Finite Group Databasebeta

← #11897601

Subgroups — #11897601

Order 1152.

628 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 107 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#10594531C211yesmaximal, characteristic, complemented
2#10594526C211yesmaximal, characteristic, complemented
3#10593756C211yesmaximal, characteristic, complemented
4#10593419C212yesmaximal
5C4×#3774C211yesmaximal, characteristic
6#10593384C211yesmaximal, characteristic, complemented
7#10593383C212yesmaximal, complemented
8#10593364C212yesmaximal, complemented
9#10593359C211yesmaximal, characteristic, complemented
10#10593359C212yesmaximal, complemented
11#10593347C211yesmaximal, characteristic, complemented
12C2×D3×Dic6—21no—
13C2×#3774C2211yescharacteristic
14#64096C2211yescharacteristic
15C3×#897—21no—
16C3×D3×C4⋊C4—21no—
17#63919C2212yes—
18#63919C2211yescharacteristic
19#63902C2212yes—
20C4×#625C2211yescharacteristic
21C4×#625C2211yescharacteristic
22C4×#625C2212yes—
23#63899—22no—
24#63873C2211yescharacteristic
25#63870C2212yes—
26#63857—21no—
27#63851—22no—
28#63777C2212yes—
29C4⋊#622C2211yescharacteristic
30C4⋊#622C2212yes—
31C4×#622C2211yescharacteristic
32#63743C2212yes—
33#63743C2211yescharacteristic
34#63742C2212yes—
35#63742C2212yes—
36#63742C2212yes—
37#63739C2212yes—
38#63739C2211yescharacteristic
39#63739C2212yes—
40#63739C2211yescharacteristic
41#5632—61no—
42#5511—61no—
43C2×#634D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—22no—
47C2×C3×Dic6—21no—
48C2×#627—22no—
49C2×#627—21no—
50C2×#625C2311yescharacteristic
51C2×#625C2311yescharacteristic
52C2×D3×Dic3—22no—
53D3×Dic6—44no—
54C2×#622C2311yescharacteristic
55C2×#622C2312yes—
56C2×#622C2311yescharacteristic
57#3774Q814yescomplemented
58C32×C4⋊C4D411yescharacteristic
59#3750D412yes—
60C4×C3⋊Dic3C2311yescharacteristic
61C4×C3⋊Dic3C2312yes—
62C3×(C2×D3)⋊C4—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—22no—
65C3×Dic3⋊C4—22no—
66#3724—21no—
67#3724C2311yescharacteristic
68#3724C2312yes—
69#3724C2312yes—
70#3724C2311yescharacteristic
71Dic3⋊Dic3—22no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—22no—
74(C2×D3)⋊Dic3—21no—
75#3384—91nomaximal, Sylow
76C2×D3×Q8—61no—
77C22×Dic6—61no—
78C3×C22⋊Q8—61no—
79C2×C3×C4⋊C4—61no—
80#944—61no—
81C4×#67—61no—
82C4×#67—61no—
83C4×#67—62no—
84#924—62no—
85#924—61no—
86#897—21no—
87#897—61no—
88#896—62no—
89#896—62no—
90D3×C4⋊C4—21no—
91#889—62no—
92#888—62no—
93#888—61no—
94#887—61no—
95#887—61no—
96#67⋊C4—62no—
97#878—62no—
98C22×C3×D3—21no—
99C22×C3×D3—21no—
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3C2×D411yescharacteristic
103C2×C3⋊Dic3C2×D412yes—
104C2×C3⋊Dic3C2411yescharacteristic
105#634—22no—
106C2×C3×Dic3—21no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—21no—
109C2×C3×Dic3—22no—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C3×C4×D3—82no—
113C3×Dic6—42no—
114#627—44no—
115#627—81no—
116#625—21no—
117#625—21no—
118#625C2×Q812yes—
119#625C2×Q812yescomplemented
120D3×Dic3—44no—
121#622—21no—
122#622—22no—
123#622C2×Q812yescomplemented
124#554—91no—
125D4×Q8—91no—
126#501—92no—
127#498—91no—
128#478—92no—
129#476—92no—
130#476—91no—
131#474—91no—
132#446—91no—
133#442—92no—
134C4×D8—91no—
135C2×C3×Q8—61no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4—62no—
139C2×#67—61no—
140C2×#67—61no—
141C22×Dic3—62no—
142D3×Q8—124no—
143C2×C4×D3—21no—
144C2×C4×D3—21no—
145C2×C4×D3—22no—
146C2×C4×D3—62no—
147C2×Dic6—21no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—62no—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6—124no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—62no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—62no—
159C3×C22⋊C4—62no—
160#217—61no—
161#217—61no—
162#217—62no—
163(C2×D3)⋊C4—22no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—62no—
167C4⋊Dic3—22no—
168C4⋊Dic3—21no—
169C4⋊Dic3—62no—
170Dic3⋊C4—22no—
171Dic3⋊C4—62no—
172Dic3⋊C4—61no—
173Dic3⋊C4—62no—
174Dic3⋊C4—61no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179C4×Dic3—62no—
180C4×Dic3—61no—
181C4×Dic3—62no—
182C4×Dic3—61no—
183C22×C32C22×D411yescharacteristic
184C2×C3×D3—22no—
185C2×C3×D3—22no—
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C2×C3×D3—41no—
