Finite Group Databasebeta

← #11773234

Subgroups — #11773234

Order 1152.

1030 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C22×C4×#157C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4C2×#63781C212yesmaximal
5C2×#63781C212yesmaximal
6C23×#157C2212yes—
7C23×#157C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C4×#157—22no—
12C2×C4×#157—24no—
13C2×C32×C4⋊C4C411yescharacteristic, complemented
14C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
15C2×#3750C411yescharacteristic, complemented
16C2×#3750C411yescharacteristic, complemented
17C4⋊C4×C3⋊D3—22no—
18C4⋊C4×C3⋊D3—22no—
19#63781—22no—
20#63781—24no—
21#63781C418yescomplemented
22C2×D3×C4⋊C4—62no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157—22no—
29C22×#157—22no—
30C22×#157—22no—
31C22×#157—22no—
32C22×#157—22no—
33C22×#157—22no—
34C22×#157C2×C414yes—
35C22×#157C2×C414yes—
36C22×#157D414yes—
37C22×#157Q814yes—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C411yescharacteristic
41C22×C3⋊Dic3C2×C411yescharacteristic
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—22no—
47C2×C4×C3⋊D3—22no—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3C2×C414yes—
54C2×C4×C3⋊D3D412yes—
55C2×C4×C3⋊D3D412yes—
56C4×#157—28no—
57C32×C4⋊C4—22no—
58C4⋊(C3⋊Dic3)—22no—
59#3750—22no—
60#3750—22no—
61#1436—91nomaximal, Sylow
62C22×C4×D3—62no—
63C22×C4×D3—62no—
64C22×C4×D3—62no—
65C2×C3×C4⋊C4—22no—
66C2×C4⋊Dic3—62no—
67C2×Dic3⋊C4—62no—
68C2×Dic3⋊C4—62no—
69D3×C4⋊C4—68no—
70D3×C4⋊C4—68no—
71C23×C32C22×C411yescharacteristic
72C22×C3⋊D3C22×C412yes—
73C22×C3⋊D3C2×D412yes—
74C22×C3⋊D3C2×D411yescharacteristic
75C22×C3⋊D3C2×D411yescharacteristic
76C22×C3⋊D3C2×Q812yes—
77C22×C3⋊D3#4112yes—
78C22×C3⋊D3#4112yes—
79C22×C3⋊D3#4112yes—
80C2×#157—24no—
81C2×#157—24no—
82C2×#157—24no—
83C2×#157—24no—
84C2×#157—24no—
85C2×#157—24no—
86C2×#157—24no—
87C2×#157—24no—
88C2×#157—24no—
89C2×#157—42no—
90C2×#157—42no—
91C2×#157—42no—
92C2×#157—42no—
93C2×#157C4⋊C418yescomplemented
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4C4212yescomplemented
100C2×C32×C4C22⋊C412yes—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3C4212yescomplemented
107C2×C3⋊Dic3C22⋊C412yes—
108C4×C3⋊D3—24no—
109C4×C3⋊D3—24no—
110C4×C3⋊D3—22no—
111C4×C3⋊D3—24no—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—42no—
115C4×C3⋊D3—41no—
116C22×C4⋊C4—91no—
117C22×C42—91no—
118C2×#95—92no—
119C2×#95—92no—
120C2×#95—91no—
121C23×D3—62no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—22no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C2×C4×D3—68no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—68no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—124no—
137C2×C4×D3—124no—
138C2×C4×D3—124no—
139C2×C4×D3—124no—
140C3×C4⋊C4—28no—
141C4⋊Dic3—68no—
142Dic3⋊C4—68no—
143Dic3⋊C4—68no—
144C22×C32C2×C4211yescharacteristic
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#11711yescharacteristic
147C22×C32C4×D412yes—
148C22×C32C4×Q812yes—
149C2×C3⋊D3C2×C4⋊C412yes—
150C2×C3⋊D3#11712yes—
151C2×C3⋊D3C4×D412yes—
152C2×C3⋊D3C4×D412yes—
153C2×C3⋊D3C4×D412yes—
154C2×C3⋊D3C4×Q812yes—
155C2×C3⋊D3#12011yescharacteristic
156C2×C3⋊D3#12112yes—
157C2×C3⋊D3C22⋊Q812yes—
158C2×C3⋊D3C22⋊Q812yes—
159C2×C3⋊D3#12312yes—
160C2×C3⋊D3#12311yescharacteristic
161C2×C3⋊D3#12411yescharacteristic
162C2×C3⋊D3#12512yes—
163C2×C3⋊D3#12612yes—
164C2×C3⋊D3C4⋊Q811yescharacteristic
165#157—28no—
166#157—44no—
167C32×C4—22no—
168C32×C4—22no—
169C32×C4—41no—
170C3⋊Dic3—22no—
171C3⋊Dic3—22no—
172C3⋊Dic3—41no—
173C23×C4—92no—
174C23×C4—91no—
175C23×C4—91no—
176C23×C4—92no—
177C23×C4—91no—
178C2×C4⋊C4—91no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—91no—
181C2×C4⋊C4—182no—
182C2×C4⋊C4—182no—
183C2×C4⋊C4#15711yescharacteristic, complemented
184C2×C42—184no—
185C2×C42—182no—
186#95—98no—
