Finite Group Databasebeta

← #11779642

Subgroups — #11779642

Order 1152.

596 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 98 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
1D4×#634C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic
3#10590287C211yesmaximal, characteristic, complemented
4#10590284C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71142—31nomaximal
9#68189—31nomaximal
10C22×#634—21no—
11C32×C4×D4C2211yescharacteristic
12D4×C3⋊Dic3—21no—
13#64133—21no—
14#64097—21no—
15#64087—22no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#832—21no—
20C3×#808—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63567—21no—
26#63566—22no—
27D4×Dic6—31no—
28D4×Dic6—31no—
29D4×Dic6—61no—
30C3×#476—31no—
31#5091—31no—
32#5079—31no—
33#5008D311yescharacteristic
34#4850—31no—
35#4681—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic
38#4486—31no—
39#4484—31no—
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3⋊Dic3—22no—
45C2×#634—22no—
46C2×#634—21no—
47C2×#634—42no—
48C2×#634—42no—
49C2×#634D411yescharacteristic
50C2×C3×Dic6—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54#3757—22no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C4⋊(C3⋊Dic3)D412yes—
58#3750—22no—
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#1637—91noSylow
67C22×Dic6—61no—
68C22×Dic6—61no—
69C22×Dic6—62no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—21no—
72C3×C4×D4C2×D311yescharacteristic
73C3×C4×D4C2×D311yescharacteristic
74D4×Dic3—62no—
75D4×Dic3—61no—
76D4×Dic3—61no—
77#924—61no—
78#924—61no—
79#924—62no—
80#888—62no—
81#888—61no—
82#888—61no—
83#878—62no—
84#878—62no—
85#878—64no—
86#869—31no—
87#869—31no—
88#869—61no—
89#869C2×D311yescharacteristic
90C4×Dic6—31no—
91C4×Dic6—31no—
92C4×Dic6—61no—
93C3×#106—61no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8—31no—
96C3×#102—61no—
97C3×C4×C8—31no—
98#835—62no—
99#832—21no—
100#818—61no—
101#816—61no—
102#816—62no—
103#810—61no—
104#808—21no—
105#807—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4×C3⋊C8C2×D311yescharacteristic
109C23×C32—21no—
110C32×D4—21no—
111C32×D4Q1612yes—
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—44no—
122#634—21no—
123#634—44no—
124#634—41no—
125#634—41no—
126#634SD1612yes—
127C2×C3×Dic3—41no—
128C3×Dic6—42no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131C3×C3⋊C8—41no—
132D4×Q8—91no—
133#487—91no—
134#477—91no—
135#476—31no—
136#332—91no—
137Q8⋊C8—91no—
138D4⋊C8—31no—
139C2×C3×Q8—61no—
140C2×C3×D4—21no—
141C2×C3×D4D1211yescharacteristic
142C2×C3×D4#6711yescharacteristic
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×Dic3—64no—
147C22×Dic3—62no—
148C22×Dic3—62no—
149C2×Dic6—21no—
150C2×Dic6—31no—
151C2×Dic6—31no—
152C2×Dic6—61no—
153C2×Dic6—62no—
154C2×Dic6—64no—
155C2×Dic6—62no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×Dic6—122no—
160C2×Dic6—122no—
161C2×Dic6—124no—
162C2×Dic6—124no—
163C2×Dic6—122no—
164C2×Dic6—122no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4D1211yescharacteristic
172C3×C4⋊C4#6711yescharacteristic
173C3×C22⋊C4—22no—
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C42—21no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#217—64no—
180#217—62no—
181#217—62no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—31no—
185C4⋊Dic3—32no—
186C4⋊Dic3—31no—
187C4⋊Dic3—32no—
188C4⋊Dic3—61no—
189C4⋊Dic3—62no—
190C4⋊Dic3—62no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193Dic3⋊C4—62no—
194Dic3⋊C4—64no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199C4×Dic3—62no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C22×C32—22no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32#12011yescharacteristic
209C32×C4—21no—
210C32×C4—41no—
211C32×C4C2×SD1611yescharacteristic
212C32×C4C2×Q1611yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C32×C4#13711yescharacteristic
215C3⋊Dic3—22no—
216C3⋊Dic3—42no—
