Finite Group Databasebeta

← #11857574

Subgroups — #11857574

Order 1152.

1565 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic, complemented
3#10594828C211yesmaximal, characteristic, complemented
4C3×#5006C212yesmaximal, complemented
5#10591231C212yesmaximal, complemented
6#10590406C218yesmaximal, complemented
7#78689—32nomaximal
8C22×#634C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×#3805C2214yes—
11#64298—22no—
12#64298—22no—
13#64298—24no—
14C2×#3795C414yescomplemented
15C2×D3×Dic6C414yescomplemented
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18#64096—22no—
19#64086C2214yes—
20C4×#634—22no—
21C3×#926C2212yes—
22#63957C2214yes—
23#63844—24no—
24C3×#806C2218yes—
25#63580C2218yes—
26C2×#1010—32no—
27#5516—32no—
28#5516—32no—
29#5516—61no—
30C3×#410—32no—
31#5240—32no—
32#5006—32no—
33#5006D312yescomplemented
34#4740—316no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3C2312yes—
37C2×#634C2×C414yes—
38C2×#634D412yes—
39C2×#634D412yes—
40C2×#634D414yes—
41C2×C3×#67C2314yes—
42C3×#235—22no—
43C3×#235—22no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12C2×C412yes—
47C2×C3×C4×D3C2×C414yes—
48C2×C3×Dic6C2×C412yes—
49C2×#627C2×C414yes—
50C2×#625C2×C414yes—
51#3805—28no—
52#3805—28no—
53C2×D3×Dic3C2×C418yes—
54#3795—28no—
55#3795—28no—
56D3×Dic6—28no—
57D3×Dic6—28no—
58C32×C4⋊C4—21no—
59C32×C22⋊C4C2312yes—
60C32×C42—21no—
61#3757C2312yes—
62C4⋊(C3⋊Dic3)—21no—
63#3750—24no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—24no—
66C3×#217C2314yes—
67C3×C4⋊Dic3—22no—
68C3×C4×Dic3—22no—
69#3724—24no—
70Dic32—24no—
71#2884—91noSylow
72C2×C3×#41—32no—
73#1010—64no—
74#1010—64no—
75#1010—64no—
76#1010—64no—
77C2×D3×Q8—34no—
78C2×#237—38no—
79C2×#237—34no—
80C2×#235—34no—
81C2×#235C2×D312yes—
82C22×Dic6—32no—
83C22×Dic6—34no—
84C22×Dic6—61no—
85C3×#117—21no—
86C3×#117—32no—
87C3×#117C2×D312yes—
88#926—32no—
89#926—61no—
90#926C2×D312yes—
91#887—64no—
92#887—64no—
93#887—64no—
94#877—38no—
95#877—38no—
96#877—64no—
97C4×Dic6—64no—
98C4×Dic6—64no—
99C4×Dic6—64no—
100C3×#99—38no—
101#834—38no—
102#806—38no—
103#806C2×D318yes—
104C23×C32C2411yescharacteristic
105C22×C3×D3C22×C414yes—
106C2×C32×C4—22no—
107C2×C32×C4C22×C412yes—
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3C22×C414yes—
113C2×C3⋊Dic3C2×D414yes—
114C2×C3⋊Dic3C2×D414yes—
115#634C22⋊C418yes—
116#634C22⋊C418yes—
117C3×#67—24no—
118C3×#67—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3C22×C414yes—
121C3×D12—22no—
122C3×D12—22no—
123C3×C4×D3—24no—
124C3×C4×D3—24no—
125C3×Dic6—22no—
126C3×Dic6—22no—
127#627—28no—
128#625—28no—
129D3×Dic3—216no—
130C2×2−1+4—91no—
131#519—91no—
132#519—91no—
133#410—32no—
134#410—98no—
135#410—92no—
136C3×#41—62no—
