Finite Group Databasebeta

← #11878722

Subgroups — #11878722

Order 1152.

1001 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 1001 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, complemented
2#10593972C211yesmaximal, characteristic
3C3×#5083C212yesmaximal, complemented
4#10591620C212yesmaximal, complemented
5#10591592C214yesmaximal, complemented
6#10591538C212yesmaximal, complemented
7#10590365C212yesmaximal, complemented
8#10590256C211yesmaximal, characteristic, complemented
9#80432—32nomaximal
10C2×Q8×C3⋊D3C2212yes—
11C2×#3798—21no—
12C32×C4⋊Q8C2211yescharacteristic
13#64153C2212yes—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3—21no—
16#64097—21no—
17#64097—21no—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2211yescharacteristic
20C2×C3×#215C2214yes—
21C3×C4×D12C2212yes—
22#63919C2211yescharacteristic
23#63916C2212yes—
24#63915—21no—
25#63914C2211yescharacteristic
26#63912—21no—
27C4×#625—21no—
28C2×#3716C2214yes—
29C3×#835C2214yes—
30C3×C4⋊(C3⋊C8)C2212yes—
31#63567C2214yes—
32#63557C2212yes—
33#63553C2212yes—
34D3×C4⋊Q8—32no—
35D3×C4⋊Q8—61no—
36#5548—32no—
37C3×#461—32no—
38#5175—34no—
39#5170—34no—
40#5083D312yescomplemented
41#5019—32no—
42#4841—32no—
43#4833—32no—
44#4806—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×D12C2312yes—
55C2×C3×C4×D3—22no—
56C2×#627—21no—
57C2×#626—22no—
58C2×#625—21no—
59C2×#625—21no—
60#3798—44no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C42C2311yescharacteristic
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66#3750—22no—
67#3750—22no—
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C3×#215—44no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8C2314yes—
75#3724—21no—
76(C2×D3)⋊Dic3—22no—
77#3716—44no—
78#3206—91noSylow
79C2×D3×Q8—34no—
80C2×D3×Q8—62no—
81C2×#235—62no—
82C2×C3×SD16—34no—
83C3×C4⋊Q8—21no—
84C3×C4⋊Q8C2×D312yes—
85C3×C4×D4—32no—
86#944—34no—
87#944—62no—
88C2×#215C2×D314yes—
89#940—32no—
90#938—32no—
91C2×#214—34no—
92C4×#67—62no—
93C2×#204—34no—
94#895—32no—
95D3×C4⋊C4—62no—
96D3×C4⋊C4—62no—
97D3×C4⋊C4—62no—
98D3×C4⋊C4—62no—
99#888—32no—
100#888—62no—
101#888—62no—
102#888—62no—
103#888—62no—
104#885—62no—
105#884—62no—
106C4×D12C2×D312yes—
107C42×D3—32no—
108C42×D3—61no—
109#869—32no—
110#869—61no—
111C3×C4⋊C8—32no—
112C3×#103—34no—
113#835C2×D314yes—
114(C2×D3)⋊C8—34no—
115#816—34no—
116C8×Dic3—34no—
117#810—34no—
118C4⋊(C3⋊C8)C2×D312yes—
119C22×C3⋊D3C2×D411yescharacteristic
120C22×C3×D3—22no—
121C32×Q8—24no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3⋊Dic3C2×D411yescharacteristic
129C2×C3⋊Dic3C2×D411yescharacteristic
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—44no—
133C4×C3⋊D3SD1614yescomplemented
134#634—24no—
135#634—44no—
136C2×C3×Dic3—22no—
137C3×D12—22no—
138C3×D12—22no—
139C3×C4×D3—44no—
140#627—42no—
141#626—44no—
142#625—42no—
143#625—42no—
144C3×C3⋊C8—24no—
145#532—91no—
146C2×C4⋊Q8—91no—
147#492—92no—
148#487—92no—
149#461—32no—
150#461—92no—
151#448—94no—
152#431—91no—
153C2×C3×Q8—22no—
154C2×C3×Q8C22×D314yes—
155C2×C3×D4—32no—
156C22×C3×C4—62no—
157C2×#67—62no—
158C2×#67—62no—
159C2×#67—62no—
160D3×Q8—124no—
161D3×Q8—124no—
162D3×Q8—128no—
163#235—128no—
164C2×D12—62no—
165C2×D12C22×D312yes—
166C2×C4×D3—22no—
167C2×C4×D3—32no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×C4×D3—64no—
174C2×C4×D3—64no—
175C2×Dic6—34no—
176C2×Dic6—62no—
177C2×Dic6—62no—
178C2×Dic6—64no—
179C2×Dic6—64no—
180C3×SD16—124no—
181C2×C3×C8—34no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—32no—
187C3×C22⋊C4—62no—
188C3×C42—21no—
189C3×C42C22×D312yes—
190#217—62no—
191#215—44no—
192#214—124no—
193(C2×D3)⋊C4—22no—
194(C2×D3)⋊C4—62no—
195C4⋊Dic3—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3—62no—
198C4⋊Dic3—62no—
199C4⋊Dic3C22×D312yes—
200Dic3⋊C4—62no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—64no—
205C4×Dic3—32no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C2×C3⋊C8C22×D314yes—
212#204—124no—
213C22×C32C22×D411yescharacteristic
214C2×C3⋊D3—21no—
215C2×C3⋊D3—21no—
216C2×C3⋊D3C2×SD1612yes—
217C2×C3×D3—42no—
218C2×C3×D3—42no—
219C2×C3×D3—42no—
220C32×C4—21no—
