Finite Group Databasebeta

← #11779442

Subgroups — #11779442

Order 1152.

476 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593956C211yesmaximal, characteristic
2#10592549C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic
5C3×#4483C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68492—31nomaximal
9#68202—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63898—21no—
15D3×C4⋊Dic3—21no—
16#63887—22no—
17#63872—21no—
18#63857—21no—
19C2×#3719—22no—
20C32×C4⋊C8C2211yescharacteristic
21#63645—21no—
22#63643—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—21no—
26#63563—21no—
27#5730—31no—
28#5543—31no—
29#5092—31no—
30#5008—31no—
31#4850—31no—
32#4850—31no—
33#4850—61no—
34#4842—31no—
35#4699—31no—
36C3×#333—31no—
37C3×D4⋊C8—31no—
38#4484—31no—
39#4483D311yescharacteristic
40#4481D311yescharacteristic, complemented
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6D412yes—
47C2×D3×Dic3—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3719—44no—
65#1632—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×D4—31no—
68#946—62no—
69C2×#216—62no—
70D4×Dic3—61no—
71C2×C4⋊Dic3—61no—
72#924—61no—
73C2×Dic12—62no—
74#897—61no—
75#893—61no—
76D3×C4⋊C4—61no—
77#890—61no—
78#890—61no—
79#878—62no—
80C4×D12C2×D311yescharacteristic
81#869—31no—
82#869—31no—
83#869—61no—
84#869C2×D311yescharacteristic
85C4×Dic6—31no—
86C4×Dic6—31no—
87C4×Dic6—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4×C8—31no—
93#832—61no—
94#821—61no—
95#818—61no—
96#818—61no—
97#818—62no—
98#817—61no—
99#816—61no—
100#816—61no—
101#816—62no—
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—21no—
111C2×C3⋊Dic3—41no—
112#634—21no—
113#634—21no—
114#634—42no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12Q1612yescomplemented
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—42no—
122D3×Dic3—82no—
123C32×C8—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126#554—91no—
127#494—91no—
128#477—91no—
129#476—91no—
130#333—31no—
131Q8⋊C8—91no—
132D4⋊C8—31no—
133C2×C3×Q8—32no—
134C2×C3×D4—31no—
135C22×C3×C4—61no—
136C22×Dic3—62no—
137C2×D12D1211yescharacteristic
138C2×C4×D3—21no—
139C2×C4×D3—62no—
140C2×Dic6—31no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×Dic6—121no—
146C2×Dic6D1212yes—
147C2×C3×C8—22no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—61no—
151C2×C3×C8—61no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C22⋊C4—61no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#217—62no—
160#216—124no—
161(C2×D3)⋊C4—21no—
162(C2×D3)⋊C4—62no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—61no—
168C4⋊Dic3—62no—
169C4⋊Dic3—62no—
170C4⋊Dic3—62no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—121no—
176C4⋊Dic3D1211yescharacteristic
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—121no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—121no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187Dic12—124no—
188C22×C32#12011yescharacteristic
189C2×C3×D3—22no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C32×C4—21no—
193C32×C4C2×Q1611yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4#13711yescharacteristic
196C32×C4#13711yescharacteristic
197C3⋊Dic3—41no—
198C3⋊Dic3—41no—
199C3⋊Dic3—81no—
200C3×Dic3—41no—
201C3×Dic3—42no—
202C2×Q16—182no—
203C4⋊Q8—31no—
204C4⋊Q8—91no—
205#125—181no—
206C22⋊Q8—182no—
207C22⋊Q8—181no—
208C4×Q8—91no—
209C4×D4—31no—
210C4×D4—181no—
211C2×C4⋊C4—181no—
212#107—181no—
213#106—181no—
214C4⋊C8—31no—
215C4⋊C8D3211yescharacteristic
