Finite Group Databasebeta

← #11779595

Subgroups — #11779595

Order 1152.

476 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 96 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#10596041C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic
3#10590287C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic
8#71158—31nomaximal
9#68253—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12#64099—21no—
13#64099—22no—
14#64078—21no—
15#64078C2211yescharacteristic
16C4×#634—21no—
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#835—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63567—21no—
26#63566—22no—
27#5570—31no—
28#5570—31no—
29#5570—61no—
30C3×#477—31no—
31#5091—31no—
32#5079—31no—
33#5021D311yescharacteristic
34#4850—31no—
35#4681—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic
38#4486—31no—
39#4484—31no—
40#4482—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×#634D411yescharacteristic
45C2×C3×Dic6—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C42—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—22no—
51C4⋊(C3⋊Dic3)—22no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D412yes—
55#3750—22no—
56#3750—21no—
57C4×C3⋊Dic3—22no—
58C4×C3⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#1636—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4×Q8—21no—
67C3×C4×Q8C2×D311yescharacteristic
68C3×C4×Q8C2×D311yescharacteristic
69Q8×Dic3—62no—
70Q8×Dic3—61no—
71Q8×Dic3—61no—
72#890—62no—
73#890—62no—
74#890—64no—
75#890—62no—
76#890—61no—
77#890—61no—
78#869—31no—
79#869—31no—
80#869—61no—
81#869—61no—
82#869—61no—
83#869—62no—
84#869C2×D311yescharacteristic
85C4×Dic6—31no—
86C4×Dic6—31no—
87C4×Dic6—61no—
88C4×Dic6—61no—
89C4×Dic6—61no—
90C4×Dic6—62no—
91C3×#107—61no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8—31no—
94C3×#103—61no—
95C3×C4×C8—31no—
96#835—21no—
97#835—62no—
98#818—61no—
99#816—61no—
100#816—62no—
101#810—61no—
102#807—21no—
103#807—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C32×Q8—21no—
108C32×Q8Q1612yes—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—22no—
117#634—21no—
118#634—21no—
119#634—41no—
120#634—41no—
121C2×C3×Dic3—41no—
122C3×Dic6—42no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125C3×C3⋊C8—41no—
126#557—91no—
127#487—91no—
128#477—31no—
129#477—91no—
130#332—91no—
131Q8⋊C8—31no—
132Q8⋊C8—91no—
133C2×C3×Q8—21no—
134C2×C3×Q8—61no—
135C2×C3×Q8D1211yescharacteristic
136C2×C3×Q8#6711yescharacteristic
137C2×Dic6—21no—
138C2×Dic6—31no—
139C2×Dic6—31no—
140C2×Dic6—61no—
141C2×Dic6—62no—
142C2×Dic6—61no—
143C2×Dic6—61no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4D1211yescharacteristic
154C3×C4⋊C4#6711yescharacteristic
155C3×C42—22no—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161C4⋊Dic3—21no—
162C4⋊Dic3—21no—
163C4⋊Dic3—31no—
164C4⋊Dic3—32no—
165C4⋊Dic3—31no—
166C4⋊Dic3—32no—
167C4⋊Dic3—61no—
168C4⋊Dic3—62no—
169C4⋊Dic3—64no—
170C4⋊Dic3—62no—
171C4⋊Dic3—62no—
172C4⋊Dic3—64no—
173C4⋊Dic3—62no—
174C4⋊Dic3—62no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178Dic3⋊C4—64no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184C4×Dic3—64no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3—62no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C22×C32#12011yescharacteristic
194C32×C4—22no—
195C32×C4—21no—
196C32×C4—41no—
197C32×C4C2×Q1611yescharacteristic
198C32×C4#13511yescharacteristic
199C32×C4#13711yescharacteristic
200C32×C4#13711yescharacteristic
201C3⋊Dic3—41no—
202C3⋊Dic3—42no—
