Finite Group Databasebeta

← #11774032

Subgroups — #11774032

Order 1152.

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

normal subgroups only

This group has 677 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
1C2×#64094C211yesmaximal, characteristic
2#10591066C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4C3×#4525C212yesmaximal, complemented
5#10589146C212yesmaximal, complemented
6#68104—32nomaximal
7C22×#638C411yescharacteristic
8C22×#634C411yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C411yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64094—21no—
15#64094—21no—
16#64094—21no—
17#64094—21no—
18C3×#830C2212yes—
19C3×#830C2212yes—
20#63572—21no—
21#63572—21no—
22#63555—21no—
23#63553—21no—
24C2×#885—32no—
25C2×#885—61no—
26#4719—32no—
27#4718—32no—
28C3×#323—32no—
29#4525D312yescomplemented
30#4468—32no—
31#4468—32no—
32C24×C32C2×C411yescharacteristic
33C23×C3⋊D3C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×#638—21no—
37C2×#638—21no—
38C2×#638—42no—
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3C2×C411yescharacteristic
41C22×C3⋊Dic3C2×C411yescharacteristic
42C2×#634—21no—
43C2×#634—21no—
44C2×#634—42no—
45C32×C22⋊C4—21no—
46C32×C22⋊C4—21no—
47#3757—21no—
48#3757—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52#3752—21no—
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#1469—91noSylow
60C22×#67—32no—
61C22×#67—61no—
62C22×Dic6—32no—
63C22×Dic6—61no—
64C2×C3×C22⋊C4—21no—
65C2×C3×C22⋊C4C2×D312yes—
66C2×#217—32no—
67C2×#217—61no—
68C2×(C2×D3)⋊C4—32no—
69C2×(C2×D3)⋊C4—32no—
70C2×(C2×D3)⋊C4—61no—
71C2×(C2×D3)⋊C4—61no—
72C2×C4×Dic3—32no—
73C2×C4×Dic3—61no—
74#885—62no—
75#885—62no—
76#885—62no—
77#885—62no—
78#885—62no—
79#885—62no—
80#885—62no—
81#885—62no—
82C3×C22⋊C8—32no—
83C3×C22⋊C8—32no—
84#830C2×D312yes—
85#830C2×D312yes—
86#815—62no—
87Dic3⋊C8—62no—
88Dic3⋊C8—62no—
89C8×Dic3—62no—
90C23×C32—21no—
91C23×C32—22no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32C22×C411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3—41no—
98C22×C3⋊D3—41no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104#638—42no—
105#638—42no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C2×C3⋊Dic3C22⋊C411yescharacteristic
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C2×C3⋊Dic3C22⋊C411yescharacteristic
114#634—42no—
115#634—42no—
116C3×C3⋊C8—42no—
117C3×C3⋊C8—42no—
118C2×#124—91no—
119#432—91no—
120#431—91no—
121#323—32no—
122#323—92no—
123C24×C3—21no—
124C24×C3C4×D312yes—
125C23×D3—32no—
126C23×D3—61no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4C4×D312yes—
130C22×C3×C4C22×D312yes—
131C2×#67—62no—
132C2×#67—62no—
133C2×#67—62no—
134C2×#67—62no—
135C2×#67—124no—
136C2×#67—124no—
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—32no—
140C22×Dic3—61no—
141C22×Dic3—61no—
142C22×Dic3—61no—
143C2×Dic6—62no—
144C2×Dic6—62no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—124no—
148C2×Dic6—124no—
149C2×C3×C8—62no—
150C2×C3×C8—62no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—22no—
155#217—62no—
156#217—62no—
157#217—62no—
158#217—62no—
159(C2×D3)⋊C4—62no—
160(C2×D3)⋊C4—62no—
161(C2×D3)⋊C4—62no—
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167C4×Dic3—32no—
168C4×Dic3—32no—
169C4×Dic3—32no—
170C4×Dic3—32no—
171C4×Dic3—61no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—61no—
175C2×C3⋊C8—22no—
176C2×C3⋊C8—22no—
177C22×C32—21no—
178C22×C32—21no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32—41no—
182C22×C32—82no—
183C22×C32C2×C22⋊C411yescharacteristic
184C22×C32#13112yes—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—82no—
189C32×C4—21no—
190C32×C4—21no—
191C32×C4—41no—
