Finite Group Databasebeta

← #11786756

Subgroups — #11786756

Order 1152.

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

normal subgroups only

This group has 492 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#10594511C211yesmaximal, characteristic
2#10593360C211yesmaximal, characteristic
3#10593344C211yesmaximal, characteristic, complemented
4C2×#63731C211yesmaximal, characteristic
5#10590582C211yesmaximal, characteristic, complemented
6#10590164C211yesmaximal, characteristic, complemented
7#10590052C211yesmaximal, characteristic, complemented
8C2×#3798C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3788C2211yescharacteristic
11#64101C2211yescharacteristic
12C3×#892—21no—
13C4×#627—21no—
14#63902—21no—
15#63900C2211yescharacteristic
16#63900C2211yescharacteristic
17D3×C4⋊Dic3—21no—
18#63880—22no—
19C2×#3712C2211yescharacteristic
20#63740—21no—
21#63739—21no—
22#63737—22no—
23#63731C414yescomplemented
24C3×#807—21no—
25#63573—21no—
26#5523—61no—
27#4881—61no—
28C22×#157—21no—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C3×C4×D3—21no—
31C2×#627D411yescharacteristic
32C2×#626—21no—
33C2×#625D411yescharacteristic
34C2×#624—21no—
35C2×#624D412yes—
36C2×D3×Dic3—22no—
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—
46C32×C4⋊C4D411yescharacteristic
47#3752—21no—
48C4⋊(C3⋊Dic3)D411yescharacteristic
49C4×C3⋊Dic3—21no—
50C3×(C2×D3)⋊C4—22no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4×Dic3—22no—
54C2×C3×C3⋊C8—21no—
55#3724—21no—
56#3724—21no—
57Dic3⋊Dic3—22no—
58#3712—21no—
59#3712C2×C412yescomplemented
60#1860—91nomaximal, Sylow
61C2×#235—61no—
62C3×#117—61no—
63C2×C4⋊Dic3—61no—
64C2×ΓL(1,𝔽25)—61no—
65#892—21no—
66#892—61no—
67#892—61no—
68D3×C4⋊C4—61no—
69D3×C4⋊C4—61no—
70D3×C4⋊C4—61no—
71#67⋊C4—62no—
72#67⋊C4—62no—
73C4×D12—62no—
74C4×Dic6—62no—
75C3×#107—61no—
76#817—61no—
77#808—61no—
78#807—21no—
79C22×C3⋊D3C2×D411yescharacteristic
80C22×C3×D3—21no—
81C2×#157—22no—
82C2×#157—41no—
83C2×#157—41no—
84C2×C32×C4—21no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3C2×D411yescharacteristic
88C4×C3⋊D3C22×C411yescharacteristic
89C4×C3⋊D3C2×Q811yescharacteristic
90C4×C3⋊D3#4111yescharacteristic
91C4×C3⋊D3#4111yescharacteristic
92C2×C3×Dic3—21no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—41no—
95C3×C4×D3—22no—
96C3×C4×D3—22no—
97#627—21no—
98#627C4⋊C412yes—
99#626—22no—
100#626—22no—
101#625—21no—
102#625C4⋊C412yes—
103#624—42no—
104#624—42no—
105D3×Dic3—82no—
106#622—41no—
107C3×C3⋊C8—22no—
108#520—91no—
109#428—91no—
110C2×#104—91no—
111#417—91no—
112#382—91no—
113#343—91no—
114#339—91no—
115C22×C3×C4—61no—
116C2×#67—61no—
117C2×#67—61no—
118C22×Dic3—62no—
119#235—62no—
120#235—62no—
121#235—62no—
122#235—62no—
123C2×D12—61no—
124C2×C4×D3—21no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—121no—
130C2×Dic6—61no—
131C2×C3×C8—61no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C22⋊C4—62no—
137C3×C42—62no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—62no—
140(C2×D3)⋊C4—121no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—121no—
149C4×Dic3—22no—
150C4×Dic3—62no—
151C4×Dic3—121no—
152C2×C3⋊C8—21no—
153ΓL(1,𝔽25)—62no—
154ΓL(1,𝔽25)—62no—
155C22×C32#12011yescharacteristic
156C2×C3⋊D3—21no—
157C2×C3⋊D3—21no—
158C2×C3⋊D3C4×D411yescharacteristic
159C2×C3⋊D3C22⋊Q811yescharacteristic
160C2×C3×D3—22no—
161C2×C3×D3—41no—
162C2×C3×D3—41no—
163#157—42no—
164C32×C4—41no—
165C32×C4C4×D411yescharacteristic
166C32×C4C22⋊Q811yescharacteristic
167C3⋊Dic3—41no—
168C3⋊Dic3C2×C4⋊C411yescharacteristic
169C3⋊Dic3#12311yescharacteristic
170C3×Dic3—22no—
171C3×Dic3—42no—
172C3×Dic3—81no—
173C2×#41—91no—
174C2×M16—91no—
