Finite Group Databasebeta

← #11785302

Subgroups — #11785302

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic
3C2×#63664C211yesmaximal, characteristic
4#10592817C211yesmaximal, characteristic, complemented
5C4×#3750C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#70355—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12Q8×C3⋊Dic3C411yescharacteristic, complemented
13Q8×C3⋊Dic3C411yescharacteristic, complemented
14D4×C3⋊Dic3—21no—
15D4×C3⋊Dic3—21no—
16D4×C3⋊Dic3C411yescharacteristic, complemented
17D4×C3⋊Dic3C411yescharacteristic, complemented
18#64135—21no—
19#64135C2211yescharacteristic
20C2×#3750—21no—
21C2×C4×C3⋊Dic3—21no—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C32×#104—22no—
26#63664—22no—
27#63658—21no—
28#63641—21no—
29#63641—21no—
30Dic3×#41—34no—
31C2×C3×#104D314yes—
32C2×#837—34no—
33#5118—34no—
34C4×Dic3⋊C4—34no—
35#4555—34no—
36#4523—34no—
37C32×#41—21no—
38C32×#41—21no—
39C32×#41D412yes—
40C32×#41Q812yes—
41C2×C32×Q8C2×C411yescharacteristic
42C2×C32×D4—21no—
43C2×C32×D4C2×C411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C32×M16—21no—
53C32×M16—21no—
54C2×C32×C8—21no—
55C32×C42—21no—
56C32×C42—21no—
57#3757—21no—
58#3757—21no—
59#3757—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64#3750—24no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3C2×C411yescharacteristic
71C4×C3⋊Dic3C2×C411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74#3748—21no—
75#3748—21no—
76C2×C3⋊(C3⋊C8)—21no—
77#1806—91noSylow
78C2×C3×#41C2×D314yes—
79C2×C3×M16C2×D314yes—
80C2×C3×C42C2×D314yes—
81Q8×Dic3—34no—
82Q8×Dic3—34no—
83D4×Dic3—34no—
84D4×Dic3—34no—
85D4×Dic3—64no—
86D4×Dic3—64no—
87#926—34no—
88#926—64no—
89C2×Dic3⋊C4—64no—
90C2×C4×Dic3—34no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—64no—
93C2×#208—34no—
94C3×#104—28no—
95#837—68no—
96C3⋊#95—64no—
97Dic3⋊C8—64no—
98Dic3⋊C8—64no—
99C23×C32—21no—
100C23×C32C2×D411yescharacteristic
101C32×Q8—21no—
102C32×Q8C4⋊C412yescomplemented
103C32×D4—22no—
104C32×D4—22no—
105C32×D4—21no—
106C32×D4C4⋊C412yescomplemented
107C2×C32×C4—21no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—42no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—42no—
128C2×C3⋊Dic3C22⋊C411yescharacteristic
129C2×C3⋊Dic3C22⋊C411yescharacteristic
130C2×C3⋊Dic3C22⋊C411yescharacteristic
131C2×C3⋊Dic3C22⋊C411yescharacteristic
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C4×#41—91no—
135#423—91no—
136C2×#104—91no—
137C2×#104C3⋊D311yescharacteristic
138C4×C4⋊C4—91no—
139#339—91no—
140#339—91no—
141C3×#41—24no—
142C3×#41—24no—
143C3×#41Dic618yes—
144C3×#41#6718yes—
145C2×C3×Q8C4×D314yes—
146C2×C3×D4—24no—
147C2×C3×D4C4×D314yes—
148C22×C3×C4—24no—
149C22×C3×C4—24no—
150C22×C3×C4C22×D314yes—
151C22×Dic3—34no—
152C22×Dic3—34no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C3×M16—24no—
157C3×M16—24no—
158C2×C3×C8—24no—
159C3×C42—24no—
160C3×C42—24no—
161#217—64no—
162#217—64no—
163#217—64no—
164C4⋊Dic3—34no—
165C4⋊Dic3—34no—
166C4⋊Dic3—64no—
167C4⋊Dic3—64no—
168Dic3⋊C4—616no—
169C4×Dic3—34no—
170C4×Dic3—34no—
171C4×Dic3—34no—
172C4×Dic3—34no—
173C4×Dic3—64no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C4×Dic3—64no—
177C4×Dic3—64no—
178#208—64no—
179#208—64no—
180C2×C3⋊C8—64no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32—22no—
184C22×C32—41no—
185C22×C32—41no—
186C22×C32C2×C22⋊C411yescharacteristic
187C22×C32#12111yescharacteristic
188C22×C32C22⋊Q811yescharacteristic
189C32×C4—22no—
190C32×C4—42no—
191C32×C4C2×C4⋊C411yescharacteristic
192C32×C4#11711yescharacteristic
193C32×C4#12111yescharacteristic
194C32×C4C22⋊Q811yescharacteristic
195C3⋊Dic3—21no—
196C3⋊Dic3—21no—
197C3⋊Dic3—21no—
198C3⋊Dic3—42no—
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C3⋊Dic3#10412yescomplemented
202C2×#41C2×C3⋊D311yescharacteristic
203C2×M16—91no—
204C2×M16C2×C3⋊D311yescharacteristic
205C4×Q8—91no—
206C4×Q8—91no—
207C4×D4—91no—
