Finite Group Databasebeta

← #11779773

Subgroups — #11779773

Order 1152.

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

normal subgroups only

This group has 542 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#10596184C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3#10590388C211yesmaximal, characteristic, complemented
4#10590307C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71206—31nomaximal
9#68406—31nomaximal
10C32×#127C2211yescharacteristic
11#64145—21no—
12#64145—21no—
13#64144—22no—
14D4×C3⋊Dic3—21no—
15D4×C3⋊Dic3—21no—
16C4×#634C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3719—21no—
20C3×#832—22no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63566—21no—
27#5713—31no—
28#5713—31no—
29#5713—61no—
30C3×#486—31no—
31#5094—31no—
32#5090—31no—
33#5070D311yescharacteristic
34#4851—31no—
35#4849—31no—
36C3×#331—31no—
37#4544D311yescharacteristic
38#4484—31no—
39#4484—31no—
40#4456—31no—
41#4456—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4D412yes—
45C22×C3⋊Dic3—22no—
46C2×#634D411yescharacteristic
47C2×#634D411yescharacteristic
48C2×C3×Dic6—21no—
49C32×C42C2311yescharacteristic
50#3757—22no—
51#3757—22no—
52#3757—22no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—21no—
56#3750—21no—
57C4×C3⋊Dic3—21no—
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—42no—
65#1640—91noSylow
66C3×C4⋊Q8—31no—
67C3×#127—21no—
68C3×#127C2×D311yescharacteristic
69C3×#127C2×D311yescharacteristic
70C2×#216—61no—
71#936—61no—
72#936—61no—
73#936—61no—
74#936—61no—
75#936—62no—
76#936—62no—
77#935—64no—
78#935—62no—
79#935—62no—
80D4×Dic3—61no—
81D4×Dic3—61no—
82D4×Dic3—61no—
83D4×Dic3—61no—
84D4×Dic3—62no—
85D4×Dic3—62no—
86C2×Dic12—61no—
87#869C2×D311yescharacteristic
88C4×Dic6—31no—
89C4×Dic6—31no—
90C4×Dic6—31no—
91C4×Dic6—31no—
92C4×Dic6—61no—
93C4×Dic6—61no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8—31no—
96C3×#102—62no—
97C3×C4×C8—31no—
98#835—61no—
99#832—22no—
100#817—61no—
101#816—61no—
102#816—61no—
103#810—61no—
104#808—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C23×C32—22no—
109C32×D4—41no—
110C32×D4—41no—
111C32×D4—41no—
112C32×D4—41no—
113C32×D4—42no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—82no—
122#634—21no—
123#634—21no—
124#634—21no—
125#634—21no—
126C2×C3×Dic3—41no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131C3×C3⋊C8—41no—
132#559—91no—
133#486—31no—
134#475—91no—
135#462—91no—
136#331—31no—
137Q8⋊C8—91no—
138Q8⋊C8—91no—
139C2×C3×Q8—61no—
140C2×C3×D4—22no—
141C2×C3×D4—22no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—22no—
147C2×C3×D4D1212yes—
148C2×C3×D4#6712yes—
149C22×Dic3—64no—
150C22×Dic3—62no—
151C22×Dic3—62no—
152C2×Dic6—21no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C42—21no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167#217—64no—
168#217—64no—
169#217—62no—
170#217—62no—
171#217—62no—
172#217—62no—
173#217—64no—
174#217—62no—
175#217—62no—
176#216—122no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191C4×Dic3—62no—
192C4×Dic3—62no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200Dic12—122no—
201C22×C32—42no—
202C22×C32—42no—
203C22×C32—42no—
204C22×C32#12011yescharacteristic
205C32×C4—21no—
206C32×C4#13511yescharacteristic
207C32×C4#13511yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4#13711yescharacteristic
210C3⋊Dic3—41no—
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3⋊Dic3—41no—
214C3×Dic3—81no—
215C2×Q16—181no—
216C4⋊Q8—31no—
217#127D3211yescharacteristic
218#124—181no—
219#124—181no—
220#123—182no—
221C4×Q8—91no—
222C4×Q8—91no—
223C4×D4—181no—
224C4×D4—181no—
225#106—181no—
226C4⋊C8—31no—
227C4⋊C8—31no—
228#103—181no—
229#103—181no—
230#102—62no—
231C4×C8—31no—
