Finite Group Databasebeta

← #11775854

Subgroups — #11775854

Order 1152.

487 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 487 conjugacy classes of subgroups — too many to draw. Only its 84 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#10593943C211yesmaximal, characteristic
2#10592404C211yesmaximal, characteristic, complemented
3#10590247C211yesmaximal, characteristic, complemented
4C3×#4465C211yesmaximal, characteristic, complemented
5C3×#4464C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#68364—31nomaximal
9#68344—31nomaximal
10C42×C3⋊D3C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#870C2211yescharacteristic
13#63916C411yescharacteristic
14#63898C411yescharacteristic
15#63881—21no—
16#63878—21no—
17#63871C411yescharacteristic
18#63862—21no—
19#63853—21no—
20#63843C411yescharacteristic
21C2×#3712—21no—
22C32×#97C2211yescharacteristic
23#63647—21no—
24#63641—21no—
25#63630C2211yescharacteristic
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28#63553—21no—
29#5691—31no—
30#5680—31no—
31#4707—31no—
32#4707—31no—
33#4705—31no—
34#4705—31no—
35#4705—61no—
36C3×#330—31no—
37C3×#329—31no—
38#4543—31no—
39#4540—31no—
40#4465—31no—
41#4465D311yescharacteristic, complemented
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×Dic6C2×C411yescharacteristic
49C2×#626—21no—
50C2×D3×Dic3—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71#3712—24no—
72#1529—91noSylow
73C3×#125—31no—
74C3×#124—31no—
75#946—31no—
76Q8×Dic3—31no—
77#938—31no—
78D4×Dic3—31no—
79C2×ΓL(1,𝔽25)—61no—
80C2×ΓL(1,𝔽25)—61no—
81#898—61no—
82#897—31no—
83#895—31no—
84#894—61no—
85#893—31no—
86#893—61no—
87#892—61no—
88#887—31no—
89#883—61no—
90#67⋊C4—61no—
91#879—61no—
92#877—61no—
93#875C2×D311yescharacteristic
94C42×D3—31no—
95C42×D3—31no—
96C42×D3—61no—
97#870C2×D311yescharacteristic
98C3×#97—21no—
99C3×#97—31no—
100C3×#97—31no—
101C3×#97C2×D311yescharacteristic
102C3×#97C2×D311yescharacteristic
103(C2×D3)⋊C8—61no—
104(C2×D3)⋊C8—61no—
105(C2×D3)⋊C8—62no—
106Dic3⋊C8—61no—
107Dic3⋊C8—61no—
108Dic3⋊C8—62no—
109C8×Dic3—61no—
110C8×Dic3—61no—
111#803—31no—
112#803—31no—
113#803—61no—
114#803C2×D311yescharacteristic
115#803C2×D311yescharacteristic
116C22×C3⋊D3C22⋊C411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C4×C3⋊D3—22no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C3×D12—41no—
131C3×Dic6—41no—
132#626—42no—
133D3×Dic3—42no—
134C32×C8—41no—
135C3⋊(C3⋊C8)—41no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—22no—
138#529—91no—
139#432—91no—
140C4×M16—91no—
141#330—31no—
142#330—91no—
143#329—31no—
144#329—91no—
145C2×C3×Q8—31no—
146C2×C3×D4—31no—
147C2×#67—61no—
148C22×Dic3—61no—
149C2×D12—61no—
150C2×D12C4×D311yescharacteristic
151C2×C4×D3—31no—
152C2×C4×D3—31no—
153C2×C4×D3—31no—
154C2×C4×D3—31no—
155C2×C4×D3—31no—
156C2×C4×D3—31no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×Dic6C4×D311yescharacteristic
162C2×C3×C8—22no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—21no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—61no—
177#217—61no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3C4×D311yescharacteristic
187C4⋊Dic3C4×D311yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192C4×Dic3—31no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—31no—
197C4×Dic3—31no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208ΓL(1,𝔽25)—64no—
209ΓL(1,𝔽25)—64no—
210C22×C32C2×C22⋊C411yescharacteristic
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3—21no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3#10412yes—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C2×M16—181no—
227#126—181no—
228#125—31no—
229#124—31no—
230#123—181no—
231C22⋊Q8—91no—
232#121—91no—
233C4×Q8—91no—
234C4×D4—91no—
235C4×D4—181no—
236#117—181no—