175C2×M16—91no—
176C4×Q8—181no—
177C4×D4—182no—
178C4×D4—181no—
179#117—61no—
180#117—91no—
181C2×C4⋊C4—91no—
182C2×C4⋊C4—91no—
183C2×C4⋊C4—181no—
184C2×C42—91no—
185#107—61no—
186#106—181no—
187#104—94no—
188#103—181no—
189#102—181no—
190#95—182no—
191C23×C3—61no—
192C22×D3—21no—
193C22×D3—61no—
194C22×D3—61no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—41no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—61no—
202C2×C3×C4—62no—
203C2×C3×C4—121no—
204#67—62no—
205#67—62no—
206#67—62no—
207#67—62no—
208C2×Dic3—21no—
209C2×Dic3—22no—
210C2×Dic3—41no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—121no—
215C2×Dic3—242no—
216D12—62no—
217D12—62no—
218C4×D3—22no—
219C4×D3—22no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—61no—
227C4×D3—61no—
228C4×D3—242no—
229C4×D3—242no—
230C4×D3—242no—
231Dic6—62no—
232Dic6—62no—
233C3×C8—62no—
234C3⋊C8—22no—
235C2×C32#38511yescharacteristic
236C2×C32#45411yescharacteristic
237C2×C32#45511yescharacteristic
238C3⋊D3—21no—
239C3⋊D3—21no—
240C3×D3—42no—
241#41—92no—
242#41—92no—
243#41—181no—
244#41—181no—
245C2×Q8—91no—
246C2×D4—91no—
247C2×D4—181no—
248C22×C4—61no—
249C22×C4—92no—
250C22×C4—91no—
251C22×C4—182no—
252C22×C4—181no—
253C22×C4—181no—
254M16—92no—
255M16—181no—
256M16—181no—
257M16—181no—
258C2×C8—61no—
259C2×C8—181no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4—91no—
263C4⋊C4—181no—
264C4⋊C4—182no—
265C4⋊C4—181no—
266C4⋊C4GO+(4,𝔽2)11yescharacteristic
267C22⋊C4—62no—
268C22⋊C4—181no—
269C42—62no—
270C42—92no—
271C42—181no—
272C42—181no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—62no—
276C22×C3—121no—
277C22×C3—121no—
278C2×D3—22no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—61no—
282C2×D3—61no—
283C2×D3—61no—
284C2×D3—61no—
285C2×D3—121no—
286C2×D3—121no—
287C2×D3—121no—
288C2×D3—121no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—42no—
294C3×C4—62no—
295C3×C4—81no—
296C3×C4—122no—
297C3×C4—241no—
298Dic3—22no—
299Dic3—42no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303Dic3—61no—
304Dic3—81no—
305Dic3—122no—
306Dic3—241no—
307C32#186011yescharacteristic, complemented, Sylow
308C23—61no—
309C23—91no—
310Q8—92no—
311Q8—181no—
312D4—92no—
313D4—182no—
314D4—182no—
315D4—181no—
316C2×C4—21no—
317C2×C4—61no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—62no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—121no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4—362no—
330C2×C4—362no—
331C2×C4—361no—
332C2×C4—361no—
333C2×C4—722no—
334C2×C4C2×GO+(4,𝔽2)11yescharacteristic
335C8—62no—
336C8—361no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—122no—
344D3—42no—
345D3—121no—
346D3—121no—
347D3—121no—
348D3—121no—
349C22—62no—
350C22—91no—
351C22—91no—
352C22—121no—
353C22—121no—
354C22—181no—
355C22—181no—
356C22#6424111yescharacteristic
357C4—41no—
358C4—62no—
359C4—91no—
360C4—91no—
361C4—122no—
362C4—241no—
363C4—362no—
364C4—361no—
365C4D32⋊Q811yescharacteristic
366C4C4×GO+(4,𝔽2)11yescharacteristic
367C3—21no—
368C3—21no—
369C2—122no—
370C2—181no—
371C2—181no—
372C2#1059339811yescharacteristic
373C2#1059346911yescharacteristic
374C2#1059347311yescharacteristic
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#1860
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
3. #10593344C2semidirect
5. #10590582C2semidirect
6. #10590164C2semidirect
7. #10590052C2semidirect
23. #63731C4semidirect
43. C4×#157C2×C4semidirect
59. #3712C2×C4semidirect
307. C32#1860semidirect

Maximal subgroups

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

subgroupindex
#105945112
#105933602
#105933442
C2×#637312
#105905822
#105901642
#105900522
#18609