Finite Group Databasebeta

← #11776301

Subgroups — #11776301

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
1D3×#869C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589348C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#70506—31nomaximal
9#68420—31nomaximal
10C2×D3×Dic6—21no—
11#64078C2211yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C42×D3C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63918—21no—
16#63918C412yes—
17D3×C4⋊Dic3—21no—
18D3×C4⋊Dic3C412yes—
19#63866—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×Dic3⋊C8—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27D3×C4⋊Q8—31no—
28C2×#869—31no—
29C3×#423—31no—
30#4925—31no—
31#4837D311yescharacteristic
32#4833—31no—
33C3×#332—31no—
34#4547—31no—
35#4486—31no—
36#4482—31no—
37#4482—31no—
38#4482—31no—
39#4482—31no—
40#4482—61no—
41#4482D311yescharacteristic, complemented
42C2×#634—21no—
43C2×C3×C4×D3C2×C411yescharacteristic
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×#627—22no—
48C2×D3×Dic3—22no—
49D3×Dic6—42no—
50D3×Dic6—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×C4×Dic3C2×C411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C3×ΓL(1,𝔽25)—42no—
64Dic3⋊Dic3—22no—
65Dic3⋊Dic3—22no—
66#1546—91noSylow
67C2×D3×Q8—61no—
68C22×Dic6—61no—
69C2×C3×M16—61no—
70C3×C4⋊Q8—31no—
71C2×C3×C42—31no—
72#944—61no—
73C2×C4⋊Dic3—32no—
74C2×C4⋊Dic3—61no—
75C2×ΓL(1,𝔽25)—21no—
76D3×C4⋊C4—32no—
77D3×C4⋊C4—61no—
78#888—32no—
79#888—61no—
80C42×D3C2×D311yescharacteristic
81#869—31no—
82#869—31no—
83#869—32no—
84#869—61no—
85#869—61no—
86#869—61no—
87#869C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8—61no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94#830—61no—
95(C2×D3)⋊C8—61no—
96Dic3⋊C8—21no—
97C8×Dic3—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—61no—
104C22×C3×D3C22⋊C411yescharacteristic
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—22no—
109#634—41no—
110#634—41no—
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×D3D812yes—
119C3×C4×D3SD1612yes—
120C3×Dic6—41no—
121C3×Dic6—41no—
122#627—44no—
123D3×Dic3—44no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127C3×C3⋊C8—41no—
128C2×C4⋊Q8—91no—
129#431—91no—
130#423—31no—
131#332—31no—
132#332—91no—
133#332—91no—
134#332—91no—
135C2×C3×Q8—61no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4—31no—
139C22×Dic3—62no—
140D3×Q8—122no—
141D3×Q8—122no—
142C2×C4×D3—62no—
143C2×C4×D3C4×D311yescharacteristic
144C2×C4×D3D1211yescharacteristic
145C2×C4×D3#6711yescharacteristic
146C2×Dic6—21no—
147C2×Dic6—62no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—62no—
151C2×Dic6—121no—
152C2×Dic6—122no—
153C2×Dic6—122no—
154C3×M16—122no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—41no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C3×C4⋊C4—32no—
161C3×C4⋊C4—61no—
162C3×C42—21no—
163C3×C42—31no—
164C3×C42—31no—
165C3×C42—31no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168C4⋊Dic3—21no—
169C4⋊Dic3—32no—
170C4⋊Dic3—32no—
171C4⋊Dic3—62no—
172C4⋊Dic3—62no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—121no—
177C4⋊Dic3C4×D312yes—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180C4×Dic3C4×D311yescharacteristic
181C4×Dic3D1211yescharacteristic
182C4×Dic3#6711yescharacteristic
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188ΓL(1,𝔽25)—42no—
189C22×C32C2×C22⋊C411yescharacteristic
190C2×C3×D3—21no—
191C2×C3×D3—21no—
192C2×C3×D3#10212yes—
193C32×C4—21no—
194C32×C4C2×D811yescharacteristic
195C32×C4C2×SD1611yescharacteristic
196C32×C4#13711yescharacteristic
197C32×C4#13711yescharacteristic
198C3⋊Dic3—42no—
199C3×Dic3—21no—
200C3×Dic3—42no—
201C3×Dic3#10112yes—
202C3×Dic3#10212yes—
203C22×Q8—181no—
204C2×M16—61no—
205C4⋊Q8—31no—
206C4⋊Q8—92no—
207C4⋊Q8—91no—
208C4⋊Q8—181no—
