Finite Group Databasebeta

← #11778788

Subgroups — #11778788

Order 1152.

639 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 639 conjugacy classes of subgroups — too many to draw. Only its 88 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
1#10595981C211yesmaximal, characteristic
2C3×#4986C211yesmaximal, characteristic, complemented
3#10591125C212yesmaximal, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589151C212yesmaximal, complemented
6#69718—31nomaximal
7#68137—31nomaximal
8C2×#3828—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10#64139—21no—
11#64139C2212yes—
12#64106—22no—
13#64104—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×C3⋊#95—21no—
16C3×C3⋊#95—21no—
17C3×C3⋊#95C2211yescharacteristic
18C3×#830C2212yes—
19#63573—22no—
20#63564—22no—
21#5510—31no—
22#5510—31no—
23#5510—61no—
24C3×#400—31no—
25#4986D311yescharacteristic, complemented
26#4968—32no—
27#4735—32no—
28C3×#324—31no—
29#4528D311yescharacteristic, complemented
30#4470—32no—
31#4451—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#638—22no—
36#3828—42no—
37#3828—42no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)D412yes—
41C2×C4×C3⋊D3—22no—
42C2×#634—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C32×C4⋊C4—22no—
46#3752—22no—
47#3752—22no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D412yes—
50C3×C4⋊Dic3—22no—
51C2×C3×C3⋊C8—22no—
52#1616—91noSylow
53C2×#235—62no—
54C2×#235—61no—
55C2×#235—61no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—31no—
58C2×C3×C4⋊C4C2×D311yescharacteristic
59C2×C3×C4⋊C4C2×D311yescharacteristic
60#930—32no—
61#930—32no—
62#930—62no—
63#930—62no—
64#930—61no—
65#930—61no—
66C2×C4⋊Dic3C2×D311yescharacteristic
67#897—62no—
68#897—62no—
69#897—64no—
70#895—62no—
71#895—62no—
72#895—64no—
73C3×C22⋊C8—32no—
74C3×#95—31no—
75C3×#95—61no—
76C3×#95—61no—
77C3⋊#95—21no—
78C3⋊#95—21no—
79C3⋊#95C2×D311yescharacteristic
80#830C2×D312yes—
81#821—62no—
82#817—62no—
83#809—62no—
84#808—62no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—22no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4SD1612yes—
93C2×C32×C4C2×D412yes—
94#638—42no—
95#638—42no—
96C2×C3⋊Dic3—22no—
97C4⋊(C3⋊D3)—42no—
98C4⋊(C3⋊D3)—42no—
99C4⋊(C3⋊D3)—81no—
100C4×C3⋊D3—44no—
101#634—42no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—42no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C3×C3⋊C8—42no—
108#537—91no—
109#481—92no—
110#400—31no—
111#327—92no—
112#324—31no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4D1211yescharacteristic
119C22×C3×C4D1211yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C2×#67—64no—
125C2×#67—62no—
126C2×#67—62no—
127C22×Dic3—21no—
128C22×Dic3—21no—
129#235—124no—
130#235—122no—
131#235—122no—
132#235—124no—
133#235—122no—
134#235—122no—
135C2×D12—32no—
136C2×D12—32no—
137C2×D12—62no—
138C2×D12—62no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—62no—
142C2×D12—61no—
143C2×D12—61no—
144C2×C4×D3—64no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×Dic6—62no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×C3×C8—62no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—62no—
155(C2×D3)⋊C4—64no—
156(C2×D3)⋊C4—62no—
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—64no—
159(C2×D3)⋊C4—62no—
160(C2×D3)⋊C4—62no—
161C4⋊Dic3—22no—
162C4⋊Dic3—32no—
163C4⋊Dic3—32no—
164C4⋊Dic3—62no—
165C4⋊Dic3—62no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C2×C3⋊C8—22no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32#12011yescharacteristic
172C22×C32C2×SD1611yescharacteristic
173C22×C32AGL(1,ℤ/8)11yescharacteristic
174C2×C3⋊D3—42no—
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C32×C4—22no—
178C32×C4—22no—
179C32×C4—41no—
180C3⋊Dic3—42no—
181C3×Dic3—81no—
182C3×Dic3—81no—
183C2×#41—181no—
184C22⋊Q8—182no—
