Finite Group Databasebeta

← #11776296

Subgroups — #11776296

Order 1152.

512 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2#10590336C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589413C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71773—31nomaximal
9#68420—31nomaximal
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#944—21no—
13C3×D3×C4⋊C4—21no—
14C3×D3×C4⋊C4C412yes—
15C3×#888—21no—
16C3×#888C412yes—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3711—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24Dic3⋊(C3⋊C8)—21no—
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27C2×C3×C4⋊Q8—31no—
28D3×C4⋊Q8D311yescharacteristic
29#4925—31no—
30#4924—31no—
31#4837—31no—
32#4833—31no—
33C3×#332—31no—
34#4547—31no—
35#4547—31no—
36#4547—31no—
37#4547—31no—
38#4547—61no—
39#4547D311yescharacteristic, complemented
40#4486—31no—
41#4482—31no—
42C2×C32×Q8—21no—
43C3×D3×Q8—42no—
44C3×D3×Q8—42no—
45C2×C3×C4×D3—22no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6—21no—
50C2×C3×Dic6—22no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4C2×C412yes—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—22no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3711—42no—
66#1546—91noSylow
67C22×C3×Q8—61no—
68C2×D3×Q8—21no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8—32no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×C4⋊Q8C2×D311yescharacteristic
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—61no—
78C2×C3×C42—31no—
79#944—21no—
80C2×#208—61no—
81C2×ΓL(1,𝔽25)—61no—
82D3×C4⋊C4—21no—
83D3×C4⋊C4Dic312yes—
84#888—21no—
85#888Dic312yes—
86C42×D3C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90#830—61no—
91(C2×D3)⋊C8—61no—
92Dic3⋊C8—61no—
93C8×Dic3—61no—
94C4⋊(C3⋊C8)—31no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—61no—
104C22×C3×D3C22⋊C411yescharacteristic
105C32×Q8—41no—
106C32×Q8—41no—
107C2×C32×C4—22no—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—22no—
112C2×C3×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic3C22⋊C411yescharacteristic
114C2×C3×Dic3C22⋊C411yescharacteristic
115C3×C4×D3—21no—
116C3×C4×D3—21no—
117C3×C4×D3—22no—
118C3×C4×D3—44no—
119C3×C4×D3D812yes—
120C3×C4×D3SD1612yes—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6—44no—
124C3⋊(C3⋊C8)—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127C3×C3⋊C8—41no—
128C2×C4⋊Q8—31no—
129#431—91no—
130#423—91no—
131#332—31no—
132#332—91no—
133#332—91no—
134#332—91no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—41no—
138C2×C3×Q8—62no—
139C2×C3×Q8—61no—
140C2×C3×Q8—122no—
141C2×C3×Q8—122no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—62no—
146D3×Q8—42no—
147D3×Q8—42no—
148C2×C4×D3—22no—
149C2×C4×D3C2×Dic311yescharacteristic
150C2×C4×D3#6711yescharacteristic
151C2×C4×D3#6711yescharacteristic
152C2×Dic6—21no—
153C2×Dic6—22no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—32no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—62no—
162C3×C4⋊C4—62no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4C4×D312yes—
165C3×C4⋊C4C2×Dic312yes—
166C3×C42—21no—
167C3×C42—31no—
168C3×C42—31no—
169C3×C42—31no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172C4⋊Dic3—21no—
173C4⋊Dic3C2×Dic312yes—
174Dic3⋊C4—22no—
175Dic3⋊C4—22no—
176C4×Dic3C2×Dic311yescharacteristic
177C4×Dic3#6711yescharacteristic
178C4×Dic3#6711yescharacteristic
179#208—122no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—121no—
187C2×C3⋊C8—121no—
188ΓL(1,𝔽25)—122no—
189C22×C32C2×C22⋊C411yescharacteristic
190C2×C3×D3—21no—
191C2×C3×D3—21no—
192C2×C3×D3#10212yes—
193C32×C4—21no—
194C32×C4—42no—
195C32×C4C2×D811yescharacteristic
196C32×C4C2×SD1611yescharacteristic
197C32×C4#13711yescharacteristic
198C32×C4#13711yescharacteristic
199C3×Dic3—21no—
200C3×Dic3—42no—
201C3×Dic3#10112yes—
202C3×Dic3#10212yes—
203C22×Q8—61no—
204C2×M16—181no—
205C4⋊Q8—32no—
206C4⋊Q8—31no—
207C4⋊Q8—61no—
208C4⋊Q8—61no—
209C4⋊Q8D3211yescharacteristic
210C2×C4⋊C4—32no—
211C2×C4⋊C4—61no—