232C23×C3—24no—
233C23×C3—22no—
234C23×C3—22no—
235C3×Q8—121no—
236C3×Q8—121no—
237C3×D4—42no—
238C3×D4—42no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—42no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—82no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—121no—
256C2×C3×C4C2×D1211yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×Dic3—41no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—244no—
276C2×Dic3—242no—
277C2×Dic3—242no—
278Dic6—41no—
279Dic6—41no—
280Dic6—61no—
281Dic6—61no—
282Dic6—61no—
283Dic6—61no—
284Dic6—61no—
285Dic6—61no—
286Dic6—61no—
287Dic6—61no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—121no—
292C3×C8—121no—
293C3×C8—121no—
294C3×C8—121no—
295C3⋊C8—41no—
296C3⋊C8—41no—
297C3⋊C8—41no—
298C2×C32—82no—
299C2×C32#44911yescharacteristic
300C2×C32#45211yescharacteristic
301C2×C32#45511yescharacteristic
302C2×Q8—61no—
303C2×Q8—91no—
304C2×Q8—91no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4#62612yes—
308C22×C4—182no—
309Q16—362no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—91no—
316C4⋊C4—91no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C22⋊C4—182no—
320C22⋊C4—182no—
321C22⋊C4—182no—
322C42—181no—
323C42—181no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—44no—
327C22×C3—44no—
328C22×C3—44no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—42no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3#88211yescharacteristic
336C22×C3#93711yescharacteristic
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—41no—
344C3×C4—241no—
345C3×C4#91111yescharacteristic
346C3×C4#91111yescharacteristic
347C3×C4#91211yescharacteristic
348C3×C4#91211yescharacteristic
349C3×C4#91511yescharacteristic
350C3×C4#91511yescharacteristic
351C3×C4#91611yescharacteristic
352C3×C4#91611yescharacteristic
353Dic3—81no—
354Dic3—122no—
355Dic3—122no—
356Dic3—122no—
357Dic3—122no—
358Dic3—121no—
359Dic3—121no—
360Dic3—121no—
361Dic3—121no—
362Dic3—121no—
363Dic3—121no—
364Dic3—121no—
365Dic3—121no—
366C32#164011yescharacteristic, complemented, Sylow
367C23—22no—
368Q8—121no—
369Q8—121no—
370Q8—181no—
371Q8—181no—
372Q8—181no—
373Q8—181no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379C2×C4—121no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—722no—
385C2×C4C2×#62611yescharacteristic
386C2×C4#381111yescharacteristic
387C2×C4#381111yescharacteristic
388C8—121no—
389C8—121no—
390C8—121no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—84no—
395C2×C3—82no—
396C2×C3—82no—
397C2×C3#474611yescharacteristic
398C2×C3#478111yescharacteristic
399C2×C3#478311yescharacteristic
400C2×C3#506111yescharacteristic
401C2×C3#515811yescharacteristic
402C2×C3#517311yescharacteristic
403C22—42no—
404C22—42no—
405C22—42no—
406C22#6398111yescharacteristic
407C4—21no—
408C4—241no—
409C4—361no—
410C4—361no—
411C4—361no—
412C4—361no—
413C4#6392711yescharacteristic
414C4#6393111yescharacteristic
415C4#6393611yescharacteristic
416C4#6393611yescharacteristic
417C3—21no—
418C3#6840611yescharacteristic, complemented
419C3#7120611yescharacteristic, complemented
420C2—82no—
421C2#1059145711yescharacteristic
422C2#1059146611yescharacteristic
423C2#1059151411yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
Fitting, prime radicalC32×#127C22
socleC22×C32#120
hypercenter#127D32
hypocenterC32#1640
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
3. #10590388C2semidirect
4. #10590307C2semidirect
6. #10589085C2semidirect
7. #10589085C2semidirect
366. C32#1640semidirect
418. C3#68406semidirect
419. C3#71206semidirect

Maximal subgroups

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

subgroupindex
#105961842
C3×#50702
#105903882
#105903072
C3×#45442
#105890852
#712063
#684063