237C2×C42—91no—
238C4⋊C8—181no—
239C22⋊C8—181no—
240#97—31no—
241#97—31no—
242#97—91no—
243#97D3211yescharacteristic
244C4×C8—181no—
245C23×C3—61no—
246C22×D3—21no—
247C22×D3—31no—
248C22×D3—31no—
249C22×D3—61no—
250C3×Q8—121no—
251C3×D4—121no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4C2×C4×D311yescharacteristic
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264#67—122no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—31no—
269C2×Dic3—31no—
270C2×Dic3—31no—
271C2×Dic3—31no—
272C2×Dic3—31no—
273C2×Dic3—31no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—122no—
278D12—41no—
279D12—122no—
280C4×D3—62no—
281C4×D3—62no—
282C4×D3—122no—
283C4×D3—122no—
284C4×D3—121no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—121no—
288C4×D3—122no—
289C4×D3—122no—
290Dic6—41no—
291C3×C8—42no—
292C3×C8—41no—
293C3×C8—41no—
294C3×C8—62no—
295C3×C8—62no—
296C3⋊C8—22no—
297C3⋊C8—22no—
298C3⋊C8—122no—
299C3⋊C8—121no—
300C3⋊C8—121no—
301C2×C32#41311yescharacteristic
302C2×C32C2×#10411yescharacteristic
303C2×C32#42111yescharacteristic
304C3⋊D3—41no—
305C3×D3—81no—
306C2×Q8—31no—
307C2×D4—31no—
308C2×D4—181no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—181no—
313M16—184no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C22⋊C4—61no—
325C22⋊C4—61no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—181no—
333C42C2×D3211yescharacteristic
334C22×C3—21no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3—121no—
338C22×C3D3×C22⋊C411yescharacteristic
339C22×C3D3×C22⋊C411yescharacteristic
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—62no—
344C2×D3—61no—
345C2×D3—61no—
346C2×D3—61no—
347C2×D3—61no—
348C2×D3—61no—
349C2×D3—61no—
350C2×D3—121no—
351C2×D3—121no—
352C3×C4—22no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—121no—
364Dic3—32no—
365Dic3—32no—
366Dic3—41no—
367Dic3—41no—
368Dic3—41no—
369Dic3—62no—
370Dic3—61no—
371Dic3—61no—
372Dic3—61no—
373Dic3—61no—
374Dic3—121no—
375Dic3—121no—
376C32#152911yescharacteristic, complemented, Sylow
377C23—61no—
378C23—91no—
379Q8—121no—
380D4—121no—
381D4—362no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—91no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—182no—
389C2×C4—361no—
390C2×C4—361no—
391C2×C4—362no—
392C2×C4C4×D3211yescharacteristic
393C2×C4#380211yescharacteristic
394C2×C4#381111yescharacteristic
395C8—41no—
396C8—62no—
397C8—62no—
398C8—361no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—241no—
403C2×C3#474511yescharacteristic
404C2×C3#475111yescharacteristic
405C2×C3D3×#10411yescharacteristic
406C2×C3D3×#10411yescharacteristic
407C2×C3#482111yescharacteristic
408C2×C3#482111yescharacteristic
409D3—81no—
410D3—122no—
411D3—121no—
412D3—121no—
413C22—121no—
414C22—121no—
415C22—121no—
416C22—181no—
417C22—181no—
418C22—181no—
419C22#6392111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—92no—
424C4—121no—
425C4—121no—
426C4—121no—
427C4—181no—
428C4—181no—
429C3—21no—
430C3#6834411yescharacteristic, complemented
431C3#6836411yescharacteristic, complemented
432C2—241no—
433C2—361no—
434C2#1059039411yescharacteristic
435C2#1059100811yescharacteristic
436C2#1059101011yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radical#63916C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1529
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. #10592404C2semidirect
3. #10590247C2semidirect
4. C3×#4465C2semidirect
5. C3×#4464C2semidirect
6. #10589088C2semidirect
7. #10589086C2semidirect
41. #4465D3semidirect
43. #4464D3semidirect
376. C32#1529semidirect
430. C3#68344semidirect
431. C3#68364semidirect

Maximal subgroups

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

subgroupindex
#105939432
#105924042
#105902472
C3×#44652
C3×#44642
#105890882
#105890862
#683643
#683443