Finite Group Databasebeta

← #11774034

Subgroups — #11774034

Order 1152.

677 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10589146C214yesmaximal, complemented
5#70828—31nomaximal
6#70784—31nomaximal
7C22×C4⋊(C3⋊D3)C411yescharacteristic
8C22×#634C411yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×#3752C412yes—
11C2×#3752C2212yes—
12#64084—21no—
13#64084—21no—
14#64084—21no—
15#64084—21no—
16C3×#830C2212yes—
17C3×#830C2212yes—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8—21no—
22C2×#875—31no—
23C2×#875—31no—
24C2×#875—61no—
25C3×#432—31no—
26C3×#431—31no—
27#4926D311yescharacteristic, complemented
28#4925D311yescharacteristic, complemented
29#4468—34no—
30#4468—34no—
31C23×C3⋊D3C2×C412yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C412yes—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—42no—
39C2×#634—21no—
40C2×#634—21no—
41C2×#634—42no—
42C32×C42D411yescharacteristic
43C32×C42D411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46#3752—22no—
47#3752—22no—
48#3752—22no—
49#3752—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52#1469—91noSylow
53C22×D12—31no—
54C22×D12—31no—
55C22×D12—61no—
56C22×Dic6—31no—
57C22×Dic6—31no—
58C22×Dic6—61no—
59C2×C3×C42—21no—
60C2×C3×C42C2×D311yescharacteristic
61C2×C3×C42C2×D311yescharacteristic
62C2×(C2×D3)⋊C4—32no—
63C2×(C2×D3)⋊C4—32no—
64C2×(C2×D3)⋊C4—32no—
65C2×(C2×D3)⋊C4—32no—
66C2×(C2×D3)⋊C4—62no—
67C2×(C2×D3)⋊C4—62no—
68#875—62no—
69#875—62no—
70#875—62no—
71#875—62no—
72#875—61no—
73#875—61no—
74#875—61no—
75#875—61no—
76#875—61no—
77#875—61no—
78#875—61no—
79#875—61no—
80C3×C4⋊C8—61no—
81C3×C4⋊C8—61no—
82C3×C22⋊C8—32no—
83C3×C22⋊C8—32no—
84C3×#97—61no—
85C3×C4×C8—61no—
86#830C2×D312yes—
87#830C2×D312yes—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)—21no—
90#803—21no—
91C4×C3⋊C8—21no—
92C23×C32C22×C411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—24no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—41no—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—42no—
108C4⋊(C3⋊D3)—42no—
109C4⋊(C3⋊D3)—42no—
110#634—42no—
111#634—42no—
112C3×C3⋊C8—42no—
113C3×C3⋊C8—42no—
114C2×#124—91no—
115#432—31no—
116#431—31no—
117#323—94no—
118C23×D3—32no—
119C23×D3—32no—
120C23×D3—62no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4C4×D311yescharacteristic
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4C4×D311yescharacteristic
127C22×C3×C4C4×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×Dic3—32no—
131C22×Dic3—32no—
132C22×Dic3—62no—
133C2×D12—62no—
134C2×D12—62no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—124no—
140C2×D12—122no—
141C2×D12—122no—
142C2×Dic6—62no—
143C2×Dic6—62no—
144C2×Dic6—61no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6—61no—
148C2×Dic6—124no—
149C2×Dic6—122no—
150C2×Dic6—122no—
151C2×C3×C8—62no—
152C2×C3×C8—62no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42—21no—
156C3×C42—21no—
157C3×C42D1211yescharacteristic
158C3×C42D1211yescharacteristic
159C3×C42D1211yescharacteristic
160C3×C42D1211yescharacteristic
161C3×C42#6711yescharacteristic
162C3×C42#6711yescharacteristic
163C3×C42#6711yescharacteristic
164C3×C42#6711yescharacteristic
165(C2×D3)⋊C4—64no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177C2×C3⋊C8—22no—
178C2×C3⋊C8—22no—
179C22×C32—21no—
180C22×C32—21no—
181C22×C32C2×C22⋊C411yescharacteristic
182C22×C32#13112yes—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—84no—
187C32×C4—21no—
188C32×C4—21no—
189C32×C4—21no—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4#10012yes—
193C3⋊Dic3—42no—
194C22×Q8—91no—
195C22×D4—91no—
196#124—181no—
197#124—181no—
198#124—181no—
199#124—181no—
200C2×C22⋊C4—92no—
201C2×C22⋊C4—92no—
202C2×C42D3211yescharacteristic
203C4⋊C8—61no—
204C4⋊C8—61no—
205C22⋊C8—32no—
206C22⋊C8—32no—
207#97—61no—
208C4×C8—61no—
209C23×C3—21no—
