Finite Group Databasebeta

← #14672103

Subgroups — #14672103

Order 2816.

490 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#13073593C211yesmaximal, characteristic
2C2×#10622186C211yesmaximal, characteristic, complemented
3C2×#10622115C211yesmaximal, characteristic
4C2×#10622115C211yesmaximal, characteristic
5#13068610C211yesmaximal, characteristic, complemented
6#101×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#356C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#67000C411yescharacteristic
10C2×#67000C2211yescharacteristic
11C2×Q8×Dic11C2211yescharacteristic
12C2×C11×#101C2211yescharacteristic
13C2×C11×#101C2211yescharacteristic
14#10622843C411yescharacteristic
15C2×#66900C2211yescharacteristic
16C2×#66900C2211yescharacteristic
17#10622731—21no—
18M16×Dic11—21no—
19#10622607—21no—
20#10622607—21no—
21#10622603—21no—
22#10622603—21no—
23#10622552C411yescharacteristic
24C4×Dic11⋊C4C411yescharacteristic
25C11×#356—22no—
26#10622192—21no—
27#10622192—21no—
28#10622186—22no—
29#10622115—22no—
30#10622115—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Q8×C11C2311yescharacteristic
33C22×D44C2×C411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11C2×C411yescharacteristic
43#67000—21no—
44#67000—21no—
45#67000—21no—
46#67000—21no—
47#67000—41no—
48#67000—41no—
49Q8×Dic11—41no—
50Q8×Dic11—41no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×C4⋊Dic11D411yescharacteristic
59C2×C4⋊Dic11D411yescharacteristic
60C2×Dic11⋊C4—21no—
61C2×C4×Dic11C2×C411yescharacteristic
62C2×C4×Dic11C2×C411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×#4318—21no—
66C2×#4318—21no—
67C11×#101—21no—
68C11×#101—21no—
69C11×#101—21no—
70C11×#101D412yes—
71#66900—21no—
72#66900—21no—
73#66900—21no—
74#66900D412yes—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78#66879—41no—
79Dic11⋊C8—41no—
80Dic11⋊C8—41no—
81C8×Dic11—41no—
82#13228—111nomaximal, Sylow
83C23×D11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11C2×D411yescharacteristic
91C2×Q8×C11C2×D411yescharacteristic
92C2×Q8×C11#4111yescharacteristic
93C2×Q8×C11#4111yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C22×Dic11C22⋊C411yescharacteristic
103C22×Dic11C22⋊C411yescharacteristic
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—41no—
107C2×D44—41no—
108C11×M16—22no—
109C11×M16—41no—
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C42×C11—21no—
119C42×C11—21no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132Dic11⋊C4—42no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141#4318—22no—
142#4318—41no—
143#4318—41no—
144#4318—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147#2545—111no—
148C2×#356—111no—
149C2×#356D1111yescharacteristic, complemented
150C2×#355—111no—
151C2×#355—111no—
152#1801—111no—
153C4×#101—111no—
154C23×C11C2×C22⋊C411yescharacteristic
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166Q8×C11—81no—
167Q8×C11—81no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12411yescharacteristic
185C2×C4×C11#12711yescharacteristic
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11#9911yescharacteristic
197C2×Dic11#9911yescharacteristic
198D44—81no—
199D44—81no—
200C8×C11—42no—
201C8×C11—81no—
202C11⋊C8—42no—
203C11⋊C8—81no—
204C2×C4⋊Q8C2×D1111yescharacteristic
205C2×#124—111no—
206C2×#124—111no—
207C2×C4×Q8—111no—
208#423—221no—
209C2×#101—111no—
210C2×#101—111no—
211C2×#101C2×D1111yescharacteristic
212C2×#101C2×D1111yescharacteristic
213C4×M16—221no—
214#396—221no—
215#396—221no—
216#391—111no—
217#390—111no—
218#388—221no—
219#388—221no—
220C4×C4⋊C4—111no—
221#356—22no—
222#356—222no—
223#355—222no—
224#355—222no—
225#343—221no—
226#343—221no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11#39011yescharacteristic
230C22×C11C2×#9911yescharacteristic
