Finite Group Databasebeta

← #11878437

Subgroups — #11878437

Order 1152.

835 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 835 conjugacy classes of subgroups — too many to draw. Only its 172 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
1C3×#5825C212yesmaximal
2#10592933C211yesmaximal, characteristic
3#10591189C212yesmaximal, complemented
4#10591188C212yesmaximal, complemented
5#10591185C214yesmaximal, complemented
6#10591102C214yesmaximal, complemented
7#83413—32nomaximal
8C2×C32×#41C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C2×#3748C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×#944—22no—
13C3×#936—22no—
14C3×#935—22no—
15C3×#935—22no—
16C3×#926C2212yes—
17C3×#924C2214yes—
18C3×#924C2214yes—
19C2×#3718C2212yes—
20C2×#3718C2212yes—
21#63657C2214yes—
22#63576C2212yes—
23#63574C2212yes—
24#63565C2214yes—
25#63565C2214yes—
26C3×#536—32no—
27#5825D312yes—
28#5234—32no—
29#5234—61no—
30#5228—34no—
31#5052—34no—
32#5051—34no—
33#5050—34no—
34#5045—34no—
35#4996—34no—
36C32×#41—41no—
37C32×#41—41no—
38C2×C32×Q8D411yescharacteristic
39C2×C32×D4D411yescharacteristic
40C2×C32×D4D412yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C3×Dic3—22no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6—42no—
46C2×C3×Dic6—42no—
47C2×C3×Dic6C2314yes—
48#3748—41no—
49C2×C3⋊(C3⋊C8)—41no—
50C2×C3⋊(C3⋊C8)C2312yes—
51C2×C3⋊(C3⋊C8)C2312yes—
52C3×#217—24no—
53C3×#217—24no—
54C3×#217—22no—
55C3×C4⋊Dic3C2314yes—
56C3×Dic3⋊C4—24no—
57C3×Dic3⋊C4—24no—
58C3×C4×Dic3—22no—
59#3718—42no—
60#3718—42no—
61#3202—91noSylow
62C2×C3×#41—21no—
63C2×C3×#41C2×D312yes—
64C22×C3×Q8—32no—
65C22×Dic6C2×D312yes—
66C3×C4⋊Q8—62no—
67C3×#124—62no—
68C3×#123—62no—
69C3×#123—62no—
70C3×C22⋊Q8—34no—
71C3×C22⋊Q8—34no—
72C3×#117—32no—
73#944—22no—
74C2×#216—34no—
75C2×#216—34no—
76#936—22no—
77#935—22no—
78#935—22no—
79#926C2×D312yes—
80#924C2×D314yes—
81#924C2×D314yes—
82C2×#208—32no—
83C2×#208—61no—
84C22×C3⋊C8—32no—
85C22×C3⋊C8—61no—
86#835—34no—
87#835—34no—
88#830—34no—
89#830—34no—
90#830—64no—
91#810—34no—
92#810—34no—
93#808—34no—
94#807—34no—
95C23×C32C2×D411yescharacteristic
96C23×C32C2×D412yes—
97C32×Q8—41no—
98C32×D4—41no—
99C32×D4—42no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4C2×D412yes—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2411yescharacteristic
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—44no—
110C3×Dic6—24no—
111C3×Dic6—24no—
112C3×Dic6—44no—
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)—22no—
115#536—32no—
116#485—94no—
117#470—92no—
118#467—92no—
119#451—94no—
120#408—91no—
121C3×#41—42no—
122C3×#41—42no—
123C3×#41—42no—
124C3×#41—42no—
125C2×C3×Q8—21no—
126C2×C3×Q8—34no—
127C2×C3×Q8—62no—
128C2×C3×Q8—122no—
129C2×C3×Q8—122no—
130C2×C3×Q8#6712yes—
131C2×C3×D4—21no—
132C2×C3×D4—22no—
133C2×C3×D4#6712yes—
134C2×C3×D4#6712yes—
135C2×C3×D4#6712yes—
136C22×C3×C4—21no—
137C22×C3×C4—22no—
138C22×C3×C4—62no—
139C22×C3×C4C22×D312yes—
140C22×C3×C4C22×D312yes—
141C22×C3×C4C22×D312yes—
142C22×Dic3—22no—
143C2×Dic6—22no—
144C2×Dic6—42no—
145C2×Dic6—42no—
146C2×Dic6C22×D314yes—
147C3×C4⋊C4—34no—
148C3×C4⋊C4—64no—
149C3×C4⋊C4—64no—
150C3×C22⋊C4—62no—
151C3×C22⋊C4—64no—
152C3×C22⋊C4—64no—
153C3×C42—62no—
154#217—24no—
155#217—24no—
156#217—22no—
157#216—124no—
158#216—124no—
159C4⋊Dic3C22×D314yes—
