Finite Group Databasebeta

← #11779924

Subgroups — #11779924

Order 1152.

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

normal subgroups only

This group has 476 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
2#10592540C211yesmaximal, characteristic
3#10590301C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#68494—31nomaximal
9#68249—31nomaximal
10C2×#3744—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63900—21no—
16#63894—21no—
17#63888—22no—
18#63871—21no—
19#63869—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63566—22no—
26#63566—21no—
27#5730—31no—
28#5579—31no—
29#5079—31no—
30#5020—31no—
31#4851—31no—
32#4841—31no—
33#4841—31no—
34#4841—61no—
35#4681—31no—
36C3×#333—31no—
37C3×Q8⋊C8—31no—
38#4484D311yescharacteristic, complemented
39#4483—31no—
40#4481D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D412yes—
47C2×#624—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50#3752—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3744—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64#3722—22no—
65#1643—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68#946—62no—
69#946—61no—
70C2×#204—61no—
71C2×#204—61no—
72C2×#204—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#869—31no—
85#869—31no—
86#869—61no—
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4×C8—31no—
94#835—61no—
95#835—62no—
96#817—61no—
97#816—61no—
98#816—61no—
99#816—62no—
100#816—62no—
101#816—61no—
102#808—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—41no—
111C4⋊(C3⋊D3)—21no—
112C4⋊(C3⋊D3)SD1612yes—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115#634—41no—
116#634—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—42no—
123#624—82no—
124C32×C8—41no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127#554—91no—
128#487—91no—
129#475—91no—
130#461—91no—
131#333—31no—
132Q8⋊C8—31no—
133D4⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—32no—
136C2×D12—31no—
137C2×D12—31no—
138C2×D12—61no—
139C2×C4×D3—61no—
140C2×C4×D3—61no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—121no—
144C2×Dic6—62no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6D1211yescharacteristic
148C2×Dic6D1212yes—
149C2×C3×C8—22no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C42—21no—
159C3×C42—61no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—62no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—121no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172C4⋊Dic3—62no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—121no—
178C4⋊Dic3—121no—
179C4⋊Dic3D1211yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184C4×Dic3—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187#204—122no—
188#204—122no—
189#204—124no—
190C22×C32#12011yescharacteristic
191C2×C3⋊D3—22no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C32×C4—21no—
195C32×C4C2×SD1611yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4#13711yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—41no—
200C3⋊Dic3—81no—
201C3×Dic3—41no—
202C3×Dic3—41no—
203C3×Dic3—42no—
204C2×SD16—181no—
205C4⋊Q8—31no—
206C4⋊Q8—91no—
207#125—181no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C4×Q8—31no—
211C4×D4—91no—
212C4×D4—181no—
213C2×C4⋊C4—181no—
214#106—181no—
215C4⋊C8—31no—
216C4⋊C8D3211yescharacteristic
217#103—181no—
218#103—181no—
219#103—182no—
220C4×C8—31no—
221C22×D3—61no—
222C22×D3—61no—
223C22×D3—121no—
224C3×Q8—61no—
225C3×Q8—61no—
226C3×Q8—122no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—62no—
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—22no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—121no—
245C2×Dic3—122no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248D12—32no—
249D12—32no—
250D12—62no—
251D12—61no—
252D12—61no—
253D12—121no—
254C4×D3—121no—
255C4×D3—121no—
256C4×D3—121no—
257C4×D3—121no—
258C4×D3—241no—
259C4×D3—241no—
260C4×D3—242no—
261C4×D3—242no—
262Dic6—21no—
263Dic6—21no—
264Dic6—42no—
265Dic6—122no—
266Dic6—122no—
267Dic6—121no—
268Dic6—121no—
269Dic6—121no—
270Dic6—121no—
271C3×C8—42no—
272C3×C8—41no—
273C3×C8—41no—
274C3×C8—121no—
275C3×C8—121no—
276C3⋊C8—41no—
277C3⋊C8—41no—
278C2×C32#44811yescharacteristic
279C2×C32#45211yescharacteristic
280C2×C32#45511yescharacteristic
281C3⋊D3—42no—
282C2×Q8—31no—
283C2×Q8—32no—
284C2×Q8—181no—
285C2×D4—91no—
286C22×C4—182no—
287C22×C4—181no—
288SD16—362no—
289C2×C8—21no—
290C2×C8—61no—
291C2×C8—61no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—91no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C22⋊C4—182no—
302C22⋊C4—181no—
303C42—61no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3#88211yescharacteristic
307C22×C3#88211yescharacteristic
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—122no—
311C2×D3—121no—
312C2×D3—121no—
313C2×D3—121no—
314C2×D3—121no—
315C2×D3—241no—
316C2×D3—241no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—121no—
325C3×C4—121no—
326C3×C4—122no—
327C3×C4#90411yescharacteristic
328C3×C4#90911yescharacteristic
329C3×C4D3×SD1611yescharacteristic
330C3×C4D3×SD1611yescharacteristic
331C3×C4#91611yescharacteristic
332C3×C4#91811yescharacteristic
333C3×C4#91811yescharacteristic
334C3×C4#91811yescharacteristic
335Dic3—41no—
336Dic3—42no—
337Dic3—41no—
338Dic3—121no—
339Dic3—121no—
340Dic3—241no—
341Dic3—242no—
342Dic3—241no—
343Dic3—241no—
344C32#164311yescharacteristic, complemented, Sylow
345C23—181no—
346Q8—61no—
347Q8—61no—
348Q8—122no—
349Q8—361no—
350Q8—361no—
351D4—92no—
352D4—181no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—62no—
356C2×C4—181no—
357C2×C4—361no—
358C2×C4—361no—
359C2×C4—361no—
360C2×C4—722no—
361C2×C4D3×D1211yescharacteristic
362C2×C4D3×D1211yescharacteristic
363C2×C4#381111yescharacteristic
364C8—41no—
365C8—121no—
366C8—121no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3#473311yescharacteristic
371C2×C3#474611yescharacteristic
372C2×C3#480611yescharacteristic
373C2×C3#480611yescharacteristic
374C2×C3#480811yescharacteristic
375C2×C3#482511yescharacteristic
376D3—122no—
377D3—122no—
378D3—242no—
379C22—182no—
380C22—361no—
381C22—361no—
382C22#6392311yescharacteristic
383C4—21no—
384C4—121no—
385C4—122no—
386C4—121no—
387C4—361no—
388C4—721no—
389C4#6380111yescharacteristic
390C4#6380611yescharacteristic
391C4#6393011yescharacteristic
392C4#6394511yescharacteristic
393C3—21no—
394C3#6824911yescharacteristic, complemented
395C3#6849411yescharacteristic, complemented
396C2—362no—
397C2#1059060611yescharacteristic
398C2#1059097011yescharacteristic
399C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1643
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
3. #10590301C2semidirect
4. #10590287C2semidirect
5. C3×#4484C2semidirect
6. C3×#4481C2semidirect
38. #4484D3semidirect
40. #4481D3semidirect
344. C32#1643semidirect
394. C3#68249semidirect
395. C3#68494semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105925402
#105903012
#105902872
C3×#44842
C3×#44812
#105890822
#684943
#682493