Finite Group Databasebeta

← C11×#21519 #14598712

Subgroups — C11×#21519 #14598712

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 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×#2932C211yesmaximal, characteristic, complemented
5C11×#2875C211yesmaximal, characteristic, complemented
6C11×#1980C211yesmaximal, characteristic, complemented
7C11×#1950C211yesmaximal, characteristic, complemented
8C11×#1929C211yesmaximal, characteristic, complemented
9C11×#1929C211yesmaximal, characteristic, complemented
10C11×#1876C211yesmaximal, characteristic, complemented
11C11×#1876C211yesmaximal, characteristic, complemented
12C11×#1806C211yesmaximal, characteristic, complemented
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1765C211yesmaximal, characteristic, complemented
15C11×#1764C211yesmaximal, 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×#435—21no—
35C11×#435—21no—
36C11×#435—21no—
37C11×#435—21no—
38C2×C11×#108C2211yescharacteristic
39C2×C11×#108C2211yescharacteristic
40C11×#423C2211yescharacteristic
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#104C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic
47C2×C11×#104C2211yescharacteristic
48C11×#416C2211yescharacteristic
49C11×#416C2211yescharacteristic
50C11×#408C2211yescharacteristic
51C11×#408C2211yescharacteristic
52C11×#405—21no—
53C11×#405—21no—
54C11×#405C2211yescharacteristic
55C11×#405C2211yescharacteristic
56C4×C11×M16—21no—
57C4×C11×M16C2211yescharacteristic
58C2×C11×#97—21no—
59C2×C11×#97C2211yescharacteristic
60C2×C11×#97C2211yescharacteristic
61C2×C4×C8×C11C2211yescharacteristic
62C4×C11×C4⋊C4C2211yescharacteristic
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—22no—
89C11×#131—22no—
90C11×#131—22no—
91C11×#131D414yescomplemented
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×C11×C4⋊C4—21no—
125C2×C42×C11—21no—
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C11×#108—22no—
130C11×#108—22no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2×C411yescharacteristic
134C11×C4⋊C8C2×C411yescharacteristic
135C11×C4⋊C8C2×C411yescharacteristic
136C11×C4⋊C8C2×C411yescharacteristic
137C11×#104—22no—
138C11×#104—22no—
139C11×#104—22no—
140C11×#104—22no—
141C11×#104—22no—
142C11×#104—22no—
143C11×#103C2×C411yescharacteristic
144C11×#103C2×C411yescharacteristic
145C11×#103C2×C411yescharacteristic
146C11×#103C2×C411yescharacteristic
147C11×#102C2×C411yescharacteristic
148C11×#102C2×C411yescharacteristic
149C11×#102C2×C411yescharacteristic
150C11×#102C2×C411yescharacteristic
151C11×C22⋊C8—21no—
152C11×C22⋊C8—21no—
153C11×C22⋊C8—21no—
154C11×C22⋊C8—21no—
155C11×#97—21no—
156C11×#97—21no—
157C11×#97—22no—
158C11×#97—21no—
159C11×#97D411yescharacteristic
160C11×#97D411yescharacteristic
161C11×#97D411yescharacteristic
162C11×#97D411yescharacteristic
163C4×C8×C11—22no—
164C4×C8×C11—21no—
165C4×C8×C11—21no—
166C4×C8×C11—21no—
167C11×#95—21no—
168#21519C1111yesmaximal, 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—24no—
211C11×M16—24no—
212C11×M16—21no—
213C11×M16—21no—
214C11×M16—21no—
215C11×M16—21no—
216C11×M16—21no—
217C11×M16—21no—
218C11×M16—42no—
219C11×M16—42no—
220C11×M16C2×D412yes—
221C11×M16#4112yes—
222C2×C8×C11—24no—
223C2×C8×C11—24no—
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×C11C22×C411yescharacteristic
237C2×C8×C11C22×C411yescharacteristic
238C2×C8×C11C22×C411yescharacteristic
239C2×C8×C11C22×C411yescharacteristic
240C2×C8×C11C2×D412yes—
241C2×C8×C11C2×D411yescharacteristic
242C2×C8×C11C2×D411yescharacteristic
243C2×C8×C11C2×D411yescharacteristic
244C2×C8×C11C2×D411yescharacteristic
245C2×C8×C11#4112yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—42no—
251C11×C4⋊C4C22×C411yescharacteristic
