Finite Group Databasebeta

← #11780450

Subgroups — #11780450

Order 1152.

521 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5555C211yesmaximal, characteristic
2C3×#5007C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic, complemented
4#10590309C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71913—31nomaximal
9#71111—31nomaximal
10C2×C3×#237—21no—
11C32×C4×D4C2211yescharacteristic
12C3×#930—21no—
13C2×C3×C4⋊Dic3—21no—
14C3×#897—21no—
15C3×#886—22no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3715—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#832—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63574—22no—
26#63565—21no—
27C3×#547—31no—
28#5555D311yescharacteristic
29C3×#474—31no—
30#5083—31no—
31#5080—31no—
32#5080—31no—
33#5019—31no—
34#5007D311yescharacteristic, complemented
35#4547—31no—
36D4⋊(C3⋊C8)—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4483—31no—
41#4482—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C22×C3×Dic3—22no—
46C3×#237—42no—
47C3×#237—42no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—22no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D412yes—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66#3715—42no—
67#1654—91noSylow
68C2×C3×#41—61no—
69C2×#237—21no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—31no—
72C3×#123—62no—
73C3×C22⋊Q8—61no—
74C3×#121—61no—
75C3×C4×D4—21no—
76C3×C4×D4—31no—
77C3×C4×D4C2×D311yescharacteristic
78C3×C4×D4C2×D311yescharacteristic
79C2×C3×C4⋊C4—61no—
80C2×#215—61no—
81C2×#214—61no—
82#930—21no—
83C2×C4⋊Dic3—21no—
84#897—21no—
85#886—22no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C3×#107—61no—
90C3×C4⋊C8—31no—
91C3×#102—61no—
92#835—61no—
93#832—21no—
94#810—61no—
95#808—62no—
96#808—62no—
97#807—21no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C23×C32—21no—
106C22×C3×D3—21no—
107C32×D4—21no—
108C32×D4SD1612yescomplemented
109C2×C32×C4—21no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C3×#67—44no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—44no—
119C2×C3×Dic3—41no—
120C3×D12—21no—
121C3×D12—21no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C3⋊(C3⋊C8)—22no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—41no—
131#547—31no—
132#498—91no—
133#474—31no—
134#461—91no—
135#332—91no—
136D4⋊C8—91no—
137D4⋊C8—91no—
138C3×#41—122no—
139C3×#41—122no—
140C2×C3×Q8—61no—
141C2×C3×Q8—61no—
142C2×C3×D4—21no—
143C2×C3×D4—31no—
144C2×C3×D4—62no—
145C2×C3×D4#6711yescharacteristic
146C2×C3×D4#6711yescharacteristic
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—41no—
150C22×C3×C4—62no—
151C22×C3×C4—61no—
152C2×#67—22no—
153C22×Dic3—22no—
154#237—42no—
155#237—42no—
156C2×D12#6711yescharacteristic
157C2×C4×D3—21no—
158C2×Dic6—21no—
159C2×Dic6—21no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4#6711yescharacteristic
169C3×C4⋊C4#6711yescharacteristic
170C3×C22⋊C4—21no—
171C3×C22⋊C4—21no—
172C3×C22⋊C4—41no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—61no—
175C3×C42—21no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178#215—122no—
179#214—122no—
180(C2×D3)⋊C4—22no—
181(C2×D3)⋊C4—21no—
182C4⋊Dic3—22no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3#6712yes—
187C4⋊Dic3#6711yescharacteristic
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194C2×C3⋊C8—121no—
195C22×C32—22no—
196C22×C32—41no—
197C22×C32—41no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C3×Dic3—42no—
209C3×Dic3—41no—
210C3×Dic3—81no—
211C2×#41—61no—
212C2×SD16—181no—
213C4⋊Q8—31no—
214C4⋊Q8—31no—
215#123—62no—
216C22⋊Q8—61no—
217#121—61no—
218C4×D4—31no—
219C4×D4D3211yescharacteristic
220C2×C4⋊C4—61no—
221#107—61no—
222#106—182no—
223C4⋊C8—31no—
224C4⋊C8—91no—
225#103—181no—
226#102—61no—
227C4×C8—91no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—41no—
231C23×C3—61no—
232C22×D3—21no—
233C3×Q8—121no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×Q8—121no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—22no—
