Finite Group Databasebeta

← C11×#11107 #14588300

Subgroups — C11×#11107 #14588300

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#107C211yesmaximal, characteristic, complemented
2C2×C11×#417C212yesmaximal
3C2×C11×#408C211yesmaximal, characteristic
4C2×C11×#343C212yesmaximal, complemented
5C2×C11×#341C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C22×C11×M16C2211yescharacteristic
8C22×C11×M16C2212yes—
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2212yes—
11C2×C11×#107—22no—
12C2×C11×#107—24no—
13C11×#417—24no—
14C11×#417—24no—
15C2×C11×#103—22no—
16C2×C11×#102—22no—
17C11×#408—22no—
18C11×#408C414yescomplemented
19C2×C11×C22⋊C8—22no—
20C11×#343—24no—
21C11×#341—22no—
22C2×C11×#41—21no—
23C2×C11×#41—21no—
24C2×C11×#41—22no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41C2×C412yes—
29C2×C11×#41Q812yes—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11—22no—
35C23×C4×C11C2311yescharacteristic
36C2×C11×M16—21no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16—22no—
41C2×C11×M16—22no—
42C2×C11×M16—22no—
43C2×C11×M16—22no—
44C2×C11×M16C2×C412yes—
45C2×C11×M16D414yes—
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—21no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C412yes—
51C22×C8×C11D412yes—
52C22×C8×C11D412yes—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D414yes—
59C11×#107—28no—
60C11×#103—28no—
61C11×#102—28no—
62C11×C22⋊C8—28no—
63#11107C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11#4111yescharacteristic
66C11×#41—24no—
67C11×#41—24no—
68C11×#41—24no—
69C11×#41—24no—
70C11×#41—42no—
71C11×#41—42no—
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11C4⋊C412yes—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11C4⋊C412yes—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—84no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×Q811yescharacteristic
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4111yescharacteristic
107C11×M16—24no—
108C11×M16—24no—
109C11×M16—24no—
110C11×M16—42no—
111C11×M16—42no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—24no—
115C2×C8×C11—22no—
116C2×C8×C11—24no—
117C2×C8×C11—24no—
118C2×C8×C11—22no—
119C2×C8×C11—42no—
120C2×C8×C11—42no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11C22⋊C414yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C22×#107C2×C1111yescharacteristic, complemented
129C2×#417C2×C1112yes—
130C2×#408C2×C1111yescharacteristic
131C2×#343C2×C1112yescomplemented
132C2×#341C2×C1111yescharacteristic, complemented
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11#11711yescharacteristic
141C23×C11#12112yes—
142C23×C11#12111yescharacteristic
143C23×C11C22⋊Q811yescharacteristic
144C23×C11#12612yes—
145Q8×C11—24no—
146Q8×C11—42no—
147D4×C11—24no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—42no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—44no—
159C2×C4×C11—84no—
160C2×C4×C11—84no—
161C2×C4×C11—84no—
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C2×C4⋊C411yescharacteristic
164C2×C4×C11C4×D412yes—
165C2×C4×C11C4×D412yes—
166C2×C4×C11#12012yes—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12112yes—
169C2×C4×C11#12112yes—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11C22⋊Q812yes—
172C2×C4×C11C22⋊Q812yes—
173C2×C4×C11C22⋊Q811yescharacteristic
174C2×C4×C11#12312yes—
175C2×C4×C11#12311yescharacteristic
176C2×C4×C11#12312yes—
177C2×C4×C11#12411yescharacteristic
178C2×C4×C11#12412yes—
179C2×C4×C11#12711yescharacteristic
180C8×C11—24no—
181C8×C11—42no—
182C8×C11—44no—
183C22×#41C22×C1111yescharacteristic
184C22×M16C22×C1111yescharacteristic
185C22×M16C22×C1112yes—
186C23×C8C22×C1111yescharacteristic
187C22×C4⋊C4C22×C1112yes—
188C2×#107—22no—
189C2×#107—24no—
190#417—24no—
191#417—24no—
192C2×#103—22no—
193C2×#102—22no—
194#408—22no—
195#408C4×C1114yescomplemented
196C2×C22⋊C8—22no—
197#343—24no—
198#341—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—24no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—44no—
205C22×C11—42no—
206C22×C11—82no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#38011yescharacteristic
210C22×C11#38812yes—
211C22×C11#39211yescharacteristic
212C22×C11#39612yes—
