Finite Group Databasebeta

← #11779646

Subgroups — #11779646

Order 1152.

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

normal subgroups only

This group has 510 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#10592541C211yesmaximal, characteristic
3#10590288C211yesmaximal, characteristic, complemented
4#10590283C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#68459—31nomaximal
9#68269—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—
19C32×C4⋊C8C2211yescharacteristic
20#63648—21no—
21#63644—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63567—22no—
26#63566—21no—
27#5727—31no—
28Q8×D12—31no—
29#5093—31no—
30#5021—31no—
31#4850—31no—
32#4842—31no—
33#4842—31no—
34#4842—61no—
35#4681—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⋊Dic3D412yes—
59C3×C4⋊Dic3D411yescharacteristic
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#1637—91noSylow
67C2×D3×Q8—61no—
68C2×D3×Q8—61no—
69C3×C4⋊Q8—31no—
70C3×C4×Q8—31no—
71#946—61no—
72#897—61no—
73#897—62no—
74#896—62no—
75#893—61no—
76#888—61no—
77C4×D12—31no—
78C4×D12—31no—
79C4×D12—61no—
80C4×D12—61no—
81#869—31no—
82#869—31no—
83#869—61no—
84#869—61no—
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×C4⋊C8—21no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4×C8—31no—
92#835—61no—
93#821—61no—
94#821—61no—
95#821—62no—
96#818—61no—
97#817—61no—
98#817—61no—
99#817—62no—
100#816—61no—
101#816—62no—
102#810—62no—
103#807—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112C4⋊(C3⋊D3)—21no—
113C4⋊(C3⋊D3)Q1612yes—
114C4×C3⋊D3—41no—
115C4×C3⋊D3—41no—
116#634—42no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C3×Dic6—21no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6SD1612yes—
124#627—44no—
125#624—44no—
126C32×C8—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129D4×Q8—91no—
130#487—91no—
131#477—91no—
132#476—91no—
133#332—31no—
134Q8⋊C8—31no—
135D4⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×Q8—61no—
138D3×Q8—122no—
139D3×Q8—122no—
140D3×Q8—122no—
141D3×Q8—122no—
142C2×D12—31no—
143C2×D12—31no—
144C2×D12—61no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—121no—
150C2×Dic6—21no—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6—61no—
154C2×Dic6—61no—
155C2×Dic6—121no—
156C2×Dic6D1211yescharacteristic
157C2×C3×C8—22no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—32no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C42—21no—
167C3×C42—61no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—61no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—121no—
175C4⋊Dic3—21no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—61no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3D1212yes—
187C4⋊Dic3D1211yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—62no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C22×C32#12011yescharacteristic
194C2×C3⋊D3—22no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—41no—
197C32×C4—21no—
198C32×C4C2×SD1611yescharacteristic
199C32×C4C2×Q1611yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4#13711yescharacteristic
202C3⋊Dic3—41no—
203C3⋊Dic3—81no—
204C3×Dic3—22no—
205C3×Dic3—42no—
206C3×Dic3—41no—
207C22×Q8—181no—
208C4⋊Q8—31no—
209C4⋊Q8—91no—
210C4⋊Q8—181no—
211C22⋊Q8—182no—
212C22⋊Q8—181no—
213C4×Q8—31no—
214C4×D4—91no—
215C4×D4—181no—
216#107—181no—
217#106—181no—
218C4⋊C8—31no—
219C4⋊C8D3211yescharacteristic
220#103—182no—
221#103—181no—
222#102—181no—
223C4×C8—31no—
224C22×D3—61no—
225C22×D3—61no—
226C22×D3—121no—
227C3×Q8—32no—
228C3×Q8—61no—
229C3×Q8—121no—
230C3×Q8—121no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—61no—
