Finite Group Databasebeta

← #11775302

Subgroups — #11775302

Order 1152.

865 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 865 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C3⋊D3×#121C211yesmaximal, characteristic
2#10591219C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4537C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#68304—32nomaximal
7C2×D4×C3⋊D3—21no—
8C2×D4×C3⋊D3C411yescharacteristic, complemented
9C22×C4×C3⋊D3C2211yescharacteristic
10C32×#121C2211yescharacteristic
11#64148—21no—
12#64147C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14#64104C411yescharacteristic, complemented
15C4⋊C4×C3⋊D3C411yescharacteristic, complemented
16#64093—21no—
17C22⋊C4×C3⋊D3—21no—
18C2×#3722—21no—
19C2×#3712—21no—
20C3×C3⋊#95C2212yescomplemented
21C3×#830C2212yescomplemented
22#63579—21no—
23#63557—21no—
24D3×#121—32no—
25D3×#121—61no—
26#4726—32no—
27#4664—32no—
28C3×#327—32no—
29#4537D312yescomplemented
30#4470—32no—
31#4451—32no—
32C23×C3⋊D3—21no—
33C23×C3⋊D3D411yescharacteristic
34C2×C32×D4—21no—
35C2×C32×D4C2×C411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C2×#638—21no—
38C2×#638—21no—
39C2×#638—21no—
40C22×C3⋊Dic3D411yescharacteristic
41D4×C3⋊D3—42no—
42D4×C3⋊D3—44no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—42no—
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C22×C3×Dic3—22no—
52C32×C4⋊C4C2×C411yescharacteristic
53C32×C22⋊C4—21no—
54#3757—21no—
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C2×C3×C3⋊C8—22no—
60#3722—42no—
61#3712—42no—
62#1510—91noSylow
63C2×D3×D4—32no—
64C2×D3×D4—61no—
65C2×D3×D4—62no—
66C2×D3×D4—62no—
67C22×C4×D3—32no—
68C22×C4×D3—61no—
69C3×#121—21no—
70C3×#121C2×D312yes—
71#939—62no—
72#939—62no—
73#938—32no—
74#938—61no—
75#930—32no—
76#930—61no—
77C2×(C2×D3)⋊C4—62no—
78C2×ΓL(1,𝔽25)—62no—
79#895—32no—
80#895—61no—
81D3×C4⋊C4—32no—
82D3×C4⋊C4—61no—
83#884—62no—
84#884—62no—
85D3×C22⋊C4—62no—
86D3×C22⋊C4—62no—
87C3×C22⋊C8—32no—
88C3×#95—32no—
89C3⋊#95—62no—
90C3⋊#95C2×D312yescomplemented
91#830C2×D312yescomplemented
92(C2×D3)⋊C8—62no—
93C23×C32—21no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—42no—
100C22×C3⋊D3—42no—
101C22×C3⋊D3—42no—
102C22×C3⋊D3C22⋊C411yescharacteristic
103C22×C3⋊D3C22⋊C411yescharacteristic
104C32×D4—41no—
105C32×D4—42no—
106C2×C32×C4—21no—
107C2×C32×C4—41no—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110#638—42no—
111#638—42no—
112#638—42no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3C22⋊C411yescharacteristic
116C2×C3⋊Dic3C22⋊C411yescharacteristic
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—42no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123C4×C3⋊D3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C3×C3⋊C8—42no—
128C2×#121—91no—
129#407—91no—
130#381—91no—
131#327—32no—
132#327—92no—
133C23×D3—32no—
134C23×D3—61no—
135C23×D3—62no—
136C23×D3—62no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—21no—
140C2×C3×D4C4×D312yes—
141C22×C3×C4—21no—
142C22×C3×C4—62no—
143C22×C3×C4C22×D312yes—
144C2×#67—62no—
145C2×#67—62no—
146C2×#67—62no—
147C2×#67—62no—
148C2×#67—62no—
149C2×#67—62no—
150C22×Dic3—22no—
151C22×Dic3—32no—
152C22×Dic3—61no—
153D3×D4—124no—
154D3×D4—124no—
155D3×D4—128no—
156D3×D4—124no—
157D3×D4—124no—
158C2×D12—32no—
159C2×D12—61no—
160C2×D12—62no—
161C2×D12—62no—
162C2×C4×D3—32no—
163C2×C4×D3—32no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×C4×D3—124no—
173C2×C4×D3—124no—
174C2×C3×C8—62no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4C4×D312yes—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179#217—62no—
180#217—62no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—124no—
186C4⋊Dic3—32no—
187C4⋊Dic3—61no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190C2×C3⋊C8—22no—
191ΓL(1,𝔽25)—124no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32C2×C22⋊C411yescharacteristic
198C22×C32AGL(1,ℤ/8)12yes—
199C2×C3⋊D3—21no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3—21no—
204C2×C3⋊D3—44no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C2×C3⋊D3—41no—
208C2×C3⋊D3—84no—
209C2×C3⋊D3#9912yes—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—41no—
213C3⋊Dic3—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3—41no—
216C3×Dic3—82no—
217C22×D4—91no—
218C22×D4—181no—
219C23×C4—91no—
220C2×M16—181no—
221#121—91no—
222#121—91no—
223#121—91no—
224#121—181no—
225#121—181no—
226#121D3211yescharacteristic
227C2×C4⋊C4—91no—
228C2×C22⋊C4—181no—
