Finite Group Databasebeta

← #11780208

Subgroups — #11780208

Order 1152.

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

normal subgroups only

This group has 522 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
1#10593904C211yesmaximal, characteristic
2#10592548C211yesmaximal, characteristic, complemented
3#10590311C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic
5C3×#4483C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68461—31nomaximal
9#68192—31nomaximal
10C2×D3×Dic6—21no—
11C2×#3746—21no—
12#64078C2211yescharacteristic
13C4×#634C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63919—21no—
17#63899—22no—
18#63898—21no—
19#63856—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63575—22no—
26#63563—21no—
27#5727—31no—
28D4×Dic6—31no—
29#5078—31no—
30#5007—31no—
31#4849—31no—
32#4849—31no—
33#4849—61no—
34#4846—31no—
35#4682—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4484—31no—
39#4483D311yescharacteristic
40#4482D311yescharacteristic, complemented
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
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)—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C4×C3⋊Dic3—21no—
58#3746—42no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3724—22no—
66(C2×D3)⋊Dic3—22no—
67#1649—91noSylow
68C2×D3×Q8—61no—
69C22×Dic6—61no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—31no—
72#946—61no—
73D4×Dic3—61no—
74#924—61no—
75C2×Dic12—61no—
76C2×Dic12—61no—
77C2×Dic12—62no—
78#896—62no—
79#893—61no—
80#888—61no—
81#888—61no—
82#878—62no—
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87#869C2×D311yescharacteristic
88C4×Dic6—31no—
89C4×Dic6—31no—
90C4×Dic6—61no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4×C8—31no—
96#832—61no—
97#821—61no—
98#818—62no—
99#818—61no—
100#816—61no—
101#816—61no—
102#816—62no—
103#807—61no—
104#807—62no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3×D3—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—41no—
114#634—21no—
115#634—41no—
116#634—41no—
117#634D812yes—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×D12—21no—
121C3×D12Q1612yescomplemented
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126#627—44no—
127D3×Dic3—44no—
128C32×C8—41no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—41no—
131D4×Q8—91no—
132#500—91no—
133#474—91no—
134#462—91no—
135#332—31no—
136Q8⋊C8—91no—
137D4⋊C8—31no—
138C2×C3×Q8—61no—
139C2×C3×D4—31no—
140C22×C3×C4—61no—
141C22×Dic3—62no—
142D3×Q8—122no—
143D3×Q8—122no—
144C2×D12D1211yescharacteristic
145C2×C4×D3—21no—
146C2×C4×D3—62no—
147C2×Dic6—21no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6—62no—
154C2×Dic6—61no—
155C2×Dic6—61no—
156C2×Dic6—122no—
157C2×Dic6—122no—
158C2×C3×C8—22no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—32no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—62no—
171(C2×D3)⋊C4—21no—
172(C2×D3)⋊C4—62no—
173C4⋊Dic3—21no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—121no—
182C4⋊Dic3—121no—
183C4⋊Dic3D1212yes—
184C4⋊Dic3D1211yescharacteristic
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—121no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C4×Dic3—121no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195Dic12—122no—
196Dic12—122no—
197Dic12—124no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—22no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4C2×D811yescharacteristic
204C32×C4C2×Q1611yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4#13711yescharacteristic
207C3⋊Dic3—22no—
208C3⋊Dic3—41no—
209C3⋊Dic3—81no—
210C3×Dic3—42no—
211C3×Dic3—41no—
212C22×Q8—181no—
213C2×Q16—181no—
214C4⋊Q8—31no—
215C4⋊Q8—91no—
216C4⋊Q8—181no—
217C22⋊Q8—182no—
218C22⋊Q8—181no—
219C4×Q8—91no—
220C4×D4—31no—
221C4×D4—181no—
222#107—181no—
223#107—182no—
224C4⋊C8—31no—
225C4⋊C8D3211yescharacteristic
226#103—181no—
227#102—181no—
