Finite Group Databasebeta

← #11780209

Subgroups — #11780209

Order 1152.

509 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593903C211yesmaximal, characteristic
2C3×#4849C211yesmaximal, characteristic, complemented
3#10590313C211yesmaximal, characteristic
4#10590312C211yesmaximal, characteristic, complemented
5#10589349C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71065—31nomaximal
9#68461—31nomaximal
10C2×#3797—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×Dic12—21no—
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63918—21no—
17#63895—22no—
18#63894—21no—
19#63871—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#816—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63576—22no—
25#63575—21no—
26#63564—21no—
27#5727—31no—
28Q8×D12—31no—
29C3×#462—31no—
30#5087—31no—
31#5078—31no—
32#5078—31no—
33#4849D311yescharacteristic, complemented
34#4846—31no—
35C3×#332—31no—
36#4535—31no—
37#4484—31no—
38#4483—31no—
39#4483—31no—
40#4483—61no—
41#4482D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×#627—22no—
48C2×#624—22no—
49#3797—42no—
50#3797—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D412yes—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C3×Dic12—42no—
65Dic3⋊Dic3—22no—
66#3722—22no—
67#1649—91noSylow
68C2×D3×Q8—61no—
69C2×D3×Q8—61no—
70C2×C3×Q16—61no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—31no—
73C3×C4×Q8—31no—
74#946—61no—
75C2×Dic12—21no—
76#897—61no—
77#897—62no—
78#896—62no—
79#893—61no—
80#888—61no—
81C4×D12—31no—
82C4×D12—31no—
83C4×D12—61no—
84C4×D12—61no—
85#869—61no—
86#869C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×#103—61no—
94#821—61no—
95#818—61no—
96#816—21no—
97#809—61no—
98#807—61no—
99#807—62no—
100#807—62no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3⋊D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C4⋊(C3⋊D3)—21no—
111C4⋊(C3⋊D3)Q1612yescomplemented
112C4×C3⋊D3—41no—
113C4×C3⋊D3—41no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C3×Dic6—21no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6D812yes—
124#627—44no—
125#624—44no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—41no—
129D4×Q8—91no—
130#500—91no—
131#474—91no—
132#462—31no—
133#332—31no—
134Q8⋊C8—91no—
135D4⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×Q8—61no—
138C2×C3×Q8—61no—
139D3×Q8—122no—
140D3×Q8—122no—
141D3×Q8—122no—
142D3×Q8—122no—
143C2×D12—31no—
144C2×D12—31no—
145C2×D12—61no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—121no—
151C2×Dic6—21no—
152C2×Dic6—21no—
153C2×Dic6—62no—
154C2×Dic6—62no—
155C2×Dic6#6711yescharacteristic
156C3×Q16—122no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—41no—
160C2×C3×C8—61no—
161C3×C4⋊C4—32no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C42—21no—
168C3×C42—61no—
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—121no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—61no—
182C4⋊Dic3—62no—
183C4⋊Dic3D1212yes—
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—62no—
187C4×Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—121no—
192Dic12—42no—
193C22×C32#12011yescharacteristic
194C2×C3⋊D3—22no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—41no—
197C32×C4—21no—
198C32×C4C2×D811yescharacteristic
199C32×C4C2×Q1611yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4#13711yescharacteristic
202C3⋊Dic3—41no—
203C3×Dic3—22no—
204C3×Dic3—42no—
205C3×Dic3—41no—
206C3×Dic3—81no—
207C22×Q8—181no—
208C2×Q16—61no—
209C4⋊Q8—31no—
210C4⋊Q8—31no—
211C4⋊Q8—181no—
212C22⋊Q8—182no—
213C22⋊Q8—181no—
214C4×Q8—31no—
215C4×D4—91no—
216C4×D4—181no—
217#107—182no—
218#107—181no—
219C4⋊C8—31no—
220C4⋊C8D3211yescharacteristic
221#103—61no—
222#102—181no—
223C4×C8—91no—
224C22×D3—61no—
225C22×D3—61no—
