Finite Group Databasebeta

← #11778369

Subgroups — #11778369

Order 1152.

579 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 579 conjugacy classes of subgroups — too many to draw. Only its 88 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#10595971C211yesmaximal, characteristic
2C3×#4979C211yesmaximal, characteristic
3#10591186C212yesmaximal
4C3×#4528C211yesmaximal, characteristic
5#10589154C212yesmaximal
6#69707—31nomaximal
7#68139—31nomaximal
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10#64135—21no—
11#64133—21no—
12#64133C2212yes—
13#64099—22no—
14#64097—22no—
15C2×C3×Dic3⋊C4—21no—
16C2×#3719—22no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20#63566—22no—
21#5500—31no—
22#5500—31no—
23#5500—61no—
24C3×#395—31no—
25#5228—32no—
26#4979D311yescharacteristic
27#4739—32no—
28C3×#324—31no—
29#4528D311yescharacteristic
30#4467—32no—
31#4452—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#634—21no—
36C2×#634D412yes—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C2×C3×Dic6—22no—
40C2×C3×Dic6—42no—
41C32×C4⋊C4—22no—
42#3757—22no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)D412yes—
47#3750—22no—
48#3750—22no—
49C4×C3⋊Dic3—22no—
50C3×Dic3⋊C4—42no—
51C2×C3×C3⋊C8—22no—
52#3719—44no—
53#1605—91noSylow
54C22×C3×Q8—31no—
55C22×Dic6C2×D311yescharacteristic
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—61no—
58C2×C3×C4⋊C4C2×D311yescharacteristic
59C2×C3×C4⋊C4C2×D311yescharacteristic
60C2×#216—62no—
61#926—62no—
62#926—61no—
63#926—61no—
64#924—32no—
65#924—32no—
66#924—62no—
67#924—62no—
68#924—61no—
69#924—61no—
70C2×Dic3⋊C4—21no—
71C2×Dic12—62no—
72#890—62no—
73#890—62no—
74#890—64no—
75#888—62no—
76#888—62no—
77#888—64no—
78C3×C22⋊C8—32no—
79C3×#95—31no—
80C3×#95—61no—
81#835—62no—
82C3⋊#95—21no—
83C3⋊#95C2×D311yescharacteristic
84#830C2×D312yes—
85#816—62no—
86C23×C32C2×D411yescharacteristic
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4Q1612yescomplemented
93C2×C32×C4C2×D412yes—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96#634—42no—
97#634—81no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C3×Dic6—24no—
105C3×Dic6—42no—
106C3×C3⋊C8—42no—
107#544—91no—
108#451—92no—
109#395—31no—
110#328—92no—
111#324—31no—
112C2×C3×Q8—62no—
113C2×C3×Q8—122no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—61no—
118C22×C3×C4—61no—
119C22×C3×C4D1211yescharacteristic
120C22×C3×C4D1211yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4#6711yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—21no—
126C22×Dic3—21no—
127C2×Dic6—22no—
128C2×Dic6—32no—
129C2×Dic6—32no—
130C2×Dic6—42no—
131C2×Dic6—62no—
132C2×Dic6—62no—
133C2×Dic6—61no—
134C2×Dic6—61no—
135C2×C3×C8—62no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—122no—
140#217—64no—
141#217—62no—
142#217—62no—
143#216—124no—
144C4⋊Dic3—32no—
145C4⋊Dic3—32no—
146C4⋊Dic3—62no—
147C4⋊Dic3—62no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—62no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—62no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156Dic3⋊C4—42no—
157Dic3⋊C4—64no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160Dic3⋊C4—64no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163C4×Dic3—64no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C2×C3⋊C8—22no—
167Dic12—124no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32#12011yescharacteristic
171C22×C32C2×Q1611yescharacteristic
172C22×C32#13711yescharacteristic
173C32×C4—22no—