203C3⋊Dic3—41no—
204C3×Dic3—81no—
205C4⋊Q8—31no—
206C4⋊Q8—91no—
207C4⋊Q8—181no—
208#125—182no—
209#125—181no—
210C4×Q8—91no—
211C4×Q8—181no—
212C4×Q8—181no—
213C4×Q8D3211yescharacteristic
214#107—61no—
215#107—181no—
216C4⋊C8—31no—
217C4⋊C8—31no—
218#103—61no—
219#103—181no—
220#103—182no—
221C4×C8—31no—
222C3×Q8—22no—
223C3×Q8—21no—
224C3×Q8—21no—
225C3×Q8—22no—
226C3×Q8—122no—
227C3×Q8Dic1212yes—
228C3×Q8#21612yes—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—121no—
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×Dic3—41no—
246C2×Dic3—62no—
247C2×Dic3—64no—
248C2×Dic3—62no—
249C2×Dic3—61no—
250C2×Dic3—62no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—62no—
254C2×Dic3—61no—
255Dic6—42no—
256Dic6—61no—
257Dic6—61no—
258Dic6—61no—
259Dic6—61no—
260Dic6—121no—
261Dic6—121no—
262Dic6—122no—
263Dic6—122no—
264Dic6—121no—
265Dic6—121no—
266Dic6—121no—
267Dic6—121no—
268C3×C8—121no—
269C3×C8—121no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—41no—
273C3⋊C8—41no—
274C2×C32#45111yescharacteristic
275C2×C32#45211yescharacteristic
276C2×C32#45411yescharacteristic
277C2×Q8—61no—
278C2×Q8—91no—
279C2×Q8—181no—
280C2×Q8#62611yescharacteristic
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—61no—
284C4⋊C4—21no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—92no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4#62611yescharacteristic
295C42—21no—
296C42—182no—
297C42—181no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3#88211yescharacteristic
301C22×C3#93711yescharacteristic
302C3×C4—24no—
303C3×C4—21no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—241no—
316C3×C4C2×Dic1211yescharacteristic
317C3×C4#90911yescharacteristic
318C3×C4#91611yescharacteristic
319C3×C4#91811yescharacteristic
320C3×C4#91811yescharacteristic
321C3×C4#91911yescharacteristic
322C3×C4C2×#21611yescharacteristic
323C3×C4#95111yescharacteristic
324Dic3—81no—
325Dic3—122no—
326Dic3—124no—
327Dic3—122no—
328Dic3—121no—
329Dic3—122no—
330Dic3—121no—
331Dic3—121no—
332Dic3—122no—
333Dic3—121no—
334C32#163611yescharacteristic, complemented, Sylow
335Q8—21no—
336Q8—122no—
337Q8—181no—
338Q8—181no—
339Q8—361no—
340Q8—361no—
341Q8#371912yes—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—121no—
345C2×C4—181no—
346C2×C4—182no—
347C2×C4—181no—
348C2×C4C2×#62611yescharacteristic
349C2×C4#381111yescharacteristic
350C2×C4#381111yescharacteristic
351C8—121no—
352C8—121no—
353C8—121no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3#473911yescharacteristic
358C2×C3#480811yescharacteristic
359C2×C3#482711yescharacteristic
360C2×C3#505011yescharacteristic
361C2×C3#518711yescharacteristic
362C2×C3#520111yescharacteristic
363C22#6398111yescharacteristic
364C4—21no—
365C4—22no—
366C4—41no—
367C4—241no—
368C4—361no—
369C4—362no—
370C4—361no—
371C4#6383111yescharacteristic
372C4C2×#371911yescharacteristic
373C4#6394511yescharacteristic
374C4#6395011yescharacteristic
375C3—21no—
376C3#6825311yescharacteristic, complemented
377C3#7115811yescharacteristic, complemented
378C2#1059119011yescharacteristic
379C2#1059160211yescharacteristic
380C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#120
hypercenterC4×Q8D32
hypocenterC32#1636
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
334. C32#1636semidirect
376. C3#68253semidirect
377. C3#71158semidirect

Maximal subgroups

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

subgroupindex
#105960412
C3×#50212
#105902872
#105902842
C3×#45352
#105890942
#105890852
#711583
#682533