Finite Group Databasebeta

← #11781779

Subgroups — #11781779

Order 1152.

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

normal subgroups only

This group has 386 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#10592706C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4#10590386C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71105—31nomaximal
9#70871—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#208—21no—
13C3×#869C2211yescharacteristic
14C2×#3719—21no—
15C2×#3719—21no—
16#63659—21no—
17#63634—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×#832—21no—
20C3×#830—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#474—31no—
26C3×#436—31no—
27#5092—31no—
28#5012D311yescharacteristic
29#5007—31no—
30#5007—31no—
31#5007—61no—
32#5007D311yescharacteristic
33#4699—31no—
34#4547—31no—
35#4486—31no—
36#4482—31no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×#208—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3719—42no—
58#3719—42no—
59#1689—91noSylow
60C2×C3×M16—61no—
61C3×C4⋊Q8—31no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C2×D311yescharacteristic
65C2×#216—61no—
66C2×#216—61no—
67C2×#208—21no—
68C2×Dic12—61no—
69C2×Dic12—61no—
70#869—31no—
71#869—31no—
72#869—61no—
73#869C2×D311yescharacteristic
74C3×#107—61no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#102—61no—
78C3×C22⋊C8—61no—
79C3×C4×C8—31no—
80#832—21no—
81#832—62no—
82#832—61no—
83#832—61no—
84#830—21no—
85#807—21no—
86#807—62no—
87#807—61no—
88#807—61no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C23×C32—21no—
96C32×D4—21no—
97C32×D4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—41no—
105#634—41no—
106#634—41no—
107C2×C3×Dic3—41no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8D812yes—
115#494—91no—
116#474—31no—
117#474—91no—
118#436—31no—
119#334—91no—
120#332—91no—
121#332—91no—
122C2×C3×Q8—61no—
123C2×C3×D4—21no—
124C2×C3×D4D1211yescharacteristic
125C2×C3×D4#6711yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C2×Dic6—21no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×Dic6—121no—
133C3×M16—122no—
134C2×C3×C8—31no—
135C2×C3×C8—31no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C4⋊C4D1211yescharacteristic
142C3×C4⋊C4#6711yescharacteristic
143C3×C22⋊C4—21no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—41no—
146C3×C42—21no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#216—122no—
150#216—122no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—62no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—121no—
159#208—42no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8#6711yescharacteristic
166C2×C3⋊C8#6711yescharacteristic
167Dic12—122no—
168Dic12—122no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32#12111yescharacteristic
173C32×C4—21no—
174C32×C4—41no—
175C32×C4C2×D811yescharacteristic
176C32×C4AGL(1,ℤ/8)11yescharacteristic
177C32×C4#13711yescharacteristic
178C32×C4#13711yescharacteristic
179C3⋊Dic3—81no—
180C3×Dic3—81no—
181C2×Q16—181no—
182C2×Q16—181no—
183C2×M16—61no—
184C4⋊Q8—31no—
185C4⋊Q8—91no—
186C4×D4D3211yescharacteristic
187#107—61no—
188#107—181no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8—91no—
192#102—61no—
193#102—181no—
194C22⋊C8—61no—
195C4×C8—31no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—41no—
199C3×Q8—121no—
200C3×Q8—121no—
201C3×D4—22no—
202C3×D4—21no—
203C3×D4—21no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—41no—
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×C4C2×D1211yescharacteristic
221C2×C3×C4#23511yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4#23711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×C3×C4C2×#6711yescharacteristic
226C2×Dic3—41no—
227C2×Dic3—122no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230Dic6—41no—
231Dic6—41no—
232Dic6—121no—
233Dic6—121no—
234Dic6—121no—
235Dic6—121no—
236Dic6—241no—
237Dic6—241no—
238C3×C8—32no—
239C3×C8—61no—
240C3×C8—121no—
241C3×C8—121no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8—41no—
245C3⋊C8—122no—
246C3⋊C8—121no—
247C3⋊C8—121no—
248C3⋊C8#21312yes—
249C2×C32—81no—
250C2×C32#45911yescharacteristic
251C2×C32#47011yescharacteristic
252C2×C32#47311yescharacteristic
253C2×Q8—61no—
254C2×Q8—181no—
255C2×D4#62611yescharacteristic
256C22×C4—21no—
257Q16—362no—
258Q16—362no—
259M16—122no—
260C2×C8—31no—
261C2×C8—31no—
262C2×C8—61no—
263C2×C8—61no—
264C2×C8—181no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4—181no—
268C4⋊C4—181no—
269C4⋊C4#62611yescharacteristic
270C22⋊C4—21no—
271C42C2×D3211yescharacteristic
272C22×C3—21no—
273C22×C3—42no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—81no—
281C22×C3—81no—
282C22×C3#93011yescharacteristic
283C22×C3#93911yescharacteristic
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—81no—
294C3×C4—241no—
295C3×C4#90911yescharacteristic
296C3×C4#90911yescharacteristic
297C3×C4D3×D811yescharacteristic
298C3×C4#91111yescharacteristic
299C3×C4C2×#21311yescharacteristic
300C3×C4#94211yescharacteristic
301C3×C4#94911yescharacteristic
302C3×C4#95111yescharacteristic
303Dic3—81no—
304Dic3—242no—
305Dic3—241no—
306Dic3—241no—
307C32#168911yescharacteristic, complemented, Sylow
308C23—21no—
309Q8—121no—
310Q8—121no—
311Q8—361no—
312Q8—361no—
313D4—21no—
314D4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—121no—
319C2×C4—361no—
320C2×C4#380411yescharacteristic
321C2×C4C2×#62611yescharacteristic
322C2×C4D3×#6711yescharacteristic
323C8—32no—
324C8—61no—
325C8—121no—
326C8—121no—
327C8—361no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—82no—
332C2×C3—81no—
333C2×C3—81no—
334C2×C3#501511yescharacteristic
335C2×C3#505211yescharacteristic
336C2×C3#513711yescharacteristic
337C2×C3#514311yescharacteristic
338C2×C3#515011yescharacteristic
339C2×C3#520411yescharacteristic
340C22—41no—
341C22—41no—
342C22—41no—
343C22#6397811yescharacteristic
344C4—21no—
345C4—41no—
346C4—241no—
347C4—721no—
348C4#6383111yescharacteristic
349C4#6383311yescharacteristic
350C4D3×#21311yescharacteristic
351C4#6392511yescharacteristic
352C3—21no—
353C3#7087111yescharacteristic, complemented
354C3#7110511yescharacteristic, complemented
355C2—81no—
356C2#1059112111yescharacteristic
357C2#1059148111yescharacteristic
358C2#1059168211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1689
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10590386C2semidirect
5. #10589097C2semidirect
6. #10589094C2semidirect
7. #10589093C2semidirect
307. C32#1689semidirect
353. C3#70871semidirect
354. C3#71105semidirect

Maximal subgroups

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

subgroupindex
#105927062
C3×#50122
C3×#50072
#105903862
#105890972
#105890942
#105890932
#711053
#708713