212C2×C42—31no—
213C4⋊C8—31no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216C4⋊C8—91no—
217C4⋊C8—181no—
218C22⋊C8—181no—
219C4×C8—181no—
220C23×C3—31no—
221C22×D3#21711yescharacteristic
222C3×Q8—41no—
223C3×Q8—41no—
224C3×Q8—41no—
225C3×Q8—41no—
226C3×Q8—81no—
227C3×Q8—81no—
228C3×Q8—124no—
229C3×Q8—121no—
230C3×Q8—121no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—32no—
239C2×C3×C4—32no—
240C2×C3×C4—31no—
241C2×C3×C4—42no—
242C2×C3×C4—62no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4—62no—
246C2×C3×C4—124no—
247C2×C3×C4C2×C4×D311yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4C22×Dic311yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×Dic3—22no—
254C2×Dic3#21711yescharacteristic
255C2×Dic3#21711yescharacteristic
256C2×Dic3#21711yescharacteristic
257C4×D3—21no—
258C4×D3—21no—
259C4×D3—22no—
260C4×D3—44no—
261C4×D3#21312yes—
262C4×D3#21412yes—
263Dic6—41no—
264Dic6—41no—
265Dic6—44no—
266C3×C8—121no—
267C3×C8—121no—
268C3⋊C8—41no—
269C3⋊C8—41no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C3⋊C8—121no—
273C3⋊C8—121no—
274C3⋊C8—241no—
275C3⋊C8—241no—
276C2×C32C2×#10111yescharacteristic
277C2×C32C2×#10211yescharacteristic
278C2×C32#41911yescharacteristic
279C3×D3—22no—
280C2×Q8—21no—
281C2×Q8—62no—
282C2×Q8—61no—
283C2×Q8—122no—
284C2×Q8—122no—
285C22×C4—31no—
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—62no—
289M16—362no—
290C2×C8—61no—
291C2×C8—61no—
292C2×C8—181no—
293C2×C8—181no—
294C4⋊C4—21no—
295C4⋊C4—32no—
296C4⋊C4—62no—
297C4⋊C4—62no—
298C4⋊C4—61no—
299C4⋊C4D3×Dic312yes—
300C42—31no—
301C42—31no—
302C42—31no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—32no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3D3×C22⋊C411yescharacteristic
309C22×C3C2×#21711yescharacteristic
310C2×D3—21no—
311C2×D3—21no—
312C2×D3#83212yes—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—32no—
320C3×C4—32no—
321C3×C4—41no—
322C3×C4—42no—
323C3×C4—42no—
324C3×C4—61no—
325C3×C4—82no—
326C3×C4—122no—
327C3×C4D3×D811yescharacteristic
328C3×C4D3×SD1611yescharacteristic
329C3×C4#91511yescharacteristic
330C3×C4#91811yescharacteristic
331C3×C4C2×#21311yescharacteristic
332C3×C4C2×#21411yescharacteristic
333C3×C4#94211yescharacteristic
334C3×C4#94211yescharacteristic
335Dic3—21no—
336Dic3—42no—
337Dic3#83212yes—
338Dic3#83612yes—
339C32#154611yescharacteristic, complemented, Sylow
340C23—31no—
341Q8—41no—
342Q8—41no—
343Q8—124no—
344Q8—121no—
345Q8—121no—
346C2×C4—22no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—32no—
350C2×C4—32no—
351C2×C4—31no—
352C2×C4—62no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—62no—
356C2×C4—124no—
357C2×C4C2×D3×Dic311yescharacteristic
358C2×C4D3×#6711yescharacteristic
359C2×C4D3×#6711yescharacteristic
360C8—121no—
361C8—121no—
362C8—361no—
363C8—361no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—62no—
368C2×C3D3×#10111yescharacteristic
369C2×C3D3×#10211yescharacteristic
370C2×C3#480211yescharacteristic
371C2×C3C2×#83211yescharacteristic
372C2×C3#522511yescharacteristic
373C2×C3C2×#83611yescharacteristic
374D3—22no—
375C22—32no—
376C22—61no—
377C22—61no—
378C22D3×#21711yescharacteristic
379C4—21no—
380C4—32no—
381C4—32no—
382C4—42no—
383C4—61no—
384C4—122no—
385C4D3×#21311yescharacteristic
386C4D3×#21411yescharacteristic
387C4#6394611yescharacteristic
388C4#6394811yescharacteristic
389C3—21no—
390C3#6842011yescharacteristic, complemented
391C3#7177311yescharacteristic, complemented
392C2—62no—
393C2D3×#83211yescharacteristic
394C2#1059155711yescharacteristic
395C2D3×#83611yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1546
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10589413C2semidirect
5. C3×#4547C2semidirect
6. #10589093C2semidirect
7. #10589092C2semidirect
39. #4547D3semidirect
339. C32#1546semidirect
390. C3#68420semidirect
391. C3#71773semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
#105903362
#105902482
#105894132
C3×#45472
#105890932
#105890922
#717733
#684203