Finite Group Databasebeta

← #11775722

Subgroups — #11775722

Order 1152.

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

normal subgroups only

This group has 503 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
1#10593976C211yesmaximal, characteristic
2C3×#4707C211yesmaximal, characteristic, complemented
3D3×#803C211yesmaximal, characteristic, complemented
4#10589330C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic, complemented
8#69858—31nomaximal
9#68361—31nomaximal
10#64084C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C42×D3C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63909C411yescharacteristic
15#63904—21no—
16#63894C411yescharacteristic
17#63868—21no—
18#63857C411yescharacteristic
19#63850—21no—
20#63844C411yescharacteristic
21#63836—21no—
22C2×D3×C3⋊C8—21no—
23C32×#97C2211yescharacteristic
24#63630C2211yescharacteristic
25C3×C8×Dic3—21no—
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28#63554—21no—
29#5691—31no—
30#5479—31no—
31C3×C4×M16—31no—
32C2×#803—31no—
33#4707D311yescharacteristic, complemented
34D3×#97—31no—
35C3×#330—31no—
36#4543—31no—
37#4465—31no—
38#4465D311yescharacteristic, complemented
39#4464—31no—
40#4464—31no—
41#4464—31no—
42#4464—31no—
43#4464—61no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×#634C2×C411yescharacteristic
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×#626—21no—
50C2×#624—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54#3752—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C3×ΓL(1,𝔽25)—24no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72D3×C3⋊C8—24no—
73#1524—91noSylow
74C2×C3×M16—61no—
75C3×#125—31no—
76C2×C3×C42—31no—
77#930—31no—
78#929—61no—
79C4×#67—61no—
80#924—31no—
81C22×C3⋊C8—61no—
82C2×ΓL(1,𝔽25)—21no—
83C2×D3×C8—61no—
84#898—61no—
85#897—31no—
86#895—31no—
87#894—61no—
88#893—31no—
89#893—61no—
90#892—61no—
91#887—31no—
92#876—61no—
93#875—31no—
94#875—31no—
95#875—61no—
96C4×D12—31no—
97#872—61no—
98C42×D3C2×D311yescharacteristic
99#870C2×D311yescharacteristic
100C4×Dic6—31no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97—31no—
104C3×#97C2×D311yescharacteristic
105C3×#97C2×D311yescharacteristic
106C3×C4×C8—61no—
107#815—61no—
108C8×Dic3—21no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C4⋊(C3⋊D3)—41no—
122#634—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×C4×D3—22no—
129C3×C4×D3—22no—
130C3×C4×D3—41no—
131#626—42no—
132#624—42no—
133C32×C8—22no—
134C3⋊(C3⋊C8)—22no—
135C3×C3⋊C8—22no—
136C3×C3⋊C8—22no—
137#529—91no—
138C4×M16—31no—
139C2×#97—91no—
140#330—31no—
141#330—91no—
142#329—91no—
143#329—91no—
144C22×C3×C4—31no—
145C22×C3×C4—31no—
146C22×C3×C4—31no—
147C2×#67—61no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×D12—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3C4×D311yescharacteristic
155C2×C4×D3D1211yescharacteristic
156C2×C4×D3#6711yescharacteristic
157C2×Dic6—31no—
158C2×Dic6—31no—
159C2×Dic6—61no—
160C3×M16—64no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C42—21no—
171C3×C42—31no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—121no—
187(C2×D3)⋊C4—121no—
188C4⋊Dic3—61no—
189C4⋊Dic3C4×D311yescharacteristic
190C4⋊Dic3C4×D311yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3C4×D311yescharacteristic
199C4×Dic3D1211yescharacteristic
200C4×Dic3#6711yescharacteristic
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—121no—
207ΓL(1,𝔽25)—24no—
208D3×C8—64no—
209C22×C32C2×C22⋊C411yescharacteristic
210C2×C3⋊D3—41no—
211C2×C3⋊D3—41no—
212C2×C3⋊D3—41no—
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C2×C3×D3#10412yes—
216C32×C4—21no—
217C32×C4—21no—
218C32×C4—21no—
219C3⋊Dic3—41no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3#10412yes—
225C2×M16—61no—
226C22×C8—181no—
227#126—181no—
228#125—31no—
229#124—91no—
230#123—181no—