235C2×C3×C4—62no—
236C2×C3×C4—61no—
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—22no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249C2×Dic3—122no—
250C2×Dic3—121no—
251C2×Dic3—121no—
252D12—32no—
253D12—32no—
254D12—62no—
255D12—61no—
256D12—61no—
257D12—121no—
258C4×D3—124no—
259C4×D3—124no—
260C4×D3—121no—
261C4×D3—121no—
262C4×D3—121no—
263C4×D3—121no—
264C4×D3—241no—
265C4×D3—241no—
266Dic6—21no—
267Dic6—41no—
268Dic6—41no—
269Dic6—124no—
270Dic6—124no—
271Dic6—122no—
272Dic6—122no—
273Dic6—242no—
274Dic6#20412yes—
275C3×C8—42no—
276C3×C8—41no—
277C3×C8—41no—
278C3×C8—121no—
279C3×C8—121no—
280C3⋊C8—41no—
281C3⋊C8—41no—
282C2×C32#45011yescharacteristic
283C2×C32#45111yescharacteristic
284C2×C32#45411yescharacteristic
285C3⋊D3—42no—
286C2×Q8—31no—
287C2×Q8—61no—
288C2×Q8—182no—
289C2×Q8—181no—
290C2×Q8—362no—
291C2×Q8—362no—
292C2×D4—91no—
293C22×C4—182no—
294C22×C4—181no—
295C2×C8—21no—
296C2×C8—61no—
297C2×C8—61no—
298C4⋊C4—32no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—91no—
303C4⋊C4—182no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C22⋊C4—182no—
307C22⋊C4—181no—
308C42—61no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3#88211yescharacteristic
312C22×C3#88211yescharacteristic
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—122no—
316C2×D3—121no—
317C2×D3—121no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—241no—
321C2×D3—241no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—62no—
330C3×C4—122no—
331C3×C4—121no—
332C3×C4C2×#20411yescharacteristic
333C3×C4#90811yescharacteristic
334C3×C4#91111yescharacteristic
335C3×C4D3×SD1611yescharacteristic
336C3×C4#91511yescharacteristic
337C3×C4#91511yescharacteristic
338C3×C4D3×Q1611yescharacteristic
339C3×C4D3×Q1611yescharacteristic
340Dic3—22no—
341Dic3—42no—
342Dic3—41no—
343Dic3—121no—
344Dic3—121no—
345Dic3—241no—
346Dic3—242no—
347Dic3—241no—
348Dic3—241no—
349C32#163711yescharacteristic, complemented, Sylow
350C23—181no—
351Q8—32no—
352Q8—61no—
353Q8—121no—
354Q8—121no—
355Q8—362no—
356Q8—364no—
357D4—92no—
358D4—181no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—62no—
362C2×C4—181no—
363C2×C4—364no—
364C2×C4—361no—
365C2×C4—361no—
366C2×C4—361no—
367C2×C4D3×D1211yescharacteristic
368C2×C4D3×D1211yescharacteristic
369C2×C4#381111yescharacteristic
370C8—41no—
371C8—121no—
372C8—121no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3#473111yescharacteristic
377C2×C3#475311yescharacteristic
378C2×C3#477611yescharacteristic
379C2×C3#480911yescharacteristic
380C2×C3#480911yescharacteristic
381C2×C3#482711yescharacteristic
382D3—122no—
383D3—122no—
384D3—242no—
385C22—182no—
386C22—361no—
387C22—361no—
388C22#6392311yescharacteristic
389C4—21no—
390C4—62no—
391C4—121no—
392C4—122no—
393C4—361no—
394C4—721no—
395C4D3×#20411yescharacteristic
396C4#6379511yescharacteristic
397C4#6393111yescharacteristic
398C4#6394411yescharacteristic
399C3—21no—
400C3#6826911yescharacteristic, complemented
401C3#6845911yescharacteristic, complemented
402C2—362no—
403C2#1059060511yescharacteristic
404C2#1059094611yescharacteristic
405C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1637
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. #10590288C2semidirect
4. #10590283C2semidirect
5. C3×#4486C2semidirect
6. C3×#4484C2semidirect
38. #4486D3semidirect
39. #4484D3semidirect
349. C32#1637semidirect
400. C3#68269semidirect
401. C3#68459semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105925412
#105902882
#105902832
C3×#44862
C3×#44842
#105890822
#684593
#682693