Finite Group Databasebeta

← #11780215

Subgroups — #11780215

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#10593903C211yesmaximal, characteristic
2#10592545C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic, complemented
4#10590311C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#68461—31nomaximal
9#68273—31nomaximal
10C2×#3797—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63895—22no—
17#63894—21no—
18#63871—21no—
19C2×#3719—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63648—21no—
22#63645—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63567—21no—
27#5727—31no—
28Q8×D12—31no—
29#5078—31no—
30#5031—31no—
31#4849—31no—
32#4846—31no—
33#4846—31no—
34#4846—61no—
35#4682—31no—
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4484D311yescharacteristic, complemented
40#4483—31no—
41#4459—31no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×#627—22no—
48C2×#624—22no—
49#3797—42no—
50#3797—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D412yes—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65#3722—22no—
66#3719—42no—
67#1649—91noSylow
68C2×D3×Q8—61no—
69C2×D3×Q8—61no—
70C3×C4⋊Q8—31no—
71C3×C4×Q8—31no—
72#946—61no—
73C2×#216—61no—
74C2×Dic12—61no—
75#897—61no—
76#897—62no—
77#896—62no—
78#893—61no—
79#888—61no—
80C4×D12—31no—
81C4×D12—31no—
82C4×D12—61no—
83C4×D12—61no—
84#869—31no—
85#869—31no—
86#869—61no—
87#869—61no—
88#869C2×D311yescharacteristic
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—21no—
91C3×C4⋊C8—31no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4×C8—31no—
95#821—61no—
96#821—61no—
97#821—62no—
98#818—61no—
99#818—61no—
100#818—62no—
101#818—62no—
102#816—61no—
103#810—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—41no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)Q1612yescomplemented
115C4×C3⋊D3—41no—
116C4×C3⋊D3—41no—
117#634—41no—
118#634—41no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C3×Dic6—21no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6D812yes—
126#627—44no—
127#624—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—31no—
137D4⋊C8—91no—
138C2×C3×Q8—31no—
139C2×C3×Q8—61no—
140D3×Q8—122no—
141D3×Q8—122no—
142D3×Q8—122no—
143D3×Q8—122no—
144C2×D12—31no—
145C2×D12—31no—
146C2×D12—61no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—121no—
152C2×Dic6—21no—
153C2×Dic6—62no—
154C2×Dic6—62no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×Dic6—121no—
158C2×Dic6D1211yescharacteristic
159C2×C3×C8—22no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—32no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C42—21no—
169C3×C42—61no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#216—122no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—121no—
178C4⋊Dic3—21no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—61no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—121no—
189C4⋊Dic3D1211yescharacteristic
190C4⋊Dic3D1212yes—
191Dic3⋊C4—21no—
192Dic3⋊C4—62no—
193C4×Dic3—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196Dic12—122no—
197C22×C32#12011yescharacteristic
198C2×C3⋊D3—22no—
199C2×C3⋊D3—41no—
200C2×C3⋊D3—41no—
201C32×C4—21no—
202C32×C4C2×D811yescharacteristic
203C32×C4C2×Q1611yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3⋊Dic3—41no—
207C3⋊Dic3—81no—
208C3×Dic3—22no—
209C3×Dic3—42no—
210C3×Dic3—41no—
211C22×Q8—181no—
212C2×Q16—181no—
213C4⋊Q8—31no—
214C4⋊Q8—91no—
215C4⋊Q8—181no—
216C22⋊Q8—182no—
217C22⋊Q8—181no—
218C4×Q8—31no—
219C4×D4—91no—
220C4×D4—181no—
221#107—182no—
222#107—181no—
223C4⋊C8—31no—
224C4⋊C8D3211yescharacteristic
225#103—181no—
226#102—181no—
227C4×C8—31no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3—121no—
231C3×Q8—32no—
232C3×Q8—61no—
233C3×Q8—121no—
