Finite Group Databasebeta

← #11786707

Subgroups — #11786707

Order 1152.

508 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 65 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#10594509C211yesmaximal, characteristic
2#10593413C211yesmaximal, characteristic, complemented
3#10593360C211yesmaximal, characteristic
4C2×#63731C211yesmaximal, characteristic
5#10590582C211yesmaximal, characteristic, complemented
6#10590164C211yesmaximal, characteristic, complemented
7#10590052C211yesmaximal, characteristic, complemented
8C2×#3798C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3788C2211yescharacteristic
11C2×#3773—22no—
12#64101C2211yescharacteristic
13C3×D3×C4⋊C4—21no—
14#63904—22no—
15C4×#625—21no—
16#63900C2211yescharacteristic
17#63900C2211yescharacteristic
18#63841—21no—
19#63838—21no—
20C2×#3712C2211yescharacteristic
21#63740—21no—
22#63739—21no—
23#63731C414yescomplemented
24C3×#807—21no—
25#63573—21no—
26#5504—61no—
27#4881—61no—
28C22×#157—21no—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C3×C4×D3—21no—
31C2×C3×C4×D3—22no—
32C2×#627D411yescharacteristic
33C2×#626—21no—
34C2×#625D411yescharacteristic
35C2×#624—21no—
36C2×#624D412yes—
37#3798—21no—
38#3798—21no—
39#3798C2×C412yes—
40#3798Q812yes—
41C2×#622—21no—
42C4×#157—21no—
43C4×#157C2×C412yescomplemented
44#3788—21no—
45#3788—21no—
46#3773—44no—
47C32×C4⋊C4D411yescharacteristic
48#3752—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C4×C3⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×Dic3⋊C4—22no—
54C2×C3×C3⋊C8—21no—
55#3724—21no—
56#3724—21no—
57(C2×D3)⋊Dic3—22no—
58Dic32—22no—
59#3712—21no—
60#3712C2×C412yescomplemented
61#1859—91nomaximal, Sylow
62C2×#235—61no—
63C2×C3×C4⋊C4—61no—
64C4×#67—62no—
65C4×#67—62no—
66#926—61no—
67C2×ΓL(1,𝔽25)—61no—
68#893—62no—
69#892—61no—
70#892—61no—
71#892—61no—
72D3×C4⋊C4—21no—
73D3×C4⋊C4—61no—
74D3×C4⋊C4—61no—
75#887—62no—
76C3×#107—61no—
77#817—61no—
78#808—61no—
79#807—21no—
80C22×C3⋊D3C2×D411yescharacteristic
81C22×C3×D3—21no—
82C2×#157—22no—
83C2×#157—22no—
84C2×#157—22no—
85C2×C32×C4—21no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3C2×D411yescharacteristic
89C4×C3⋊D3C22×C411yescharacteristic
90C4×C3⋊D3C2×Q811yescharacteristic
91C4×C3⋊D3#4111yescharacteristic
92C4×C3⋊D3#4111yescharacteristic
93C2×C3×Dic3—21no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—41no—
96C3×C4×D3—22no—
97C3×C4×D3—22no—
98C3×C4×D3—82no—
99#627—21no—
100#627C4⋊C412yescomplemented
101#626—22no—
102#626—22no—
103#625—21no—
104#625C4⋊C412yescomplemented
105#624—42no—
106#624—42no—
107#622—41no—
108C3×C3⋊C8—22no—
109#520—91no—
110#428—91no—
111C2×#104—91no—
112#417—91no—
113#384—91no—
114#343—91no—
115#339—91no—
116C22×C3×C4—61no—
117C22×C3×C4—62no—
118C2×#67—61no—
119C2×#67—61no—
120#235—62no—
121#235—62no—
122#235—62no—
123#235—62no—
124C2×D12—61no—
125C2×C4×D3—21no—
126C2×C4×D3—22no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—62no—
130C2×C4×D3—121no—
131C2×Dic6—61no—
132C2×C3×C8—61no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138#217—62no—
139(C2×D3)⋊C4—62no—
140(C2×D3)⋊C4—62no—
141(C2×D3)⋊C4—121no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146Dic3⋊C4—22no—
147Dic3⋊C4—62no—
148Dic3⋊C4—121no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—121no—
153C2×C3⋊C8—21no—
154ΓL(1,𝔽25)—62no—
155ΓL(1,𝔽25)—62no—
156C22×C32#12011yescharacteristic
157C2×C3⋊D3—21no—
158C2×C3⋊D3—21no—
159C2×C3⋊D3C4×D411yescharacteristic
160C2×C3⋊D3C22⋊Q811yescharacteristic
161C2×C3×D3—22no—
162C2×C3×D3—41no—
163C2×C3×D3—41no—
164#157—24no—
165C32×C4—41no—
166C32×C4C4×D411yescharacteristic
167C32×C4C22⋊Q811yescharacteristic
168C3⋊Dic3—41no—
169C3⋊Dic3C2×C4⋊C411yescharacteristic
170C3⋊Dic3#12311yescharacteristic
171C3×Dic3—22no—
172C3×Dic3—42no—
173C3×Dic3—81no—
174C2×#41—91no—
175C2×M16—91no—
176C2×M16—91no—