231C22⋊Q8—91no—
232#121—91no—
233C4×Q8—91no—
234C4×D4—91no—
235C4×D4—181no—
236#117—181no—
237C2×C42—31no—
238#97—31no—
239#97—31no—
240#97—91no—
241#97—181no—
242#97D3211yescharacteristic
243C4×C8—61no—
244C23×C3—31no—
245C22×D3—61no—
246C22×D3—61no—
247C22×D3—121no—
248C22×D3(C2×D3)⋊C411yescharacteristic
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—31no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4C2×C4×D311yescharacteristic
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—122no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—121no—
272C2×Dic3(C2×D3)⋊C411yescharacteristic
273C2×Dic3(C2×D3)⋊C411yescharacteristic
274C2×Dic3(C2×D3)⋊C411yescharacteristic
275D12—121no—
276D12—121no—
277D12—122no—
278D12—241no—
279C4×D3—22no—
280C4×D3—22no—
281C4×D3—41no—
282C4×D3—122no—
283C4×D3—122no—
284Dic6—121no—
285Dic6—121no—
286Dic6—241no—
287C3×C8—22no—
288C3×C8—22no—
289C3×C8—42no—
290C3×C8—62no—
291C3×C8—62no—
292C3⋊C8—22no—
293C3⋊C8—22no—
294C3⋊C8—62no—
295C3⋊C8—62no—
296C3⋊C8—122no—
297C2×C32#41311yescharacteristic
298C2×C32C2×#10411yescharacteristic
299C2×C32C2×#10411yescharacteristic
300C3⋊D3—81no—
301C3×D3—22no—
302C2×Q8—91no—
303C2×D4—91no—
304C2×D4—181no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—181no—
309M16—64no—
310C2×C8—21no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—184no—
314C2×C8—181no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C22⋊C4—181no—
322C22⋊C4—181no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C42—31no—
327C42—31no—
328C42—31no—
329C42—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—32no—
333C22×C3—61no—
334C22×C3—61no—
335C22×C3D3×C22⋊C411yescharacteristic
336C22×C3C2×(C2×D3)⋊C411yescharacteristic
337C2×D3—21no—
338C2×D3—21no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—241no—
346C2×D3—241no—
347C2×D3—241no—
348C2×D3#80512yes—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—32no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—61no—
360C3×C4—61no—
361C3×C4—121no—
362C3×C4—121no—
363Dic3—21no—
364Dic3—21no—
365Dic3—41no—
366Dic3—41no—
367Dic3—121no—
368Dic3—121no—
369Dic3—241no—
370Dic3#82512yes—
371C32#152411yescharacteristic, complemented, Sylow
372C23—31no—
373C23—181no—
374Q8—361no—
375D4—361no—
376D4—362no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—121no—
385C2×C4—181no—
386C2×C4—362no—
387C2×C4C4×D3211yescharacteristic
388C2×C4D3×D1211yescharacteristic
389C2×C4D3×#6711yescharacteristic
390C8—22no—
391C8—62no—
392C8—62no—
393C8—182no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—62no—
398C2×C3#475111yescharacteristic
399C2×C3D3×#10411yescharacteristic
400C2×C3D3×#10411yescharacteristic
401C2×C3C2×#80511yescharacteristic
402C2×C3#513211yescharacteristic
403C2×C3C2×#82511yescharacteristic
404D3—22no—
405D3—241no—
406D3—241no—
407D3—481no—
408C22—32no—
409C22—61no—
410C22—61no—
411C22—361no—
412C22—361no—
413C22—361no—
414C22D3×(C2×D3)⋊C411yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—32no—
419C4—61no—
420C4—61no—
421C4—121no—
422C4—121no—
423C4—361no—
424C3—21no—
425C3#6836111yescharacteristic, complemented
426C3#6985811yescharacteristic, complemented
427C2—62no—
428C2—721no—
429C2D3×#80511yescharacteristic
430C2D3×#82511yescharacteristic
431C2#1059100711yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radical#63909C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#4707C2semidirect
3. D3×#803C2semidirect
4. #10589330C2semidirect
5. C3×#4465C2semidirect
6. #10589088C2semidirect
7. #10589087C2semidirect
33. #4707D3semidirect
38. #4465D3semidirect
371. C32#1524semidirect
425. C3#68361semidirect
426. C3#69858semidirect

Maximal subgroups

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

subgroupindex
#105939762
C3×#47072
D3×#8032
#105893302
C3×#44652
#105890882
#105890872
#698583
#683613