252C11×C4⋊C4C22×C411yescharacteristic
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—21no—
264C42×C11—21no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11C22×C411yescharacteristic
268C42×C11C22×C411yescharacteristic
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271#3035C2×C1111yescharacteristic
272C2×#444C2×C1111yescharacteristic, complemented
273C2×#443C2×C1111yescharacteristic, complemented
274#2932C2×C1111yescharacteristic, complemented
275#2875C2×C1111yescharacteristic, complemented
276#1980C2×C1111yescharacteristic, complemented
277#1950C2×C1111yescharacteristic, complemented
278#1929C2×C1111yescharacteristic, complemented
279#1929C2×C1111yescharacteristic, complemented
280#1876C2×C1111yescharacteristic, complemented
281#1876C2×C1111yescharacteristic, complemented
282#1806C2×C1111yescharacteristic, complemented
283#1771C2×C1111yescharacteristic, complemented
284#1765C2×C1111yescharacteristic, complemented
285#1764C2×C1111yescharacteristic, complemented
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11C2×#4111yescharacteristic
290Q8×C11—21no—
291Q8×C11—21no—
292Q8×C11—21no—
293Q8×C11—21no—
294Q8×C11—21no—
295Q8×C11C4×D412yes—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—21no—
299D4×C11—21no—
300D4×C11—21no—
301D4×C11—21no—
302D4×C11—21no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—81no—
308D4×C11—81no—
309D4×C11C4×D412yes—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
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×C11—81no—
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11C23×C411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C8×C11—21no—
342C8×C11—21no—
343C8×C11—21no—
344C8×C11—21no—
345C8×C11—22no—
346C8×C11—21no—
347C8×C11—22no—
348C8×C11—21no—
349C8×C11—41no—
350C8×C11—41no—
351C8×C11#12112yes—
352C8×C11#12112yes—
353C2×#135C22×C1111yescharacteristic
354C2×#135C22×C1111yescharacteristic
355C2×#131C22×C1111yescharacteristic
356C2×#131C22×C1111yescharacteristic
357C2×#131C22×C1111yescharacteristic
358C2×#131C22×C1111yescharacteristic
359#532C22×C1111yescharacteristic
360C4×#41C22×C1111yescharacteristic
361#464C4×C1111yescharacteristic, complemented
362#464C4×C1111yescharacteristic, complemented
363#463C4×C1111yescharacteristic, complemented
364#463C4×C1111yescharacteristic, complemented
365#462C4×C1111yescharacteristic, complemented
366#461C4×C1111yescharacteristic, complemented
367#460C4×C1111yescharacteristic, complemented
368#459C4×C1111yescharacteristic, complemented
369#444—24no—
370#443—24no—
371#435—21no—
372#435—21no—
373#435—21no—
374#435—21no—
375C2×#108C22×C1111yescharacteristic
376C2×#108C22×C1111yescharacteristic
377#423C22×C1111yescharacteristic
378C2×C4⋊C8C22×C1111yescharacteristic
379C2×#104C22×C1111yescharacteristic
380C2×#104C22×C1111yescharacteristic
381C2×#104C22×C1111yescharacteristic
382C2×#104C22×C1111yescharacteristic
383C2×#104C22×C1111yescharacteristic
384C2×#104C22×C1111yescharacteristic
385#416C22×C1111yescharacteristic
386#416C22×C1111yescharacteristic
387#408C22×C1111yescharacteristic
388#408C22×C1111yescharacteristic
389#405—21no—
390#405—21no—
391#405C22×C1111yescharacteristic
392#405C22×C1111yescharacteristic
393C4×M16—21no—
394C4×M16C22×C1111yescharacteristic
395C2×#97—21no—
396C2×#97C22×C1111yescharacteristic
397C2×#97C22×C1111yescharacteristic
398C2×C4×C8C22×C1111yescharacteristic
399C4×C4⋊C4C22×C1111yescharacteristic
400#341C22×C1111yescharacteristic
401#341C22×C1111yescharacteristic
402#339C22×C1111yescharacteristic
403#339C22×C1111yescharacteristic
404#336C22×C1111yescharacteristic
405#336C22×C1111yescharacteristic
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—22no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11C2×C4×D411yescharacteristic
