Finite Group Databasebeta

← #11780015

Subgroups — #11780015

Order 1152.

449 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 449 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic62C211yesmaximal, characteristic
2#10592380C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic
4#10590301C211yesmaximal, characteristic
5C3×#4456C211yesmaximal, characteristic
6C3×#4456C211yesmaximal, characteristic
7#10589096C211yesmaximal, characteristic
8#68271—31nomaximal
9#68255—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63918—21no—
15#63918—21no—
16Dic3×Dic6—21no—
17Dic3×Dic6—21no—
18#63840—22no—
19C2×#3719—21no—
20C32×C4×C8C2211yescharacteristic
21#63643—22no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63566—21no—
27Q8×Dic6—31no—
28Q8×Dic6—31no—
29#5031—31no—
30#5020—31no—
31#4851—31no—
32#4849—31no—
33#4681—31no—
34#4681—31no—
35#4681—61no—
36C3×Q8⋊C8—31no—
37C3×Q8⋊C8—31no—
38#4481—31no—
39#4481—31no—
40#4456D311yescharacteristic
41#4456D311yescharacteristic
42C2×#634—21no—
43C2×#634D412yes—
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D411yescharacteristic
46C2×#627—22no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×C4⋊Dic3D411yescharacteristic
55C3×Dic3⋊C4—21no—
56C3×Dic3⋊C4—21no—
57C3×C4×Dic3—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3719—42no—
65#1645—91noSylow
66C3×C4×Q8—31no—
67C3×C4×Q8—31no—
68Q8×Dic3—61no—
69Q8×Dic3—61no—
70C2×#216—61no—
71C2×Dic12—61no—
72#888—61no—
73#888—61no—
74#888—62no—
75#888—62no—
76#869—31no—
77#869—31no—
78#869—31no—
79#869—31no—
80#869—61no—
81#869—61no—
82#869—61no—
83#869—61no—
84C4×Dic6—61no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90C3×C4×C8—21no—
91C3×C4×C8C2×D311yescharacteristic
92C3×C4×C8C2×D311yescharacteristic
93#835—61no—
94#817—61no—
95#816—62no—
96#816—62no—
97#816—64no—
98#816—61no—
99#816—61no—
100#810—61no—
101#808—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—41no—
109#634—42no—
110#634—41no—
111#634—41no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C3×Dic6—21no—
117C3×Dic6—21no—
118C3×Dic6SD1612yes—
119C3×Dic6Q1612yescomplemented
120#627—82no—
121C32×C8—41no—
122C3×C3⋊C8—41no—
123C3×C3⋊C8—41no—
124Q82—91no—
125#487—91no—
126#475—91no—
127#462—91no—
128#333—91no—
129Q8⋊C8—31no—
130Q8⋊C8—31no—
131C2×C3×Q8—31no—
132C2×C3×Q8—31no—
133C2×Dic6—32no—
134C2×Dic6—32no—
135C2×Dic6—62no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×Dic6—121no—
141C2×Dic6D1211yescharacteristic
142C2×Dic6D1211yescharacteristic
143C2×C3×C8—22no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C42—21no—
153C3×C42—61no—
154C3×C42—61no—
155C3×C42C22×D311yescharacteristic
156C3×C42C22×D311yescharacteristic
157#216—122no—
158C4⋊Dic3—62no—
159C4⋊Dic3—62no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—62no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3—61no—
169C4⋊Dic3—121no—
170C4⋊Dic3—121no—
171C4⋊Dic3—121no—
172C4⋊Dic3D1211yescharacteristic
173C4⋊Dic3D1211yescharacteristic
174Dic3⋊C4—21no—
175Dic3⋊C4—21no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178C4×Dic3—21no—
179C4×Dic3—21no—
180C4×Dic3—62no—
181C4×Dic3—62no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184Dic12—122no—
185C22×C32#12011yescharacteristic
186C32×C4—21no—
187C32×C4C2×SD1611yescharacteristic
188C32×C4C2×Q1611yescharacteristic
189C32×C4#13711yescharacteristic
190C32×C4#13711yescharacteristic
191C3⋊Dic3—42no—
192C3⋊Dic3—81no—
193C3×Dic3—22no—
194C3×Dic3—22no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C2×Q16—181no—