216#103—181no—
217#102—181no—
218C4×C8—31no—
219C23×C3—61no—
220C22×D3—21no—
221C3×Q8—122no—
222C3×D4—32no—
223C3×D4—61no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—61no—
228C2×C3×C4—62no—
229C2×C3×C4—121no—
230C2×C3×C4—121no—
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—22no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245C2×Dic3—122no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248C2×Dic3—242no—
249D12—21no—
250D12Dic1212yescomplemented
251C4×D3—41no—
252C4×D3—41no—
253C4×D3—242no—
254Dic6—42no—
255Dic6—62no—
256Dic6—61no—
257Dic6—61no—
258Dic6—61no—
259Dic6—61no—
260Dic6—121no—
261Dic6—122no—
262Dic6—122no—
263Dic6—242no—
264C3×C8—42no—
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—62no—
268C3×C8—121no—
269C3⋊C8—22no—
270C3⋊C8—41no—
271C2×C32#45111yescharacteristic
272C2×C32#45211yescharacteristic
273C2×C32#45311yescharacteristic
274C3×D3—42no—
275C2×Q8—32no—
276C2×Q8—91no—
277C2×Q8—181no—
278C2×D4—31no—
279C22×C4—61no—
280C22×C4—182no—
281Q16—364no—
282C2×C8—21no—
283C2×C8—61no—
284C2×C8—61no—
285C4⋊C4—31no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C22⋊C4—61no—
295C22⋊C4—182no—
296C42—181no—
297C42C2×D3211yescharacteristic
298C22×C3—21no—
299C22×C3—62no—
300C22×C3—121no—
301C22×C3—121no—
302C22×C3#88211yescharacteristic
303C22×C3#88211yescharacteristic
304C2×D3—22no—
305C2×D3—41no—
306C2×D3—41no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—41no—
314C3×C4—121no—
315C3×C4—122no—
316C3×C4C2×Dic1211yescharacteristic
317C3×C4#90911yescharacteristic
318C3×C4#91211yescharacteristic
319C3×C4#91511yescharacteristic
320C3×C4#91511yescharacteristic
321C3×C4#91611yescharacteristic
322C3×C4D3×Q1611yescharacteristic
323C3×C4#91811yescharacteristic
324Dic3—42no—
325Dic3—41no—
326Dic3—122no—
327Dic3—121no—
328Dic3—121no—
329Dic3—121no—
330Dic3—121no—
331Dic3—241no—
332Dic3—242no—
333Dic3—241no—
334Dic3—241no—
335C32#163211yescharacteristic, complemented, Sylow
336C23—61no—
337Q8—122no—
338Q8—181no—
339Q8—181no—
340Q8—362no—
341D4—32no—
342D4—61no—
343C2×C4—61no—
344C2×C4—62no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—361no—
350C2×C4—722no—
351C2×C4D3×D1211yescharacteristic
352C2×C4D3×D1211yescharacteristic
353C2×C4#381111yescharacteristic
354C8—41no—
355C8—62no—
356C8—121no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—122no—
361C2×C3#473911yescharacteristic
362C2×C3#474711yescharacteristic
363C2×C3#478311yescharacteristic
364C2×C3#480811yescharacteristic
365C2×C3#480911yescharacteristic
366C2×C3#482211yescharacteristic
367D3—42no—
368C22—62no—
369C22—121no—
370C22—121no—
371C22#6392311yescharacteristic
372C4—21no—
373C4—122no—
374C4—121no—
375C4—361no—
376C4—361no—
377C4—721no—
378C4D3×Dic1211yescharacteristic
379C4#6380011yescharacteristic
380C4#6393611yescharacteristic
381C4#6395111yescharacteristic
382C3—21no—
383C3#6820211yescharacteristic, complemented
384C3#6849211yescharacteristic, complemented
385C2—122no—
386C2#1059061811yescharacteristic
387C2#1059095211yescharacteristic
388C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
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. #10592549C2semidirect
3. #10590386C2semidirect
6. C3×#4481C2semidirect
7. #10589085C2semidirect
40. #4481D3semidirect
118. C3×D12Q16semidirect
250. D12Dic12semidirect
335. C32#1632semidirect
383. C3#68202semidirect
384. C3#68492semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105925492
#105903862
#105902682
C3×#44832
C3×#44812
#105890852
#684923
#682023