Finite Group Databasebeta

← #11869012

Subgroups — #11869012

Order 1152.

670 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 111 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#10594606C211yesmaximal, characteristic
2#10594508C211yesmaximal, characteristic, complemented
3#10593755C211yesmaximal, characteristic, complemented
4#10593394C211yesmaximal, characteristic, complemented
5#10593389C211yesmaximal, characteristic, complemented
6#10593367C212yesmaximal, complemented
7#10593365C211yesmaximal, characteristic
8#10593364C212yesmaximal, complemented
9#10593363C211yesmaximal, characteristic
10#10593359C212yesmaximal, complemented
11#10593350C212yesmaximal, complemented
12C2×#3802C2211yescharacteristic
13C2×#3788C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15#64101C2211yescharacteristic
16C3×#893—21no—
17C3×#890—21no—
18D3×(C2×D3)⋊C4—22no—
19#63919C2212yescomplemented
20#63918—21no—
21#63902C2212yes—
22C4×#625C2212yes—
23#63900C2211yescharacteristic
24#63895—22no—
25Dic3×D12—21no—
26#63874C2211yescharacteristic
27#63874C2211yescharacteristic
28#63870C2212yescomplemented
29#63779C2212yescomplemented
30C4⋊#622C2212yescomplemented
31#63743C2211yescharacteristic, complemented
32#63743C2212yescomplemented
33#63743C2211yescharacteristic, complemented
34#63742C2212yescomplemented
35#63742C2211yescharacteristic, complemented
36#63742C2211yescharacteristic, complemented
37#63739C2212yes—
38#63739C2212yes—
39#63739C2212yes—
40#63739C2212yes—
41#5689—61no—
42#5545—61no—
43C22×D32—21no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×D12—21no—
46C2×C3×C4×D3—22no—
47C2×#627—22no—
48C2×#625C2312yes—
49C2×#624—21no—
50C2×D3×Dic3—22no—
51#3802—22no—
52#3802Q814yescomplemented
53C2×#622C2311yescharacteristic
54C2×#622C2311yescharacteristic
55C2×#622C2312yes—
56#3788—22no—
57#3787—22no—
58C32×C4⋊C4D411yescharacteristic
59#3752D412yes—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C4×C3⋊Dic3C2312yes—
62C3×(C2×D3)⋊C4—22no—
63C3×C4⋊Dic3—22no—
64C3×C4⋊Dic3—21no—
65C3×Dic3⋊C4—22no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68#3724C2311yescharacteristic
69#3724C2312yes—
70#3724C2311yescharacteristic
71#3724C2311yescharacteristic
72#3724C2311yescharacteristic
73Dic3⋊Dic3—22no—
74#3722—21no—
75#3722—21no—
76(C2×D3)⋊Dic3—22no—
77#3081—91nomaximal, Sylow
78C2×D3×D4—61no—
79C3×#125—61no—
80C3×C4×D4—61no—
81D4×Dic3—61no—
82C4×#67—62no—
83C2×(C2×D3)⋊C4—62no—
84#897—62no—
85#896—62no—
86#893—21no—
87#892—61no—
88#892—61no—
89D3×C4⋊C4—61no—
90#890—21no—
91#889—62no—
92#888—62no—
93#888—61no—
94#67⋊C4—62no—
95D3×C22⋊C4—62no—
96C4×D12—61no—
97#872—61no—
98#872—61no—
99#869—61no—
100C22×C3⋊D3C2×D411yescharacteristic
101C22×C3×D3—22no—
102C2×D32—24no—
103C2×D32—81no—
104C2×D32—81no—
105C2×C32×C4C2×D412yes—
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3C2×D412yes—
108C2×C3⋊Dic3C2411yescharacteristic
109C4×C3⋊D3C2×Q812yes—
110C4×C3⋊D3#4112yes—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C3×D12—24no—
117C3×C4×D3—82no—
118#627—82no—
119#625—22no—
120#625C2×Q814yes—
121#624—81no—
122D3×Dic3—82no—
123#622—21no—
124#622—21no—
125#622—22no—
126#544—91no—
127#518—91no—
128#478—92no—
129#478—92no—
130#476—92no—
131#474—92no—
132#428—91no—
133#427—91no—
134#424—91no—
135#418—91no—
136C2×#102—91no—
137C23×D3—62no—
138C2×C3×D4—61no—
139C22×C3×C4—62no—
140C2×#67—62no—
141C22×Dic3—62no—
142D3×D4—64no—
143D3×D4—64no—
144C2×D12—21no—
145C2×C4×D3—22no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×Dic6—62no—
151C2×Dic6—62no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—62no—
156C3×C4⋊C4—62no—
157C3×C22⋊C4—62no—
158C3×C42—61no—
159C3×C42—61no—
160#217—62no—
161(C2×D3)⋊C4—22no—
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—62no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—61no—
167(C2×D3)⋊C4—61no—
168(C2×D3)⋊C4—62no—
169C4⋊Dic3—21no—
170C4⋊Dic3—22no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—62no—
174Dic3⋊C4—22no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181C4×Dic3—21no—
182C4×Dic3—21no—
183C4×Dic3—62no—
184C4×Dic3—62no—
185C22×C32C22×D411yescharacteristic
186C2×C3⋊D3—21no—
187C2×C3⋊D3—21no—
188C2×C3⋊D3C22⋊Q812yes—
189C2×C3×D3—24no—
190C2×C3×D3—42no—
191C2×C3×D3—42no—
192D32—84no—
