Finite Group Databasebeta

← #11777901

Subgroups — #11777901

Order 1152.

385 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3755C211yesmaximal, characteristic
2C3×#5024C211yesmaximal, characteristic, complemented
3#10590338C211yesmaximal, characteristic
4C3×#4535C211yesmaximal, characteristic, complemented
5#10589100C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic
7#10589079C211yesmaximal, characteristic, complemented
8#70955—31nomaximal
9#68226—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3755C411yescharacteristic
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×#3712—21no—
14#63662C411yescharacteristic
15#63636C411yescharacteristic
16#63635C411yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#803—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63557—21no—
25C3×#446—31no—
26C4×#215—31no—
27C4×#215—31no—
28C4×#215—61no—
29#5024D311yescharacteristic, complemented
30#4838—31no—
31#4688—31no—
32C3×Q8⋊C8—31no—
33#4535D311yescharacteristic, complemented
34#4483—31no—
35#4479—31no—
36#4479—31no—
37#4459—31no—
38#4454—31no—
39#4454—31no—
40C2×C32×Q8C2×C411yescharacteristic
41C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47#3755—22no—
48#3752—21no—
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
51C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3712—42no—
58#1592—91noSylow
59C3×C4×Q8—21no—
60C3×C4×Q8C2×D311yescharacteristic
61C3×C4×Q8C2×D311yescharacteristic
62C2×#215—31no—
63C2×#215—31no—
64C2×#215—61no—
65C2×ΓL(1,𝔽25)—61no—
66C2×ΓL(1,𝔽25)—61no—
67C4×D12—31no—
68C4×D12—31no—
69C4×D12—61no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—61no—
73C3×#97—61no—
74C3×C4×C8—31no—
75C3×C4×C8—31no—
76#835—31no—
77#835—31no—
78#835—61no—
79(C2×D3)⋊C8—61no—
80(C2×D3)⋊C8—61no—
81#809—31no—
82#809—31no—
83#809—61no—
84#808—31no—
85#808—31no—
86#808—61no—
87C4⋊(C3⋊C8)—21no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90#803—21no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C4×C3⋊C8C2×D311yescharacteristic
95C4×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊D3—21no—
97C32×Q8—21no—
98C32×Q8—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—21no—
105C4⋊(C3⋊D3)—21no—
106C4⋊(C3⋊D3)—21no—
107C4×C3⋊D3—41no—
108C4×C3⋊D3—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)M1612yescomplemented
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#446—31no—
117C4×SD16—91no—
118#436—91no—
119#335—91no—
120Q8⋊C8—31no—
121D4⋊C8—91no—
122#322—91no—
123C2×C3×Q8—21no—
124C2×C3×Q8C4×D311yescharacteristic
125C2×C3×Q8C4×D311yescharacteristic
126C2×D12—31no—
127C2×D12—31no—
128C2×D12—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—121no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—41no—
141C3×C4⋊C4C4×D311yescharacteristic
142C3×C4⋊C4C4×D311yescharacteristic
143C3×C42—21no—
144C3×C42—21no—
145C3×C42—21no—
146C3×C42—41no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#215—62no—
150#215—62no—
151#215—64no—
152(C2×D3)⋊C4—61no—
153(C2×D3)⋊C4—61no—
154(C2×D3)⋊C4—121no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157C4⋊Dic3—61no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8#6711yescharacteristic
168C2×C3⋊C8#6711yescharacteristic
169ΓL(1,𝔽25)—122no—
170ΓL(1,𝔽25)—122no—
171C22×C32C4×D411yescharacteristic
172C2×C3⋊D3—41no—
173C2×C3⋊D3—41no—
174C2×C3⋊D3—41no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4—41no—
178C32×C4C2×M1611yescharacteristic
179C32×C4#13111yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4#13711yescharacteristic
182C3⋊Dic3—41no—
183C2×SD16—91no—
184C2×M16—181no—
185C4×Q8D3211yescharacteristic
186C4×D4—91no—
187#106—91no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—61no—