137C3×#41—62no—
138C3×#41—62no—
139C3×#41—62no—
140C2×C3×Q8—32no—
141C2×C3×D4—34no—
142C2×C3×D4—32no—
143C22×C3×C4—21no—
144C22×C3×C4—34no—
145C22×C3×C4C22×D312yes—
146C2×#67—38no—
147C2×#67C22×D314yes—
148C22×Dic3—34no—
149C22×Dic3—38no—
150C22×Dic3—62no—
151D3×Q8—68no—
152D3×Q8—68no—
153#237—68no—
154#237—68no—
155#237—616no—
156#237—616no—
157#235—22no—
158#235—22no—
159#235—22no—
160#235—22no—
161#235—68no—
162#235—68no—
163C2×D12C4×D312yes—
164C2×C4×D3—38no—
165C2×C4×D3C4×D314yes—
166C2×Dic6—34no—
167C2×Dic6—34no—
168C2×Dic6—34no—
169C2×Dic6—34no—
170C2×Dic6—34no—
171C2×Dic6—34no—
172C2×Dic6—38no—
173C2×Dic6—62no—
174C2×Dic6—62no—
175C2×Dic6—64no—
176C2×Dic6—64no—
177C2×Dic6—68no—
178C2×Dic6—68no—
179C2×Dic6C4×D312yes—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—62no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—34no—
185C3×C22⋊C4C22×D314yes—
186C3×C42—22no—
187C3×C42—22no—
188C3×C42—62no—
189#217—34no—
190#217—62no—
191#217C22×D314yes—
192C4⋊Dic3—22no—
193C4⋊Dic3—62no—
194C4⋊Dic3—62no—
195Dic3⋊C4—68no—
196Dic3⋊C4—68no—
197Dic3⋊C4—68no—
198C4×Dic3—22no—
199C4×Dic3—68no—
200C4×Dic3—68no—
201C4×Dic3—68no—
202C4×Dic3—62no—
203C4×Dic3—62no—
204C22×C32—41no—
205C22×C32C23×C411yescharacteristic
206C22×C32C22×D411yescharacteristic
207C22×C32C22×D411yescharacteristic
208C2×C3×D3—24no—
209C2×C3×D3—44no—
210C32×C4—42no—
211C32×C4C2×C22⋊C412yes—
212C32×C4C2×C22⋊C412yes—
213C3⋊Dic3—42no—
214C3⋊Dic3C2×C22⋊C418yes—
215C3×Dic3—24no—
216C3×Dic3—44no—
2172−1+4—184no—
2182−1+4—182no—
2192−1+4—182no—
220C2×#41—32no—
221C2×#41—94no—
222C2×#41—94no—
223C22×Q8—94no—
224C22×Q8—91no—
225C4×Q8—182no—
226C4×Q8—184no—
227C4×Q8—182no—
228#117—32no—
229#117—94no—
230#117—91no—
231#117—94no—
232#117D3211yescharacteristic
233#99—38no—
234#99—98no—
235C23×C3—21no—
236C23×C3—34no—
237C23×C3C23×D312yes—
238C22×D3C2×C4×D314yes—
239C3×Q8—62no—
240C3×Q8—62no—
241C3×D4—64no—
242C3×D4—64no—
243C3×D4—62no—
244C3×D4—62no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—34no—
252C2×C3×C4—64no—
253C2×C3×C4—64no—
254C2×C3×C4—64no—
255C2×C3×C4C2×C4×D312yes—
256C2×C3×C4C2×C4×D312yes—
257C2×C3×C4D3×D412yes—
258C2×C3×C4D3×D412yes—
259C2×C3×C4D3×D412yes—
260C2×C3×C4D3×D412yes—
261#67—24no—
262#67—24no—
263#67—616no—
264C2×Dic3—24no—
265C2×Dic3—38no—
266C2×Dic3—38no—
267C2×Dic3—38no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—616no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3C2×C4×D314yes—
275D12—22no—
276D12—22no—
277C4×D3—24no—
278C4×D3—24no—
279C4×D3—616no—
280Dic6—22no—
281Dic6—22no—
282Dic6—38no—
283Dic6—38no—
284Dic6—38no—
285Dic6—38no—
286Dic6—68no—
287Dic6—68no—
288Dic6—616no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32C22×C22⋊C411yescharacteristic