231C22×C11#41011yescharacteristic
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—42no—
246C4×C11—81no—
247Dic11—21no—
248Dic11—21no—
249Dic11—41no—
250Dic11—41no—
251Dic11—41no—
252Dic11—81no—
253C22×Q8C4×D1111yescharacteristic
254C22×Q8C22×D1111yescharacteristic
255C22×D4—111no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—221no—
259C2×M16—221no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264#124—221no—
265#124—221no—
266#124—221no—
267#124—221no—
268#124—441no—
269#124—441no—
270C4×Q8—441no—
271C4×Q8—441no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—221no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C42—111no—
285C2×C42—111no—
286C2×C42—111no—
287C2×C42—111no—
288C2×C42C4×D1111yescharacteristic
289C4⋊C8—441no—
290C4⋊C8—441no—
291#101—21no—
292#101—21no—
293#101—21no—
294#101—112no—
295#101—221no—
296#101—221no—
297#101—221no—
298#101C22⋊D1112yes—
299#97—441no—
300C4×C8—441no—
301#95—221no—
302#95—221no—
303#95—221no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11#196411yescharacteristic
307C2×C11#213211yescharacteristic
308C2×C11#213311yescharacteristic
309D11—161no—
310C24—221no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8#433911yescharacteristic
318C2×Q8D4×D1111yescharacteristic
319C2×Q8#434111yescharacteristic
320C2×Q8C2×C22⋊D1111yescharacteristic
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4—441no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—221no—
332C22×C4C2×C4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335M16—22no—
336M16—41no—
337M16—41no—
338M16—41no—
339M16—222no—
340M16—441no—
341M16—441no—
342M16—441no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—441no—
346C2×C8—441no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C4⋊C4—442no—
355C22⋊C4—442no—
356C22⋊C4—442no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C22⋊C4—442no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C42—21no—
365C42—21no—
366C42—221no—
367C42—221no—
368C42—221no—
369C42—221no—
370C42—221no—
371C42—221no—
372C42—221no—
373C42—221no—
374C11#1322811yescharacteristic, complemented, Sylow
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23—441no—
380C23—441no—
381C23—441no—
382C23C22⋊C4×D1111yescharacteristic
383Q8—41no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—81no—
388Q8—81no—
389D4—881no—
390D4—881no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—111no—
404C2×C4—111no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4(C22⋊D11)⋊C411yescharacteristic
416C2×C4#6693711yescharacteristic
417C2×C4#6693811yescharacteristic
418C2×C4C4×C22⋊D1111yescharacteristic
419C2×C4#6699211yescharacteristic
420C2×C4#6699311yescharacteristic
421C8—42no—
422C8—81no—
423C8—442no—
424C8—881no—
425C22—21no—
426C22—21no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22—881no—
431C22—881no—
432C22—881no—
433C22—881no—
434C22#1062235311yescharacteristic
435C22D11×#9911yescharacteristic
436C22#1062257011yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—81no—
445C4—221no—
446C4—221no—
447C4—441no—
448C4—441no—
449C4—441no—
450C4—881no—
451C2—21no—
452C2—21no—
453C2—1761no—
454C2#1306945011yescharacteristic
455C2#1307030011yescharacteristic
456C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#356C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC22×Q8×C11C23
hypercenterC2×#356D11
hypocenterC11#13228
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
2. C2×#10622186C2semidirect
5. #13068610C2semidirect
6. #101×Dic11C2semidirect
7. C2×C11×#356C2semidirect
149. C2×#356D11semidirect
374. C11#13228semidirect

Maximal subgroups

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

subgroupindex
#130735932
C2×#106221862
C2×#106221152
#130686102
#101×Dic112
C2×C11×#3562
#1322811