191#103—91no—
192#102—91no—
193C22⋊C8—181no—
194#97—61no—
195C4×C8—31no—
196C4×C8—31no—
197C4×C8—91no—
198C22×D3—61no—
199C22×D3—61no—
200C22×D3—121no—
201C3×Q8—22no—
202C3×Q8—21no—
203C3×Q8—21no—
204C3×Q8—21no—
205C3×Q8—21no—
206C3×Q8—41no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4C2×C4×D311yescharacteristic
217C2×C3×C4C2×C4×D311yescharacteristic
218C2×C3×C4#23511yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4#23711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—121no—
225D12—62no—
226D12—61no—
227D12—61no—
228D12—61no—
229D12—61no—
230D12—121no—
231C4×D3—121no—
232C4×D3—121no—
233C4×D3—121no—
234C4×D3—121no—
235C4×D3—241no—
236C4×D3—241no—
237C3×C8—61no—
238C3×C8—61no—
239C3×C8—121no—
240C3×C8—121no—
241C3×C8—121no—
242C3⋊C8—21no—
243C3⋊C8—21no—
244C3⋊C8—32no—
245C3⋊C8—32no—
246C3⋊C8—41no—
247C3⋊C8—41no—
248C3⋊C8—41no—
249C3⋊C8—62no—
250C3⋊C8—61no—
251C3⋊C8—61no—
252C3⋊C8—121no—
253C2×C32#43611yescharacteristic
254C2×C32#44011yescharacteristic
255C2×C32#44411yescharacteristic
256C3⋊D3—81no—
257C2×Q8#62411yescharacteristic
258C2×D4—91no—
259C22×C4—181no—
260SD16—182no—
261M16—362no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—61no—
267C2×C8—91no—
268C2×C8—91no—
269C4⋊C4—21no—
270C4⋊C4—91no—
271C4⋊C4#62411yescharacteristic
272C22⋊C4—181no—
273C42—21no—
274C42C2×D3211yescharacteristic
275C22×C3—21no—
276C22×C3#67⋊C411yescharacteristic
277C22×C3C4×#6711yescharacteristic
278C2×D3—122no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—121no—
284C2×D3—121no—
285C2×D3—241no—
286C2×D3—241no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—81no—
300C3×C4#90111yescharacteristic
301C3×C4D3×M1611yescharacteristic
302C3×C4D3×M1611yescharacteristic
303C3×C4#90711yescharacteristic
304C3×C4#91411yescharacteristic
305C3×C4#91811yescharacteristic
306C3×C4#94211yescharacteristic
307C3×C4#94911yescharacteristic
308Dic3—121no—
309Dic3—121no—
310Dic3—241no—
311C32#159211yescharacteristic, complemented, Sylow
312C23—181no—
313Q8—21no—
314Q8—21no—
315D4—181no—
316D4—181no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—181no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4#380411yescharacteristic
323C2×C4C2×#62411yescharacteristic
324C2×C4D3×#6711yescharacteristic
325C8—61no—
326C8—61no—
327C8—92no—
328C8—121no—
329C8—121no—
330C8—121no—
331C8—181no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3#472911yescharacteristic
336C2×C3#481711yescharacteristic
337C2×C3#482311yescharacteristic
338C2×C3#502611yescharacteristic
339C2×C3#512811yescharacteristic
340C2×C3#514511yescharacteristic
341D3—242no—
342D3—241no—
343D3—241no—
344C22—361no—
345C22—361no—
346C22—361no—
347C22#6395211yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—361no—
352C4#6381711yescharacteristic
353C4#6381811yescharacteristic
354C4#6393911yescharacteristic
355C4#6394811yescharacteristic
356C3—21no—
357C3#6822611yescharacteristic, complemented
358C3#7095511yescharacteristic, complemented
359C2—721no—
360C2#1059105111yescharacteristic
361C2#1059154011yescharacteristic
362C2#1059166311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C4×D4
prime radicalC2×C4⋊(C3⋊D3)C2×C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1592
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5024C2semidirect
4. C3×#4535C2semidirect
5. #10589100C2semidirect
7. #10589079C2semidirect
29. #5024D3semidirect
33. #4535D3semidirect
110. C3⋊(C3⋊C8)M16semidirect
311. C32#1592semidirect
357. C3#68226semidirect
358. C3#70955semidirect

Maximal subgroups

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

subgroupindex
C4×#37552
C3×#50242
#105903382
C3×#45352
#105891002
#105890822
#105890792
#709553
#682263