213C22×C11#39711yescharacteristic
214C22×C11#47212yes—
215C22×C11#47312yes—
216C4×C11—42no—
217C4×C11—84no—
218C4×C11#38512yes—
219C4×C11#38611yescharacteristic
220C4×C11#39011yescharacteristic
221C4×C11#39311yescharacteristic
222C4×C11#39412yes—
223C4×C11#39911yescharacteristic
224C2×#41—21no—
225C2×#41—21no—
226C2×#41—22no—
227C2×#41—22no—
228C2×#41—22no—
229C2×#41—22no—
230C2×#41C2×C4×C1112yes—
231C2×#41Q8×C1112yes—
232C22×Q8D4×C1111yescharacteristic
233C22×D4—21no—
234C22×D4D4×C1111yescharacteristic
235C23×C4—21no—
236C23×C4—22no—
237C23×C4C23×C1111yescharacteristic
238C2×M16—21no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16C2×C4×C1112yes—
247C2×M16D4×C1114yes—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—21no—
251C22×C8—22no—
252C22×C8C2×C4×C1112yes—
253C22×C8D4×C1112yes—
254C22×C8D4×C1112yes—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4D4×C1114yes—
261#107—28no—
262#103—28no—
263#102—28no—
264C22⋊C8—28no—
265C2×C11—22no—
266C2×C11—22no—
267C2×C11—82no—
268C2×C11#143911yescharacteristic
269C2×C11#181612yes—
270C2×C11#201811yescharacteristic
271C2×C11#202011yescharacteristic
272C2×C11#207812yes—
273C24—21no—
274C24C11×#4111yescharacteristic
275#41—24no—
276#41—24no—
277#41—24no—
278#41—24no—
279#41—42no—
280#41—42no—
281#41—42no—
282#41—42no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8C11×C4⋊C412yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4C11×C4⋊C412yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—84no—
306C22×C4C22×C4×C1111yescharacteristic
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1112yes—
312C22×C4C2×Q8×C1111yescharacteristic
313C22×C4C11×#4112yes—
314C22×C4C11×#4112yes—
315C22×C4C11×#4111yescharacteristic
316M16—24no—
317M16—24no—
318M16—24no—
319M16—42no—
320M16—42no—
321M16—42no—
322C2×C8—24no—
323C2×C8—22no—
324C2×C8—24no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—24no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8C11×C22⋊C414yes—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C11#1110711yescharacteristic, direct product factor, Sylow
338C23—22no—
339C23—22no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—42no—
344C23—42no—
345C23C11×#11711yescharacteristic
346C23C11×#12112yes—
347C23C11×#12111yescharacteristic
348C23C11×C22⋊Q811yescharacteristic
349C23C11×#12612yes—
350Q8—24no—
351Q8—42no—
352D4—24no—
353D4—44no—
354D4—44no—
355D4—42no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—84no—
365C2×C4—84no—
366C2×C4—84no—
367C2×C4C2×C11×C22⋊C411yescharacteristic
368C2×C4C2×C11×C4⋊C411yescharacteristic
369C2×C4C4×D4×C1112yes—
370C2×C4C4×D4×C1112yes—
371C2×C4C11×#12012yes—
372C2×C4C11×#12011yescharacteristic
373C2×C4C11×#12112yes—
374C2×C4C11×#12112yes—
375C2×C4C11×#12111yescharacteristic
376C2×C4C11×C22⋊Q812yes—
377C2×C4C11×C22⋊Q812yes—
378C2×C4C11×C22⋊Q811yescharacteristic
379C2×C4C11×#12312yes—
380C2×C4C11×#12311yescharacteristic
381C2×C4C11×#12312yes—
382C2×C4C11×#12411yescharacteristic
383C2×C4C11×#12412yes—
384C2×C4C11×#12711yescharacteristic
385C8—24no—
386C8—42no—
387C8—44no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—24no—
393C22—42no—
394C22—44no—
395C22—81no—
396C22—81no—
397C22—82no—
398C22C11×#38011yescharacteristic
399C22C11×#38812yes—
400C22C11×#39211yescharacteristic
401C22C11×#39612yes—
402C22C11×#39711yescharacteristic
403C22C11×#47212yes—
404C22C11×#47312yes—
405C4—42no—
406C4—84no—
407C4C11×#38512yes—
408C4C11×#38611yescharacteristic
409C4C11×#39011yescharacteristic
410C4C11×#39311yescharacteristic
411C4C11×#39412yes—
412C4C11×#39911yescharacteristic
413C2—22no—
414C2—22no—
415C2—82no—
416C2C11×#143911yescharacteristic
417C2C11×#181612yes—
418C2C11×#201811yescharacteristic
419C2C11×#202011yescharacteristic
420C2C11×#207812yes—
subgroupG/H
center, socleC23×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#107C2semidirect
4. C2×C11×#343C2semidirect
5. C2×C11×#341C2semidirect
18. C11×#408C4semidirect
63. #11107C11direct (N × H)
128. C22×#107C2×C11semidirect
131. C2×#343C2×C11semidirect
132. C2×#341C2×C11semidirect
195. #408C4×C11semidirect
337. C11#11107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1072
C2×C11×#4172
C2×C11×#4082
C2×C11×#3432
C2×C11×#3412
#1110711