190C32×C4—22no—
191C32×C4AGL(1,ℤ/8)12yes—
192C3⋊Dic3—22no—
193C3⋊Dic3—21no—
194C3⋊Dic3C22×Q811yescharacteristic
195C3⋊Dic32−1+411yescharacteristic
196C3×Dic3—42no—
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—42no—
200C22×Q8—181no—
201C2×D8—91no—
202C4⋊Q8—92no—
203C4⋊Q8—91no—
204C4⋊Q8—91no—
205#125—92no—
206C22⋊Q8—61no—
207C22⋊Q8—182no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C4×Q8—91no—
211C4×D4—92no—
212C4×D4—91no—
213C4×D4—91no—
214C4×D4—92no—
215C2×C4⋊C4—61no—
216#107—91no—
217#107—92no—
218#106—92no—
219#106—92no—
220#106—92no—
221C4⋊C8—91no—
222C4⋊C8—92no—
223#102—91no—
224#102—91no—
225#102—92no—
226#102—92no—
227#97—92no—
228C4×C8—91no—
229C23×C3—61no—
230C23×C3—61no—
231C22×D3—21no—
232C22×D3—21no—
233C3×Q8—122no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—61no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4—61no—
242C2×C3×C4—122no—
243C2×C3×C4—122no—
244C2×C3×C4—242no—
245#67—62no—
246#67—62no—
247#67—62no—
248#67—62no—
249C2×Dic3—21no—
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—21no—
253C2×Dic3—62no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—62no—
258C2×Dic3—61no—
259C2×Dic3—124no—
260C4×D3—42no—
261C4×D3—42no—
262C4×D3—82no—
263C4×D3—124no—
264Dic6—42no—
265Dic6—64no—
266Dic6—122no—
267Dic6—124no—
268Dic6—124no—
269Dic6—242no—
270C2×C32D4×Q811yescharacteristic
271C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
272C2×C32#57711yescharacteristic
273C3×D3—42no—
274C3×D3—42no—
275C2×Q8—61no—
276C2×Q8—91no—
277C2×Q8—182no—
278C2×Q8—181no—
279C2×Q8—364no—
280C2×D4—91no—
281C2×D4—91no—
282C22×C4—61no—
283C22×C4—61no—
284C22×C4—62no—
285C22×C4—182no—
286D8—94no—
287C2×C8—91no—
288C2×C8—91no—
289C2×C8—92no—
290C4⋊C4—62no—
291C4⋊C4—61no—
292C4⋊C4—62no—
293C4⋊C4—92no—
294C4⋊C4—92no—
295C4⋊C4—91no—
296C4⋊C4—91no—
297C4⋊C4—92no—
298C4⋊C4—182no—
299C4⋊C4—181no—
300C4⋊C4GO+(4,𝔽2)11yescharacteristic
301C22⋊C4—62no—
302C22⋊C4—181no—
303C22⋊C4—182no—
304C22⋊C4—181no—
305C42—91no—
306C42—92no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—62no—
310C22×C3—62no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3—121no—
315C2×D3—22no—
316C2×D3—22no—
317C2×D3—41no—
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—41no—
321C3×C4—22no—
322C3×C4—22no—
323C3×C4—42no—
324C3×C4—42no—
325C3×C4—121no—
326C3×C4—122no—
327C3×C4—122no—
328C3×C4—121no—
329Dic3—42no—
330Dic3—41no—
331Dic3—42no—
332Dic3—41no—
333Dic3—61no—
334Dic3—61no—
335Dic3—61no—
336Dic3—61no—
337Dic3—64no—
338Dic3—122no—
339Dic3—121no—
340Dic3—121no—
341C32#338411yescharacteristic, complemented, Sylow
342C23—61no—
343C23—61no—
344Q8—122no—
345Q8—182no—
346Q8—364no—
347Q8—721no—
348D4—92no—
349D4—92no—
350D4—181no—
351D4—181no—
352C2×C4—62no—
353C2×C4—61no—
354C2×C4—62no—
355C2×C4—61no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—92no—
359C2×C4—122no—
360C2×C4—122no—
361C2×C4—242no—
362C2×C4—364no—
363C2×C4C2×GO+(4,𝔽2)12yes—
364C2×C4C2×GO+(4,𝔽2)11yescharacteristic
365C8—92no—
366C8—181no—
367C8—182no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—122no—
375C2×C3—122no—
376D3—42no—
377D3—42no—
378C22—62no—
379C22—62no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22—121no—
384C22C22×GO+(4,𝔽2)11yescharacteristic
385C4—22no—
386C4—91no—
387C4—91no—
388C4—121no—
389C4—121no—
390C4—122no—
391C4—122no—
392C4—182no—
393C4—181no—
394C4#6422412yes—
395C3—21no—
396C3—21no—
397C2—122no—
398C2—122no—
399C2C2×#6422411yescharacteristic
400C2#1059651511yescharacteristic
401C2Q8×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#3774C22
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#3384
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10594531C2semidirect
2. #10594526C2semidirect
3. #10593756C2semidirect
6. #10593384C2semidirect
7. #10593383C2semidirect
8. #10593364C2semidirect
9. #10593359C2semidirect
10. #10593359C2semidirect
11. #10593347C2semidirect
57. #3774Q8semidirect
119. #625C2×Q8semidirect
123. #622C2×Q8semidirect
341. C32#3384semidirect

Maximal subgroups

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

subgroupindex
#105945312
#105945262
#105937562
#105934192
C4×#37742
#105933842
#105933832
#105933642
#105933592
#105933472
#33849