198C4⋊Q8—91no—
199C4⋊Q8—91no—
200C4⋊Q8—181no—
201C4⋊Q8—181no—
202C4⋊Q8—182no—
203C4×Q8—31no—
204C4×Q8—31no—
205C4×Q8—181no—
206C4×Q8—181no—
207#106—181no—
208C4⋊C8—31no—
209C4⋊C8—31no—
210#103—181no—
211#103—182no—
212#103—181no—
213C4×C8D3211yescharacteristic
214C3×Q8—32no—
215C3×Q8—32no—
216C3×Q8—61no—
217C3×Q8—61no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—61no—
225C2×C3×C4C2×D1211yescharacteristic
226C2×C3×C4C2×D1211yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—122no—
238C2×Dic3—122no—
239C2×Dic3—121no—
240C2×Dic3—121no—
241Dic6—21no—
242Dic6—21no—
243Dic6—122no—
244Dic6—122no—
245Dic6—124no—
246Dic6—121no—
247Dic6—121no—
248Dic6—121no—
249Dic6—121no—
250Dic6—241no—
251Dic6—241no—
252Dic6—242no—
253Dic6—242no—
254Dic6#20412yes—
255Dic6Dic1212yescomplemented
256C3×C8—42no—
257C3×C8—41no—
258C3×C8—41no—
259C3×C8—121no—
260C3×C8—121no—
261C3⋊C8—41no—
262C3⋊C8—41no—
263C2×C32#44811yescharacteristic
264C2×C32#45111yescharacteristic
265C2×C32#45511yescharacteristic
266C2×Q8—31no—
267C2×Q8—31no—
268C2×Q8—92no—
269C2×Q8—182no—
270C2×Q8—181no—
271Q16—362no—
272C2×C8—21no—
273C2×C8—61no—
274C2×C8—61no—
275C4⋊C4—31no—
276C4⋊C4—31no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C4⋊C4—181no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C42—61no—
286C42—61no—
287C42—182no—
288C42C2×D3211yescharacteristic
289C22×C3—21no—
290C22×C3#88211yescharacteristic
291C22×C3#88211yescharacteristic
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—62no—
300C3×C4—62no—
301C3×C4—121no—
302C3×C4—121no—
303C3×C4C2×#20411yescharacteristic
304C3×C4C2×Dic1211yescharacteristic
305C3×C4#90911yescharacteristic
306C3×C4#90911yescharacteristic
307C3×C4D3×SD1611yescharacteristic
308C3×C4#91511yescharacteristic
309C3×C4D3×Q1611yescharacteristic
310C3×C4#91811yescharacteristic
311Dic3—22no—
312Dic3—22no—
313Dic3—41no—
314Dic3—41no—
315Dic3—122no—
316Dic3—122no—
317Dic3—242no—
318Dic3—242no—
319Dic3—241no—
320Dic3—241no—
321C32#164511yescharacteristic, complemented, Sylow
322Q8—32no—
323Q8—32no—
324Q8—61no—
325Q8—61no—
326Q8—362no—
327Q8—361no—
328Q8—361no—
329Q8—722no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—182no—
335C2×C4—361no—
336C2×C4D3×D1211yescharacteristic
337C2×C4D3×D1211yescharacteristic
338C2×C4#381111yescharacteristic
339C8—41no—
340C8—121no—
341C8—121no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#473811yescharacteristic
346C2×C3#473911yescharacteristic
347C2×C3#480611yescharacteristic
348C2×C3#480911yescharacteristic
349C2×C3#482511yescharacteristic
350C2×C3#482511yescharacteristic
351C22#6392311yescharacteristic
352C4—21no—
353C4—62no—
354C4—62no—
355C4—121no—
356C4—121no—
357C4—362no—
358C4—721no—
359C4D3×#20411yescharacteristic
360C4D3×Dic1211yescharacteristic
361C4#6380011yescharacteristic
362C4#6380111yescharacteristic
363C3—21no—
364C3#6825511yescharacteristic, complemented
365C3#6827111yescharacteristic, complemented
366C2#1059039811yescharacteristic
367C2#1059095111yescharacteristic
368C2#1059095211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#120
hypercenterC4×C8D32
hypocenterC32#1645
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
119. C3×Dic6Q16semidirect
255. Dic6Dic12semidirect
321. C32#1645semidirect
364. C3#68255semidirect
365. C3#68271semidirect

Maximal subgroups

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

subgroupindex
Dic622
#105923802
#105903852
#105903012
C3×#44562
#105890962
#682713
#682553