×C1111yescharacteristic
689C2×C4C4×D4×C1111yescharacteristic
690C2×C4C4×D4×C1111yescharacteristic
691C2×C4C4×D4×C1111yescharacteristic
692C2×C4C23×C4×C1111yescharacteristic
693C2×C4C22×D4×C1111yescharacteristic
694C2×C4C22×D4×C1111yescharacteristic
695C2×C4C2×C11×#4111yescharacteristic
696C2×C4C11×H(5,𝔽2)11yescharacteristic
697C2×C4C11×2−1+411yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—21no—
705C8—21no—
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×C4×D4×C1111yescharacteristic
722C22C11×#54711yescharacteristic
723C22C11×#55311yescharacteristic
724C4—21no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—22no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4C2×C4×D4×C1111yescharacteristic
736C4C11×#52011yescharacteristic
737C4D42×C1111yescharacteristic
738C4C11×#54811yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2C11×#236111yescharacteristic
745C2C11×#295511yescharacteristic
746C2C11×#295711yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#3035C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#444C2semidirect
3. C2×C11×#443C2semidirect
4. C11×#2935C2semidirect
5. C11×#2906C2semidirect
6. C11×#1963C2semidirect
7. C11×#1950C2semidirect
8. C11×#1938C2semidirect
9. C11×#1937C2semidirect
10. C11×#1876C2semidirect
11. C11×#1876C2semidirect
12. C11×#1866C2semidirect
13. C11×#1866C2semidirect
14. C11×#1768C2semidirect
15. C11×#1759C2semidirect
24. C11×#464C4semidirect
25. C11×#464C4semidirect
26. C11×#463C4semidirect
27. C11×#463C4semidirect
28. C11×#462C4semidirect
29. C11×#461C4semidirect
30. C11×#460C4semidirect
31. C11×#459C4semidirect
149. C11×#104D4semidirect
168. #23017C11direct (N × H)
271. C2×#444C2×C11semidirect
272. C2×#443C2×C11semidirect
273. #2935C2×C11semidirect
274. #2906C2×C11semidirect
275. #1963C2×C11semidirect
276. #1950C2×C11semidirect
277. #1938C2×C11semidirect
278. #1937C2×C11semidirect
279. #1876C2×C11semidirect
280. #1876C2×C11semidirect
281. #1866C2×C11semidirect
282. #1866C2×C11semidirect
283. #1768C2×C11semidirect
284. #1759C2×C11semidirect
360. #464C4×C11semidirect
361. #464C4×C11semidirect
362. #463C4×C11semidirect
363. #463C4×C11semidirect
364. #462C4×C11semidirect
365. #461C4×C11semidirect
366. #460C4×C11semidirect
367. #459C4×C11semidirect
514. #104D4×C11semidirect
642. C11#23017direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30352
C2×C11×#4442
C2×C11×#4432
C11×#29352
C11×#29062
C11×#19632
C11×#19502
C11×#19382
C11×#19372
C11×#18762
C11×#18662
C11×#17682
C11×#17592
#2301711