Finite Group Databasebeta

← #11906302

Subgroups — #11906302

Order 1152.

2077 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×#5470C212yesmaximal
3#10595052C212yesmaximal
4#10594828C212yesmaximal
5#10594813C214yesmaximal
6#10594810C214yesmaximal
7#10593864C214yesmaximal, complemented
8#10593856C214yesmaximal, complemented
9#10593852C218yesmaximal, complemented
10#86258—32nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C4×#634C2214yes—
17C4×#634C2214yes—
18C3×#926C2214yes—
19C3×#924C2214yes—
20C3×#924C2214yes—
21C3×#870C2214yes—
22C3×#869C2212yes—
23C3×#869C2212yes—
24C3×C4×Dic6C2214yes—
25C3×C4×Dic6C2214yes—
26#63982C2218yes—
27#63957C2218yes—
28#63919C2214yes—
29#63918C2218yes—
30#63873C2214yes—
31#63870C2218yes—
32#63869C2218yes—
33#63847C22116yes—
34#63844C2218yes—
35#63844C2218yes—
36#63843C2218yes—
37#63839C22116yes—
38#63838C2218yes—
39C3×#533—32no—
40#5722—34no—
41#5721—34no—
42#5685—38no—
43#5623—38no—
44#5622—38no—
45#5567—38no—
46#5567—34no—
47Q8×Dic6—34no—
48#5519—34no—
49#5516—34no—
50#5470D312yes—
51C2×C4×Dic6—32no—
52C2×C4×Dic6—61no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C2×#634Q818yescomplemented
59C2×#634C2314yes—
60C2×C3×Dic6C2314yes—
61C2×C3×Dic6C2314yes—
62C2×#627C2318yes—
63C32×C42C2312yes—
64C32×C42C2312yes—
65C4⋊(C3⋊Dic3)C2314yes—
66#3750C2318yes—
67C4×C3⋊Dic3C2314yes—
68C4×C3⋊Dic3C2314yes—
69C3×#217C2318yes—
70C3×C4⋊Dic3C2314yes—
71C3×C4⋊Dic3C2314yes—
72C3×C4⋊Dic3C2314yes—
73C3×C4⋊Dic3C2314yes—
74C3×Dic3⋊C4C2318yes—
75C3×Dic3⋊C4C2318yes—
76C3×C4×Dic3C2318yes—
77#3724C2318yes—
78#3724C2318yes—
79#3724C2318yes—
80Dic3⋊Dic3C23116yes—
81Dic32C23116yes—
82#3502—91noSylow
83C22×Dic6—32no—
84C22×Dic6—61no—
85C3×C4⋊Q8—32no—
86C3×C4⋊Q8—32no—
87C3×#125—34no—
88C3×C22⋊Q8—34no—
89C3×C22⋊Q8—34no—
90C3×C4×Q8—34no—
91C3×C4×Q8—34no—
92C3×#117—34no—
93C2×C3×C42—21no—
94C2×C3×C42C2×D312yes—
95Q8×Dic3—38no—
96#944—38no—
97#944—316no—
98#926C2×D314yes—
99C2×C4⋊Dic3—32no—
100C2×C4⋊Dic3—61no—
101#924C2×D314yes—
102#924C2×D314yes—
103C2×Dic3⋊C4—34no—
104C2×Dic3⋊C4—62no—
105C2×C4×Dic3—34no—
106C2×C4×Dic3—62no—
107#890—38no—
108#889—316no—
109#889—316no—
110#889—316no—
111#888—316no—
112#888—38no—
113#888—38no—
114#887—38no—
115#887—316no—
116#887—38no—
117#887—38no—
118#878—316no—
119#877—316no—
120#870—38no—
121#870C2×D314yes—
122#869—38no—
123#869C2×D312yes—
124#869C2×D312yes—
125C4×Dic6—34no—
126C4×Dic6—34no—
127C4×Dic6—34no—
128C4×Dic6—34no—
129C4×Dic6—38no—
130C4×Dic6—38no—
131C4×Dic6—64no—
132C4×Dic6—64no—
133C4×Dic6C2×D314yes—
134C4×Dic6C2×D314yes—
135C23×C32C2411yescharacteristic
136C2×C32×C4—22no—
137C2×C32×C4—41no—