293C3×D3—44no—
294#41—62no—
295#41—62no—
296#41—62no—
297#41—62no—
298#41—188no—
299#41—188no—
300#41—188no—
301#41—188no—
302C2×Q8—32no—
303C2×Q8—94no—
304C2×Q8—94no—
305C2×Q8—94no—
306C2×Q8—92no—
307C2×Q8—92no—
308C2×Q8—188no—
309C2×Q8—188no—
310C2×D4—34no—
311C2×D4—32no—
312C2×D4—94no—
313C22×C4—34no—
314C22×C4—98no—
315C22×C4—92no—
316C22×C4C2×D3211yescharacteristic
317C4⋊C4—21no—
318C4⋊C4—62no—
319C4⋊C4—184no—
320C4⋊C4—184no—
321C4⋊C4—181no—
322C22⋊C4—34no—
323C22⋊C4—92no—
324C22⋊C4C2×D3212yes—
325C42—21no—
326C42—62no—
327C42—184no—
328C42—184no—
329C42—181no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—64no—
336C22×C3—124no—
337C22×C3C22×C4×D312yes—
338C22×C3C2×D3×D412yes—
339C22×C3C2×D3×D412yes—
340C2×D3—24no—
341C2×D3—44no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—44no—
345C3×C4—44no—
346C3×C4—64no—
347C3×C4—124no—
348C3×C4D3×C22⋊C412yes—
349C3×C4D3×C22⋊C412yes—
350C3×C4D3×C22⋊C412yes—
351C3×C4D3×C22⋊C412yes—
352Dic3—24no—
353Dic3—316no—
354Dic3—44no—
355Dic3—68no—
356Dic3—124no—
357Dic3—124no—
358C32#288411yescharacteristic, complemented, Sylow
359C23—34no—
360C23C22×D3211yescharacteristic
361Q8—62no—
362Q8—62no—
363Q8—98no—
364Q8—98no—
365Q8—188no—
366D4—64no—
367D4—64no—
368D4—62no—
369D4—62no—
370D4—188no—
371C2×C4—22no—
372C2×C4—34no—
373C2×C4—64no—
374C2×C4—64no—
375C2×C4—64no—
376C2×C4—94no—
377C2×C4—94no—
378C2×C4—94no—
379C2×C4—1816no—
380C2×C4—182no—
381C2×C4C4×D3212yes—
382C2×C4#380212yes—
383C2×C4#381111yescharacteristic
384C2×C4#381111yescharacteristic
385C2×C3—22no—
386C2×C3—22no—
387C2×C3—22no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—41no—
391C2×C3—41no—
392C2×C3—124no—
393C2×C3C2×D3×C22⋊C412yes—
394D3—44no—
395C22—41no—
396C22—64no—
397C22—124no—
398C22C2×C4×D3211yescharacteristic
399C22C2×#380211yescharacteristic
400C22C2×#381111yescharacteristic
401C4—42no—
402C4—64no—
403C4—98no—
404C4—124no—
405C4—362no—
406C4#6392112yes—
407C4#6392112yes—
408C3—21no—
409C3#7868912yescomplemented
410C2—21no—
411C2—21no—
412C2—21no—
413C2—124no—
414C2C2×#6392111yescharacteristic
subgroupG/H
centerC2C2×#63921
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC32×#117C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#64298C2
cosocleC23×C32C24
hypercenter#117D32
hypocenterC32#2884
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595987C2semidirect
3. #10594828C2semidirect
4. C3×#5006C2semidirect
5. #10591231C2semidirect
6. #10590406C2semidirect
14. C2×#3795C4semidirect
15. C2×D3×Dic6C4semidirect
33. #5006D3semidirect
358. C32#2884semidirect
409. C3#78689semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
#105959872
#105948282
C3×#50062
#105912312
#105904062
#786893