226C22×D3—121no—
227C3×Q8—32no—
228C3×Q8—61no—
229C3×Q8—121no—
230C3×Q8—121no—
231C3×Q8—121no—
232C3×Q8—121no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4—121no—
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—22no—
248C2×Dic3—21no—
249C2×Dic3—41no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—121no—
253D12—32no—
254D12—32no—
255D12—62no—
256D12—61no—
257D12—61no—
258D12—121no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—121no—
262C4×D3—121no—
263C4×D3—121no—
264C4×D3—121no—
265C4×D3—241no—
266C4×D3—241no—
267Dic6—21no—
268Dic6—41no—
269Dic6—41no—
270Dic6—41no—
271Dic6—41no—
272Dic6—124no—
273Dic6—124no—
274Dic6#21312yes—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—81no—
278C3×C8—121no—
279C3⋊C8—41no—
280C3⋊C8—62no—
281C3⋊C8—62no—
282C3⋊C8—122no—
283C2×C32#44711yescharacteristic
284C2×C32#45111yescharacteristic
285C2×C32#45611yescharacteristic
286C3⋊D3—42no—
287C2×Q8—31no—
288C2×Q8—61no—
289C2×Q8—61no—
290C2×Q8—182no—
291C2×Q8—362no—
292C2×Q8—362no—
293C2×D4—91no—
294C22×C4—182no—
295C22×C4—181no—
296Q16—122no—
297C2×C8—21no—
298C2×C8—61no—
299C2×C8—181no—
300C4⋊C4—32no—
301C4⋊C4—31no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—91no—
307C4⋊C4—182no—
308C22⋊C4—182no—
309C22⋊C4—181no—
310C42—61no—
311C42C2×D3211yescharacteristic
312C22×C3—21no—
313C22×C3#88211yescharacteristic
314C22×C3#93711yescharacteristic
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—122no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—121no—
322C2×D3—241no—
323C2×D3—241no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—62no—
332C3×C4—121no—
333C3×C4—122no—
334C3×C4—241no—
335C3×C4D3×D811yescharacteristic
336C3×C4#91411yescharacteristic
337C3×C4#91511yescharacteristic
338C3×C4D3×Q1611yescharacteristic
339C3×C4D3×Q1611yescharacteristic
340C3×C4#91811yescharacteristic
341C3×C4C2×#21311yescharacteristic
342C3×C4#94911yescharacteristic
343Dic3—22no—
344Dic3—41no—
345Dic3—42no—
346Dic3—81no—
347Dic3—121no—
348Dic3—121no—
349Dic3—241no—
350C32#164911yescharacteristic, complemented, Sylow
351C23—181no—
352Q8—32no—
353Q8—61no—
354Q8—121no—
355Q8—121no—
356Q8—121no—
357Q8—121no—
358Q8—364no—
359D4—92no—
360D4—181no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—62no—
364C2×C4—121no—
365C2×C4—181no—
366C2×C4—364no—
367C2×C4—361no—
368C2×C4—361no—
369C2×C4D3×D1211yescharacteristic
370C2×C4#380211yescharacteristic
371C2×C4D3×#6711yescharacteristic
372C8—41no—
373C8—121no—
374C8—182no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3#475211yescharacteristic
379C2×C3#477311yescharacteristic
380C2×C3#480911yescharacteristic
381C2×C3#503611yescharacteristic
382C2×C3#518611yescharacteristic
383C2×C3#520511yescharacteristic
384D3—122no—
385D3—122no—
386D3—242no—
387C22—182no—
388C22—361no—
389C22—361no—
390C22#6392211yescharacteristic
391C4—21no—
392C4—62no—
393C4—121no—
394C4—122no—
395C4—241no—
396C4—361no—
397C4#6380211yescharacteristic
398C4#6381111yescharacteristic
399C4D3×#21311yescharacteristic
400C4#6393911yescharacteristic
401C3—21no—
402C3#6846111yescharacteristic, complemented
403C3#7106511yescharacteristic, complemented
404C2—362no—
405C2#1059059511yescharacteristic
406C2#1059095011yescharacteristic
407C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1649
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. C3×#4849C2semidirect
4. #10590312C2semidirect
6. C3×#4482C2semidirect
7. #10589083C2semidirect
33. #4849D3semidirect
41. #4482D3semidirect
111. C4⋊(C3⋊D3)Q16semidirect
350. C32#1649semidirect
402. C3#68461semidirect
403. C3#71065semidirect

Maximal subgroups

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

subgroupindex
#105939032
C3×#48492
#105903132
#105903122
#105893492
C3×#44822
#105890832
#710653
#684613