418C22×C11#52911yescharacteristic
419C22×C11#53211yescharacteristic
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—22no—
425C4×C11—42no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—81no—
431C4×C11C2×C4×D411yescharacteristic
432C4×C11C4×#4111yescharacteristic
433C4×C11C2×#12111yescharacteristic
434C4×C11#52511yescharacteristic
435C2×#41C23×C1111yescharacteristic
436C2×#41C23×C1111yescharacteristic
437C2×#41C23×C1111yescharacteristic
438#135—22no—
439#135—22no—
440#135—22no—
441#135—22no—
442C2×Q16C2×C4×C1111yescharacteristic
443C2×Q16C2×C4×C1111yescharacteristic
444C2×SD16C2×C4×C1111yescharacteristic
445C2×SD16C2×C4×C1111yescharacteristic
446C2×SD16C2×C4×C1111yescharacteristic
447C2×SD16C2×C4×C1111yescharacteristic
448C2×D8C2×C4×C1111yescharacteristic
449C2×D8C2×C4×C1111yescharacteristic
450#131—22no—
451#131—22no—
452#131—22no—
453#131—22no—
454#131—22no—
455#131—22no—
456#131—22no—
457#131D4×C1114yescomplemented
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16C23×C1111yescharacteristic
463C2×M16C23×C1111yescharacteristic
464C2×M16C23×C1111yescharacteristic
465C2×M16C23×C1111yescharacteristic
466C22×C8—21no—
467C22×C8—21no—
468C22×C8—21no—
469C22×C8—21no—
470C22×C8C23×C1111yescharacteristic
471C22×C8C23×C1111yescharacteristic
472C22×C8C23×C1111yescharacteristic
473C22×C8C23×C1111yescharacteristic
474C4⋊Q8C2×C4×C1111yescharacteristic
475#127C2×C4×C1111yescharacteristic
476#124C2×C4×C1111yescharacteristic
477#124C2×C4×C1111yescharacteristic
478#121—21no—
479#121—21no—
480C4×Q8C2×C4×C1111yescharacteristic
481C4×Q8C2×C4×C1111yescharacteristic
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4C2×C4×C1111yescharacteristic
487C4×D4C2×C4×C1111yescharacteristic
488#117—21no—
489#117C23×C1111yescharacteristic
490C2×C4⋊C4—21no—
491C2×C42—21no—
492C2×C42C23×C1111yescharacteristic
493C2×C42C23×C1111yescharacteristic
494C2×C42C23×C1111yescharacteristic
495#108—22no—
496#108—22no—
497C4⋊C8—21no—
498C4⋊C8—21no—
499C4⋊C8C2×C4×C1111yescharacteristic
500C4⋊C8C2×C4×C1111yescharacteristic
501C4⋊C8C2×C4×C1111yescharacteristic
502C4⋊C8C2×C4×C1111yescharacteristic
503#104—22no—
504#104—22no—
505#104—22no—
506#104—22no—
507#104—22no—
508#104—22no—
509#103C2×C4×C1111yescharacteristic
510#103C2×C4×C1111yescharacteristic
511#103C2×C4×C1111yescharacteristic
512#103C2×C4×C1111yescharacteristic
513#102C2×C4×C1111yescharacteristic
514#102C2×C4×C1111yescharacteristic
515#102C2×C4×C1111yescharacteristic
516#102C2×C4×C1111yescharacteristic
517C22⋊C8—21no—
518C22⋊C8—21no—
519C22⋊C8—21no—
520C22⋊C8—21no—
521#97—21no—
522#97—21no—
523#97—22no—
524#97—21no—
525#97D4×C1111yescharacteristic
526#97D4×C1111yescharacteristic
527#97D4×C1111yescharacteristic
528#97D4×C1111yescharacteristic
529C4×C8—22no—
530C4×C8—21no—
531C4×C8—21no—
532C4×C8—21no—
533#95—21no—
534C2×C11—21no—
535C2×C11—21no—
536C2×C11—42no—
537C2×C11—81no—
538C2×C11—81no—
539C2×C11C4×#12111yescharacteristic
540C2×C11#295611yescharacteristic
541C2×C11#295711yescharacteristic
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#41—21no—
552#41C2×D4×C1112yes—
553#41C11×#4112yes—
554C2×Q8C22×C4×C1111yescharacteristic
555C2×Q8C22×C4×C1111yescharacteristic
556C2×Q8C22×C4×C1111yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×C4×C1111yescharacteristic
563C2×D4C22×C4×C1111yescharacteristic
564C2×D4C22×C4×C1111yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4C11×#4111yescharacteristic
573C22×C4C11×#4111yescharacteristic
574C22×C4C24×C1111yescharacteristic
575Q16—22no—
576Q16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581D8—22no—
582D8—22no—
583M16—24no—
584M16—21no—
585M16—21no—
586M16—24no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—21no—
591M16—42no—
592M16—42no—
