Finite Group Databasebeta

← #11779500

Subgroups — #11779500

Order 1152.

554 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 88 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#10596034C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71145—31nomaximal
9#68203—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64147—21no—
12#64139—21no—
13#64135—21no—
14#64101—21no—
15#64094—22no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3719—22no—
20C3×#832—21no—
21C3×#808—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—21no—
26#63564—21no—
27#5563—31no—
28#5563—31no—
29#5563—61no—
30C3×#476—31no—
31#5092—31no—
32#5084—31no—
33#5008D311yescharacteristic, complemented
34#4842—31no—
35#4699—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4483—31no—
39#4481—31no—
40#4481—31no—
41#4459—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#638—22no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×#634D412yes—
48C2×C3×Dic6—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3757—22no—
53#3752—22no—
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C4×C3⋊Dic3—22no—
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#1634—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×D4—21no—
68C3×C4×D4C2×D311yescharacteristic
69C3×C4×D4C2×D311yescharacteristic
70C2×#216—62no—
71#938—62no—
72#938—61no—
73#938—61no—
74#930—61no—
75#930—61no—
76#930—62no—
77#926—61no—
78#926—61no—
79#926—62no—
80C2×Dic12—62no—
81#892—62no—
82#892—61no—
83#892—61no—
84#885—62no—
85#885—62no—
86#885—64no—
87C4×D12—31no—
88C4×D12—31no—
89C4×D12—61no—
90#869—31no—
91#869—31no—
92#869—61no—
93#869C2×D311yescharacteristic
94C3×#106—61no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8—31no—
97C3×#102—61no—
98C3×C4×C8—31no—
99#832—21no—
100#821—61no—
101#817—61no—
102#809—61no—
103#808—21no—
104#808—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C23×C32—21no—
109C22×C3⋊D3—21no—
110C32×D4—21no—
111C32×D4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118#638—82no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125#634—42no—
126C2×C3×Dic3—41no—
127C3×Dic6—42no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#555—91no—
132#494—91no—
133#476—31no—
134#476—91no—
135#333—91no—
136D4⋊C8—31no—
137D4⋊C8—91no—
138C2×C3×Q8—61no—
139C2×C3×D4—21no—
140C2×C3×D4D1211yescharacteristic
141C2×C3×D4#6711yescharacteristic
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C2×#67—64no—
146C2×#67—62no—
147C2×#67—62no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×C4×D3—62no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×Dic6—21no—
155C2×Dic6—32no—
156C2×Dic6—32no—
157C2×Dic6—62no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4D1211yescharacteristic
165C3×C4⋊C4#6711yescharacteristic
166C3×C22⋊C4—22no—
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C42—21no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#217—64no—
173#217—62no—
174#217—62no—
175#216—124no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—64no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—61no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4×Dic3—64no—
194C4×Dic3—62no—
195C4×Dic3—62no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199Dic12—124no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32#12011yescharacteristic
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4#13511yescharacteristic
210C32×C4#13511yescharacteristic
211C32×C4#13711yescharacteristic
212C32×C4#13711yescharacteristic
213C3⋊Dic3—41no—
214C3⋊Dic3—42no—
215C3×Dic3—81no—
216C2×Q16—182no—
217C4⋊Q8—31no—
218C4⋊Q8—91no—
219#124—182no—
220#121—181no—
221#121—181no—
222C4×D4—91no—
223C4×D4D3211yescharacteristic
224#117—181no—
225#117—181no—
226#106—61no—
227#106—181no—
228C4⋊C8—31no—
229C4⋊C8—31no—
230#102—61no—
231#102—181no—
232C4×C8—31no—
233C23×C3—22no—