193C32×C4—22no—
194C32×C4C22⋊Q812yes—
195C3⋊Dic3—22no—
196C3⋊Dic3C22×Q811yescharacteristic
197C3⋊Dic3C2×#4111yescharacteristic
198C3×Dic3—41no—
199C3×Dic3—42no—
200C3×Dic3—41no—
201C3×Dic3—41no—
202C3×Dic3—41no—
203C22×D4—91no—
204C2×M16—91no—
205C22×C8—91no—
206C4⋊Q8—92no—
207C4⋊Q8—181no—
208#125—61no—
209#125—92no—
210C22⋊Q8—182no—
211C4×D4—61no—
212C4×D4—92no—
213C4×D4—92no—
214C4×D4—181no—
215#117—91no—
216#117—91no—
217#117—91no—
218C2×C4⋊C4—91no—
219C2×C22⋊C4—182no—
220#107—91no—
221#107—91no—
222#107—92no—
223#106—91no—
224#106—91no—
225#106—92no—
226C4⋊C8—92no—
227C4⋊C8—92no—
228#102—92no—
229#102—92no—
230#102—92no—
231#102—92no—
232C23×C3—62no—
233C22×D3—22no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—68no—
237C22×D3—242no—
238C22×D3—242no—
239C3×D4—64no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—62no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—242no—
250#67—64no—
251#67—64no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—22no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—242no—
262D12—24no—
263C4×D3—62no—
264C4×D3—62no—
265C4×D3—62no—
266C4×D3—62no—
267C4×D3—82no—
268C4×D3—242no—
269C4×D3—242no—
270Dic6—242no—
271Dic6—242no—
272C2×C32C2×C22⋊Q811yescharacteristic
273C2×C32#57611yescharacteristic
274C2×C32#57711yescharacteristic
275C3⋊D3—22no—
276C3×D3—44no—
277C24—181no—
278C2×Q8—182no—
279C2×D4—61no—
280C2×D4—94no—
281C2×D4—92no—
282C2×D4—182no—
283C22×C4—62no—
284C22×C4—91no—
285C22×C4—181no—
286C22×C4—182no—
287M16—182no—
288C2×C8—91no—
289C2×C8—92no—
290C2×C8—91no—
291C2×C8—182no—
292C4⋊C4—61no—
293C4⋊C4—62no—
294C4⋊C4—62no—
295C4⋊C4—92no—
296C4⋊C4—91no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—91no—
300C4⋊C4—91no—
301C4⋊C4—182no—
302C4⋊C4GO+(4,𝔽2)11yescharacteristic
303C22⋊C4—62no—
304C22⋊C4—92no—
305C22⋊C4—181no—
306C22⋊C4—181no—
307C22⋊C4—182no—
308C42—61no—
309C42—61no—
310C42—92no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—64no—
314C22×C3—122no—
315C22×C3—122no—
316C2×D3—24no—
317C2×D3—42no—
318C2×D3—42no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—121no—
322C2×D3—121no—
323C2×D3—121no—
324C2×D3—121no—
325C2×D3—248no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—42no—
329C3×C4—42no—
330C3×C4—121no—
331C3×C4—122no—
332C3×C4—121no—
333C3×C4—121no—
334C3×C4—121no—
335Dic3—41no—
336Dic3—42no—
337Dic3—41no—
338Dic3—41no—
339Dic3—41no—
340Dic3—61no—
341Dic3—61no—
342Dic3—61no—
343Dic3—61no—
344Dic3—122no—
345Dic3—122no—
346C32#308111yescharacteristic, complemented, Sylow
347C23—62no—
348C23—91no—
349C23—184no—
350C23—721no—
351C23—721no—
352Q8—722no—
353D4—64no—
354D4—94no—
355D4—182no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—62no—
361C2×C4—91no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—242no—
366C2×C4—721no—
367C2×C4—722no—
368C2×C4C2×GO+(4,𝔽2)12yes—
369C2×C4C2×GO+(4,𝔽2)11yescharacteristic
370C8—181no—
371C8—181no—
372C8—182no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—124no—
380D3—44no—
381D3—122no—
382D3—122no—
383C22—64no—
384C22—92no—
385C22—122no—
386C22—122no—
387C22—181no—
388C22—181no—
389C22—724no—
390C22C22×GO+(4,𝔽2)11yescharacteristic
391C4—22no—
392C4—91no—
393C4—91no—
394C4—121no—
395C4—121no—
396C4—121no—
397C4—122no—
398C4—121no—
399C4—182no—
400C4D32⋊Q812yes—
401C3—21no—
402C3—21no—
403C2—124no—
404C2—182no—
405C2C2×D32⋊Q811yescharacteristic
406C2#1059651511yescharacteristic
407C2#1059652211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#3081
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
2. #10594508C2semidirect
3. #10593755C2semidirect
4. #10593394C2semidirect
5. #10593389C2semidirect
6. #10593367C2semidirect
8. #10593364C2semidirect
10. #10593359C2semidirect
11. #10593350C2semidirect
19. #63919C22semidirect
28. #63870C22semidirect
29. #63779C22semidirect
30. C4⋊#622C22semidirect
31. #63743C22semidirect
32. #63743C22semidirect
33. #63743C22semidirect
34. #63742C22semidirect
35. #63742C22semidirect
36. #63742C22semidirect
52. #3802Q8semidirect
346. C32#3081semidirect

Maximal subgroups

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

subgroupindex
#105946062
#105945082
#105937552
#105933942
#105933892
#105933672
#105933652
#105933642
#105933632
#105933592
#105933502
#30819