Finite Group Databasebeta

← #11775723

Subgroups — #11775723

Order 1152.

539 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592406C211yesmaximal, characteristic, complemented
3#10590322C211yesmaximal, characteristic, complemented
4C3×#4465C211yesmaximal, characteristic, complemented
5C3×#4464C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#68361—31nomaximal
9#68341—31nomaximal
10C2×#3743—21no—
11C42×C3⋊D3C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63916C411yescharacteristic
15#63898C411yescharacteristic
16#63881—21no—
17#63878—21no—
18#63871C411yescharacteristic
19#63862—21no—
20#63853—21no—
21#63843C411yescharacteristic
22C2×#3710—21no—
23C32×#97C2211yescharacteristic
24C8×C3⋊Dic3—21no—
25#63630C2211yescharacteristic
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28#63555—21no—
29#5691—31no—
30#5680—31no—
31#4707—31no—
32#4707—31no—
33#4707—61no—
34D3×#97—31no—
35D3×#97—31no—
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—
57#3743—24no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#3710—24no—
73#1524—91noSylow
74C3×#125—31no—
75C3×#124—31no—
76#946—31no—
77Q8×Dic3—31no—
78#938—31no—
79D4×Dic3—31no—
80C2×ΓL(1,𝔽25)—61no—
81C2×ΓL(1,𝔽25)—61no—
82C2×ΓL(1,𝔽25)—62no—
83C2×D3×C8—61no—
84C2×D3×C8—61no—
85#898—61no—
86#897—31no—
87#895—31no—
88#894—61no—
89#893—31no—
90#893—61no—
91#892—61no—
92#887—31no—
93#883—61no—
94#67⋊C4—61no—
95#879—61no—
96#877—61no—
97#875C2×D311yescharacteristic
98C42×D3—31no—
99C42×D3—31no—
100C42×D3—61no—
101#870C2×D311yescharacteristic
102C3×#97—21no—
103C3×#97—31no—
104C3×#97—31no—
105C3×#97C2×D311yescharacteristic
106C3×#97C2×D311yescharacteristic
107#815—61no—
108#815—61no—
109C8×Dic3—61no—
110C8×Dic3—61no—
111C8×Dic3—62no—
112#803—31no—
113#803—31no—
114#803—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3⋊D3C22⋊C411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C3×D12—41no—
132C3×Dic6—41no—
133#626—42no—
134D3×Dic3—42no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—22no—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—22no—
139#529—91no—
140C4×M16—91no—
141C2×#97—91no—
142#330—31no—
143#330—91no—
144#329—31no—
145#329—91no—
146C2×C3×Q8—31no—
147C2×C3×D4—31no—
148C2×#67—61no—
149C22×Dic3—61no—
150C2×D12—61no—
151C2×D12C4×D311yescharacteristic
152C2×C4×D3—31no—
153C2×C4×D3—31no—
154C2×C4×D3—31no—
155C2×C4×D3—31no—
156C2×C4×D3—31no—
157C2×C4×D3—31no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×Dic6C4×D311yescharacteristic
163C2×C3×C8—22no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—21no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—61no—
178#217—61no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3C4×D311yescharacteristic
188C4⋊Dic3C4×D311yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—31no—
197C4×Dic3—31no—
198C4×Dic3—31no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209ΓL(1,𝔽25)—64no—
210ΓL(1,𝔽25)—64no—
211ΓL(1,𝔽25)—68no—
212D3×C8—64no—
213D3×C8—64no—
214C22×C32C2×C22⋊C411yescharacteristic
215C2×C3⋊D3—21no—
216C2×C3⋊D3—21no—
217C2×C3⋊D3#10412yes—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3#10412yes—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C2×M16—181no—
231C22×C8—181no—
232#126—181no—
233#125—31no—
234#124—31no—
235#123—181no—
236C22⋊Q8—91no—
237#121—91no—
238C4×Q8—91no—
239C4×D4—91no—
240C4×D4—181no—
241#117—181no—
242C2×C42—91no—
243#97—31no—
244#97—31no—
245#97—91no—
246#97—181no—
247#97D3211yescharacteristic
248C4×C8—181no—
249C23×C3—61no—
250C22×D3—21no—
251C22×D3—31no—
252C22×D3—31no—
253C22×D3—61no—
254C3×Q8—121no—
