Finite Group Databasebeta

← #14671323

Subgroups — #14671323

Order 2816.

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

normal subgroups only

This group has 676 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
2C2×#10622186C212yesmaximal, complemented
3#13068540C211yesmaximal, characteristic
4#13066743C212yesmaximal, complemented
5C11×#2434C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C2×C11×C4⋊Q8C411yescharacteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C411yescharacteristic
10C22×#4318—21no—
11C11×#395—21no—
12C11×#395—21no—
13C11×#391C411yescharacteristic
14C11×#391C2211yescharacteristic
15C11×#385—21no—
16C11×#385—21no—
17C4×C11×C22⋊C4C411yescharacteristic
18C2×#66900—21no—
19C2×#66900—24no—
20C2×#66900—21no—
21C2×#66900C2212yes—
22C2×#66900C2212yes—
23#10622820—21no—
24#10622186—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×C11C2×C411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11D411yescharacteristic
34C22×Q8×C11C2311yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—42no—
41C11×C22⋊Q8—41no—
42C11×C22⋊Q8—41no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2×C411yescharacteristic
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#66900D414yes—
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13094—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—22no—
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×C11—41no—
92C2×Q8×C11—41no—
93C2×Q8×C11C2×D412yes—
94C2×Q8×C11#4112yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11C22⋊C411yescharacteristic
113C22×C4×C11C22⋊C411yescharacteristic
114C22×C4×C11C22⋊C411yescharacteristic
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C11×C4⋊C4—42no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11—22no—
129C42×C11—41no—
130#4318—24no—
131#4318—44no—
132#4318—42no—
133#4318—42no—
134#4318—42no—
135C2×C11⋊C8—44no—
136C2×C11⋊C8—42no—
137C2×C11⋊C8—42no—
138C22×#101—111no—
139#2434D1111yescharacteristic
140C2×#356—112no—
141#1784—111no—
142#1394—112no—
143C23×C11—22no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11#9911yescharacteristic
148C23×C11#9911yescharacteristic
149C23×C11C2×C22⋊C411yescharacteristic
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—44no—
153Q8×C11—44no—
154Q8×C11—42no—
155Q8×C11—42no—
156Q8×C11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
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—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11#9912yes—
191C2×C4×C11C4×D412yes—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12112yes—
194C2×C4×C11#12311yescharacteristic
195C11⋊C8—44no—
196C11⋊C8—82no—
197C23×Q8C2×D1111yescharacteristic
198C22×M16—221no—
199C2×C4⋊Q8Dic1111yescharacteristic
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×C22⋊Q8Dic1111yescharacteristic
202C2×#101—112no—
203C2×#101—112no—
204C2×#101—224no—
205C2×#101—221no—
206C2×#101—221no—
207#407—221no—
208#395—21no—
209#395—21no—
210#391Dic1111yescharacteristic
211#391C2×D1111yescharacteristic
212#385—21no—
213#385—21no—
214C4×C22⋊C4Dic1111yescharacteristic
215#356—224no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—42no—
224C22×C11—42no—
225C22×C11#35612yescomplemented
226C22×C11#38611yescharacteristic
227C22×C11C2×#9911yescharacteristic
228C22×C11C2×#9911yescharacteristic
229C4×C11—22no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—81no—
239C4×C11—81no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—41no—
243C22×Q8—41no—
244C22×Q8—42no—
245C22×Q8C2×Dic1111yescharacteristic
246C22×Q8C2×Dic1111yescharacteristic
247C22×Q8C22⋊D1111yescharacteristic
248C22×Q8C22⋊D1111yescharacteristic
249C22×Q8C22×D1111yescharacteristic
250C23×C4C2×Dic1111yescharacteristic
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22⋊D1111yescharacteristic
253C2×M16—224no—
254C2×M16—222no—
255C2×M16—222no—
256C2×M16—441no—
257C2×M16—442no—
258C22×C8—441no—
259C4⋊Q8—22no—
260C4⋊Q8—22no—
261C4⋊Q8—42no—
262C22⋊Q8—41no—
263C22⋊Q8—41no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C2×Dic1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42C2×Dic1111yescharacteristic
273C2×C42C2×Dic1111yescharacteristic
274#101—114no—
275#101—224no—
276#101—222no—
277#101—222no—
278#101—222no—
279#101—442no—
280C22⋊C8—441no—
281C22⋊C8—441no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—22no—
290C2×C11—41no—
291C2×C11#189811yescharacteristic
292C2×C11C2×#35611yescharacteristic
293C2×C11#213311yescharacteristic
294C24C22⋊Dic1111yescharacteristic
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—44no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8D4×D1112yes—
315C2×Q8#434112yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C22⋊Dic1111yescharacteristic
334C22×C4C22⋊Dic1111yescharacteristic
335C22×C4C22⋊Dic1111yescharacteristic
336C22×C4C22×Dic1111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339M16—224no—
340M16—444no—
341M16—442no—
342M16—442no—
343M16—442no—
344C2×C8—444no—
345C2×C8—442no—
346C2×C8—442no—
347C4⋊C4—41no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—42no—
354C22⋊C4—24no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C42—22no—
358C42—41no—
359C11#1309411yescharacteristic, complemented, Sylow
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23#6689811yescharacteristic
365C23#6689811yescharacteristic
366C23C2×C22⋊Dic1111yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—44no—
370Q8—44no—
371Q8—42no—
372Q8—42no—
373Q8—82no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4#6689812yes—
408C2×C4D4×Dic1112yes—
409C2×C4#6698811yescharacteristic
410C2×C4#6699011yescharacteristic
411C2×C4#6699212yes—
412C8—444no—
413C8—882no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22#1062218612yescomplemented
424C22C2×#6689811yescharacteristic
425C22C2×#6689811yescharacteristic
426C22#1062283311yescharacteristic
427C4—21no—
428C4—22no—
429C4—22no—
430C4—21no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—41no—
435C4—41no—
436C4—81no—
437C4—81no—
438C2—21no—
439C2—21no—
440C2—22no—
441C2—41no—
442C2#1306907011yescharacteristic
443C2C2×#1062218611yescharacteristic
444C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#2434C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC22×Q8×C11C23
hypercenter#2434D11
hypocenterC11#13094
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #2434

Complements

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

NH ≅ G/Ntype
2. C2×#10622186C2semidirect
4. #13066743C2semidirect
225. C22×C11#356semidirect
359. C11#13094semidirect
423. C22#10622186semidirect

Maximal subgroups

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

subgroupindex
C22×#669002
C2×#106221862
#130685402
#130667432
C11×#24342
#1309411