208C4×D4—91no—
209C4×D4—181no—
210C4×D4—181no—
211#117—91no—
212#117—181no—
213C2×C4⋊C4—181no—
214C2×C42—91no—
215C2×C42—91no—
216C2×C42—181no—
217C2×C42C2×C3⋊D311yescharacteristic
218C4⋊C8—181no—
219C4⋊C8—181no—
220#104—22no—
221#104—182no—
222#95—181no—
223C23×C3—24no—
224C23×C3D3×D414yes—
225C3×Q8—24no—
226C3×Q8Dic3⋊C418yescomplemented
227C3×D4—28no—
228C3×D4—28no—
229C3×D4—24no—
230C3×D4Dic3⋊C418yescomplemented
231C2×C3×C4—24no—
232C2×C3×C4—28no—
233C2×C3×C4—28no—
234C2×C3×C4—28no—
235C2×C3×C4—44no—
236C2×C3×C4—44no—
237C2×C3×C4C2×Dic614yes—
238C2×C3×C4C2×C4×D314yes—
239C2×C3×C4D3×D414yes—
240C2×C3×C4#23714yes—
241C2×C3×C4#23714yes—
242C2×C3×C4C2×#6714yes—
243C2×Dic3—34no—
244C2×Dic3—34no—
245C2×Dic3—34no—
246C2×Dic3—34no—
247C2×Dic3—68no—
248C2×Dic3—68no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—128no—
252C2×Dic3—124no—
253C2×Dic3—128no—
254C2×Dic3—124no—
255C2×Dic3—124no—
256C3×C8—44no—
257C3⋊C8—124no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32—42no—
261C2×C32#38011yescharacteristic
262C2×C32C2×#10411yescharacteristic
263C2×C32#42111yescharacteristic
264#41—21no—
265#41—21no—
266#41#63412yes—
267#41#63812yes—
268C2×Q8C4×C3⋊D311yescharacteristic
269C2×D4—21no—
270C2×D4C4×C3⋊D311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4C22×C3⋊D311yescharacteristic
279M16—21no—
280M16—21no—
281M16—181no—
282M16—181no—
283C2×C8—21no—
284C2×C8—181no—
285C4⋊C4—91no—
286C4⋊C4—91no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4—184no—
290C22⋊C4—181no—
291C22⋊C4—181no—
292C22⋊C4—181no—
293C42—21no—
294C42—21no—
295C42—91no—
296C42—91no—
297C42—91no—
298C42—91no—
299C42—181no—
300C42—181no—
301C42—181no—
302C42—181no—
303C42—181no—
304C22×C3—24no—
305C22×C3—24no—
306C22×C3—28no—
307C22×C3—44no—
308C22×C3—44no—
309C22×C3#87814yes—
310C22×C3D3×C22⋊C414yes—
311C22×C3#93914yes—
312C3×C4—28no—
313C3×C4—48no—
314C3×C4#87714yes—
315C3×C4#87814yes—
316C3×C4C2×Dic3⋊C414yes—
317C3×C4#93914yes—
318Dic3—38no—
319Dic3—64no—
320Dic3—64no—
321Dic3—64no—
322Dic3—128no—
323Dic3—124no—
324Dic3—124no—
325C32#180611yescharacteristic, complemented, Sylow
326C23—21no—
327C23D4×C3⋊D311yescharacteristic
328Q8—21no—
329Q8#375012yescomplemented
330D4—22no—
331D4—22no—
332D4—21no—
333D4#375012yescomplemented
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—362no—
349C2×C4—361no—
350C2×C4—362no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4C2×#63411yescharacteristic
354C2×C4C2×C4×C3⋊D311yescharacteristic
355C2×C4D4×C3⋊D311yescharacteristic
356C2×C4#383011yescharacteristic
357C2×C4#383011yescharacteristic
358C2×C4C2×#63811yescharacteristic
359C8—41no—
360C8—361no—
361C2×C3—24no—
362C2×C3—24no—
363C2×C3—48no—
364C2×C3D3×#10414yes—
365C2×C3#482114yes—
366C2×C3#494214yes—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22#6408711yescharacteristic
373C22C22⋊C4×C3⋊D311yescharacteristic
374C22#6414811yescharacteristic
375C4—22no—
376C4—42no—
377C4—92no—
378C4—181no—
379C4—181no—
380C4—181no—
381C4—362no—
382C4—361no—
383C4—361no—
384C4#6408611yescharacteristic
385C4#6408711yescharacteristic
386C4C2×#375011yescharacteristic
387C4#6414811yescharacteristic
388C3#7035514yescomplemented
389C2—21no—
390C2—21no—
391C2—42no—
392C2C3⋊D3×#10411yescharacteristic
393C2#1059252011yescharacteristic
394C2#1059264111yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
4. #10592817C2semidirect
5. C4×#3750C2semidirect
6. #10589421C2semidirect
7. #10589389C2semidirect
12. Q8×C3⋊Dic3C4semidirect
13. Q8×C3⋊Dic3C4semidirect
16. D4×C3⋊Dic3C4semidirect
17. D4×C3⋊Dic3C4semidirect
102. C32×Q8C4⋊C4semidirect
106. C32×D4C4⋊C4semidirect
201. C3⋊Dic3#104semidirect
226. C3×Q8Dic3⋊C4semidirect
230. C3×D4Dic3⋊C4semidirect
325. C32#1806semidirect
329. Q8#3750semidirect
333. D4#3750semidirect
388. C3#70355semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×C32×#1042
C2×#636642
#105928172
C4×#37502
#105894212
#105893892
#703553