255C3×D4—121no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×C4×D311yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268#67—122no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—31no—
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—31no—
276C2×Dic3—31no—
277C2×Dic3—31no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—122no—
282D12—41no—
283D12—122no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—64no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—121no—
292C4×D3—121no—
293C4×D3—122no—
294Dic6—41no—
295C3×C8—24no—
296C3×C8—22no—
297C3×C8—22no—
298C3×C8—62no—
299C3×C8—62no—
300C3⋊C8—22no—
301C3⋊C8—22no—
302C3⋊C8—64no—
303C3⋊C8—62no—
304C3⋊C8—62no—
305C2×C32#41311yescharacteristic
306C2×C32C2×#10411yescharacteristic
307C2×C32C2×#10411yescharacteristic
308C3⋊D3—22no—
309C3×D3—81no—
310C2×Q8—31no—
311C2×D4—31no—
312C2×D4—181no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—181no—
317M16—184no—
318C2×C8—21no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—184no—
322C2×C8—181no—
323C4⋊C4—31no—
324C4⋊C4—31no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C22⋊C4—61no—
330C22⋊C4—61no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C42—91no—
335C42—91no—
336C42—91no—
337C42—181no—
338C42C2×D3211yescharacteristic
339C22×C3—21no—
340C22×C3—121no—
341C22×C3—121no—
342C22×C3—121no—
343C22×C3D3×C22⋊C411yescharacteristic
344C22×C3D3×C22⋊C411yescharacteristic
345C2×D3—32no—
346C2×D3—32no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—62no—
351C2×D3—61no—
352C2×D3—61no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—121no—
356C2×D3—121no—
357C3×C4—22no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—121no—
369Dic3—32no—
370Dic3—32no—
371Dic3—41no—
372Dic3—41no—
373Dic3—41no—
374Dic3—62no—
375Dic3—62no—
376Dic3—62no—
377Dic3—61no—
378Dic3—61no—
379Dic3—61no—
380Dic3—61no—
381C32#152411yescharacteristic, complemented, Sylow
382C23—61no—
383C23—91no—
384Q8—121no—
385D4—121no—
386D4—362no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—91no—
391C2×C4—91no—
392C2×C4—91no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—361no—
396C2×C4—362no—
397C2×C4C4×D3211yescharacteristic
398C2×C4#380211yescharacteristic
399C2×C4#381111yescharacteristic
400C8—22no—
401C8—62no—
402C8—62no—
403C8—182no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—241no—
408C2×C3#474511yescharacteristic
409C2×C3#475111yescharacteristic
410C2×C3D3×#10411yescharacteristic
411C2×C3D3×#10411yescharacteristic
412C2×C3D3×#10411yescharacteristic
413C2×C3D3×#10411yescharacteristic
414D3—62no—
415D3—62no—
416D3—81no—
417D3—122no—
418C22—92no—
419C22—121no—
420C22—121no—
421C22—121no—
422C22—181no—
423C22—181no—
424C22#6392111yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—92no—
429C4—121no—
430C4—121no—
431C4—121no—
432C4—181no—
433C4—181no—
434C3—21no—
435C3#6834111yescharacteristic, complemented
436C3#6836111yescharacteristic, complemented
437C2—182no—
438C2—241no—
439C2#1059039311yescharacteristic
440C2#1059100811yescharacteristic
441C2#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#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. #10592406C2semidirect
3. #10590322C2semidirect
4. C3×#4465C2semidirect
5. C3×#4464C2semidirect
6. #10589088C2semidirect
7. #10589086C2semidirect
41. #4465D3semidirect
43. #4464D3semidirect
381. C32#1524semidirect
435. C3#68341semidirect
436. C3#68361semidirect

Maximal subgroups

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

subgroupindex
#105939432
#105924062
#105903222
C3×#44652
C3×#44642
#105890882
#105890862
#683613
#683413