Finite Group Databasebeta

← #11785330

Subgroups — #11785330

Order 1152.

530 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#3798C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3C2×#63731C212yesmaximal
4#10590340C211yesmaximal, characteristic, complemented
5#10590047C212yesmaximal, complemented
6C2×#3798C2211yescharacteristic
7C2×C4⋊#157—21no—
8C2×C4×#157C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×C42×D3—21no—
11C4×#627C411yescharacteristic, complemented
12C4×#627C411yescharacteristic, complemented
13C4×#626—21no—
14C4×#626—21no—
15C4×#625C411yescharacteristic, complemented
16C4×#625C411yescharacteristic, complemented
17#63874C2211yescharacteristic
18#63855—21no—
19C2×#3712C2212yes—
20#63781—21no—
21#63731—24no—
22C3×C4⋊(C3⋊C8)—21no—
23#63572—21no—
24C4×#235—61no—
25#4837—61no—
26C22×#157—22no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C3×C4×D3—21no—
31C2×C3×C4×D3—21no—
32C2×C3×C4×D3—21no—
33C2×#627C2×C411yescharacteristic
34C2×#626—21no—
35C2×#625C2×C411yescharacteristic
36#3798—21no—
37#3798—21no—
38#3798D412yes—
39#3798Q812yes—
40C4⋊#157—24no—
41C4×#157—22no—
42C4×#157—22no—
43C32×C42D411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C3×C4×Dic3—21no—
48C3×C4×Dic3—21no—
49C3×C4×Dic3—21no—
50C2×C3×C3⋊C8—22no—
51#3724C2×C411yescharacteristic
52#3724C2×C411yescharacteristic
53Dic3⋊Dic3—21no—
54Dic3⋊Dic3—21no—
55#3722—21no—
56(C2×D3)⋊Dic3—21no—
57(C2×D3)⋊Dic3—21no—
58#3712—22no—
59#3712—22no—
60#1806—91nomaximal, Sylow
61C2×#235—61no—
62C2×C3×C42—61no—
63C4×#67—61no—
64C4×#67—61no—
65C4×#67—61no—
66C4×#67—61no—
67#926—61no—
68C2×ΓL(1,𝔽25)—62no—
69C4×D12—61no—
70C4×D12—61no—
71#872—61no—
72#872—61no—
73C42×D3—21no—
74C42×D3—61no—
75C42×D3—61no—
76C4×Dic6—61no—
77C4×Dic6—61no—
78C3×C4⋊C8—61no—
79Dic3⋊C8—62no—
80C4⋊(C3⋊C8)—21no—
81C22×C3⋊D3C2×D411yescharacteristic
82C22×C3×D3—21no—
83C2×#157—24no—
84C2×#157—42no—
85C2×#157—42no—
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22×C411yescharacteristic
92C4×C3⋊D3—22no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3C2×D411yescharacteristic
95C4×C3⋊D3C2×Q811yescharacteristic
96C4×C3⋊D3#4111yescharacteristic
97C4×C3⋊D3#4111yescharacteristic
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C3×C4×D3—22no—
102C3×C4×D3—22no—
103C3×C4×D3—42no—
104C3×C4×D3—42no—
105#627—21no—
106#627C4⋊C412yescomplemented
107#626—22no—
108#626—22no—
109#625—21no—
110#625C4⋊C412yescomplemented
111C3×C3⋊C8—42no—
112C4×#41—91no—
113#423—91no—
114C2×#104—92no—
115C4×C4⋊C4—91no—
116#339—92no—
117C22×C3×C4—61no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C2×#67—61no—
121C2×#67—61no—
122#235—62no—
123#235—62no—
124#235—62no—
125#235—62no—
126C2×D12—61no—
127C2×C4×D3—21no—
128C2×C4×D3—21no—
129C2×C4×D3—21no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×Dic6—61no—
137C2×C3×C8—62no—
138C3×C42—21no—
139C3×C42—21no—
140C3×C42—61no—
141C3×C42—61no—
142C3×C42—61no—
143#217—61no—
144#217—61no—
145(C2×D3)⋊C4—61no—
146(C2×D3)⋊C4—61no—
147(C2×D3)⋊C4—61no—
148(C2×D3)⋊C4—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151Dic3⋊C4—61no—
152Dic3⋊C4—61no—
153Dic3⋊C4—61no—
154Dic3⋊C4—61no—
155C4×Dic3—21no—
156C4×Dic3—21no—
157C4×Dic3—21no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C2×C3⋊C8—22no—
165ΓL(1,𝔽25)—122no—
166ΓL(1,𝔽25)—122no—
167C22×C32C2×C22⋊C411yescharacteristic
168C2×C3⋊D3—21no—
169C2×C3⋊D3—21no—
170C2×C3⋊D3#12111yescharacteristic
171C2×C3⋊D3C22⋊Q811yescharacteristic
172C2×C3×D3—22no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175#157—44no—
176C32×C4—21no—
177C32×C4#10412yescomplemented
178C32×C4#12111yescharacteristic
179C32×C4C22⋊Q811yescharacteristic
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3C2×C4⋊C411yescharacteristic
183C3⋊Dic3#11711yescharacteristic
184C3×Dic3—22no—
185C3×Dic3—41no—
186C3×Dic3—41no—
