Finite Group Databasebeta

← #11779469

Subgroups — #11779469

Order 1152.

518 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 98 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
1Q8×#634C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic
3#10590386C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic
6#10589096C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic
8#71161—31nomaximal
9#68267—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12#64097—22no—
13#64097—21no—
14#64078—21no—
15#64078C2211yescharacteristic
16C4×#634—21no—
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3719—22no—
20C3×#835—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—21no—
26#63567—21no—
27Q8×Dic6—31no—
28Q8×Dic6—31no—
29Q8×Dic6—61no—
30C3×#477—31no—
31#5092—31no—
32#5091—31no—
33#5021D311yescharacteristic
34#4850—31no—
35#4699—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic
38#4484—31no—
39#4481—31no—
40#4481—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—22no—
44C2×#634D411yescharacteristic
45C2×#634D412yes—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—22no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—22no—
56#3750—21no—
57C4×C3⋊Dic3—22no—
58C4×C3⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3719—44no—
65#1633—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—21no—
68C3×C4×Q8C2×D311yescharacteristic
69C3×C4×Q8C2×D311yescharacteristic
70Q8×Dic3—62no—
71Q8×Dic3—61no—
72Q8×Dic3—61no—
73C2×#216—62no—
74C2×Dic12—62no—
75#888—62no—
76#888—62no—
77#888—64no—
78#888—62no—
79#888—61no—
80#888—61no—
81#869—31no—
82#869—31no—
83#869—61no—
84#869—61no—
85#869—61no—
86#869—62no—
87#869C2×D311yescharacteristic
88C4×Dic6—31no—
89C4×Dic6—31no—
90C4×Dic6—61no—
91C4×Dic6—61no—
92C4×Dic6—61no—
93C4×Dic6—62no—
94C3×#107—61no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8—31no—
97C3×#103—61no—
98C3×C4×C8—31no—
99#835—21no—
100#818—61no—
101#816—61no—
102#810—61no—
103#807—21no—
104#807—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C32×Q8—21no—
109C32×Q8Q1612yescomplemented
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—21no—
118#634—21no—
119#634—42no—
120#634—82no—
121#634Q1612yescomplemented
122C2×C3×Dic3—41no—
123C3×Dic6—42no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127Q82—91no—
128#494—91no—
129#477—31no—
130#477—91no—
131#333—91no—
132Q8⋊C8—31no—
133Q8⋊C8—91no—
134C2×C3×Q8—21no—
135C2×C3×Q8—61no—
136C2×C3×Q8D1211yescharacteristic
137C2×C3×Q8#6711yescharacteristic
138C2×Dic6—21no—
139C2×Dic6—31no—
140C2×Dic6—31no—
141C2×Dic6—32no—
142C2×Dic6—32no—
143C2×Dic6—61no—
144C2×Dic6—62no—
145C2×Dic6—64no—
146C2×Dic6—62no—
147C2×Dic6—62no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C2×C3×C8—61no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4D1211yescharacteristic
158C3×C4⋊C4#6711yescharacteristic
159C3×C42—22no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#216—124no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—61no—
171C4⋊Dic3—62no—
172C4⋊Dic3—64no—
173C4⋊Dic3—62no—
174C4⋊Dic3—62no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180Dic3⋊C4—64no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186C4×Dic3—64no—
187C4×Dic3—62no—
188C4×Dic3—62no—
189C4×Dic3—62no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195Dic12—124no—
196C22×C32#12011yescharacteristic
197C32×C4—22no—
198C32×C4—21no—
199C32×C4—41no—
200C32×C4C2×Q1611yescharacteristic
201C32×C4C2×Q1611yescharacteristic
202C32×C4#13711yescharacteristic
203C32×C4#13711yescharacteristic
204C3⋊Dic3—22no—
205C3⋊Dic3—42no—
206C3⋊Dic3—41no—
207C3×Dic3—81no—
208C2×Q16—182no—
209C4⋊Q8—31no—
210C4⋊Q8—91no—
211C4⋊Q8—181no—
