Finite Group Databasebeta

← #11878739

Subgroups — #11878739

Order 1152.

728 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 109 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#10593972C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4#10593442C212yesmaximal, complemented
5#10593437C214yesmaximal, complemented
6#10593436C214yesmaximal, complemented
7#10593379C212yesmaximal, complemented
8C2×#3798—21no—
9C2×#3797C2212yes—
10C2×#3775C2218yes—
11C42×C3⋊D3C2211yescharacteristic
12C3×C4×D12—21no—
13C3×#869—21no—
14#63919C2212yes—
15#63919C2212yes—
16#63919C2211yescharacteristic
17#63916—21no—
18#63915—21no—
19#63914C2211yescharacteristic
20#63912C2212yes—
21C4×#625C2212yes—
22#63900—21no—
23#63900—21no—
24#63873—21no—
25#63778C2212yes—
26C4⋊#622C2212yes—
27C4×#622C2212yes—
28#63740C2218yes—
29D3×C4⋊Q8—61no—
30#5548—61no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C3×D12—21no—
35C2×C3×C4×D3—22no—
36C2×C3×Dic6—22no—
37C2×#627—21no—
38C2×#627C2314yes—
39C2×#626—22no—
40C2×#625—21no—
41C2×#625C2312yes—
42C2×#624—22no—
43#3798—44no—
44#3797—44no—
45C2×#622C2314yes—
46#3775—48no—
47C32×C42D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51C3×(C2×D3)⋊C4—22no—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—21no—
55#3724—22no—
56#3724—22no—
57#3724C2312yes—
58(C2×D3)⋊Dic3—22no—
59#3206—91nomaximal, Sylow
60C2×D3×Q8—62no—
61C2×#235—62no—
62C3×C4⋊Q8—61no—
63C3×C4×D4—61no—
64#944—62no—
65#940—61no—
66#938—61no—
67C4×#67—62no—
68#895—61no—
69D3×C4⋊C4—62no—
70D3×C4⋊C4—62no—
71#888—62no—
72#888—62no—
73#888—61no—
74#885—62no—
75#884—62no—
76C4×D12—21no—
77C42×D3—61no—
78C42×D3—61no—
79#869—21no—
80C22×C3⋊D3C2×D411yescharacteristic
81C22×C3×D3—22no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C2×C3⋊Dic3C2411yescharacteristic
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3SD1614yescomplemented
91C2×C3×Dic3—22no—
92C2×C3×Dic3—24no—
93C3×D12—42no—
94C3×C4×D3—44no—
95C3×Dic6—44no—
96#627—28no—
97#627—42no—
98#626—44no—
99#625—24no—
100#625—42no—
101#624—44no—
102#622—24no—
103#532—91no—
104C2×C4⋊Q8—91no—
105#492—92no—
106#487—92no—
107#461—94no—
108#448—94no—
109#431—91no—
110C2×C3×Q8—62no—
111C2×C3×D4—61no—
112C22×C3×C4—62no—
113C2×#67—62no—
114C2×#67—62no—
115C2×#67—62no—
116D3×Q8—128no—
117#235—128no—
118C2×D12—21no—
119C2×D12—62no—
120C2×C4×D3—22no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—64no—
128C2×Dic6—22no—
129C2×Dic6—64no—
130C2×Dic6—62no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—62no—
133C3×C4⋊C4—61no—
134C3×C22⋊C4—62no—
135C3×C42—21no—
136C3×C42—21no—
137#217—62no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—62no—
140C4⋊Dic3—22no—
141C4⋊Dic3—22no—
142C4⋊Dic3—21no—
143Dic3⋊C4—62no—
144Dic3⋊C4—64no—
145Dic3⋊C4—64no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C22×C32C22×D411yescharacteristic
153C2×C3⋊D3—21no—
154C2×C3⋊D3—21no—
155C2×C3⋊D3C2×SD1612yes—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C2×C3×D3—42no—
159C32×C4—21no—
160C32×C4C2×SD1612yes—
161C32×C4#13712yes—
162C3⋊Dic3—21no—
163C3⋊Dic3C2×SD1612yes—
164C3⋊Dic3H(5,𝔽2)12yes—
165C3×Dic3—44no—
166C3×Dic3—42no—
167C2×#41—181no—
168C22×Q8—92no—
169C2×SD16—98no—
170C4⋊Q8—61no—
171C4⋊Q8—91no—
