Finite Group Databasebeta

← #11878912

Subgroups — #11878912

Order 1152.

913 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 913 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593882C211yesmaximal, characteristic
3C3×#5090C212yesmaximal, complemented
4#10591628C212yesmaximal, complemented
5#10591603C214yesmaximal
6#10591538C212yesmaximal, complemented
7#10590385C212yesmaximal, complemented
8#10590256C211yesmaximal, characteristic
9#80480—32nomaximal
10C2×Q8×C3⋊D3C2212yes—
11C32×C4⋊Q8C2211yescharacteristic
12#64153C2212yes—
13C4⋊C4×C3⋊D3—21no—
14C4⋊C4×C3⋊D3—21no—
15#64097—21no—
16#64097—21no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2211yescharacteristic
19C2×C3×#216C2214yes—
20C3×C4×Dic6C2212yes—
21#63919C2211yescharacteristic
22C4×#627—21no—
23#63874—21no—
24#63873C2211yescharacteristic
25#63871C2212yes—
26#63870—21no—
27#63865—21no—
28C2×#3719C2214yes—
29C3×#835C2214yes—
30C3×C4⋊(C3⋊C8)C2212yes—
31#63567C2214yes—
32#63557C2212yes—
33#63553C2212yes—
34D3×C4⋊Q8—32no—
35D3×C4⋊Q8—61no—
36#5578—32no—
37C3×#462—32no—
38#5186—34no—
39#5183—34no—
40#5090D312yescomplemented
41#5031—32no—
42#4849—32no—
43#4833—32no—
44#4809—34no—
45#4792—34no—
46C2×C32×Q8C2312yes—
47Q8×C3⋊D3—44no—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3C2311yescharacteristic
52C2×#634—22no—
53C2×#634C2312yes—
54C2×C3×Dic6C2312yes—
55C2×#627—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C42C2311yescharacteristic
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61#3750—22no—
62#3750—22no—
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C3×#216—44no—
67C3×C4⋊Dic3C2312yes—
68C3×Dic3⋊C4—22no—
69C3×C4×Dic3—22no—
70C2×C3×C3⋊C8C2314yes—
71#3724—21no—
72#3724—21no—
73#3724—21no—
74Dic3⋊Dic3—22no—
75#3722—22no—
76#3719—44no—
77#3209—91noSylow
78C2×D3×Q8—34no—
79C2×D3×Q8—62no—
80C2×C3×Q16—34no—
81C3×C4⋊Q8—21no—
82C3×C4⋊Q8C2×D312yes—
83C3×C4×Q8—32no—
84#946—32no—
85#944—34no—
86#944—32no—
87#944—62no—
88C2×#216—34no—
89C2×#216C2×D314yes—
90C2×Dic12—34no—
91#897—32no—
92#896—62no—
93D3×C4⋊C4—62no—
94D3×C4⋊C4—62no—
95D3×C4⋊C4—62no—
96D3×C4⋊C4—62no—
97#889—62no—
98#888—32no—
99#888—62no—
100#888—62no—
101#888—62no—
102#888—62no—
103#872—62no—
104C42×D3—32no—
105C42×D3—61no—
106#869—32no—
107#869—61no—
108C4×Dic6—62no—
109C4×Dic6C2×D312yes—
110C3×C4⋊C8—32no—
111C3×#103—34no—
112#835C2×D314yes—
113(C2×D3)⋊C8—34no—
114#816—34no—
115C8×Dic3—34no—
116#810—34no—
117C4⋊(C3⋊C8)C2×D312yes—
118C22×C3⋊D3C2×D411yescharacteristic
119C32×Q8—24no—
120C2×C32×C4—22no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D411yescharacteristic
128C4×C3⋊D3—22no—
129C4×C3⋊D3—22no—
130C4×C3⋊D3—44no—
131C4×C3⋊D3Q1614yescomplemented
132#634—24no—
133#634—44no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138#627—42no—
139C3×C3⋊C8—24no—
140#533—91no—
141C2×C4⋊Q8—91no—
142#494—92no—
143#487—92no—
144#462—32no—
145#462—92no—
146#451—94no—
147#431—91no—
148C2×C3×Q8—22no—
149C2×C3×Q8—32no—
150C2×C3×Q8C22×D314yes—
151D3×Q8—124no—
152D3×Q8—124no—
153D3×Q8—128no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—32no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C2×Dic6—34no—
163C2×Dic6—62no—
164C2×Dic6—62no—
165C2×Dic6—64no—
166C2×Dic6—64no—
167C2×Dic6C22×D312yes—
168C3×Q16—124no—
169C2×C3×C8—34no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—62no—
176C3×C42—21no—
177C3×C42—62no—
178C3×C42C22×D312yes—
179#216—44no—
180#216—124no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3C22×D312yes—
189Dic3⋊C4—22no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—22no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C2×C3⋊C8C22×D314yes—