177C4×Q8—181no—
178C4×D4—182no—
179C4×D4—181no—
180#117—91no—
181#117—181no—
182C2×C4⋊C4—61no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—182no—
186C2×C42—91no—
187#107—61no—
188#106—181no—
189#104—94no—
190#103—181no—
191#102—181no—
192C23×C3—61no—
193C22×D3—21no—
194C22×D3—61no—
195C22×D3—61no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—41no—
200C2×C3×C4—62no—
201C2×C3×C4—62no—
202C2×C3×C4—61no—
203C2×C3×C4—62no—
204C2×C3×C4—121no—
205C2×C3×C4—242no—
206#67—62no—
207#67—62no—
208#67—62no—
209#67—62no—
210C2×Dic3—21no—
211C2×Dic3—22no—
212C2×Dic3—41no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—62no—
216C2×Dic3—121no—
217D12—62no—
218D12—62no—
219C4×D3—22no—
220C4×D3—22no—
221C4×D3—61no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—61no—
227C4×D3—61no—
228C4×D3—61no—
229C4×D3—82no—
230C4×D3—242no—
231C4×D3—242no—
232Dic6—62no—
233Dic6—62no—
234C3×C8—62no—
235C3⋊C8—22no—
236C2×C32#38511yescharacteristic
237C2×C32#45311yescharacteristic
238C2×C32#45611yescharacteristic
239C3⋊D3—21no—
240C3⋊D3—21no—
241C3×D3—42no—
242#41—92no—
243#41—92no—
244#41—181no—
245#41—181no—
246C2×Q8—91no—
247C2×D4—91no—
248C2×D4—181no—
249C22×C4—62no—
250C22×C4—61no—
251C22×C4—92no—
252C22×C4—91no—
253C22×C4—181no—
254C22×C4—181no—
255M16—92no—
256M16—181no—
257M16—181no—
258M16—181no—
259C2×C8—61no—
260C2×C8—181no—
261C4⋊C4—62no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4—91no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4—364no—
268C4⋊C4GO+(4,𝔽2)11yescharacteristic
269C22⋊C4—181no—
270C22⋊C4—182no—
271C42—92no—
272C42—181no—
273C42—182no—
274C42—181no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—62no—
278C22×C3—121no—
279C22×C3—121no—
280C2×D3—22no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3—61no—
284C2×D3—61no—
285C2×D3—61no—
286C2×D3—61no—
287C2×D3—121no—
288C2×D3—121no—
289C2×D3—121no—
290C2×D3—121no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—42no—
296C3×C4—62no—
297C3×C4—81no—
298C3×C4—122no—
299C3×C4—241no—
300Dic3—22no—
301Dic3—42no—
302Dic3—61no—
303Dic3—61no—
304Dic3—61no—
305Dic3—61no—
306Dic3—81no—
307Dic3—122no—
308Dic3—241no—
309C32#185911yescharacteristic, complemented, Sylow
310C23—61no—
311C23—91no—
312Q8—92no—
313Q8—181no—
314D4—92no—
315D4—182no—
316D4—182no—
317D4—181no—
318C2×C4—21no—
319C2×C4—61no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—62no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—121no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4—181no—
333C2×C4—242no—
334C2×C4—362no—
335C2×C4—362no—
336C2×C4C2×GO+(4,𝔽2)11yescharacteristic
337C8—62no—
338C8—361no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—122no—
346D3—42no—
347D3—121no—
348D3—121no—
349D3—121no—
350D3—121no—
351C22—62no—
352C22—91no—
353C22—91no—
354C22—121no—
355C22—121no—
356C22—181no—
357C22—181no—
358C22#6424111yescharacteristic
359C4—41no—
360C4—62no—
361C4—91no—
362C4—91no—
363C4—122no—
364C4—184no—
365C4—241no—
366C4—361no—
367C4D32⋊Q811yescharacteristic
368C4C4×GO+(4,𝔽2)11yescharacteristic
369C3—21no—
370C3—21no—
371C2—122no—
372C2—181no—
373C2—181no—
374C2#1059339811yescharacteristic
375C2#1059346311yescharacteristic
376C2#1059348411yescharacteristic
subgroupG/H
centerC22#64241
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#120
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1859
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593413C2semidirect
5. #10590582C2semidirect
6. #10590164C2semidirect
7. #10590052C2semidirect
23. #63731C4semidirect
43. C4×#157C2×C4semidirect
60. #3712C2×C4semidirect
100. #627C4⋊C4semidirect
104. #625C4⋊C4semidirect
309. C32#1859semidirect

Maximal subgroups

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

subgroupindex
#105945092
#105934132
#105933602
C2×#637312
#105905822
#105901642
#105900522
#18599