Finite Group Databasebeta

← #11779441

Subgroups — #11779441

Order 1152.

469 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593958C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic, complemented
3#10590387C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic
5#10589349C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71156—31nomaximal
9#68492—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63900—21no—
15#63894—21no—
16#63888—22no—
17#63871—21no—
18#63869—21no—
19C2×#3718—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#818—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63573—21no—
26#63564—21no—
27#5730—31no—
28#5579—31no—
29C3×#477—31no—
30#5092—31no—
31#5092—31no—
32#5084—31no—
33#4850D311yescharacteristic, complemented
34#4842—31no—
35C3×#333—31no—
36#4535—31no—
37#4484—31no—
38#4483—31no—
39#4483—31no—
40#4483—61no—
41#4481D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D412yes—
47C2×#624—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50#3752—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63#3722—22no—
64#3718—44no—
65#1632—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4×Q8—31no—
69#946—62no—
70#946—61no—
71C2×#216—62no—
72C2×#216—62no—
73#897—61no—
74#896—62no—
75#893—61no—
76D3×C4⋊C4—61no—
77D3×C4⋊C4—61no—
78#890—61no—
79C4×D12—31no—
80C4×D12—31no—
81C4×D12—61no—
82C4×D12—61no—
83#870—61no—
84#869C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×#103—61no—
93#821—61no—
94#818—21no—
95#817—61no—
96#816—21no—
97#809—61no—
98#808—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3⋊D3—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C4⋊(C3⋊D3)—21no—
109C4⋊(C3⋊D3)Q1612yescomplemented
110C4×C3⋊D3—41no—
111C4×C3⋊D3—41no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×Dic6—21no—
117C3×Dic6—21no—
118C3×Dic6—42no—
119C3×Dic6—42no—
120#624—82no—
121C32×C8—41no—
122C3⋊(C3⋊C8)—22no—
123C3×C3⋊C8—41no—
124#554—91no—
125#494—91no—
126#477—31no—
127#476—91no—
128#333—31no—
129Q8⋊C8—91no—
130D4⋊C8—91no—
131C2×C3×Q8—31no—
132C2×C3×Q8—32no—
133C2×C3×Q8—61no—
134C2×D12—31no—
135C2×D12—31no—
136C2×D12—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—121no—
142C2×Dic6—21no—
143C2×Dic6D1212yes—
144C2×Dic6#6711yescharacteristic
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—41no—
148C2×C3×C8—61no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C42—21no—
156C3×C42—61no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#216—124no—
160#216—124no—
161(C2×D3)⋊C4—62no—
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—61no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—121no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—61no—
173C4⋊Dic3—62no—
174C4⋊Dic3#6711yescharacteristic
175Dic3⋊C4—21no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179C4×Dic3—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C22×C32#12011yescharacteristic
185C2×C3⋊D3—22no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C32×C4—21no—
189C32×C4C2×Q1611yescharacteristic
190C32×C4#13511yescharacteristic
191C32×C4#13711yescharacteristic
192C32×C4#13711yescharacteristic
193C3⋊Dic3—41no—
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—42no—
197C3×Dic3—81no—
198C2×Q16—182no—
199C4⋊Q8—31no—
200C4⋊Q8—31no—
201#125—181no—
202C22⋊Q8—182no—
203C22⋊Q8—181no—
204C4×Q8—31no—
205C4×D4—91no—
206C4×D4—181no—
207C2×C4⋊C4—181no—
208#107—61no—
209#106—181no—
210C4⋊C8—31no—
211C4⋊C8D3211yescharacteristic
212#103—61no—
213#102—181no—
214C4×C8—91no—
215C22×D3—61no—
216C22×D3—61no—
217C22×D3—121no—
218C3×Q8—61no—
219C3×Q8—61no—
