Finite Group Databasebeta

← #14671313

Subgroups — #14671313

Order 2816.

702 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66900C211yesmaximal, characteristic, complemented
2C2×#10622180C212yesmaximal, complemented
3#13068540C211yesmaximal, characteristic, complemented
4#13066743C212yesmaximal, complemented
5C11×#2436C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C2×C11×#124C411yescharacteristic
8C2×C11×#124C2211yescharacteristic
9C2×C11×#121C411yescharacteristic
10C22×#4318—21no—
11C11×#393—21no—
12C11×#393—21no—
13C11×#391C411yescharacteristic
14C11×#391C2211yescharacteristic
15C11×#386—21no—
16C11×#386—21no—
17C4×C11×C22⋊C4C411yescharacteristic
18C2×#66900—21no—
19C2×#66900—24no—
20C2×#66900—21no—
21C2×#66900C2212yes—
22C2×#66900C2212yes—
23#10622820—21no—
24#10622180—24no—
25C22×Q8×C11—22no—
26C22×Q8×C11—22no—
27C22×Q8×C11—41no—
28C22×Q8×C11—41no—
29C22×Q8×C11—42no—
30C22×Q8×C11C2×C411yescharacteristic
31C22×Q8×C11D411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C11×#124—22no—
40C11×#124—22no—
41C11×#124—42no—
42C11×#121—41no—
43C11×#121—41no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×#4318—24no—
54C2×#4318—22no—
55C2×#4318—22no—
56C2×#4318—41no—
57C2×#4318—42no—
58C22×C11⋊C8—41no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#66900—24no—
65#66900—22no—
66#66900—22no—
67#66900—22no—
68#66900—42no—
69#66900D414yescomplemented
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13092—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11C22⋊C411yescharacteristic
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C2×Q8×C11—44no—
90C2×Q8×C11—44no—
91C2×Q8×C11C2×D412yes—
92C2×Q8×C11#4112yes—
93C2×D4×C11—22no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—44no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11C22⋊C411yescharacteristic
116C22×C4×C11C22⋊C411yescharacteristic
117C22×C4×C11C22⋊C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C11×C4⋊C4—41no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—41no—
129C42×C11—22no—
130C42×C11—41no—
131#4318—24no—
132#4318—44no—
133#4318—42no—
134#4318—42no—
135#4318—42no—
136C2×C11⋊C8—44no—
137C2×C11⋊C8—42no—
138C2×C11⋊C8—42no—
139C22×#101—111no—
140#2436D1111yescharacteristic
141C2×#355—112no—
142#1784—111no—
143#1394—112no—
144C23×C11—22no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11#9911yescharacteristic
154C23×C11#9911yescharacteristic
155C23×C11C2×C22⋊C411yescharacteristic
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—44no—
159Q8×C11—44no—
160Q8×C11—42no—
161Q8×C11—42no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11#9912yes—
196C2×C4×C11C4×D412yes—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12112yes—
199C2×C4×C11#12311yescharacteristic
200C11⋊C8—44no—
201C11⋊C8—82no—
202C23×Q8C2×D1111yescharacteristic
203C22×M16—221no—
204C2×#124Dic1111yescharacteristic
205C2×#124C2×D1111yescharacteristic
206C2×#121Dic1111yescharacteristic
207C2×#101—112no—
208C2×#101—112no—
209C2×#101—224no—
210C2×#101—221no—
211C2×#101—221no—
212#407—221no—
213#393—21no—
214#393—21no—
215#391Dic1111yescharacteristic
216#391C2×D1111yescharacteristic
217#386—21no—
218#386—21no—
219C4×C22⋊C4Dic1111yescharacteristic
220#355—224no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11#35512yescomplemented
236C22×C11#38611yescharacteristic
237C22×C11C2×#9911yescharacteristic
238C22×C11C2×#9911yescharacteristic
239C4×C11—22no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—22no—