192C3⋊Dic3—21no—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3—41no—
196C3⋊Dic3#10012yes—
197C22×Q8—91no—
198C22×D4—91no—
199#124—181no—
200#124—181no—
201#124—181no—
202#124—181no—
203C2×C22⋊C4—91no—
204C2×C22⋊C4—91no—
205C2×C22⋊C4—91no—
206C2×C22⋊C4D3211yescharacteristic
207C2×C42—91no—
208C4⋊C8—181no—
209C4⋊C8—181no—
210C22⋊C8—32no—
211C22⋊C8—32no—
212#97—181no—
213C4×C8—181no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—21no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3—42no—
222C23×C3—42no—
223C23×C3—42no—
224C23×C3C2×C4×D312yes—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—122no—
230C22×D3—122no—
231C22×D3—122no—
232C22×D3—122no—
233C22×D3—122no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4D3×D412yes—
243C2×C3×C4D3×D412yes—
244#67—124no—
245#67—124no—
246#67—124no—
247#67—124no—
248C2×Dic3—32no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—122no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265Dic6—124no—
266Dic6—124no—
267Dic6—124no—
268Dic6—124no—
269C3×C8—122no—
270C3×C8—122no—
271C3⋊C8—42no—
272C3⋊C8—42no—
273C2×C32—22no—
274C2×C32—81no—
275C2×C32#40811yescharacteristic
276C2×C32#41011yescharacteristic
277C2×C32C2×#10011yescharacteristic
278C3⋊D3—81no—
279C24—91no—
280C24#62411yescharacteristic
281C2×Q8—181no—
282C2×Q8—181no—
283C2×Q8—362no—
284C2×D4—181no—
285C2×D4—181no—
286C2×D4—362no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4#62411yescharacteristic
291C22×C4C2×D3211yescharacteristic
292C2×C8—62no—
293C2×C8—62no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—181no—
297C22⋊C4—181no—
298C22⋊C4—181no—
299C22⋊C4—181no—
300C22⋊C4—181no—
301C22⋊C4—181no—
302C42—91no—
303C42—91no—
304C42—91no—
305C42—91no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—42no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—82no—
319C22×C3—82no—
320C22×C3—84no—
321C22×C3D3×C22⋊C412yes—
322C22×C3#90112yes—
323C22×C3#90712yes—
324C2×D3—122no—
325C2×D3—122no—
326C2×D3—122no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—244no—
331C2×D3—242no—
332C2×D3—242no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—42no—
338C3×C4—42no—
339Dic3—34no—
340Dic3—62no—
341Dic3—62no—
342Dic3—62no—
343Dic3—62no—
344Dic3—62no—
345Dic3—121no—
346Dic3—121no—
347Dic3—122no—
348Dic3—122no—
349C32#146911yescharacteristic, complemented, Sylow
350C23—21no—
351C23—22no—
352C23—41no—
353C23—41no—
354C23—181no—
355C23—182no—
356C23—361no—
357C23—361no—
358C23C2×#62411yescharacteristic
359Q8—362no—
360Q8—362no—
361D4—362no—
362D4—362no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—181no—
373C2×C4—361no—
374C2×C4#381111yescharacteristic
375C2×C4#381111yescharacteristic
376C8—122no—
377C8—122no—
378C2×C3—24no—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—82no—
385C2×C3—82no—
386C2×C3#472712yes—
387C2×C3#474012yes—
388C2×C3D3×#10012yes—
389D3—242no—
390D3—242no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—82no—
397C22—361no—
398C22—361no—
399C22—361no—
400C22—722no—
401C22#6381712yes—
402C22#6397411yescharacteristic
403C4—21no—
404C4—21no—
405C4—41no—
406C4—92no—
407C4—181no—
408C4—181no—
409C4—181no—
410C4—361no—
411C3—21no—
412C3#6810412yescomplemented
413C2—22no—
414C2—81no—
415C2—721no—
416C2#1059115311yescharacteristic
417C2#1059150311yescharacteristic
418C2#1059152911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1469
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591066C2semidirect
3. #10591061C2semidirect
4. C3×#4525C2semidirect
5. #10589146C2semidirect
29. #4525D3semidirect
349. C32#1469semidirect
412. C3#68104semidirect

Maximal subgroups

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

subgroupindex
C2×#640942
#105910662
#105910612
C3×#45252
#105891462
#681043