234C3×Q8—121no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—61no—
239C2×C3×C4—62no—
240C2×C3×C4—61no—
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—22no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—121no—
253C2×Dic3—122no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256D12—32no—
257D12—32no—
258D12—62no—
259D12—61no—
260D12—61no—
261D12—121no—
262C4×D3—124no—
263C4×D3—124no—
264C4×D3—121no—
265C4×D3—121no—
266C4×D3—121no—
267C4×D3—121no—
268C4×D3—241no—
269C4×D3—241no—
270Dic6—21no—
271Dic6—41no—
272Dic6—41no—
273Dic6—124no—
274Dic6—124no—
275Dic6—121no—
276Dic6—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—241no—
280Dic6—241no—
281Dic6D2412yes—
282C3×C8—42no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—62no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C2×C32#44711yescharacteristic
290C2×C32#45111yescharacteristic
291C2×C32#45611yescharacteristic
292C3⋊D3—42no—
293C2×Q8—31no—
294C2×Q8—61no—
295C2×Q8—182no—
296C2×Q8—181no—
297C2×Q8—362no—
298C2×Q8—362no—
299C2×D4—91no—
300C22×C4—182no—
301C22×C4—181no—
302Q16—362no—
303C2×C8—21no—
304C2×C8—61no—
305C2×C8—61no—
306C4⋊C4—31no—
307C4⋊C4—32no—
308C4⋊C4—61no—
309C4⋊C4—61no—
310C4⋊C4—91no—
311C4⋊C4—182no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C22⋊C4—182no—
315C22⋊C4—181no—
316C42—61no—
317C42C2×D3211yescharacteristic
318C22×C3—21no—
319C22×C3#88211yescharacteristic
320C22×C3#88211yescharacteristic
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—122no—
324C2×D3—121no—
325C2×D3—121no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—241no—
329C2×D3—241no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—41no—
337C3×C4—62no—
338C3×C4—122no—
339C3×C4—121no—
340C3×C4C2×D2411yescharacteristic
341C3×C4#90811yescharacteristic
342C3×C4D3×D811yescharacteristic
343C3×C4#91411yescharacteristic
344C3×C4#91511yescharacteristic
345C3×C4#91511yescharacteristic
346C3×C4D3×Q1611yescharacteristic
347C3×C4D3×Q1611yescharacteristic
348Dic3—22no—
349Dic3—42no—
350Dic3—41no—
351Dic3—121no—
352Dic3—121no—
353Dic3—241no—
354Dic3—242no—
355Dic3—241no—
356Dic3—241no—
357C32#164911yescharacteristic, complemented, Sylow
358C23—181no—
359Q8—32no—
360Q8—61no—
361Q8—121no—
362Q8—121no—
363Q8—364no—
364Q8—361no—
365Q8—361no—
366D4—92no—
367D4—181no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—62no—
371C2×C4—181no—
372C2×C4—364no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4—361no—
376C2×C4D3×D1211yescharacteristic
377C2×C4D3×D1211yescharacteristic
378C2×C4#381111yescharacteristic
379C8—41no—
380C8—62no—
381C8—121no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3#473211yescharacteristic
386C2×C3#475211yescharacteristic
387C2×C3#477311yescharacteristic
388C2×C3#480911yescharacteristic
389C2×C3#480911yescharacteristic
390C2×C3#482611yescharacteristic
391D3—122no—
392D3—122no—
393D3—242no—
394C22—182no—
395C22—361no—
396C22—361no—
397C22#6392311yescharacteristic
398C4—21no—
399C4—62no—
400C4—121no—
401C4—122no—
402C4—361no—
403C4—721no—
404C4D3×D2411yescharacteristic
405C4#6379411yescharacteristic
406C4#6393111yescharacteristic
407C4#6394411yescharacteristic
408C3—21no—
409C3#6827311yescharacteristic, complemented
410C3#6846111yescharacteristic, complemented
411C2—362no—
412C2#1059060511yescharacteristic
413C2#1059094711yescharacteristic
414C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
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
3. #10590385C2semidirect
4. #10590311C2semidirect
5. C3×#4486C2semidirect
6. C3×#4484C2semidirect
38. #4486D3semidirect
39. #4484D3semidirect
114. C4⋊(C3⋊D3)Q16semidirect
357. C32#1649semidirect
409. C3#68273semidirect
410. C3#68461semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105925452
#105903852
#105903112
C3×#44862
C3×#44842
#105890822
#684613
#682733