221C32×C4—42no—
222C32×C4C2×SD1612yes—
223C32×C4H(5,𝔽2)12yes—
224C3⋊Dic3—21no—
225C3⋊Dic3—42no—
226C3⋊Dic3C2×SD1612yes—
227C3⋊Dic3#13712yes—
228C3×Dic3—42no—
229C2×#41—181no—
230C22×Q8—92no—
231C2×SD16—34no—
232C2×SD16—94no—
233C4⋊Q8—91no—
234C4⋊Q8—92no—
235C4⋊Q8—91no—
236C4⋊Q8—181no—
237C4⋊Q8—181no—
238C4⋊Q8D3211yescharacteristic
239#127—91no—
240#124—181no—
241#121—92no—
242#121—181no—
243C4×D4—32no—
244C4×D4—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C42—91no—
248C4⋊C8—32no—
249#103—34no—
250#103—94no—
251C22⋊C8—92no—
252C4×C8—92no—
253C23×C3—62no—
254C22×D3—22no—
255C22×D3—32no—
256C22×D3—61no—
257C3×Q8—24no—
258C3×Q8—24no—
259C3×Q8—44no—
260C3×D4—62no—
261C3×D4—62no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—62no—
268C2×C3×C4—124no—
269C2×C3×C4D3×D412yes—
270C2×C3×C4D3×D412yes—
271C2×C3×C4C23×D312yes—
272#67—124no—
273#67—124no—
274#67—124no—
275C2×Dic3—22no—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—32no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284D12—22no—
285D12—22no—
286D12—124no—
287C4×D3—38no—
288C4×D3—44no—
289C4×D3—64no—
290C4×D3—64no—
291C4×D3—64no—
292C4×D3—64no—
293C4×D3—62no—
294C4×D3—62no—
295C4×D3—128no—
296C4×D3—128no—
297Dic6—64no—
298Dic6—64no—
299Dic6—124no—
300Dic6—124no—
301Dic6—128no—
302Dic6—128no—
303C3×C8—64no—
304C3⋊C8—24no—
305C2×C32#53511yescharacteristic
306C2×C32C22×SD1611yescharacteristic
307C2×C32C2×#13711yescharacteristic
308C3⋊D3—22no—
309C3×D3—82no—
310#41—364no—
311C2×Q8—92no—
312C2×Q8—182no—
313C2×Q8—181no—
314C2×Q8—364no—
315C2×Q8C2×D3212yes—
316C2×D4—32no—
317C2×D4—182no—
318C2×D4—181no—
319C2×D4—181no—
320C22×C4—62no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—182no—
325SD16—124no—
326SD16—364no—
327C2×C8—34no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—32no—
331C4⋊C4—182no—
332C4⋊C4—182no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C22⋊C4—62no—
337C22⋊C4—182no—
338C42—91no—
339C42—91no—
340C42—91no—
341C42C2×D3211yescharacteristic
342C22×C3—21no—
343C22×C3—122no—
344C22×C3—122no—
345C22×C3—122no—
346C22×C3C2×D3×D412yes—
347C2×D3—34no—
348C2×D3—42no—
349C2×D3—42no—
350C2×D3—42no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—62no—
354C2×D3—62no—
355C2×D3—62no—
356C3×C4—22no—
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—44no—
361C3×C4—44no—
362C3×C4—122no—
363C3×C4D3×SD1614yes—
364C3×C4#100412yes—
365C3×C4#100912yes—
366Dic3—34no—
367Dic3—34no—
368Dic3—42no—
369Dic3—62no—
370Dic3—62no—
371Dic3—62no—
372Dic3—62no—
373Dic3—124no—
374Dic3—124no—
375C32#320611yescharacteristic, complemented, Sylow
376C23—62no—
377C23—91no—
378Q8—24no—
379Q8—184no—
380Q8—364no—
381Q8—362no—
382D4—62no—
383D4—62no—
384D4—362no—
385D4—362no—
386D4—364no—
387C2×C4—22no—
388C2×C4—62no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—94no—
392C2×C4—91no—
393C2×C4—124no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—364no—
398C2×C4#381111yescharacteristic
399C2×C4#381111yescharacteristic
400C2×C4C22×D3211yescharacteristic
401C8—64no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—242no—
406C2×C3#560712yes—
407C2×C3C2×D3×SD1612yes—
408C2×C3D3×#13712yes—
409D3—64no—
410D3—64no—
411D3—82no—
412C22—92no—
413C22—122no—
414C22—122no—
415C22—122no—
416C22—181no—
417C22—181no—
418C22C2×#381111yescharacteristic
419C4—21no—
420C4—42no—
421C4—92no—
422C4—92no—
423C4—122no—
424C4—181no—
425C4—362no—
426C4#6394012yes—
427C4#6431412yes—
428C3—21no—
429C3#8043212yescomplemented
430C2—182no—
431C2—242no—
432C2#1059524111yescharacteristic
433C2C2×#6394011yescharacteristic
434C2#1059532211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593972C2
hypercenterC4⋊Q8D32
hypocenterC32#3206
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
1. C3⋊D3×C4⋊Q8C2semidirect
3. C3×#5083C2semidirect
4. #10591620C2semidirect
5. #10591592C2semidirect
6. #10591538C2semidirect
7. #10590365C2semidirect
8. #10590256C2semidirect
40. #5083D3semidirect
133. C4×C3⋊D3SD16semidirect
375. C32#3206semidirect
429. C3#80432semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105939722
C3×#50832
#105916202
#105915922
#105915382
#105903652
#105902562
#804323