Finite Group Databasebeta

← #11780245

Subgroups — #11780245

Order 1152.

449 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 449 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#5732C211yesmaximal, characteristic
2#10592777C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic
4#10590301C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic
8#71933—31nomaximal
9#68437—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#947—21no—
13C3×Q8×Dic3—21no—
14C3×#898—22no—
15C3×#897—21no—
16C3×#892—21no—
17C3×C4×D12C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3716—21no—
20#63634—22no—
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63566—21no—
27C3×#556—31no—
28#5732D311yescharacteristic
29#5078—31no—
30#5078—31no—
31#5078—61no—
32#5020—31no—
33#5019—31no—
34#4851—31no—
35#4841—31no—
36C3×#332—31no—
37#4547D311yescharacteristic, complemented
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4484—31no—
41#4483—31no—
42C2×C32×Q8—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4D412yes—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—22no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—22no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3716—42no—
65#1650—91noSylow
66C3×C4⋊Q8—21no—
67C3×C4⋊Q8C2×D311yescharacteristic
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×#126—62no—
70C3×#124—61no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—31no—
73C3×C4×Q8—61no—
74C3×C4×D4—31no—
75C3×#117—61no—
76#947—21no—
77Q8×Dic3—21no—
78C2×#214—61no—
79C2×#204—61no—
80#898—22no—
81#897—21no—
82#892—21no—
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90#835—61no—
91#817—61no—
92#816—61no—
93#816—61no—
94#810—61no—
95#808—61no—
96#807—64no—
97#807—62no—
98#807—62no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—31no—
102C4×C3⋊C8—31no—
103C4×C3⋊C8—61no—
104C22×C3×D3—21no—
105C32×Q8—41no—
106C32×Q8—41no—
107C2×C32×C4—22no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—41no—
112#634—41no—
113#634—41no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3⋊(C3⋊C8)—22no—
124C3×C3⋊C8—41no—
125C3×C3⋊C8—41no—
126#556—31no—
127#500—91no—
128#475—91no—
129#461—91no—
130#332—31no—
131Q8⋊C8—91no—
132D4⋊C8—91no—
133C2×C3×Q8—21no—
134C2×C3×Q8—21no—
135C2×C3×Q8—31no—
136C2×C3×Q8—41no—
137C2×C3×D4—31no—
138C22×C3×C4—61no—
139C2×D12#6711yescharacteristic
140C2×C4×D3—21no—
141C2×Dic6—61no—
142C2×Dic6—61no—
143C2×Dic6—121no—
144C2×Dic6#6711yescharacteristic
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—62no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4D1212yes—
156C3×C4⋊C4#6712yes—
157C3×C22⋊C4—62no—
158C3×C22⋊C4—62no—
159C3×C22⋊C4—61no—
160C3×C42—21no—
161C3×C42—62no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#214—122no—
166(C2×D3)⋊C4—22no—
167(C2×D3)⋊C4—22no—
168(C2×D3)⋊C4—21no—
169C4⋊Dic3—22no—
170C4⋊Dic3—62no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—121no—
176C4⋊Dic3#6711yescharacteristic
177C4⋊Dic3#6711yescharacteristic
178Dic3⋊C4—21no—
179C4×Dic3—22no—
180C4×Dic3—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186#204—122no—
187C22×C32#12011yescharacteristic
188C2×C3×D3—41no—
189C2×C3×D3—41no—
190C2×C3×D3—41no—
191C32×C4—21no—
192C32×C4—42no—
193C32×C4#13511yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4#13711yescharacteristic
197C3⋊Dic3—81no—
198C3×Dic3—41no—
199C3×Dic3—41no—
200C3×Dic3—41no—
201C2×SD16—181no—
202C4⋊Q8—91no—
203C4⋊Q8D3211yescharacteristic
204#126—62no—
205#124—61no—
206C22⋊Q8—61no—
207C4×Q8—31no—
208C4×Q8—61no—
209C4×D4—31no—