593M16C2×D4×C1112yes—
594M16C11×#4112yes—
595C2×C8—24no—
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—24no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8C22×C4×C1111yescharacteristic
610C2×C8C22×C4×C1111yescharacteristic
611C2×C8C22×C4×C1111yescharacteristic
612C2×C8C22×C4×C1111yescharacteristic
613C2×C8C2×D4×C1111yescharacteristic
614C2×C8C2×D4×C1111yescharacteristic
615C2×C8C2×D4×C1112yes—
616C2×C8C2×D4×C1111yescharacteristic
617C2×C8C2×D4×C1111yescharacteristic
618C2×C8C11×#4112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4C22×C4×C1111yescharacteristic
625C4⋊C4C22×C4×C1111yescharacteristic
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42C22×C4×C1111yescharacteristic
641C42C22×C4×C1111yescharacteristic
642C42C2×D4×C1111yescharacteristic
643C42C2×D4×C1111yescharacteristic
644C11#2151911yescharacteristic, direct product factor, Sylow
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×C11×#4111yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8C4×D4×C1112yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4C4×D4×C1112yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
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—41no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4C4×D4×C1111yescharacteristic
691C2×C4C4×D4×C1111yescharacteristic
692C2×C4C4×D4×C1111yescharacteristic
693C2×C4C4×D4×C1111yescharacteristic
694C2×C4C23×C4×C1111yescharacteristic
695C2×C4C22×D4×C1111yescharacteristic
696C2×C4C22×D4×C1111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C2×C11×#4111yescharacteristic
699C2×C4C2×C11×#4111yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—22no—
705C8—21no—
706C8—22no—
707C8—21no—
708C8—41no—
709C8—41no—
710C8C11×#12112yes—
711C8C11×#12112yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×C4×D4×C1111yescharacteristic
724C22C11×#52911yescharacteristic
725C22C11×#53211yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—22no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4C2×C4×D4×C1111yescharacteristic
738C4C4×C11×#4111yescharacteristic
739C4C2×C11×#12111yescharacteristic
740C4C11×#52511yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2C4×C11×#12111yescharacteristic
747C2C11×#295611yescharacteristic
748C2C11×#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×#97 ◁ 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×#2932C2semidirect
5. C11×#2875C2semidirect
6. C11×#1980C2semidirect
7. C11×#1950C2semidirect
8. C11×#1929C2semidirect
9. C11×#1929C2semidirect
10. C11×#1876C2semidirect
11. C11×#1876C2semidirect
12. C11×#1806C2semidirect
13. C11×#1771C2semidirect
14. C11×#1765C2semidirect
15. C11×#1764C2semidirect
24. C11×#464C4semidirect
25. C11×#464C4semidirect
26. C11×#463C4semidirect
27. C11×#463C4semidirect
28. C11×#462C4semidirect
29. C11×#461C4semidirect
30. C11×#460C4semidirect
31. C11×#459C4semidirect
91. C11×#131D4semidirect
168. #21519C11direct (N × H)
272. C2×#444C2×C11semidirect
273. C2×#443C2×C11semidirect
274. #2932C2×C11semidirect
275. #2875C2×C11semidirect
276. #1980C2×C11semidirect
277. #1950C2×C11semidirect
278. #1929C2×C11semidirect
279. #1929C2×C11semidirect
280. #1876C2×C11semidirect
281. #1876C2×C11semidirect
282. #1806C2×C11semidirect
283. #1771C2×C11semidirect
284. #1765C2×C11semidirect
285. #1764C2×C11semidirect
361. #464C4×C11semidirect
362. #464C4×C11semidirect
363. #463C4×C11semidirect
364. #463C4×C11semidirect
365. #462C4×C11semidirect
366. #461C4×C11semidirect
367. #460C4×C11semidirect
368. #459C4×C11semidirect
457. #131D4×C11semidirect
644. C11#21519direct (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×#29322
C11×#28752
C11×#19802
C11×#19502
C11×#19292
C11×#18762
C11×#18062
C11×#17712
C11×#17652
C11×#17642
#2151911