174C32×C4—22no—
175C32×C4—41no—
176C3⋊Dic3—42no—
177C3⋊Dic3—42no—
178C3×Dic3—42no—
179C3×Dic3—42no—
180C22×Q8—31no—
181C2×Q16—182no—
182C4⋊Q8—182no—
183#125—182no—
184C22⋊Q8—92no—
185C22⋊Q8—181no—
186#117—181no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4D3211yescharacteristic
189#103—182no—
190C22⋊C8—32no—
191#95—31no—
192#95—61no—
193C23×C3—21no—
194C23×C3C2×D1211yescharacteristic
195C23×C3C2×#6711yescharacteristic
196C3×Q8—64no—
197C3×Q8—122no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—81no—
216C2×C3×C4—81no—
217C2×C3×C4—121no—
218C2×C3×C4—121no—
219C2×C3×C4—121no—
220C2×C3×C4—121no—
221C2×C3×C4Dic1212yescomplemented
222C2×C3×C4#21612yescomplemented
223C2×C3×C4D3×D412yes—
224C2×C3×C4D3×D412yes—
225C2×Dic3—22no—
226C2×Dic3—22no—
227C2×Dic3—41no—
228C2×Dic3—41no—
229C2×Dic3—41no—
230C2×Dic3—41no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237Dic6—24no—
238Dic6—42no—
239Dic6—122no—
240Dic6—122no—
241Dic6—242no—
242Dic6—242no—
243Dic6—241no—
244Dic6—241no—
245C3×C8—122no—
246C3⋊C8—42no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32#45111yescharacteristic
250C2×C32#45611yescharacteristic
251C2×C32B(4,𝔽2)11yescharacteristic
252C2×Q8—62no—
253C2×Q8—92no—
254C2×Q8—122no—
255C2×Q8—181no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4#62611yescharacteristic
259C22×C4#62611yescharacteristic
260C22×C4C2×D3211yescharacteristic
261Q16—364no—
262C2×C8—62no—
263C4⋊C4—22no—
264C4⋊C4—92no—
265C4⋊C4—122no—
266C4⋊C4—181no—
267C4⋊C4—181no—
268C4⋊C4—181no—
269C4⋊C4—182no—
270C4⋊C4—182no—
271C22⋊C4—182no—
272C42—182no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3#88211yescharacteristic
283C22×C3C2×Dic1211yescharacteristic
284C22×C3#90911yescharacteristic
285C22×C3#93711yescharacteristic
286C22×C3C2×#21611yescharacteristic
287C22×C3#95111yescharacteristic
288C3×C4—24no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—42no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—122no—
298C3×C4—122no—
299Dic3—42no—
300Dic3—42no—
301Dic3—124no—
302Dic3—124no—
303Dic3—122no—
304Dic3—122no—
305Dic3—122no—
306Dic3—122no—
307C32#160511yescharacteristic, complemented, Sylow
308C23C2×#62611yescharacteristic
309Q8—64no—
310Q8—122no—
311Q8—362no—
312Q8—721no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—182no—
325C2×C4—182no—
326C2×C4#371912yescomplemented
327C2×C4#381112yes—
328C8—122no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—41no—
337C2×C3—41no—
338C2×C3#473911yescharacteristic
339C2×C3#474111yescharacteristic
340C2×C3#475211yescharacteristic
341C2×C3#503211yescharacteristic
342C2×C3#505011yescharacteristic
343C2×C3#509511yescharacteristic
344C22—21no—
345C22—21no—
346C22#6383111yescharacteristic
347C22C2×#371911yescharacteristic
348C22#6398111yescharacteristic
349C4—22no—
350C4—22no—
351C4—41no—
352C4—122no—
353C4—122no—
354C4—362no—
355C4—362no—
356C3—21no—
357C3#6813911yescharacteristic, complemented
358C3#6970711yescharacteristic, complemented
359C2—21no—
360C2—21no—
361C2#1059119011yescharacteristic
362C2#1059153211yescharacteristic
363C2#1059165011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
92. C2×C32×C4Q16semidirect
221. C2×C3×C4Dic12semidirect
222. C2×C3×C4#216semidirect
307. C32#1605semidirect
326. C2×C4#3719semidirect
357. C3#68139semidirect
358. C3#69707semidirect

Maximal subgroups

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

subgroupindex
#105959712
C3×#49792
#105911862
C3×#45282
#105891542
#697073
#681393