209C4⋊Q8—181no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4—181no—
212C2×C42—31no—
213C4⋊C8—31no—
214C4⋊C8—31no—
215C4⋊C8—61no—
216C4⋊C8—91no—
217C4⋊C8D3211yescharacteristic
218C22⋊C8—181no—
219C4×C8—181no—
220C23×C3—31no—
221C22×D3(C2×D3)⋊C411yescharacteristic
222C3×Q8—121no—
223C3×Q8—121no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—32no—
230C2×C3×C4—32no—
231C2×C3×C4—31no—
232C2×C3×C4—62no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—62no—
236C2×C3×C4C2×C4×D311yescharacteristic
237C2×C3×C4C2×C4×D311yescharacteristic
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×Dic3—22no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—122no—
246C2×Dic3—124no—
247C2×Dic3(C2×D3)⋊C411yescharacteristic
248C2×Dic3(C2×D3)⋊C411yescharacteristic
249C2×Dic3(C2×D3)⋊C411yescharacteristic
250C4×D3—21no—
251C4×D3—21no—
252C4×D3—22no—
253C4×D3—124no—
254C4×D3#21312yes—
255C4×D3#21512yes—
256Dic6—41no—
257Dic6—41no—
258Dic6—124no—
259Dic6—121no—
260Dic6—121no—
261Dic6—121no—
262Dic6—121no—
263Dic6—124no—
264Dic6—241no—
265Dic6—241no—
266C3×C8—41no—
267C3×C8—41no—
268C3×C8—81no—
269C3×C8—121no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—41no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C3⋊C8—241no—
276C2×C32C2×#10111yescharacteristic
277C2×C32C2×#10211yescharacteristic
278C2×C32#41911yescharacteristic
279C3×D3—22no—
280C2×Q8—61no—
281C2×Q8—182no—
282C2×Q8—181no—
283C2×Q8—362no—
284C2×Q8—362no—
285C22×C4—31no—
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—182no—
289M16—122no—
290C2×C8—21no—
291C2×C8—61no—
292C2×C8—61no—
293C2×C8—181no—
294C4⋊C4—32no—
295C4⋊C4—61no—
296C4⋊C4—92no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4—181no—
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×(C2×D3)⋊C411yescharacteristic
310C2×D3—21no—
311C2×D3—21no—
312C2×D3#80912yes—
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—61no—
323C3×C4—122no—
324C3×C4#90911yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4D3×D811yescharacteristic
327C3×C4D3×SD1611yescharacteristic
328C3×C4#91511yescharacteristic
329C3×C4#91811yescharacteristic
330C3×C4C2×#21311yescharacteristic
331C3×C4C2×#21511yescharacteristic
332Dic3—21no—
333Dic3—42no—
334Dic3—122no—
335Dic3—122no—
336Dic3—242no—
337Dic3#80912yes—
338Dic3#82412yes—
339C32#154611yescharacteristic, complemented, Sylow
340C23—31no—
341Q8—121no—
342Q8—121no—
343Q8—364no—
344Q8—361no—
345Q8—361no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—32no—
349C2×C4—32no—
350C2×C4—31no—
351C2×C4—62no—
352C2×C4—61no—
353C2×C4—61no—
354C2×C4—62no—
355C2×C4—182no—
356C2×C4—364no—
357C2×C4C4×D3211yescharacteristic
358C2×C4D3×D1211yescharacteristic
359C2×C4D3×#6711yescharacteristic
360C8—41no—
361C8—121no—
362C8—121no—
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×#80911yescharacteristic
372C2×C3#512011yescharacteristic
373C2×C3C2×#82411yescharacteristic
374D3—22no—
375C22—32no—
376C22—61no—
377C22—61no—
378C22D3×(C2×D3)⋊C411yescharacteristic
379C4—21no—
380C4—32no—
381C4—32no—
382C4—61no—
383C4—122no—
384C4—362no—
385C4#6380011yescharacteristic
386C4#6380111yescharacteristic
387C4D3×#21311yescharacteristic
388C4D3×#21511yescharacteristic
389C3—21no—
390C3#6842011yescharacteristic, complemented
391C3#7050611yescharacteristic, complemented
392C2—62no—
393C2D3×#80911yescharacteristic
394C2#1059094811yescharacteristic
395C2D3×#82411yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1546
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10589348C2semidirect
5. C3×#4482C2semidirect
6. #10589094C2semidirect
7. #10589093C2semidirect
41. #4482D3semidirect
339. C32#1546semidirect
390. C3#68420semidirect
391. C3#70506semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
C3×#48372
#105902482
#105893482
C3×#44822
#105890942
#105890932
#705063
#684203