Finite Group Databasebeta

← #11789876

Subgroups — #11789876

Order 1152.

426 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#63777C211yesmaximal, characteristic
2C2×#63740C211yesmaximal, characteristic
3C2×#63740C211yesmaximal, characteristic
4#10591396C211yesmaximal, characteristic
5#10591328C211yesmaximal, characteristic
6#10590075C211yesmaximal, characteristic
7#10590075C211yesmaximal, characteristic
8C22×#627C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16#63777—22no—
17#63740—22no—
18#63740C414yescomplemented
19C3×C3⋊#95—21no—
20C3×C3⋊#95—21no—
21#63579—21no—
22#4647—61no—
23#4646—61no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3⋊Dic3C2311yescharacteristic
27C22×C3×Dic3—21no—
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C2×#627—21no—
32C2×#627—21no—
33C2×#627—21no—
34C2×#627—21no—
35C2×#627—21no—
36C2×#627C2×C412yes—
37C2×#622—21no—
38C2×#622—21no—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622C2×C412yes—
42C2×#622D412yes—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3—21no—
45#3724—21no—
46#3724—21no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50#3724C2×C412yes—
51Dic3⋊Dic3—42no—
52#1935—91nomaximal, Sylow
53C22×Dic6—61no—
54C2×C4⋊Dic3—61no—
55C2×Dic3⋊C4—61no—
56C2×Dic3⋊C4—61no—
57C2×Dic3⋊C4—61no—
58C2×Dic3⋊C4—61no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61C3×#95—61no—
62C3×#95—61no—
63C3⋊#95—21no—
64C3⋊#95—21no—
65C3⋊#95—61no—
66C3⋊#95—61no—
67C23×C32C2×D411yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C22×C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3#4111yescharacteristic
77C2×C3⋊Dic3#4111yescharacteristic
78C2×C3⋊Dic3#4111yescharacteristic
79C2×C3⋊Dic3#4111yescharacteristic
80C2×C3×Dic3—22no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—41no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92#627—22no—
93#627—22no—
94#627—41no—
95#627—41no—
96#622—22no—
97#622—22no—
98C2×#103—91no—
99C2×#103—91no—
100C2×#97—91no—
101#391—91no—
102#389—91no—
103#340—91no—
104#340—91no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—61no—
108C22×C3×C4—61no—
109C22×C3×C4—61no—
110C22×C3×C4—61no—
111C22×Dic3—21no—
112C22×Dic3—21no—
113C22×Dic3—21no—
114C22×Dic3—21no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C2×Dic6—62no—
120C2×Dic6—62no—
121C2×Dic6—121no—
122C2×Dic6—121no—
123C2×Dic6—121no—
124C2×Dic6—121no—
125C4⋊Dic3—122no—
126Dic3⋊C4—62no—
127Dic3⋊C4—62no—
128Dic3⋊C4—121no—
129Dic3⋊C4—121no—
130Dic3⋊C4—121no—
131Dic3⋊C4—121no—
132Dic3⋊C4—122no—
133C4×Dic3—121no—
134C4×Dic3—121no—
135C4×Dic3—121no—
136C4×Dic3—121no—
137C22×C32C4×D411yescharacteristic
138C22×C32#12111yescharacteristic
139C22×C32#12411yescharacteristic
140C22×C32AGL(1,ℤ/8)11yescharacteristic
141C22×C32#13711yescharacteristic
142C22×C32#13711yescharacteristic
143C22×C32#13711yescharacteristic
144C32×C4—41no—
145C3⋊Dic3—41no—
146C3⋊Dic3#11711yescharacteristic
147C3⋊Dic3C4×D411yescharacteristic
148C3⋊Dic3#12311yescharacteristic
149C3⋊Dic3#12611yescharacteristic
150C3×Dic3—42no—
151C3×Dic3—42no—
152C3×Dic3—81no—
153C3×Dic3—81no—
154C22×Q8—91no—
155C22×C8—91no—
156C22×C8—91no—
157C2×C4⋊C4—91no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—181no—
161C2×C42—91no—