185#121—92no—
186#121—182no—
187#121—181no—
188C2×C4⋊C4—31no—
189C2×C4⋊C4D3211yescharacteristic
190#106—182no—
191#102—182no—
192C22⋊C8—32no—
193#95—31no—
194#95—61no—
195#95—61no—
196C23×C3—21no—
197C23×C3C2×D1211yescharacteristic
198C23×C3C2×#6711yescharacteristic
199C22×D3—64no—
200C22×D3—62no—
201C22×D3—62no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—81no—
218C2×C3×C4—81no—
219C2×C3×C4—121no—
220C2×C3×C4—121no—
221C2×C3×C4—122no—
222C2×C3×C4—121no—
223C2×C3×C4—121no—
224C2×C3×C4#20412yes—
225C2×C3×C4#21512yes—
226C2×C3×C4D3×D412yes—
227C2×C3×C4D3×D412yes—
228#67—124no—
229#67—124no—
230#67—122no—
231#67—122no—
232#67—122no—
233#67—122no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3—42no—
237C2×Dic3—41no—
238C2×Dic3—41no—
239C2×Dic3—64no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242D12—122no—
243D12—122no—
244D12—124no—
245D12—122no—
246D12—122no—
247D12—242no—
248D12—242no—
249D12—241no—
250D12—241no—
251C4×D3—128no—
252C4×D3—124no—
253C4×D3—124no—
254Dic6—124no—
255Dic6—122no—
256Dic6—122no—
257C3×C8—122no—
258C3⋊C8—42no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32#45011yescharacteristic
262C2×C32#45411yescharacteristic
263C2×C32#45811yescharacteristic
264C3⋊D3—82no—
265#41—362no—
266#41—362no—
267C2×Q8—181no—
268C2×D4—92no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—182no—
272C22×C4—61no—
273C22×C4—61no—
274C22×C4—182no—
275C22×C4#62611yescharacteristic
276C22×C4#62611yescharacteristic
277C22×C4C2×D3211yescharacteristic
278C2×C8—62no—
279C4⋊C4—22no—
280C4⋊C4—62no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3#88211yescharacteristic
295C22×C3C2×#20411yescharacteristic
296C22×C3#90811yescharacteristic
297C22×C3#93711yescharacteristic
298C22×C3C2×#21511yescharacteristic
299C22×C3#94911yescharacteristic
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C2×D3—122no—
304C2×D3—122no—
305C2×D3—122no—
306C2×D3—122no—
307C2×D3—122no—
308C2×D3—122no—
309C3×C4—24no—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—42no—
315C3×C4—42no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—241no—
319C3×C4—241no—
320Dic3—81no—
321Dic3—81no—
322Dic3—124no—
323Dic3—122no—
324Dic3—122no—
325C32#161611yescharacteristic, complemented, Sylow
326C23—182no—
327C23C2×#62611yescharacteristic
328Q8—362no—
329D4—362no—
330D4—362no—
331D4—362no—
332D4—362no—
333D4—721no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—121no—
340C2×C4—121no—
341C2×C4—122no—
342C2×C4—121no—
343C2×C4—121no—
344C2×C4—182no—
345C2×C4—364no—
346C2×C4#371712yes—
347C2×C4#381112yes—
348C8—122no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3#473111yescharacteristic
359C2×C3#474211yescharacteristic
360C2×C3#475311yescharacteristic
361C2×C3#504611yescharacteristic
362C2×C3#505311yescharacteristic
363C2×C3#506211yescharacteristic
364D3—244no—
365D3—242no—
366D3—242no—
367C22—21no—
368C22—21no—
369C22—362no—
370C22—362no—
371C22—362no—
372C22#6382511yescharacteristic
373C22C2×#371711yescharacteristic
374C22#6398111yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—241no—
379C4—241no—
380C4—362no—
381C3—21no—
382C3#6813711yescharacteristic, complemented
383C3#6971811yescharacteristic, complemented
384C2—21no—
385C2—21no—
386C2—722no—
387C2#1059118311yescharacteristic
388C2#1059153511yescharacteristic
389C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#10595981C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4986C2semidirect
3. #10591125C2semidirect
4. C3×#4528C2semidirect
5. #10589151C2semidirect
25. #4986D3semidirect
29. #4528D3semidirect
325. C32#1616semidirect
382. C3#68137semidirect
383. C3#69718semidirect

Maximal subgroups

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

subgroupindex
#105959812
C3×#49862
#105911252
C3×#45282
#105891512
#697183
#681373