Finite Group Databasebeta

← #14671278

Subgroups — #14671278

Order 2816.

724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#10622853C211yesmaximal, characteristic
2C2×#10622177C212yesmaximal, complemented
3#13068544C211yesmaximal, characteristic
4#13066734C212yesmaximal, complemented
5C11×#2406C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×C11×#123C411yescharacteristic, complemented
8C2×C11×#123C2211yescharacteristic
9C22×C11×C4⋊C4C411yescharacteristic, complemented
10C2×#66979—21no—
11C11×#395—21no—
12C11×#394—21no—
13C11×#386C411yescharacteristic, complemented
14C11×#386C2211yescharacteristic
15C11×#385—21no—
16C11×#385—21no—
17C11×#381C411yescharacteristic, complemented
18#10622853—24no—
19C2×#66900—21no—
20C2×#66898—21no—
21C2×#66898C2212yes—
22C2×#66897C2212yes—
23#10622820—21no—
24#10622177—24no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—41no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C11×#123—22no—
40C11×#123—22no—
41C11×#123—42no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2×C411yescharacteristic
54C2×C22⋊Dic11—22no—
55#66979—24no—
56#66979—42no—
57C2×C4⋊Dic11—41no—
58C2×C4×Dic11—41no—
59C2×#4318—22no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#66900—42no—
65#66898—24no—
66#66898—22no—
67#66898D414yes—
68#66897—22no—
69#66897—22no—
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13085—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C24×C11C22×C411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C11×#41—44no—
77C11×#41—44no—
78C11×#41—44no—
79C11×#41—44no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—41no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11C2×D412yes—
93C2×D4×C11#4112yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—42no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11C22⋊C411yescharacteristic
117C22×C4×C11C22⋊C411yescharacteristic
118C22×C4×C11C22⋊C411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×Dic11—42no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C22⋊Dic11—24no—
134C22⋊Dic11—42no—
135C4⋊Dic11—44no—
136C4×Dic11—44no—
137#4318—42no—
138#4318—42no—
139C2×C11⋊C8—42no—
140C2×#410—111no—
141#2406D1111yescharacteristic
142C2×#352—112no—
143#1785—111no—
144#1390—112no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11C2×C22⋊C411yescharacteristic
159C23×C11C4×D412yes—
160C23×C11#12011yescharacteristic
161C23×C11#12311yescharacteristic
162Q8×C11—44no—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—44no—
166D4×C11—42no—
167D4×C11—42no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
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—22no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—82no—
200C2×C4×C11#9911yescharacteristic
201C2×C4×C11#9911yescharacteristic
202C2×C4×C11#9912yes—
203C2×C4×C11#12112yes—
204C2×Dic11—44no—
205C2×Dic11—82no—
206C2×Dic11—82no—
207C11⋊C8—82no—
208C22×#41C2×D1111yescharacteristic
209C2×#123Dic1111yescharacteristic, complemented
210C2×#123C2×D1111yescharacteristic
211C2×#117—221no—
212C22×C4⋊C4Dic1111yescharacteristic, complemented
213C2×#101—221no—
214C2×#100—112no—
215#410—224no—
216C2×#99—112no—
217C2×#99—221no—
218#407—221no—
219#395—21no—
220#394—21no—
221#386Dic1111yescharacteristic, complemented
222#386C2×D1111yescharacteristic
223#385—21no—
224#385—21no—
225#381Dic1111yescharacteristic, complemented
226#352—224no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—42no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#38611yescharacteristic
247C22×C11C2×#9911yescharacteristic
248C22×C11C2×#9911yescharacteristic
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—42no—
254C4×C11—41no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11—81no—
258Dic11—84no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—41no—
262C2×#41—41no—
263C2×#41—42no—
264C22×Q8C22⋊D1111yescharacteristic
265C22×D4C2×Dic1111yescharacteristic
266C22×D4C22⋊D1111yescharacteristic
267C22×D4C22×D1111yescharacteristic
268C23×C4C2×Dic1111yescharacteristic
269C23×C4C2×Dic1111yescharacteristic
270C23×C4C2×Dic1111yescharacteristic
271C23×C4C22⋊D1111yescharacteristic
272C23×C4C22⋊D1111yescharacteristic
273C2×M16—222no—
274#123—22no—
275#123—22no—
276#123—42no—
277#117—224no—
278#117—442no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—441no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4C2×Dic1111yescharacteristic
292C2×C22⋊C4C2×Dic1111yescharacteristic
293C2×C42—441no—
294#101—442no—
295#100—222no—
296#100—222no—
297#99—114no—
298#99—224no—
299#99—222no—
300C22⋊C8—441no—
301C22⋊C8—441no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306C2×C11—21no—
307C2×C11—21no—
308C2×C11—41no—
309C2×C11—42no—
310C2×C11—41no—
311C2×C11—81no—
312C2×C11#189811yescharacteristic
313C2×C11#212011yescharacteristic
314C2×C11#212311yescharacteristic
315C24C22⋊Dic1111yescharacteristic
316C24C22×Dic1111yescharacteristic
317C24C2×C22⋊D1111yescharacteristic
318#41—44no—
319#41—44no—
320#41—44no—
321#41—44no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4D4×D1112yes—
335C2×D4#434112yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—442no—
359C22×C4C22⋊Dic1111yescharacteristic
360C22×C4C22⋊Dic1111yescharacteristic
361C22×C4C22⋊Dic1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363M16—442no—
364M16—442no—
365C2×C8—442no—
366C4⋊C4—42no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—444no—
372C22⋊C4—22no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—224no—
380C22⋊C4—442no—
381C42—444no—
382C11#1308511yescharacteristic, complemented, Sylow
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23D4×Dic1112yes—
397C23#6698811yescharacteristic
398C23#6699011yescharacteristic
399C23C2×C22⋊Dic1111yescharacteristic
400Q8—44no—
401D4—42no—
402D4—42no—
403D4—44no—
404D4—42no—
405D4—42no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—444no—
439C2×C4—882no—
440C2×C4—882no—
441C2×C4#6689812yes—
442C2×C4#6689811yescharacteristic
443C2×C4#6689811yescharacteristic
444C2×C4#6699212yes—
445C8—882no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—42no—
452C22—41no—
453C22—41no—
454C22—42no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22—81no—
465C22C2×#6689811yescharacteristic
466C22C2×#6689811yescharacteristic
467C22#1062283311yescharacteristic
468C4—22no—
469C4—21no—
470C4—21no—
471C4—22no—
472C4—41no—
473C4—42no—
474C4—81no—
475C4—81no—
476C4—81no—
477C4—884no—
478C2—21no—
479C2—21no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—81no—
484C2#1306907011yescharacteristic
485C2#1307025711yescharacteristic
486C2#1307027011yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2406C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×D4×C11C23
hypercenter#2406D11
hypocenterC11#13085
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2406

Complements

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

NH ≅ G/Ntype
2. C2×#10622177C2semidirect
4. #13066734C2semidirect
7. C2×C11×#123C4semidirect
9. C22×C11×C4⋊C4C4semidirect
13. C11×#386C4semidirect
17. C11×#381C4semidirect
209. C2×#123Dic11semidirect
212. C22×C4⋊C4Dic11semidirect
221. #386Dic11semidirect
225. #381Dic11semidirect
382. C11#13085semidirect

Maximal subgroups

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

subgroupindex
C2×#106228532
C2×#106221772
#130685442
#130667342
C11×#24062
#1308511