212C4⋊Q8—182no—
213C4⋊Q8—181no—
214C4×Q8—91no—
215C4×Q8—181no—
216C4×Q8—181no—
217C4×Q8D3211yescharacteristic
218#107—61no—
219#107—181no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222#103—61no—
223#103—181no—
224C4×C8—31no—
225C3×Q8—22no—
226C3×Q8—21no—
227C3×Q8—21no—
228C3×Q8—22no—
229C3×Q8—122no—
230C3×Q8Dic1212yescomplemented
231C3×Q8#21612yescomplemented
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—121no—
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×Dic3—41no—
249C2×Dic3—62no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—62no—
253C2×Dic3—64no—
254C2×Dic3—61no—
255C2×Dic3—62no—
256C2×Dic3—61no—
257C2×Dic3—62no—
258Dic6—32no—
259Dic6—32no—
260Dic6—42no—
261Dic6—62no—
262Dic6—62no—
263Dic6—61no—
264Dic6—61no—
265Dic6—122no—
266Dic6—122no—
267Dic6—242no—
268Dic6—244no—
269Dic6—242no—
270Dic6—242no—
271C3×C8—62no—
272C3×C8—121no—
273C3×C8—121no—
274C3⋊C8—22no—
275C3⋊C8—41no—
276C3⋊C8—41no—
277C2×C32#45111yescharacteristic
278C2×C32#45111yescharacteristic
279C2×C32#45311yescharacteristic
280C2×Q8—61no—
281C2×Q8—91no—
282C2×Q8—92no—
283C2×Q8—182no—
284C2×Q8#62611yescharacteristic
285Q16—364no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—61no—
289C4⋊C4—21no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—91no—
293C4⋊C4—182no—
294C4⋊C4—182no—
295C4⋊C4—181no—
296C4⋊C4—181no—
297C4⋊C4—181no—
298C4⋊C4#62611yescharacteristic
299C42—21no—
300C42—182no—
301C42—181no—
302C42C2×D3211yescharacteristic
303C22×C3—21no—
304C22×C3#88211yescharacteristic
305C22×C3#93711yescharacteristic
306C3×C4—24no—
307C3×C4—21no—
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—42no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—241no—
320C3×C4C2×Dic1211yescharacteristic
321C3×C4#90911yescharacteristic
322C3×C4#91511yescharacteristic
323C3×C4D3×Q1611yescharacteristic
324C3×C4D3×Q1611yescharacteristic
325C3×C4#91811yescharacteristic
326C3×C4C2×#21611yescharacteristic
327C3×C4#95111yescharacteristic
328Dic3—64no—
329Dic3—62no—
330Dic3—62no—
331Dic3—81no—
332Dic3—124no—
333Dic3—122no—
334Dic3—122no—
335Dic3—121no—
336Dic3—122no—
337Dic3—121no—
338C32#163311yescharacteristic, complemented, Sylow
339Q8—21no—
340Q8—92no—
341Q8—122no—
342Q8—181no—
343Q8—362no—
344Q8—722no—
345Q8#371912yescomplemented
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—121no—
349C2×C4—181no—
350C2×C4—181no—
351C2×C4—182no—
352C2×C4C2×#62611yescharacteristic
353C2×C4#381111yescharacteristic
354C2×C4#381111yescharacteristic
355C8—62no—
356C8—121no—
357C8—121no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3#473911yescharacteristic
362C2×C3#480911yescharacteristic
363C2×C3#482211yescharacteristic
364C2×C3#505011yescharacteristic
365C2×C3#518611yescharacteristic
366C2×C3#519811yescharacteristic
367C22#6398111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—182no—
372C4—241no—
373C4—362no—
374C4—361no—
375C4#6383111yescharacteristic
376C4C2×#371911yescharacteristic
377C4#6394411yescharacteristic
378C4#6395111yescharacteristic
379C3—21no—
380C3#6826711yescharacteristic, complemented
381C3#7116111yescharacteristic, complemented
382C2#1059119011yescharacteristic
383C2#1059160311yescharacteristic
384C2#1059166711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#120
hypercenterC4×Q8D32
hypocenterC32#1633
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
109. C32×Q8Q16semidirect
121. #634Q16semidirect
230. C3×Q8Dic12semidirect
231. C3×Q8#216semidirect
338. C32#1633semidirect
345. Q8#3719semidirect
380. C3#68267semidirect
381. C3#71161semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#50212
#105903862
#105902842
C3×#45352
#105890962
#105890852
#711613
#682673