217C3⋊Dic3—41no—
218C3×Dic3—81no—
219C22×Q8—181no—
220C4⋊Q8—31no—
221C4⋊Q8—91no—
222C4⋊Q8—181no—
223C22⋊Q8—182no—
224C22⋊Q8—181no—
225C4×Q8—91no—
226C4×D4—181no—
227C4×D4D3211yescharacteristic
228#107—181no—
229#106—61no—
230C4⋊C8—31no—
231C4⋊C8—31no—
232#103—181no—
233#103—182no—
234#102—61no—
235C4×C8—31no—
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—21no—
239C3×Q8—122no—
240C3×D4—22no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—22no—
244C3×D4Dic1212yes—
245C3×D4#21612yes—
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
265C2×Dic3—41no—
266C2×Dic3—62no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—62no—
270C2×Dic3—64no—
271C2×Dic3—61no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—62no—
275C2×Dic3—128no—
276C2×Dic3—124no—
277C2×Dic3—124no—
278Dic6—32no—
279Dic6—32no—
280Dic6—42no—
281Dic6—62no—
282Dic6—62no—
283Dic6—61no—
284Dic6—61no—
285Dic6—128no—
286Dic6—124no—
287Dic6—124no—
288Dic6—122no—
289Dic6—122no—
290Dic6—121no—
291Dic6—121no—
292Dic6—121no—
293Dic6—121no—
294C3×C8—121no—
295C3×C8—121no—
296C3×C8—121no—
297C3⋊C8—41no—
298C3⋊C8—41no—
299C3⋊C8—41no—
300C2×C32—42no—
301C2×C32#45011yescharacteristic
302C2×C32#45111yescharacteristic
303C2×C32#45411yescharacteristic
304C2×Q8—61no—
305C2×Q8—91no—
306C2×Q8—182no—
307C2×Q8—181no—
308C2×Q8—362no—
309C2×Q8—362no—
310C2×D4#62611yescharacteristic
311C22×C4—21no—
312C22×C4—182no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—92no—
319C4⋊C4—91no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4#62611yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—182no—
326C42—181no—
327C42C2×D3211yescharacteristic
328C22×C3—24no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3#88211yescharacteristic
339C22×C3#93711yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—42no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—241no—
351C3×C4C2×Dic1211yescharacteristic
352C3×C4#90911yescharacteristic
353C3×C4#91111yescharacteristic
354C3×C4D3×SD1611yescharacteristic
355C3×C4D3×SD1611yescharacteristic
356C3×C4#91411yescharacteristic
357C3×C4C2×#21611yescharacteristic
358C3×C4#95111yescharacteristic
359Dic3—64no—
360Dic3—62no—
361Dic3—62no—
362Dic3—81no—
363Dic3—124no—
364Dic3—122no—
365Dic3—122no—
366Dic3—121no—
367Dic3—122no—
368Dic3—121no—
369C32#163711yescharacteristic, complemented, Sylow
370C23—21no—
371Q8—92no—
372Q8—122no—
373Q8—181no—
374Q8—364no—
375Q8—361no—
376Q8—361no—
377D4—21no—
378D4#371912yes—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—121no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4—182no—
386C2×C4—364no—
387C2×C4C2×#62611yescharacteristic
388C2×C4#381111yescharacteristic
389C2×C4#381111yescharacteristic
390C8—121no—
391C8—121no—
392C8—121no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—44no—
397C2×C3—42no—
398C2×C3—42no—
399C2×C3#473911yescharacteristic
400C2×C3#477611yescharacteristic
401C2×C3#482711yescharacteristic
402C2×C3#505011yescharacteristic
403C2×C3#516911yescharacteristic
404C2×C3#520111yescharacteristic
405C22—22no—
406C22—41no—
407C22—41no—
408C22#6398111yescharacteristic
409C4—21no—
410C4—41no—
411C4—182no—
412C4—241no—
413C4—361no—
414C4—362no—
415C4#6383111yescharacteristic
416C4C2×#371911yescharacteristic
417C4#6393011yescharacteristic
418C4#6393711yescharacteristic
419C3—21no—
420C3#6818911yescharacteristic, complemented
421C3#7114211yescharacteristic, complemented
422C2—42no—
423C2#1059119011yescharacteristic
424C2#1059146711yescharacteristic
425C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1637
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
3. #10590287C2semidirect
4. #10590284C2semidirect
6. #10589094C2semidirect
7. #10589085C2semidirect
369. C32#1637semidirect
420. C3#68189semidirect
421. C3#71142semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#50082
#105902872
#105902842
C3×D4⋊(C3⋊C8)2
#105890942
#105890852
#711423
#681893