229C2×C22⋊C4—181no—
230C22⋊C8—32no—
231C22⋊C8—181no—
232#95—32no—
233#95—181no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3D3×D412yes—
238C22×D3—32no—
239C22×D3—32no—
240C22×D3—61no—
241C22×D3—61no—
242C22×D3—64no—
243C22×D3—64no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—122no—
249C22×D3—124no—
250C22×D3—122no—
251C22×D3—122no—
252C22×D3—124no—
253C22×D3—124no—
254C22×D3—124no—
255C22×D3—124no—
256C22×D3—124no—
257C3×D4—42no—
258C3×D4—42no—
259C3×D4—44no—
260C3×D4—42no—
261C3×D4—42no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—122no—
269C2×C3×C4—122no—
270C2×C3×C4—122no—
271C2×C3×C4C2×C4×D312yes—
272C2×C3×C4D3×D412yes—
273#67—124no—
274#67—124no—
275#67—124no—
276#67—124no—
277#67—124no—
278#67—122no—
279#67—122no—
280C2×Dic3—32no—
281C2×Dic3—32no—
282C2×Dic3—42no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291D12—122no—
292D12—122no—
293D12—124no—
294D12—124no—
295C4×D3—64no—
296C4×D3—64no—
297C4×D3—64no—
298C4×D3—122no—
299C4×D3—122no—
300C4×D3—122no—
301C4×D3—122no—
302C4×D3—122no—
303C4×D3—124no—
304C4×D3—124no—
305C3×C8—122no—
306C3⋊C8—42no—
307C2×C32—22no—
308C2×C32—81no—
309C2×C32C2×#9911yescharacteristic
310C2×C32#41811yescharacteristic
311C2×C32#42111yescharacteristic
312C3⋊D3—22no—
313C3⋊D3—41no—
314C3⋊D3—81no—
315C24—91no—
316C24—181no—
317C2×D4—21no—
318C2×D4—91no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—362no—
324C2×D4—364no—
325C2×D4#62411yescharacteristic
326C22×C4—62no—
327C22×C4—91no—
328C22×C4—91no—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—181no—
333C22×C4—362no—
334C22×C4C2×D3211yescharacteristic
335M16—362no—
336C2×C8—62no—
337C4⋊C4—91no—
338C4⋊C4—181no—
339C4⋊C4#62411yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—181no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C22⋊C4—362no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3D3×C22⋊C412yes—
358C22×C3#91112yes—
359C22×C3#91412yes—
360C2×D3—34no—
361C2×D3—62no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C2×D3—62no—
367C2×D3—62no—
368C2×D3—62no—
369C2×D3—62no—
370C2×D3—121no—
371C2×D3—121no—
372C2×D3—124no—
373C2×D3—124no—
374C2×D3—128no—
375C2×D3—122no—
376C2×D3—122no—
377C2×D3—122no—
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—248no—
382C2×D3—248no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—41no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—242no—
390Dic3—62no—
391Dic3—62no—
392Dic3—62no—
393Dic3—82no—
394Dic3—121no—
395Dic3—122no—
396Dic3—122no—
397C32#151011yescharacteristic, complemented, Sylow
398C23—21no—
399C23—91no—
400C23—91no—
401C23—182no—
402C23—182no—
403C23—181no—
404C23—361no—
405C23—362no—
406C23—362no—
407C23—362no—
408C23#381111yescharacteristic
409D4—41no—
410D4—42no—
411D4—361no—
412D4—362no—
413D4—362no—
414D4—362no—
415D4—362no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—122no—
421C2×C4—122no—
422C2×C4—122no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—181no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4—362no—
429C2×C4—361no—
430C2×C4C2×#62411yescharacteristic
431C2×C4#381111yescharacteristic
432C8—122no—
433C2×C3—22no—
434C2×C3—22no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—42no—
439C2×C3—82no—
440C2×C3—82no—
441C2×C3D3×#9912yes—
442C2×C3#477012yes—
443C2×C3#482112yes—
444D3—64no—
445D3—64no—
446D3—122no—
447D3—122no—
448D3—242no—
449D3—242no—
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—92no—
456C22—181no—
457C22—181no—
458C22—181no—
459C22—181no—
460C22—181no—
461C22—364no—
462C22—361no—
463C22—361no—
464C22—361no—
465C22—724no—
466C22#6393712yes—
467C22#6397411yescharacteristic
468C4—21no—
469C4—21no—
470C4—41no—
471C4—181no—
472C4—181no—
473C4—242no—
474C4—361no—
475C3—21no—
476C3#6830412yescomplemented
477C2—22no—
478C2—81no—
479C2—182no—
480C2—361no—
481C2—721no—
482C2#1059142611yescharacteristic
483C2#1059152711yescharacteristic
484C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#121C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591219C2semidirect
3. #10591159C2semidirect
4. C3×#4537C2semidirect
5. #10589151C2semidirect
8. C2×D4×C3⋊D3C4semidirect
12. #64147C4semidirect
14. #64104C4semidirect
15. C4⋊C4×C3⋊D3C4semidirect
20. C3×C3⋊#95C22semidirect
21. C3×#830C22semidirect
29. #4537D3semidirect
90. C3⋊#95C2×D3semidirect
91. #830C2×D3semidirect
397. C32#1510semidirect
476. C3#68304semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
#105912192
#105911592
C3×#45372
#105891512
#683043