138C2×C32×C4C2×Q814yes—
139C2×C32×C4C2411yescharacteristic
140C2×C32×C4C2412yes—
141C2×C32×C4C2412yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3C2×Q818yes—
145C2×C3⋊Dic3C2414yes—
146C2×C3⋊Dic3C2414yes—
147#634C2×Q8116yes—
148C2×C3×Dic3C2418yes—
149C2×C3×Dic3C2418yes—
150C3×Dic6—28no—
151C3×Dic6—44no—
152#627—48no—
153Q82—94no—
154#557—98no—
155#557—94no—
156#544—92no—
157#544—94no—
158#533—32no—
159#533—94no—
160#519—92no—
161C2×C4×Q8—91no—
162C2×C3×Q8—34no—
163C2×C3×Q8—34no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4C22×D312yes—
168C22×C3×C4C22×D312yes—
169C22×C3×C4C22×D312yes—
170C22×Dic3—34no—
171C22×Dic3—34no—
172C22×Dic3—62no—
173C22×Dic3—62no—
174C2×Dic6—316no—
175C2×Dic6—34no—
176C2×Dic6—34no—
177C2×Dic6—316no—
178C2×Dic6—64no—
179C2×Dic6—68no—
180C2×Dic6C22×D314yes—
181C2×Dic6C22×D314yes—
182C3×C4⋊C4—34no—
183C3×C4⋊C4—34no—
184C3×C4⋊C4—38no—
185C3×C4⋊C4—34no—
186C3×C4⋊C4—38no—
187C3×C4⋊C4—34no—
188C3×C22⋊C4—38no—
189C3×C42—22no—
190C3×C42—22no—
191C3×C42—38no—
192C3×C42C22×D312yes—
193C3×C42C22×D312yes—
194C3×C42C22×D312yes—
195C3×C42C22×D312yes—
196#217C22×D318yes—
197C4⋊Dic3—34no—
198C4⋊Dic3—34no—
199C4⋊Dic3—316no—
200C4⋊Dic3—64no—
201C4⋊Dic3C22×D314yes—
202C4⋊Dic3C22×D314yes—
203C4⋊Dic3C22×D314yes—
204C4⋊Dic3C22×D314yes—
205Dic3⋊C4—38no—
206Dic3⋊C4—38no—
207Dic3⋊C4—316no—
208Dic3⋊C4—316no—
209Dic3⋊C4—316no—
210Dic3⋊C4—316no—
211Dic3⋊C4—68no—
212Dic3⋊C4C22×D318yes—
213Dic3⋊C4C22×D318yes—
214C4×Dic3—38no—
215C4×Dic3—38no—
216C4×Dic3—316no—
217C4×Dic3—316no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C4×Dic3C22×D318yes—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32C22×Q812yes—
224C22×C32C2511yescharacteristic
225C32×C4—21no—
226C32×C4—22no—
227C32×C4C22×Q814yes—
228C32×C42−1+412yes—
229C3⋊Dic3—24no—
230C3⋊Dic3C22×Q818yes—
231C3×Dic3—28no—
232C3×Dic3—28no—
233C22×Q8—91no—
234C4⋊Q8—32no—
235C4⋊Q8—32no—
236C4⋊Q8—98no—
237C4⋊Q8—94no—
238C4⋊Q8—916no—
239C4⋊Q8—94no—
240#125—34no—
241#125—98no—
242#125—98no—
243#125—916no—
244C22⋊Q8—34no—
245C22⋊Q8—34no—
246C22⋊Q8—98no—
247C4×Q8—34no—
248C4×Q8—34no—
249C4×Q8—98no—
250C4×Q8—98no—
251C4×Q8—98no—
252C4×Q8—98no—
253C4×Q8—94no—
254C4×Q8—94no—
255#117—34no—
256#117—98no—
257C2×C4⋊C4—92no—
258C2×C4⋊C4—91no—
259C2×C42—92no—
260C2×C42D3211yescharacteristic
261C23×C3—21no—
262C23×C3C23×D312yes—
263C3×Q8—68no—
264C3×Q8—124no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—38no—
273C2×C3×C4—38no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4D3×Q818yes—
277C2×C3×C4C23×D312yes—
278C2×C3×C4C23×D312yes—
279C2×C3×C4C23×D312yes—
280C2×C3×C4C23×D312yes—