228C4×C8—31no—
229C23×C3—61no—
230C22×D3—21no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×D4—32no—
234C3×D4—61no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—61no—
239C2×C3×C4—62no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4C2×D1211yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×Dic3—21no—
249C2×Dic3—22no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256C2×Dic3—124no—
257C2×Dic3—122no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260D12—21no—
261D12Dic1212yescomplemented
262C4×D3—41no—
263C4×D3—41no—
264C4×D3—124no—
265Dic6—32no—
266Dic6—32no—
267Dic6—41no—
268Dic6—41no—
269Dic6—62no—
270Dic6—61no—
271Dic6—61no—
272Dic6—121no—
273Dic6—124no—
274Dic6—124no—
275Dic6—122no—
276Dic6—122no—
277Dic6—121no—
278Dic6—121no—
279Dic6—121no—
280Dic6—121no—
281C3×C8—42no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8—121no—
286C3⋊C8—22no—
287C3⋊C8—41no—
288C2×C32#44711yescharacteristic
289C2×C32#45111yescharacteristic
290C2×C32#45611yescharacteristic
291C3×D3—42no—
292C2×Q8—61no—
293C2×Q8—91no—
294C2×Q8—182no—
295C2×Q8—181no—
296C2×Q8—362no—
297C2×Q8—362no—
298C2×D4—31no—
299C22×C4—61no—
300C22×C4—182no—
301Q16—362no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—61no—
305C4⋊C4—31no—
306C4⋊C4—32no—
307C4⋊C4—61no—
308C4⋊C4—91no—
309C4⋊C4—182no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C22⋊C4—61no—
314C22⋊C4—182no—
315C42—181no—
316C42C2×D3211yescharacteristic
317C22×C3—21no—
318C22×C3—62no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3#88211yescharacteristic
322C22×C3#88211yescharacteristic
323C2×D3—22no—
324C2×D3—41no—
325C2×D3—41no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—41no—
333C3×C4—121no—
334C3×C4—122no—
335C3×C4C2×Dic1211yescharacteristic
336C3×C4#90911yescharacteristic
337C3×C4D3×D811yescharacteristic
338C3×C4D3×D811yescharacteristic
339C3×C4#91411yescharacteristic
340C3×C4#91411yescharacteristic
341C3×C4#91511yescharacteristic
342C3×C4D3×Q1611yescharacteristic
343Dic3—42no—
344Dic3—41no—
345Dic3—62no—
346Dic3—62no—
347Dic3—122no—
348Dic3—121no—
349Dic3—121no—
350Dic3—241no—
351Dic3—242no—
352Dic3—241no—
353Dic3—241no—
354C32#164911yescharacteristic, complemented, Sylow
355C23—61no—
356Q8—92no—
357Q8—121no—
358Q8—121no—
359Q8—181no—
360Q8—364no—
361Q8—361no—
362Q8—361no—
363D4—32no—
364D4—61no—
365C2×C4—61no—
366C2×C4—62no—
367C2×C4—121no—
368C2×C4—121no—
369C2×C4—181no—
370C2×C4—181no—
371C2×C4—364no—
372C2×C4—361no—
373C2×C4D3×D1211yescharacteristic
374C2×C4D3×D1211yescharacteristic
375C2×C4#381111yescharacteristic
376C8—41no—
377C8—62no—
378C8—121no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—122no—
383C2×C3#473911yescharacteristic
384C2×C3#475211yescharacteristic
385C2×C3#477311yescharacteristic
386C2×C3#477311yescharacteristic
387C2×C3#480911yescharacteristic
388C2×C3#482611yescharacteristic
389D3—42no—
390C22—62no—
391C22—121no—
392C22—121no—
393C22#6392311yescharacteristic
394C4—21no—
395C4—121no—
396C4—122no—
397C4—182no—
398C4—361no—
399C4—721no—
400C4D3×Dic1211yescharacteristic
401C4#6380011yescharacteristic
402C4#6392611yescharacteristic
403C4#6394111yescharacteristic
404C3—21no—
405C3#6819211yescharacteristic, complemented
406C3#6846111yescharacteristic, complemented
407C2—122no—
408C2#1059059811yescharacteristic
409C2#1059095211yescharacteristic
410C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1649
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592548C2semidirect
3. #10590311C2semidirect
6. C3×#4482C2semidirect
7. #10589085C2semidirect
40. #4482D3semidirect
121. C3×D12Q16semidirect
261. D12Dic12semidirect
354. C32#1649semidirect
405. C3#68192semidirect
406. C3#68461semidirect

Maximal subgroups

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

subgroupindex
#105939042
#105925482
#105903112
#105902722
C3×#44832
C3×#44822
#105890852
#684613
#681923