210#117—61no—
211#107—182no—
212#106—181no—
213C4⋊C8—31no—
214C4⋊C8—31no—
215#103—181no—
216#103—181no—
217C4×C8—91no—
218C23×C3—61no—
219C22×D3—21no—
220C3×Q8—41no—
221C3×Q8—41no—
222C3×Q8—41no—
223C3×Q8—41no—
224C3×Q8—61no—
225C3×Q8—61no—
226C3×Q8—81no—
227C3×Q8—81no—
228C3×D4—61no—
229C3×D4—61no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—42no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—61no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—122no—
251C2×Dic3—121no—
252C2×Dic3—121no—
253D12—21no—
254D12—21no—
255C4×D3—41no—
256C4×D3—41no—
257Dic6—21no—
258Dic6—21no—
259Dic6—121no—
260Dic6—121no—
261Dic6—121no—
262Dic6—121no—
263Dic6—241no—
264Dic6—241no—
265C3×C8—121no—
266C3×C8—121no—
267C3⋊C8—41no—
268C3⋊C8—41no—
269C3⋊C8—64no—
270C3⋊C8—62no—
271C3⋊C8—62no—
272C2×C32#44911yescharacteristic
273C2×C32#45211yescharacteristic
274C2×C32#45611yescharacteristic
275C3×D3—81no—
276C2×Q8—21no—
277C2×Q8—31no—
278C2×Q8—181no—
279C2×D4—31no—
280C22×C4—61no—
281SD16—362no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—181no—
285C4⋊C4—21no—
286C4⋊C4—31no—
287C4⋊C4—31no—
288C4⋊C4—62no—
289C4⋊C4—61no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4#62612yes—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—61no—
296C42—62no—
297C42—61no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3—121no—
301C22×C3—121no—
302C22×C3—121no—
303C22×C3#88211yescharacteristic
304C22×C3#95311yescharacteristic
305C2×D3—41no—
306C2×D3—41no—
307C2×D3—41no—
308C3×C4—22no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—42no—
316C3×C4—42no—
317C3×C4—82no—
318C3×C4—121no—
319C3×C4—121no—
320C3×C4—121no—
321C3×C4#91111yescharacteristic
322C3×C4#91611yescharacteristic
323C3×C4#91611yescharacteristic
324C3×C4#91811yescharacteristic
325C3×C4#94911yescharacteristic
326C3×C4#95011yescharacteristic
327C3×C4#95011yescharacteristic
328C3×C4#95111yescharacteristic
329Dic3—41no—
330Dic3—41no—
331Dic3—41no—
332Dic3—242no—
333Dic3—241no—
334Dic3—241no—
335C32#165011yescharacteristic, complemented, Sylow
336C23—61no—
337Q8—41no—
338Q8—41no—
339Q8—61no—
340Q8—61no—
341Q8—361no—
342Q8—361no—
343D4—61no—
344D4—61no—
345C2×C4—22no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—121no—
350C2×C4—121no—
351C2×C4—361no—
352C2×C4C2×#62611yescharacteristic
353C2×C4D3×#6711yescharacteristic
354C2×C4D3×#6711yescharacteristic
355C8—121no—
356C8—121no—
357C8—182no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—241no—
362C2×C3#475211yescharacteristic
363C2×C3#478111yescharacteristic
364C2×C3#480811yescharacteristic
365C2×C3#523811yescharacteristic
366C2×C3#523911yescharacteristic
367C2×C3#524611yescharacteristic
368D3—81no—
369C22—121no—
370C22—121no—
371C22—121no—
372C22#6397711yescharacteristic
373C4—21no—
374C4—42no—
375C4—121no—
376C4—121no—
377C4—121no—
378C4—721no—
379C4#6392511yescharacteristic
380C4#6393511yescharacteristic
381C4#6394311yescharacteristic
382C4#6394711yescharacteristic
383C3—21no—
384C3#6843711yescharacteristic, complemented
385C3#7193311yescharacteristic, complemented
386C2—241no—
387C2#1059145211yescharacteristic
388C2#1059159911yescharacteristic
389C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592777C2semidirect
4. #10590301C2semidirect
5. C3×#4547C2semidirect
6. #10589083C2semidirect
37. #4547D3semidirect
335. C32#1650semidirect
384. C3#68437semidirect
385. C3#71933semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105927772
#105903652
#105903012
C3×#45472
#105890832
#105890802
#719333
#684373