240C3×D4—41no—
241C3×D4—61no—
242C3×D4—61no—
243C3×D4—124no—
244C3×D4#21412yescomplemented
245C3×D4#21512yescomplemented
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—61no—
257C2×C3×C4—62no—
258C2×C3×C4—81no—
259C2×C3×C4—81no—
260C2×C3×C4—124no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270#67—44no—
271C2×Dic3—22no—
272C2×Dic3—21no—
273C2×Dic3—44no—
274C2×Dic3—41no—
275D12—21no—
276D12—21no—
277C4×D3—41no—
278C4×D3—41no—
279Dic6—41no—
280Dic6—41no—
281Dic6—41no—
282Dic6—41no—
283C3×C8—121no—
284C3⋊C8—41no—
285C3⋊C8—62no—
286C3⋊C8—62no—
287C3⋊C8—122no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C3⋊C8—241no—
291C2×C32—42no—
292C2×C32#44911yescharacteristic
293C2×C32#45011yescharacteristic
294C2×C32#45611yescharacteristic
295C3×D3—81no—
296#41—122no—
297#41—122no—
298C2×Q8—61no—
299C2×Q8—61no—
300C2×D4—31no—
301C2×D4—62no—
302C2×D4#62511yescharacteristic
303C22×C4—21no—
304C22×C4—62no—
305C22×C4—61no—
306SD16—362no—
307C2×C8—61no—
308C2×C8—181no—
309C2×C8—181no—
310C4⋊C4—31no—
311C4⋊C4—32no—
312C4⋊C4—62no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4#62511yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—62no—
319C22⋊C4—61no—
320C42C2×D3211yescharacteristic
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—42no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—81no—
330C22×C3—81no—
331C22×C3—121no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3#93711yescharacteristic
335C22×C3#95311yescharacteristic
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—81no—
349C3×C4—121no—
350C3×C4—122no—
351C3×C4—241no—
352C3×C4#91111yescharacteristic
353C3×C4#91211yescharacteristic
354C3×C4#93211yescharacteristic
355C3×C4C2×#21411yescharacteristic
356C3×C4C2×#21511yescharacteristic
357C3×C4#94911yescharacteristic
358C3×C4#94911yescharacteristic
359C3×C4#95011yescharacteristic
360Dic3—42no—
361Dic3—41no—
362Dic3—81no—
363C32#165411yescharacteristic, complemented, Sylow
364C23—21no—
365C23—61no—
366Q8—121no—
367Q8—121no—
368Q8—121no—
369Q8—121no—
370D4—21no—
371D4—61no—
372D4—61no—
373D4—124no—
374D4#371512yescomplemented
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—61no—
379C2×C4—62no—
380C2×C4—124no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4C2×#62511yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C2×C4D3×#6711yescharacteristic
387C8—121no—
388C8—182no—
389C8—361no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—42no—
394C2×C3—42no—
395C2×C3—82no—
396C2×C3—241no—
397C2×C3#504611yescharacteristic
398C2×C3#515811yescharacteristic
399C2×C3#520511yescharacteristic
400C2×C3#521811yescharacteristic
401C2×C3#523811yescharacteristic
402C2×C3#524611yescharacteristic
403D3—81no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—121no—
408C22—121no—
409C22—121no—
410C22#6397611yescharacteristic
411C4—21no—
412C4—41no—
413C4—121no—
414C4—122no—
415C4—241no—
416C4#6382311yescharacteristic
417C4C2×#371511yescharacteristic
418C4#6392511yescharacteristic
419C4#6393311yescharacteristic
420C3—21no—
421C3#7111111yescharacteristic, complemented
422C3#7191311yescharacteristic, complemented
423C2—42no—
424C2—241no—
425C2#1059116911yescharacteristic
426C2#1059145011yescharacteristic
427C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5555C2
hypercenterC4×D4D32
hypocenterC32#1654
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5007C2semidirect
3. #10590363C2semidirect
4. #10590309C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589093C2semidirect
7. #10589080C2semidirect
34. #5007D3semidirect
108. C32×D4SD16semidirect
244. C3×D4#214semidirect
245. C3×D4#215semidirect
363. C32#1654semidirect
374. D4#3715semidirect
421. C3#71111semidirect
422. C3#71913semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×#50072
#105903632
#105903092
D4⋊(C3⋊(C3⋊C8))2
#105890932
#105890802
#719133
#711113