172C4⋊Q8—92no—
173C4⋊Q8—92no—
174C4⋊Q8—181no—
175#127—91no—
176#124—181no—
177#121—92no—
178#121—181no—
179C4×D4—61no—
180C4×D4—92no—
181C2×C4⋊C4—181no—
182C2×C4⋊C4—181no—
183C2×C42—91no—
184C4⋊C8—92no—
185#103—98no—
186C22⋊C8—92no—
187C4×C8—92no—
188C23×C3—62no—
189C22×D3—22no—
190C22×D3—61no—
191C22×D3—61no—
192C3×Q8—124no—
193C3×D4—122no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—64no—
201C2×C3×C4—62no—
202C2×C3×C4—124no—
203#67—124no—
204#67—124no—
205#67—124no—
206C2×Dic3—24no—
207C2×Dic3—22no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214D12—42no—
215D12—124no—
216C4×D3—44no—
217C4×D3—64no—
218C4×D3—64no—
219C4×D3—64no—
220C4×D3—64no—
221C4×D3—122no—
222C4×D3—122no—
223C4×D3—128no—
224Dic6—44no—
225Dic6—128no—
226Dic6—124no—
227C2×C32#53511yescharacteristic
228C2×C32C22×SD1611yescharacteristic
229C2×C32C2×#13711yescharacteristic
230C3⋊D3—22no—
231C3×D3—82no—
232#41—364no—
233C2×Q8—62no—
234C2×Q8—94no—
235C2×Q8—181no—
236C2×Q8—364no—
237C2×D4—61no—
238C2×D4—92no—
239C2×D4—182no—
240C2×D4—181no—
241C22×C4—62no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—182no—
246SD16—368no—
247C2×C8—94no—
248C4⋊C4—62no—
249C4⋊C4—62no—
250C4⋊C4—61no—
251C4⋊C4—92no—
252C4⋊C4—182no—
253C4⋊C4—182no—
254C22⋊C4—62no—
255C22⋊C4—182no—
256C42—91no—
257C42—91no—
258C42—91no—
259C42GO+(4,𝔽2)11yescharacteristic
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—122no—
263C22×C3—122no—
264C22×C3—122no—
265C2×D3—42no—
266C2×D3—42no—
267C2×D3—42no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—121no—
273C2×D3—121no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—41no—
280C3×C4—124no—
281C3×C4—122no—
282Dic3—44no—
283Dic3—42no—
284Dic3—62no—
285Dic3—62no—
286Dic3—62no—
287Dic3—62no—
288Dic3—62no—
289Dic3—121no—
290C32#320611yescharacteristic, complemented, Sylow
291C23—62no—
292C23—91no—
293Q8—124no—
294Q8—188no—
295Q8—362no—
296D4—122no—
297D4—184no—
298D4—362no—
299D4—364no—
300C2×C4—62no—
301C2×C4—64no—
302C2×C4—91no—
303C2×C4—91no—
304C2×C4—94no—
305C2×C4—91no—
306C2×C4—124no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—364no—
310C2×C4C2×GO+(4,𝔽2)11yescharacteristic
311C2×C4C2×GO+(4,𝔽2)11yescharacteristic
312C2×C4C2×GO+(4,𝔽2)11yescharacteristic
313C8—184no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—242no—
321D3—64no—
322D3—82no—
323D3—122no—
324C22—92no—
325C22—122no—
326C22—122no—
327C22—122no—
328C22—181no—
329C22—181no—
330C22C22×GO+(4,𝔽2)11yescharacteristic
331C4—21no—
332C4—92no—
333C4—92no—
334C4—122no—
335C4—124no—
336C4—181no—
337C4#6422612yes—
338C4#6422712yes—
339C3—21no—
340C3—21no—
341C2—182no—
342C2—242no—
343C2C2×#6422611yescharacteristic
344C2C2×#6422711yescharacteristic
345C2#1059651211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radical#10593972C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3206
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593909C2semidirect
3. #10593727C2semidirect
4. #10593442C2semidirect
5. #10593437C2semidirect
6. #10593436C2semidirect
7. #10593379C2semidirect
90. C4×C3⋊D3SD16semidirect
290. C32#3206semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105939092
#105937272
#105934422
#105934372
#105934362
#105933792
#32069