220C3×Q8—122no—
221C3×Q8—122no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—61no—
226C2×C3×C4—61no—
227C2×C3×C4—62no—
228C2×C3×C4—121no—
229C2×C3×C4C2×D1211yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×Dic3—22no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—41no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—121no—
242D12—32no—
243D12—32no—
244D12—62no—
245D12—61no—
246D12—61no—
247D12—121no—
248C4×D3—121no—
249C4×D3—121no—
250C4×D3—121no—
251C4×D3—121no—
252C4×D3—241no—
253C4×D3—241no—
254C4×D3—242no—
255C4×D3—242no—
256Dic6—21no—
257Dic6—21no—
258Dic6—42no—
259Dic6—42no—
260C3×C8—41no—
261C3×C8—41no—
262C3×C8—81no—
263C3×C8—121no—
264C3⋊C8—41no—
265C3⋊C8—62no—
266C3⋊C8—62no—
267C3⋊C8—122no—
268C2×C32#45111yescharacteristic
269C2×C32#45211yescharacteristic
270C2×C32#45311yescharacteristic
271C3⋊D3—42no—
272C2×Q8—32no—
273C2×Q8—31no—
274C2×Q8—61no—
275C2×D4—91no—
276C22×C4—182no—
277C22×C4—181no—
278Q16—364no—
279C2×C8—21no—
280C2×C8—61no—
281C2×C8—181no—
282C4⋊C4—31no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C22⋊C4—182no—
292C22⋊C4—181no—
293C42—61no—
294C42C2×D3211yescharacteristic
295C22×C3—21no—
296C22×C3#88211yescharacteristic
297C22×C3#93711yescharacteristic
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—122no—
301C2×D3—121no—
302C2×D3—121no—
303C2×D3—121no—
304C2×D3—121no—
305C2×D3—241no—
306C2×D3—241no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—41no—
314C3×C4—122no—
315C3×C4—121no—
316C3×C4—121no—
317C3×C4—241no—
318C3×C4#91511yescharacteristic
319C3×C4#91611yescharacteristic
320C3×C4D3×Q1611yescharacteristic
321C3×C4D3×Q1611yescharacteristic
322C3×C4#91811yescharacteristic
323C3×C4#91811yescharacteristic
324C3×C4#94211yescharacteristic
325C3×C4#95011yescharacteristic
326Dic3—41no—
327Dic3—42no—
328Dic3—41no—
329Dic3—81no—
330Dic3—121no—
331Dic3—121no—
332Dic3—241no—
333C32#163211yescharacteristic, complemented, Sylow
334C23—181no—
335Q8—61no—
336Q8—61no—
337Q8—122no—
338Q8—122no—
339D4—92no—
340D4—181no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—62no—
344C2×C4—121no—
345C2×C4—181no—
346C2×C4—361no—
347C2×C4—361no—
348C2×C4—722no—
349C2×C4D3×D1211yescharacteristic
350C2×C4#380211yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—41no—
353C8—121no—
354C8—182no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3#474711yescharacteristic
359C2×C3#480811yescharacteristic
360C2×C3#480911yescharacteristic
361C2×C3#504711yescharacteristic
362C2×C3#518611yescharacteristic
363C2×C3#519811yescharacteristic
364D3—122no—
365D3—122no—
366D3—242no—
367C22—182no—
368C22—361no—
369C22—361no—
370C22#6392211yescharacteristic
371C4—21no—
372C4—121no—
373C4—122no—
374C4—121no—
375C4—241no—
376C4—361no—
377C4#6380211yescharacteristic
378C4#6381111yescharacteristic
379C4#6393511yescharacteristic
380C4#6394811yescharacteristic
381C3—21no—
382C3#6849211yescharacteristic, complemented
383C3#7115611yescharacteristic, complemented
384C2—362no—
385C2#1059061611yescharacteristic
386C2#1059095011yescharacteristic
387C2#1059101411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1632
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4850C2semidirect
3. #10590387C2semidirect
6. C3×#4481C2semidirect
7. #10589083C2semidirect
33. #4850D3semidirect
41. #4481D3semidirect
109. C4⋊(C3⋊D3)Q16semidirect
333. C32#1632semidirect
382. C3#68492semidirect
383. C3#71156semidirect

Maximal subgroups

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

subgroupindex
#105939582
C3×#48502
#105903872
#105903002
#105893492
C3×#44812
#105890832
#711563
#684923