281C2×C3×C4C23×D312yes—
282C2×C3×C4C23×D312yes—
283C2×Dic3—316no—
284C2×Dic3—38no—
285C2×Dic3—38no—
286C2×Dic3—68no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—124no—
290C2×Dic3—124no—
291C2×Dic3C23×D318yes—
292C2×Dic3C23×D318yes—
293Dic6—28no—
294Dic6—316no—
295Dic6—316no—
296Dic6—44no—
297Dic6—616no—
298Dic6—1216no—
299C2×C32—22no—
300C2×C32C23×Q811yescharacteristic
301C2×C32C2×2−1+411yescharacteristic
302C2×C32#58511yescharacteristic
303C2×Q8—34no—
304C2×Q8—34no—
305C2×Q8—98no—
306C2×Q8—94no—
307C2×Q8—98no—
308C22×C4—92no—
309C22×C4—92no—
310C22×C4C2×D3211yescharacteristic
311C22×C4C2×D3211yescharacteristic
312C22×C4C2×D3211yescharacteristic
313C4⋊C4—34no—
314C4⋊C4—34no—
315C4⋊C4—38no—
316C4⋊C4—34no—
317C4⋊C4—38no—
318C4⋊C4—34no—
319C4⋊C4—98no—
320C4⋊C4—98no—
321C4⋊C4—98no—
322C4⋊C4—916no—
323C4⋊C4—98no—
324C4⋊C4—94no—
325C22⋊C4—38no—
326C42—38no—
327C42—916no—
328C42—94no—
329C42—94no—
330C42C2×D3212yes—
331C42C2×D3212yes—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3C2×D3×Q814yes—
339C22×C3C24×D312yes—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—24no—
346C3×C4—42no—
347C3×C4—68no—
348C3×C4—68no—
349C3×C4C2×D3×Q814yes—
350C3×C4C2×D3×Q814yes—
351C3×C4#101014yes—
352Dic3—28no—
353Dic3—28no—
354Dic3—316no—
355Dic3—68no—
356Dic3—68no—
357Dic3—124no—
358C32#350211yescharacteristic, complemented, Sylow
359C23C22×D3211yescharacteristic
360Q8—68no—
361Q8—916no—
362Q8—124no—
363Q8—368no—
364C2×C4—22no—
365C2×C4—38no—
366C2×C4—38no—
367C2×C4—41no—
368C2×C4—98no—
369C2×C4—94no—
370C2×C4—94no—
371C2×C4—362no—
372C2×C4#379714yes—
373C2×C4C22×D3211yescharacteristic
374C2×C4C22×D3212yes—
375C2×C4C22×D3211yescharacteristic
376C2×C4C22×D3212yes—
377C2×C3—24no—
378C2×C3—24no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3C22×D3×Q812yes—
383C2×C3C2×#101012yes—
384C2×C3#596412yes—
385C22—21no—
386C22—21no—
387C22C2×#379712yes—
388C22C23×D3211yescharacteristic
389C4—21no—
390C4—22no—
391C4—68no—
392C4—68no—
393C4—98no—
394C4—184no—
395C4#6429812yes—
396C4C2×#379714yes—
397C3—21no—
398C3#8625812yescomplemented
399C2—22no—
400C2C2×#6429811yescharacteristic
401C2C22×#379711yescharacteristic
402C2#1059666911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
prime radicalC23×C32C24
hypercenterC2×C42D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
7. #10593864C2semidirect
8. #10593856C2semidirect
9. #10593852C2semidirect
58. C2×#634Q8semidirect
358. C32#3502semidirect
398. C3#86258semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#54702
#105950522
#105948282
#105948132
#105948102
#105938642
#105938562
#105938522
#862583