234C23×C3—21no—
235C23×C3—21no—
236C22×D3—62no—
237C22×D3—61no—
238C22×D3—61no—
239C3×Q8—122no—
240C3×D4—21no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4—41no—
245C3×D4—41no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—121no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265#67—244no—
266#67—242no—
267#67—242no—
268C2×Dic3—41no—
269C2×Dic3—62no—
270C2×Dic3—64no—
271C2×Dic3—61no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—62no—
275D12—61no—
276D12—61no—
277D12—61no—
278D12—61no—
279D12—121no—
280D12—121no—
281C4×D3—122no—
282C4×D3—122no—
283C4×D3—121no—
284C4×D3—121no—
285C4×D3—121no—
286C4×D3—121no—
287Dic6—42no—
288Dic6—122no—
289Dic6—122no—
290Dic6—242no—
291C3×C8—62no—
292C3×C8—121no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—41no—
296C3⋊C8—41no—
297C2×C32—81no—
298C2×C32#45211yescharacteristic
299C2×C32#45211yescharacteristic
300C2×C32#45311yescharacteristic
301C3⋊D3—81no—
302C2×Q8—61no—
303C2×Q8—92no—
304C2×D4—91no—
305C2×D4—182no—
306C2×D4#62611yescharacteristic
307C22×C4—21no—
308C22×C4—181no—
309Q16—364no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—91no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4#62611yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—182no—
321C22⋊C4—182no—
322C22⋊C4—181no—
323C42—182no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3#88211yescharacteristic
336C22×C3#93711yescharacteristic
337C2×D3—122no—
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—42no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—241no—
357C3×C4#90411yescharacteristic
358C3×C4#90911yescharacteristic
359C3×C4#91211yescharacteristic
360C3×C4#91511yescharacteristic
361C3×C4#91511yescharacteristic
362C3×C4#91611yescharacteristic
363C3×C4#94211yescharacteristic
364C3×C4#95011yescharacteristic
365Dic3—81no—
366Dic3—124no—
367Dic3—122no—
368Dic3—122no—
369Dic3—121no—
370Dic3—121no—
371Dic3—122no—
372C32#163411yescharacteristic, complemented, Sylow
373C23—21no—
374C23—181no—
375Q8—122no—
376Q8—362no—
377D4—21no—
378D4—21no—
379D4—181no—
380D4—181no—
381D4—722no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—121no—
386C2×C4—181no—
387C2×C4—182no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4C2×#62611yescharacteristic
391C2×C4#381111yescharacteristic
392C2×C4#381111yescharacteristic
393C8—62no—
394C8—121no—
395C8—121no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—82no—
400C2×C3—81no—
401C2×C3—81no—
402C2×C3#473311yescharacteristic
403C2×C3#478311yescharacteristic
404C2×C3#482211yescharacteristic
405C2×C3#504711yescharacteristic
406C2×C3#517311yescharacteristic
407C2×C3#519811yescharacteristic
408D3—242no—
409D3—241no—
410D3—241no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—361no—
415C22—361no—
416C22—361no—
417C22#6398111yescharacteristic
418C4—21no—
419C4—41no—
420C4—241no—
421C4—362no—
422C4—361no—
423C4#6382911yescharacteristic
424C4#6383311yescharacteristic
425C4#6393111yescharacteristic
426C4#6393611yescharacteristic
427C3—21no—
428C3#6820311yescharacteristic, complemented
429C3#7114511yescharacteristic, complemented
430C2—81no—
431C2—721no—
432C2#1059118411yescharacteristic
433C2#1059146611yescharacteristic
434C2#1059166711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radical#10596034C2
hypercenterC4×D4D32
hypocenterC32#1634
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×#5008C2semidirect
3. #10590386C2semidirect
4. #10590300C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589096C2semidirect
7. #10589082C2semidirect
33. #5008D3semidirect
37. D4⋊(C3⋊C8)D3semidirect
372. C32#1634semidirect
428. C3#68203semidirect
429. C3#71145semidirect

Maximal subgroups

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

subgroupindex
#105960342
C3×#50082
#105903862
#105903002
C3×D4⋊(C3⋊C8)2
#105890962
#105890822
#711453
#682033