Finite Group Databasebeta

← #11794599

Subgroups — #11794599

Order 1152.

426 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4⋊#622C211yesmaximal, characteristic
2C2×#63743C211yesmaximal, characteristic
3C2×#63740C211yesmaximal, characteristic
4C2×#63740C211yesmaximal, characteristic
5#10591396C211yesmaximal, characteristic
6#10591328C211yesmaximal, characteristic
7#10590075C211yesmaximal, characteristic
8C22×#627C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16C4⋊#622—22no—
17#63743—22no—
18#63740—22no—
19#63740—22no—
20C3×C3⋊#95—21no—
21C3×C3⋊#95—21no—
22#63579—21no—
23#4647—61no—
24#4646—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C2×#627—21no—
33C2×#627—21no—
34C2×#627—21no—
35C2×#627—21no—
36C2×#627—21no—
37C2×#627Q812yes—
38C2×#622—21no—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622—21no—
42C2×#622—21no—
43C2×#622D412yes—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3—21no—
46#3724—21no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50#3724—21no—
51#3724D412yes—
52Dic3⋊Dic3—42no—
53#2068—91nomaximal, Sylow
54C22×Dic6—61no—
55C2×C4⋊Dic3—61no—
56C2×Dic3⋊C4—61no—
57C2×Dic3⋊C4—61no—
58C2×Dic3⋊C4—61no—
59C2×Dic3⋊C4—61no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—61no—
62C3×#95—61no—
63C3×#95—61no—
64C3⋊#95—21no—
65C3⋊#95—21no—
66C3⋊#95—61no—
67C3⋊#95—61no—
68C23×C32C2×D411yescharacteristic
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4Q1612yes—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×Q811yescharacteristic
78C2×C3⋊Dic3#4111yescharacteristic
79C2×C3⋊Dic3#4111yescharacteristic
80C2×C3⋊Dic3#4111yescharacteristic
81C2×C3×Dic3—22no—
82C2×C3×Dic3—22no—
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—
92C2×C3×Dic3—41no—
93#627—22no—
94#627—22no—
95#627—41no—
96#627—41no—
97#622—22no—
98#622—41no—
99C2×#107—91no—
100C2×C4⋊C8—91no—
101C2×#103—91no—
102C2×#103—91no—
103#391—91no—
104#389—91no—
105#340—91no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—61no—
109C22×C3×C4—61no—
110C22×C3×C4—61no—
111C22×C3×C4—61no—
112C22×Dic3—21no—
113C22×Dic3—21no—
114C22×Dic3—21no—
115C22×Dic3—21no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×Dic6—121no—
123C2×Dic6—121no—
124C2×Dic6—121no—
125C2×Dic6—121no—
126C4⋊Dic3—122no—
127Dic3⋊C4—62no—
128Dic3⋊C4—62no—
129Dic3⋊C4—121no—
130Dic3⋊C4—121no—
131Dic3⋊C4—121no—
132Dic3⋊C4—121no—
133Dic3⋊C4—122no—
134C4×Dic3—121no—
135C4×Dic3—121no—
136C4×Dic3—121no—
137C4×Dic3—121no—
138C22×C32#12111yescharacteristic
139C22×C32#12111yescharacteristic
140C22×C32C22⋊Q811yescharacteristic
141C22×C32C2×Q1611yescharacteristic
142C22×C32#13511yescharacteristic
143C22×C32AGL(1,ℤ/8)11yescharacteristic
144C22×C32#13711yescharacteristic
145C32×C4—22no—
146C3⋊Dic3—41no—
147C3⋊Dic3#12111yescharacteristic
148C3⋊Dic3C22⋊Q811yescharacteristic
149C3⋊Dic3C22⋊Q811yescharacteristic
150C3⋊Dic3#12611yescharacteristic
151C3×Dic3—42no—
152C3×Dic3—42no—
153C3×Dic3—81no—
154C3×Dic3—81no—
155C22×Q8—91no—
156C22×C8—91no—
157C22×C8—91no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—181no—
162C2×C42—91no—
163#107—182no—
164C4⋊C8—182no—
165#103—182no—
166#103—182no—
167#95—61no—
168#95—61no—
169#95—181no—
170C23×C3—21no—
171C23×C3—21no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—62no—
179C2×C3×C4—62no—
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×C3×C4—121no—
189C2×C3×C4—121no—
190C2×Dic3—22no—
191C2×Dic3—22no—
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—41no—
201C2×Dic3—41no—
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—61no—
213C2×Dic3—61no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219C2×Dic3—121no—
220Dic6—122no—
221Dic6—122no—
222Dic6—122no—
223Dic6—122no—
224C2×C32#39611yescharacteristic
225C2×C32#46211yescharacteristic
226C2×C32#46311yescharacteristic
227C2×C32#46711yescharacteristic
228C2×C32#46811yescharacteristic
229C2×C32#47711yescharacteristic
230C2×C32#47911yescharacteristic
231C2×Q8—92no—
232C2×Q8—181no—
233C2×Q8—181no—
234C2×Q8—181no—
235C2×Q8—181no—
236C2×Q8—181no—
237C22×C4—61no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4—61no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4GO+(4,𝔽2)11yescharacteristic
244C2×C8—92no—
245C2×C8—181no—
246C2×C8—181no—
247C2×C8—181no—
248C2×C8—181no—
249C2×C8—181no—
250C4⋊C4—92no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C4⋊C4—362no—
257C42—181no—
258C42—181no—
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—
271C22×C3—21no—
272C22×C3—21no—
273C3×C4—42no—
274C3×C4—42no—
275C3×C4—122no—
276C3×C4—122no—
277C3×C4—241no—
278C3×C4—241no—
279Dic3—42no—
280Dic3—42no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—61no—
285Dic3—61no—
286Dic3—61no—
287Dic3—61no—
288Dic3—61no—
289Dic3—81no—
290Dic3—81no—
291Dic3—122no—
292Dic3—122no—
293C32#206811yescharacteristic, complemented, Sylow
294C23C2×GO+(4,𝔽2)11yescharacteristic
295Q8—182no—
296Q8—182no—
297Q8—361no—
298Q8—361no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
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—121no—
319C2×C4—181no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4#377612yes—
323C8—182no—
324C8—361no—
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—
337C2×C3—21no—
338C2×C3—21no—
339C22D32⋊Q811yescharacteristic
340C22#6422411yescharacteristic
341C22#6422611yescharacteristic
342C22#6423011yescharacteristic
343C22#6423711yescharacteristic
344C22C2×#377611yescharacteristic
345C22#6424211yescharacteristic
346C4—22no—
347C4—91no—
348C4—91no—
349C4—91no—
350C4—91no—
351C4—122no—
352C4—122no—
353C4—241no—
354C4—241no—
355C4—361no—
356C3—21no—
357C3—21no—
358C2#1059337311yescharacteristic
359C2#1059339311yescharacteristic
360C2#1059340611yescharacteristic
361C2#1059342811yescharacteristic
362C2#1059344111yescharacteristic
363C2#1059344711yescharacteristic
364C2#1059352711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊Dic3C23
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2068
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
293. C32#2068semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#6222
C2×#637432
C2×#637402
#105913962
#105913282
#105900752
#20689