187C2×#41—91no—
188C2×M16—92no—
189C4×Q8—91no—
190C4×Q8—91no—
191C4×D4—91no—
192C4×D4—91no—
193C4×D4—181no—
194C4×D4—181no—
195#117—91no—
196#117—181no—
197C2×C4⋊C4—181no—
198C2×C42—61no—
199C2×C42—91no—
200C2×C42—92no—
201C4⋊C8—61no—
202C4⋊C8—181no—
203#104—184no—
204#95—181no—
205C23×C3—61no—
206C22×D3—21no—
207C22×D3—61no—
208C22×D3—61no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—61no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—122no—
221C2×C3×C4—122no—
222#67—62no—
223#67—62no—
224#67—62no—
225#67—62no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235D12—62no—
236D12—62no—
237C4×D3—22no—
238C4×D3—22no—
239C4×D3—42no—
240C4×D3—42no—
241C4×D3—61no—
242C4×D3—61no—
243C4×D3—61no—
244C4×D3—61no—
245C4×D3—61no—
246C4×D3—61no—
247C4×D3—61no—
248C4×D3—61no—
249C4×D3—122no—
250C4×D3—122no—
251C4×D3—122no—
252C4×D3—122no—
253Dic6—62no—
254Dic6—62no—
255C3×C8—122no—
256C3⋊C8—42no—
257C2×C32#38011yescharacteristic
258C2×C32C2×#10411yescharacteristic
259C2×C32#42111yescharacteristic
260C3⋊D3—21no—
261C3⋊D3—21no—
262C3×D3—42no—
263#41—92no—
264#41—92no—
265#41—181no—
266#41—181no—
267C2×Q8—91no—
268C2×D4—91no—
269C2×D4—181no—
270C22×C4—61no—
271C22×C4—61no—
272C22×C4—61no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—182no—
277M16—182no—
278M16—182no—
279C2×C8—62no—
280C4⋊C4—91no—
281C4⋊C4—91no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—184no—
285C22⋊C4—181no—
286C22⋊C4—181no—
287C22⋊C4—181no—
288C42—61no—
289C42—61no—
290C42—61no—
291C42—91no—
292C42—91no—
293C42—91no—
294C42—182no—
295C42—182no—
296C42GO+(4,𝔽2)11yescharacteristic
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—62no—
300C22×C3—121no—
301C22×C3—121no—
302C2×D3—22no—
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—61no—
306C2×D3—61no—
307C2×D3—61no—
308C2×D3—61no—
309C2×D3—121no—
310C2×D3—121no—
311C2×D3—121no—
312C2×D3—121no—
313C3×C4—22no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—41no—
321C3×C4—62no—
322C3×C4—121no—
323C3×C4—121no—
324Dic3—22no—
325Dic3—41no—
326Dic3—41no—
327Dic3—61no—
328Dic3—61no—
329Dic3—61no—
330Dic3—61no—
331Dic3—62no—
332Dic3—121no—
333Dic3—121no—
334Dic3—121no—
335C32#180611yescharacteristic, complemented, Sylow
336C23—61no—
337C23—91no—
338Q8—92no—
339Q8—181no—
340D4—92no—
341D4—182no—
342D4—182no—
343D4—181no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—91no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—91no—
355C2×C4—91no—
356C2×C4—122no—
357C2×C4—122no—
358C2×C4—182no—
359C2×C4—184no—
360C2×C4—361no—
361C2×C4—362no—
362C2×C4—362no—
363C2×C4D32⋊C411yescharacteristic
364C2×C4D32⋊C411yescharacteristic
365C2×C4C2×GO+(4,𝔽2)11yescharacteristic
366C8—122no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—122no—
374D3—42no—
375D3—121no—
376D3—121no—
377D3—121no—
378D3—121no—
379C22—62no—
380C22—91no—
381C22—91no—
382C22—121no—
383C22—121no—
384C22—181no—
385C22—181no—
386C22C2×D32⋊C411yescharacteristic
387C4—21no—
388C4—62no—
389C4—91no—
390C4—91no—
391C4—121no—
392C4—121no—
393C4—181no—
394C4—181no—
395C4—364no—
396C4#6373112yescomplemented
397C4D32⋊Q811yescharacteristic
398C4#6423011yescharacteristic
399C3—21no—
400C3—21no—
401C2—122no—
402C2—181no—
403C2—181no—
404C2C2×#6373111yescharacteristic
405C2#1059332311yescharacteristic
406C2#1059340311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1806
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
4. #10590340C2semidirect
5. #10590047C2semidirect
11. C4×#627C4semidirect
12. C4×#627C4semidirect
15. C4×#625C4semidirect
16. C4×#625C4semidirect
106. #627C4⋊C4semidirect
110. #625C4⋊C4semidirect
177. C32×C4#104semidirect
335. C32#1806semidirect
396. C4#63731semidirect

Maximal subgroups

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

subgroupindex
C4×#37982
C4×C4⋊#1572
C2×#637312
#105903402
#105900472
#18069