162#103—94no—
163#103—182no—
164#97—182no—
165#95—61no—
166#95—61no—
167#95—181no—
168C23×C3—21no—
169C23×C3—21no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4—62no—
177C2×C3×C4—62no—
178C2×C3×C4—121no—
179C2×C3×C4—121no—
180C2×C3×C4—121no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4—121no—
184C2×C3×C4—121no—
185C2×C3×C4—121no—
186C2×C3×C4—121no—
187C2×C3×C4—121no—
188C2×Dic3—22no—
189C2×Dic3—22no—
190C2×Dic3—41no—
191C2×Dic3—41no—
192C2×Dic3—41no—
193C2×Dic3—41no—
194C2×Dic3—41no—
195C2×Dic3—41no—
196C2×Dic3—41no—
197C2×Dic3—41no—
198C2×Dic3—41no—
199C2×Dic3—41no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218Dic6—122no—
219Dic6—122no—
220Dic6—122no—
221Dic6—122no—
222C2×C32#38811yescharacteristic
223C2×C32#44011yescharacteristic
224C2×C32#44111yescharacteristic
225C2×C32#46811yescharacteristic
226C2×C32#47011yescharacteristic
227C2×C32#48911yescharacteristic
228C2×C32#49111yescharacteristic
229C2×Q8—92no—
230C2×Q8—181no—
231C2×Q8—181no—
232C2×Q8—181no—
233C2×Q8—181no—
234C2×Q8—181no—
235C22×C4—61no—
236C22×C4—61no—
237C22×C4—61no—
238C22×C4—61no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4GO+(4,𝔽2)11yescharacteristic
242C2×C8—92no—
243C2×C8—92no—
244C2×C8—181no—
245C2×C8—181no—
246C2×C8—181no—
247C2×C8—181no—
248C4⋊C4—92no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—362no—
255C42—181no—
256C42—181no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C3×C4—42no—
272C3×C4—42no—
273C3×C4—122no—
274C3×C4—122no—
275C3×C4—241no—
276C3×C4—241no—
277Dic3—42no—
278Dic3—42no—
279Dic3—61no—
280Dic3—61no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—61no—
285Dic3—61no—
286Dic3—61no—
287Dic3—81no—
288Dic3—81no—
289Dic3—122no—
290Dic3—122no—
291C32#193511yescharacteristic, complemented, Sylow
292C23C2×GO+(4,𝔽2)11yescharacteristic
293Q8—182no—
294Q8—182no—
295Q8—361no—
296Q8—361no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—62no—
301C2×C4—62no—
302C2×C4—91no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—121no—
309C2×C4—121no—
310C2×C4—121no—
311C2×C4—121no—
312C2×C4—121no—
313C2×C4—121no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4—121no—
317C2×C4—121no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—181no—
321C8—182no—
322C8—182no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C22#6422111yescharacteristic
338C22#6422411yescharacteristic
339C22#6422611yescharacteristic
340C22C4×GO+(4,𝔽2)11yescharacteristic
341C22#6423911yescharacteristic
342C22#6423911yescharacteristic
343C22#6424211yescharacteristic
344C4—41no—
345C4—91no—
346C4—91no—
347C4—91no—
348C4—91no—
349C4—122no—
350C4—122no—
351C4—241no—
352C4—241no—
353C4—361no—
354C3—21no—
355C3—21no—
356C2#1059336211yescharacteristic
357C2#1059336911yescharacteristic
358C2#1059337811yescharacteristic
359C2#1059340011yescharacteristic
360C2#1059343211yescharacteristic
361C2#1059344111yescharacteristic
362C2#1059350811yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1935
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
18. #63740C4semidirect
291. C32#1935semidirect

Maximal subgroups

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

subgroupindex
C2×#637772
C2×#637402
#105913962
#105913282
#105900752
#19359