Finite Group Databasebeta

← #11780121

Subgroups — #11780121

Order 1152.

534 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593896C211yesmaximal, characteristic
2#10592545C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590311C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68436—31nomaximal
9#68208—31nomaximal
10C2×#3796—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63909—21no—
16#63890—22no—
17D3×C4⋊Dic3—21no—
18#63871—21no—
19C2×#3716—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63648—21no—
22#63645—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63567—21no—
27#5726—31no—
28#5555—31no—
29#5078—31no—
30#5019—31no—
31#4846—31no—
32#4846—31no—
33#4846—61no—
34#4841—31no—
35#4682—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4483—31no—
40#4483D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×#626—22no—
49C2×D3×Dic3—22no—
50#3796—42no—
51#3796—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65#3722—22no—
66#3716—42no—
67#1647—91noSylow
68C2×#239—61no—
69C2×#237—61no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—31no—
72#946—61no—
73C2×#214—61no—
74#930—61no—
75C2×C4⋊Dic3—61no—
76C2×#204—61no—
77#897—61no—
78#895—61no—
79#894—62no—
80D3×C4⋊C4—61no—
81#886—62no—
82C4×D12—31no—
83C4×D12—31no—
84C4×D12—61no—
85C4×D12C2×D311yescharacteristic
86#869—31no—
87#869—31no—
88#869—61no—
89#869C2×D311yescharacteristic
90C3×C4⋊C8—21no—
91C3×C4⋊C8—31no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4×C8—31no—
95#821—61no—
96#821—61no—
97#821—62no—
98#818—61no—
99#818—61no—
100#818—62no—
101#818—62no—
102#816—61no—
103#810—61no—
104#807—62no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3×D3—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—41no—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—21no—
116C4×C3⋊D3—41no—
117C4×C3⋊D3—41no—
118#634—41no—
119#634—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C3×D12—21no—
123C3×D12D812yes—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128#626—44no—
129D3×Dic3—44no—
130C32×C8—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#547—91no—
134#500—91no—
135#474—91no—
136#461—91no—
137#332—31no—
138D4⋊C8—31no—
139D4⋊C8—91no—
140C2×C3×Q8—61no—
141C2×C3×D4—31no—
142C22×C3×C4—61no—
143C2×#67—62no—
144C22×Dic3—62no—
145#239—122no—
146#239—122no—
147#237—122no—
148#237—122no—
149C2×D12—31no—
150C2×D12—31no—
151C2×D12—61no—
152C2×D12—62no—
153C2×D12D1211yescharacteristic
154C2×C4×D3—21no—
155C2×C4×D3—62no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—121no—
159C2×Dic6—21no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—121no—
163C2×C3×C8—22no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—32no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C42—21no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#214—122no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—121no—
182C4⋊Dic3—21no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—61no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—121no—
193C4⋊Dic3D1211yescharacteristic
194C4⋊Dic3D1212yes—
195Dic3⋊C4—62no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198#204—122no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—41no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C2×C3×D3—22no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C32×C4—21no—
207C32×C4C2×D811yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4#13711yescharacteristic
211C3⋊Dic3—41no—
212C3⋊Dic3—81no—
213C3×Dic3—42no—
214C3×Dic3—41no—
215C2×#41—181no—
216C2×SD16—181no—
217C4⋊Q8—31no—
218C4⋊Q8—91no—
219#123—182no—
220C22⋊Q8—181no—
221#121—181no—
222C4×D4—31no—
223C4×D4—91no—
224C2×C4⋊C4—181no—
225#107—182no—
226#107—181no—
227C4⋊C8—31no—
228C4⋊C8D3211yescharacteristic
229#103—181no—
230#102—181no—
231C4×C8—31no—
232C23×C3—61no—
233C22×D3—21no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—121no—
237C3×Q8—121no—
238C3×Q8—121no—
239C3×D4—32no—
240C3×D4—61no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—62no—