243C4×C11—22no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11—81no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—41no—
252C22×Q8—41no—
253C22×Q8—42no—
254C22×Q8C2×Dic1111yescharacteristic
255C22×Q8C22⋊D1111yescharacteristic
256C22×Q8C22⋊D1111yescharacteristic
257C22×Q8C22×D1111yescharacteristic
258C22×D4—21no—
259C22×D4C2×Dic1111yescharacteristic
260C23×C4C2×Dic1111yescharacteristic
261C23×C4C22⋊D1111yescharacteristic
262C23×C4C22⋊D1111yescharacteristic
263C2×M16—224no—
264C2×M16—222no—
265C2×M16—222no—
266C2×M16—441no—
267C2×M16—442no—
268C22×C8—441no—
269#124—22no—
270#124—22no—
271#124—42no—
272#121—41no—
273#121—41no—
274C2×C4⋊C4C2×Dic1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42C2×Dic1111yescharacteristic
282C2×C42C2×Dic1111yescharacteristic
283#101—114no—
284#101—224no—
285#101—222no—
286#101—222no—
287#101—222no—
288#101—442no—
289C22⋊C8—441no—
290C22⋊C8—441no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—22no—
299C2×C11—41no—
300C2×C11—161no—
301C2×C11#189811yescharacteristic
302C2×C11C2×#35511yescharacteristic
303C2×C11#213311yescharacteristic
304C24—21no—
305C24C22⋊Dic1111yescharacteristic
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—22no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—44no—
319C2×Q8—44no—
320C2×Q8—44no—
321C2×Q8—44no—
322C2×Q8D4×D1112yes—
323C2×Q8#434112yes—
324C2×D4—22no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—44no—
328C2×D4—41no—
329C2×D4—41no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4C22⋊Dic1111yescharacteristic
347C22×C4C22⋊Dic1111yescharacteristic
348C22×C4C22⋊Dic1111yescharacteristic
349C22×C4C22×Dic1111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352M16—224no—
353M16—444no—
354M16—442no—
355M16—442no—
356M16—442no—
357C2×C8—444no—
358C2×C8—442no—
359C2×C8—442no—
360C4⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—42no—
368C42—22no—
369C42—41no—
370C11#1309211yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23#6689811yescharacteristic
381C23#6689811yescharacteristic
382C23C2×C22⋊Dic1111yescharacteristic
383Q8—42no—
384Q8—42no—
385Q8—44no—
386Q8—44no—
387Q8—42no—
388Q8—42no—
389D4—82no—
390D4—82no—
391D4—82no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4#6689812yes—
423C2×C4D4×Dic1112yes—
424C2×C4#6698811yescharacteristic
425C2×C4#6699011yescharacteristic
426C2×C4#6699212yes—
427C8—444no—
428C8—882no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—82no—
439C22—82no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22#1062218012yescomplemented
444C22C2×#6689811yescharacteristic
445C22C2×#6689811yescharacteristic
446C22#1062283311yescharacteristic
447C4—21no—
448C4—22no—
449C4—22no—
450C4—21no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—81no—
456C4—81no—
457C2—21no—
458C2—21no—
459C2—22no—
460C2—41no—
461C2—161no—
462C2#1306907011yescharacteristic
463C2C2×#1062218011yescharacteristic
464C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#2436C2
socleC22×C11C2×#99
prime radicalC2×C11×#121C4
cosocleC22×Q8×C11C23
hypercenter#2436D11
hypocenterC11#13092
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #2436

Complements

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

NH ≅ G/Ntype
1. C22×#66900C2semidirect
2. C2×#10622180C2semidirect
3. #13068540C2semidirect
4. #13066743C2semidirect
69. #66900D4semidirect
235. C22×C11#355semidirect
370. C11#13092semidirect
443. C22#10622180semidirect

Maximal subgroups

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

subgroupindex
C22×#669002
C2×#106221802
#130685402
#130667432
C11×#24362
#1309211