206Dic12—124no—
207C22×C32C22×D411yescharacteristic
208C2×C3⋊D3—21no—
209C2×C3⋊D3—21no—
210C2×C3⋊D3C2×Q1612yes—
211C32×C4—21no—
212C32×C4—42no—
213C32×C4C2×Q1612yes—
214C32×C4H(5,𝔽2)12yes—
215C3⋊Dic3—21no—
216C3⋊Dic3—42no—
217C3⋊Dic3C2×Q1612yes—
218C3⋊Dic3#13712yes—
219C3×Dic3—42no—
220C3×Dic3—42no—
221C22×Q8—92no—
222C2×Q16—34no—
223C2×Q16—94no—
224C4⋊Q8—91no—
225C4⋊Q8—91no—
226C4⋊Q8—92no—
227C4⋊Q8—91no—
228C4⋊Q8—181no—
229C4⋊Q8—181no—
230C4⋊Q8D3211yescharacteristic
231#125—181no—
232C22⋊Q8—92no—
233C22⋊Q8—181no—
234C4×Q8—32no—
235C4×Q8—181no—
236#117—181no—
237C2×C4⋊C4—181no—
238C2×C4⋊C4—181no—
239C2×C42—91no—
240C4⋊C8—32no—
241#103—34no—
242#103—94no—
243C22⋊C8—92no—
244C4×C8—92no—
245C22×D3—32no—
246C22×D3—61no—
247C3×Q8—24no—
248C3×Q8—24no—
249C3×Q8—44no—
250C3×Q8—62no—
251C3×Q8—62no—
252C2×C3×C4—24no—
253C2×C3×C4—24no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4D3×D412yes—
260C2×C3×C4D3×D412yes—
261C2×C3×C4C23×D312yes—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—32no—
265C2×Dic3—32no—
266C2×Dic3—32no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C4×D3—38no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—64no—
276C4×D3—64no—
277C4×D3—62no—
278C4×D3—62no—
279C4×D3—128no—
280C4×D3—128no—
281Dic6—22no—
282Dic6—22no—
283Dic6—64no—
284Dic6—64no—
285Dic6—124no—
286Dic6—124no—
287Dic6—128no—
288Dic6—128no—
289C3×C8—64no—
290C3⋊C8—24no—
291C2×C32#53511yescharacteristic
292C2×C32C22×Q1611yescharacteristic
293C2×C32C2×#13711yescharacteristic
294C3⋊D3—22no—
295C2×Q8—32no—
296C2×Q8—92no—
297C2×Q8—182no—
298C2×Q8—181no—
299C2×Q8—364no—
300C2×Q8C2×D3212yes—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—182no—
305Q16—124no—
306Q16—364no—
307C2×C8—34no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—32no—
311C4⋊C4—62no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4—182no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C22⋊C4—182no—
321C42—62no—
322C42—91no—
323C42—91no—
324C42—91no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3C2×D3×D412yes—
328C2×D3—34no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—44no—
339C3×C4—44no—
340C3×C4—122no—
341C3×C4—122no—
342C3×C4D3×Q1614yes—
343C3×C4#100412yes—
344C3×C4#100912yes—
345Dic3—34no—
346Dic3—34no—
347Dic3—42no—
348Dic3—42no—
349Dic3—62no—
350Dic3—62no—
351Dic3—62no—
352Dic3—62no—
353Dic3—124no—
354Dic3—124no—
355C32#320911yescharacteristic, complemented, Sylow
356C23—91no—
357Q8—24no—
358Q8—62no—
359Q8—62no—
360Q8—184no—
361Q8—364no—
362Q8—362no—
363C2×C4—22no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—94no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—364no—
374C2×C4#381111yescharacteristic
375C2×C4#381111yescharacteristic
376C2×C4C22×D3211yescharacteristic
377C8—64no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3#560712yes—
382C2×C3C2×D3×Q1612yes—
383C2×C3D3×#13712yes—
384D3—64no—
385D3—64no—
386C22—92no—
387C22—181no—
388C22—181no—
389C22C2×#381111yescharacteristic
390C4—21no—
391C4—42no—
392C4—92no—
393C4—92no—
394C4—122no—
395C4—122no—
396C4—181no—
397C4—362no—
398C4#6394412yes—
399C4#6431412yes—
400C3—21no—
401C3#8048012yescomplemented
402C2—182no—
403C2#1059524111yescharacteristic
404C2#1059532211yescharacteristic
405C2C2×#6394411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5090C2semidirect
4. #10591628C2semidirect
6. #10591538C2semidirect
7. #10590385C2semidirect
40. #5090D3semidirect
131. C4×C3⋊D3Q16semidirect
355. C32#3209semidirect
401. C3#80480semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105938822
C3×#50902
#105916282
#105916032
#105915382
#105903852
#105902562
#804803