245C2×C3×C4—61no—
246C2×C3×C4—121no—
247C2×C3×C4—121no—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254#67—124no—
255C2×Dic3—21no—
256C2×Dic3—22no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—121no—
260C2×Dic3—124no—
261C2×Dic3—122no—
262C2×Dic3—121no—
263C2×Dic3—121no—
264D12—21no—
265D12—62no—
266D12—61no—
267D12—61no—
268D12—61no—
269D12—61no—
270D12—121no—
271D12—124no—
272D12D2412yes—
273C4×D3—41no—
274C4×D3—41no—
275C4×D3—124no—
276C4×D3—121no—
277C4×D3—121no—
278C4×D3—121no—
279C4×D3—121no—
280C4×D3—241no—
281C4×D3—241no—
282Dic6—41no—
283Dic6—41no—
284Dic6—121no—
285Dic6—121no—
286Dic6—121no—
287Dic6—121no—
288Dic6—241no—
289Dic6—241no—
290C3×C8—42no—
291C3×C8—41no—
292C3×C8—41no—
293C3×C8—62no—
294C3×C8—121no—
295C3⋊C8—22no—
296C3⋊C8—41no—
297C2×C32#44711yescharacteristic
298C2×C32#45211yescharacteristic
299C2×C32#45611yescharacteristic
300C3⋊D3—81no—
301C3×D3—42no—
302#41—362no—
303#41—362no—
304C2×Q8—61no—
305C2×Q8—181no—
306C2×D4—31no—
307C2×D4—91no—
308C2×D4—182no—
309C22×C4—61no—
310C22×C4—182no—
311C22×C4—181no—
312SD16—362no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—61no—
316C4⋊C4—31no—
317C4⋊C4—32no—
318C4⋊C4—61no—
319C4⋊C4—91no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C22⋊C4—61no—
324C22⋊C4—182no—
325C22⋊C4—181no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—62no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3#88211yescharacteristic
332C22×C3#88211yescharacteristic
333C2×D3—22no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—122no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—241no—
344C2×D3—241no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—122no—
353C3×C4—121no—
354C3×C4C2×D2411yescharacteristic
355C3×C4#90811yescharacteristic
356C3×C4D3×D811yescharacteristic
357C3×C4#91211yescharacteristic
358C3×C4#91411yescharacteristic
359C3×C4#91511yescharacteristic
360C3×C4#91611yescharacteristic
361C3×C4#91811yescharacteristic
362Dic3—42no—
363Dic3—41no—
364Dic3—121no—
365Dic3—121no—
366Dic3—241no—
367Dic3—242no—
368Dic3—241no—
369Dic3—241no—
370C32#164711yescharacteristic, complemented, Sylow
371C23—61no—
372C23—181no—
373Q8—121no—
374Q8—121no—
375Q8—361no—
376Q8—361no—
377D4—32no—
378D4—61no—
379D4—181no—
380D4—181no—
381D4—364no—
382C2×C4—61no—
383C2×C4—62no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—181no—
387C2×C4—364no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4—361no—
391C2×C4D3×D1211yescharacteristic
392C2×C4D3×D1211yescharacteristic
393C2×C4#381111yescharacteristic
394C8—41no—
395C8—62no—
396C8—121no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—122no—
401C2×C3#473211yescharacteristic
402C2×C3#475211yescharacteristic
403C2×C3#477311yescharacteristic
404C2×C3#478311yescharacteristic
405C2×C3#480811yescharacteristic
406C2×C3#482611yescharacteristic
407D3—42no—
408D3—242no—
409D3—241no—
410D3—241no—
411C22—62no—
412C22—121no—
413C22—121no—
414C22—361no—
415C22—361no—
416C22—361no—
417C22#6392311yescharacteristic
418C4—21no—
419C4—121no—
420C4—122no—
421C4—361no—
422C4—721no—
423C4D3×D2411yescharacteristic
424C4#6379411yescharacteristic
425C4#6393611yescharacteristic
426C4#6395111yescharacteristic
427C3—21no—
428C3#6820811yescharacteristic, complemented
429C3#6843611yescharacteristic, complemented
430C2—122no—
431C2—721no—
432C2#1059061811yescharacteristic
433C2#1059094711yescharacteristic
434C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593896C2
hypercenterC4⋊C8D32
hypocenterC32#1647
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592545C2semidirect
3. #10590365C2semidirect
4. #10590311C2semidirect
5. C3×#4486C2semidirect
6. C3×#4483C2semidirect
7. #10589082C2semidirect
38. #4486D3semidirect
40. #4483D3semidirect
370. C32#1647semidirect
428. C3#68208semidirect
429. C3#68436semidirect

Maximal subgroups

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

subgroupindex
#105938962
#105925452
#105903652
#105903112
C3×#44862
C3×#44832
#105890822
#684363
#682083