187#95—184no—
188#95—182no—
189C23×C3—22no—
190C22×D3—64no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—64no—
197C22×D3—64no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—124no—
211C2×Dic3—124no—
212C4×D3—616no—
213C4×D3—616no—
214C4×D3—124no—
215C4×D3—128no—
216C4×D3—124no—
217C4×D3—124no—
218C4×D3—128no—
219C4×D3—124no—
220C2×C32C4×C22⋊C411yescharacteristic
221C2×C32C4×C4⋊C412yes—
222C2×C32#38611yescharacteristic
223C2×C32#38712yes—
224C2×C32#39111yescharacteristic
225C3⋊D3#38512yes—
226C3⋊D3#38712yes—
227C3⋊D3#38812yes—
228C3⋊D3#38912yes—
229C24—91no—
230C22×C4—94no—
231C22×C4—94no—
232C22×C4—94no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—94no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—94no—
239C22×C4—91no—
240C22×C4—182no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4—182no—
244C22×C4—182no—
245C22×C4—182no—
246C22×C4—181no—
247C22×C4—181no—
248C22×C4—182no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—182no—
252C22×C4—182no—
253C22×C4—182no—
254C22×C4—182no—
255C22×C4—182no—
256C22×C4—182no—
257C22×C4—182no—
258C22×C4—182no—
259C22×C4C2×#15711yescharacteristic
260C22×C4C2×#15711yescharacteristic
261C22×C4C2×#15711yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—182no—
264C4⋊C4—182no—
265C4⋊C4—182no—
266C42—188no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—24no—
270C22×C3—24no—
271C22×C3—22no—
272C2×D3—64no—
273C2×D3—64no—
274C2×D3—62no—
275C2×D3—64no—
276C2×D3—62no—
277C2×D3—64no—
278C2×D3—64no—
279C2×D3—64no—
280C2×D3—64no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—64no—
284C2×D3—62no—
285C2×D3—64no—
286C2×D3—64no—
287C2×D3—62no—
288C3×C4—28no—
289C3×C4—44no—
290C3×C4—44no—
291Dic3—68no—
292Dic3—124no—
293Dic3—124no—
294C32#143611yescharacteristic, complemented, Sylow
295C23—92no—
296C23—92no—
297C23—92no—
298C23—92no—
299C23—92no—
300C23—92no—
301C23—91no—
302C23—91no—
303C23C22×#15711yescharacteristic
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—98no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—182no—
313C2×C4—184no—
314C2×C4—184no—
315C2×C4—184no—
316C2×C4—182no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4—184no—
320C2×C4—184no—
321C2×C4—184no—
322C2×C4—184no—
323C2×C4—181no—
324C2×C4—182no—
325C2×C4—181no—
326C2×C4—184no—
327C2×C4—184no—
328C2×C4—184no—
329C2×C4—182no—
330C2×C4—181no—
331C2×C4—361no—
332C2×C4—362no—
333C2×C4—361no—
334C2×C4—362no—
335C2×C4—362no—
336C2×C4—362no—
337C2×C4—362no—
338C2×C4C4×#15712yescomplemented
339C2×C4C22⋊#15712yes—
340C2×C3—22no—
341C2×C3—22no—
342C2×C3—22no—
343C2×C3—24no—
344C2×C3—24no—
345D3—64no—
346D3—64no—
347D3—64no—
348D3—64no—
349C22—92no—
350C22—92no—
351C22—91no—
352C22—92no—
353C22—91no—
354C22—92no—
355C22—91no—
356C22—91no—
357C22—92no—
358C22—92no—
359C22—92no—
360C22—92no—
361C22—92no—
362C22—92no—
363C22—92no—
364C22—92no—
365C22C2×C4×#15711yescharacteristic
366C22#6428611yescharacteristic
367C22D4×#15712yes—
368C22Q8×#15712yes—
369C22C2×C22⋊#15711yescharacteristic
370C4—22no—
371C4—22no—
372C4—41no—
373C4—188no—
374C4—182no—
375C4—182no—
376C4—364no—
377C4—361no—
378C3—22no—
379C2—92no—
380C2—92no—
381C2—92no—
382C2—92no—
383C2C4⋊C4×#15712yes—
384C2#1059375812yes—
385C2C4×C22⋊#15711yescharacteristic
386C2#1059382611yescharacteristic
387C2#1059383711yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C4⋊C4C4
socleC23×C32C22×C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. C2×C32×C4⋊C4C4semidirect
14. C2×C4⋊(C3⋊Dic3)C4semidirect
15. C2×#3750C4semidirect
16. C2×#3750C4semidirect
21. #63781C4semidirect
93. C2×#157C4⋊C4semidirect
99. C2×C32×C4C42semidirect
106. C2×C3⋊Dic3C42semidirect
183. C2×C4⋊C4#157semidirect
294. C32#1436semidirect
338. C2×C4C4×#157semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×C4⋊C4×C3⋊D32
C2×#637812
#14369