160Dic3⋊C4—24no—
161Dic3⋊C4—24no—
162C4×Dic3—22no—
163#208—122no—
164#208—122no—
165C2×C3⋊C8—34no—
166C2×C3⋊C8—34no—
167C2×C3⋊C8—62no—
168C2×C3⋊C8—62no—
169C2×C3⋊C8—122no—
170C2×C3⋊C8—122no—
171C22×C32—21no—
172C22×C32—22no—
173C22×C32—22no—
174C22×C32—24no—
175C22×C32C22×D411yescharacteristic
176C32×C4—21no—
177C32×C4—22no—
178C32×C4H(5,𝔽2)11yescharacteristic
179C32×C4H(5,𝔽2)11yescharacteristic
180C3×Dic3—44no—
181C3×Dic3—44no—
182C2×#41D3211yescharacteristic
183C22×Q8—32no—
184C2×Q16—92no—
185C2×Q16—92no—
186C2×M16—91no—
187C22×C8—91no—
188C4⋊Q8—62no—
189#124—62no—
190#123—62no—
191#123—62no—
192C22⋊Q8—34no—
193C22⋊Q8—34no—
194#117—32no—
195#107—92no—
196#106—92no—
197#103—94no—
198#103—94no—
199C22⋊C8—94no—
200C23×C3—21no—
201C23×C3—22no—
202C23×C3C2×#6712yes—
203C23×C3C2×#6712yes—
204C23×C3C2×#6712yes—
205C3×Q8—42no—
206C3×Q8—42no—
207C3×Q8—64no—
208C3×Q8—64no—
209C3×Q8—124no—
210C3×D4—42no—
211C3×D4—42no—
212C3×D4—42no—
213C3×D4—42no—
214C3×D4—44no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—124no—
231C2×C3×C4C2×#6712yes—
232C2×C3×C4C2×#6712yes—
233C2×C3×C4C2×#6712yes—
234C2×C3×C4C23×D312yes—
235C2×Dic3—24no—
236C2×Dic3—24no—
237C2×Dic3—44no—
238Dic6—24no—
239Dic6—24no—
240Dic6—44no—
241C3⋊C8—64no—
242C3⋊C8—64no—
243C3⋊C8—122no—
244C3⋊C8—122no—
245C2×C32—41no—
246C2×C32—42no—
247C2×C32#53411yescharacteristic
248C2×C32#57812yes—
249#41—41no—
250#41—41no—
251C2×Q8—34no—
252C2×Q8—62no—
253C2×Q8—122no—
254C2×Q8—122no—
255C2×Q8#62511yescharacteristic
256C2×D4#62511yescharacteristic
257C2×D4#62512yes—
258C22×C4—62no—
259C22×C4C2×D3212yes—
260C22×C4C2×D3211yescharacteristic
261Q16—362no—
262Q16—362no—
263M16—361no—
264C2×C8—92no—
265C2×C8—92no—
266C2×C8—361no—
267C4⋊C4—34no—
268C4⋊C4—64no—
269C4⋊C4—64no—
270C22⋊C4—62no—
271C22⋊C4—64no—
272C22⋊C4—64no—
273C42—62no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—24no—
279C22×C3—24no—
280C22×C3—24no—
281C22×C3—21no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—44no—
285C22×C3C22×#6712yes—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—42no—
293C3×C4—124no—
294C3×C4—124no—
295C3×C4#100412yes—
296C3×C4#100412yes—
297Dic3—44no—
298Dic3—44no—
299C32#320211yescharacteristic, complemented, Sylow
300C23C2×#62511yescharacteristic
301C23C2×#62512yes—
302Q8—41no—
303Q8—64no—
304Q8—64no—
305Q8—124no—
306D4—42no—
307D4—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—64no—
313C2×C4—64no—
314C2×C4—124no—
315C2×C4C2×#62512yes—
316C2×C4C2×#62511yescharacteristic
317C2×C4C22×D3211yescharacteristic
318C8—182no—
319C8—182no—
320C2×C3—22no—
321C2×C3—21no—
322C2×C3—42no—
323C2×C3—42no—
324C2×C3—42no—
325C2×C3—42no—
326C2×C3—82no—
327C2×C3#580412yes—
328C2×C3#583814yes—
329C22—22no—
330C22—24no—
331C22—22no—
332C22—21no—
333C22C22×#62511yescharacteristic
334C4—22no—
335C4—21no—
336C4—124no—
337C4—124no—
338C4#6433011yescharacteristic
339C4#6433011yescharacteristic
340C3—21no—
341C3#8341312yescomplemented
342C2—41no—
343C2—42no—
344C2#1059544512yes—
345C2#1059551811yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #10591189C2semidirect
4. #10591188C2semidirect
5. #10591185C2semidirect
6. #10591102C2semidirect
299. C32#3202semidirect
341. C3#83413semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
#105929332
#105911892
#105911882
#105911852
#105911022
#834133