210C23×C3C2×C4×D311yescharacteristic
211C23×C3C2×C4×D311yescharacteristic
212C22×D3—64no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—124no—
218C22×D3—124no—
219C22×D3—124no—
220C22×D3—122no—
221C22×D3—122no—
222C22×D3—122no—
223C22×D3—122no—
224C2×C3×C4—24no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—42no—
239C2×C3×C4(C2×D3)⋊C411yescharacteristic
240C2×C3×C4(C2×D3)⋊C411yescharacteristic
241C2×C3×C4(C2×D3)⋊C411yescharacteristic
242C2×C3×C4(C2×D3)⋊C411yescharacteristic
243C2×C3×C4(C2×D3)⋊C411yescharacteristic
244C2×C3×C4(C2×D3)⋊C411yescharacteristic
245C2×C3×C4(C2×D3)⋊C411yescharacteristic
246C2×C3×C4(C2×D3)⋊C411yescharacteristic
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×Dic3—64no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—124no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257D12—124no—
258D12—122no—
259D12—122no—
260D12—124no—
261D12—122no—
262D12—122no—
263Dic6—124no—
264Dic6—122no—
265Dic6—122no—
266Dic6—124no—
267Dic6—122no—
268Dic6—122no—
269C3×C8—122no—
270C3×C8—122no—
271C3⋊C8—42no—
272C3⋊C8—42no—
273C2×C32—22no—
274C2×C32#40811yescharacteristic
275C2×C32#41011yescharacteristic
276C2×C32C2×#10011yescharacteristic
277C3⋊D3—82no—
278C24—92no—
279C2×Q8—181no—
280C2×Q8—181no—
281C2×Q8—362no—
282C2×D4—181no—
283C2×D4—181no—
284C2×D4—362no—
285C22×C4—92no—
286C22×C4#62411yescharacteristic
287C22×C4#62411yescharacteristic
288C22×C4C2×D3211yescharacteristic
289C2×C8—62no—
290C2×C8—62no—
291C22⋊C4—182no—
292C22⋊C4—182no—
293C22⋊C4—182no—
294C22⋊C4—182no—
295C42#62611yescharacteristic
296C42#62611yescharacteristic
297C42#62611yescharacteristic
298C42#62611yescharacteristic
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—21no—
307C22×C3#90112yes—
308C22×C3#90712yes—
309C22×C3C2×(C2×D3)⋊C411yescharacteristic
310C22×C3C2×(C2×D3)⋊C411yescharacteristic
311C2×D3—124no—
312C2×D3—124no—
313C2×D3—124no—
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—122no—
320C2×D3—248no—
321C2×D3—244no—
322C2×D3—244no—
323C3×C4—22no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—22no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4#82312yes—
340C3×C4#82312yes—
341Dic3—124no—
342Dic3—122no—
343Dic3—122no—
344C32#146911yescharacteristic, complemented, Sylow
345C23—182no—
346C23—184no—
347C23—362no—
348C23—362no—
349C23C2×#62411yescharacteristic
350Q8—362no—
351Q8—362no—
352D4—362no—
353D4—362no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—182no—
358C2×C4—362no—
359C2×C4#372211yescharacteristic
360C2×C4#372211yescharacteristic
361C2×C4#372211yescharacteristic
362C2×C4#372211yescharacteristic
363C2×C4C2×#62611yescharacteristic
364C2×C4C2×#62611yescharacteristic
365C8—122no—
366C8—122no—
367C2×C3—24no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3#500611yescharacteristic
374C2×C3#500611yescharacteristic
375C2×C3#511011yescharacteristic
376C2×C3#512911yescharacteristic
377C2×C3C2×#82311yescharacteristic
378C2×C3C2×#82311yescharacteristic
379D3—244no—
380D3—242no—
381D3—242no—
382C22—21no—
383C22—21no—
384C22—362no—
385C22—362no—
386C22—362no—
387C22—724no—
388C22#6381712yes—
389C22C2×#372211yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—362no—
396C4#6355912yes—
397C3—21no—
398C3#7078411yescharacteristic, complemented
399C3#7082811yescharacteristic, complemented
400C2—22no—
401C2—722no—
402C2#1059107311yescharacteristic
403C2C2×#6355911yescharacteristic
404C2#1059123211yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1469
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4926C2semidirect
3. C3×#4925C2semidirect
4. #10589146C2semidirect
27. #4926D3semidirect
28. #4925D3semidirect
344. C32#1469semidirect
398. C3#70784semidirect
399. C3#70828semidirect

Maximal subgroups

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

subgroupindex
C2×#640842
C3×#49262
C3×#49252
#105891462
#708283
#707843