Finite Group Databasebeta

← #11722963

Subgroups — #11722963

Order 864.

570 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C2×#6292C211yesmaximal, characteristic, complemented
2C2×#6291C211yesmaximal, characteristic, complemented
3C2×#6289C211yesmaximal, characteristic, complemented
4C2×C3×#626C211yesmaximal, characteristic, complemented
5#88814C211yesmaximal, characteristic, complemented
6C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#63958—31nomaximal
9#63916—31nomaximal
10#63910—31nomaximal
11C22×C3⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C3⋊D3C2211yescharacteristic
13C22×C32×D3C2211yescharacteristic
14C2×C3×C3⋊Dic3C2211yescharacteristic
15C2×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18#6292—22no—
19#6291—22no—
20#6289—22no—
21C3×#626—22no—
22C2×#638—31no—
23C2×C4⋊(C3⋊D3)—31no—
24C2×C4×C3⋊D3—31no—
25C2×C3×#67—31no—
26C2×C3×D12—31no—
27C2×#626—31no—
28C2×#626—31no—
29C2×#626—31no—
30C2×#626—31no—
31C2×#626—61no—
32C2×#626—61no—
33C2×#626D311yescharacteristic, complemented
34C2×#624—31no—
35C2×#624—31no—
36C2×#624—61no—
37C3×#217—31no—
38C3×(C2×D3)⋊C4—31no—
39C3×C4⋊Dic3—31no—
40C3×Dic3⋊C4—31no—
41Dic3⋊Dic3D311yescharacteristic, complemented
42#3722—31no—
43(C2×D3)⋊Dic3—31no—
44(C2×D3)⋊Dic3—31no—
45(C2×D3)⋊Dic3D311yescharacteristic, complemented
46C22×C33C2311yescharacteristic
47C2×C3⋊(C3⋊D3)—21no—
48C2×C3⋊(C3⋊D3)—21no—
49C2×C3⋊(C3⋊D3)D412yescomplemented
50C2×C3×C3⋊D3—21no—
51C2×C3×C3⋊D3—21no—
52C2×C3×C3⋊D3—21no—
53C2×C32×D3—21no—
54C2×C32×D3—21no—
55C2×C32×D3—21no—
56C3×C3⋊Dic3—21no—
57C3×C3⋊Dic3—21no—
58C32×Dic3—21no—
59C32×Dic3D412yescomplemented
60#938—91no—
61#895—91no—
62#884—91no—
63C23×C32—31no—
64C22×C3⋊D3—31no—
65C22×C3⋊D3—31no—
66C22×C3⋊D3—31no—
67C22×C3⋊D3—61no—
68C22×C3⋊D3—61no—
69C22×C3⋊D3—61no—
70C22×C3⋊D3—121no—
71C22×C3⋊D3C2×D311yescharacteristic
72C22×C3×D3—21no—
73C22×C3×D3—31no—
74C22×C3×D3—31no—
75C22×C3×D3—61no—
76C22×C3×D3C2×D311yescharacteristic
77C22×C3×D3C2×D311yescharacteristic
78C2×C32×C4—31no—
79C2×C32×C4—31no—
80#638—62no—
81C2×C3⋊Dic3C2×D311yescharacteristic
82C2×C3⋊Dic3C2×D311yescharacteristic
83C4⋊(C3⋊D3)—62no—
84C4×C3⋊D3—62no—
85C3×#67—62no—
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—31no—
89C2×C3×Dic3—31no—
90C2×C3×Dic3—31no—
91C2×C3×Dic3—31no—
92C2×C3×Dic3—61no—
93C2×C3×Dic3—61no—
94C2×C3×Dic3C2×D311yescharacteristic
95C2×C3×Dic3C2×D311yescharacteristic
96C2×C3×Dic3C2×D311yescharacteristic
97C2×C3×Dic3C2×D311yescharacteristic
98C3×D12—62no—
99#626—22no—
100#626—62no—
101#626—62no—
102#626—64no—
103#626—62no—
104#626—62no—
105#626—64no—
106#624—64no—
107#624—62no—
108#624—62no—
109C2×C33C2×D411yescharacteristic
110C2×C33C2×D411yescharacteristic
111C2×C33#4111yescharacteristic
112C3⋊(C3⋊D3)—22no—
113C3×C3⋊D3—41no—
114C32×D3—41no—
115C2×C3×D4—91no—
116C2×#67—31no—
117C2×#67—91no—
118C2×#67—91no—
119C2×#67—91no—
120C2×#67—181no—
121C2×D12—31no—
122C2×D12—91no—
123C2×D12—91no—
124C2×D12—91no—
125C2×D12—181no—
126C2×C4×D3—91no—
127C2×C4×D3—91no—
128C2×C4×D3—91no—
129C2×C4×D3—181no—
130C3×C4⋊C4—91no—
131C3×C22⋊C4—91no—
132#217—31no—
133#217—91no—
134(C2×D3)⋊C4—31no—
135(C2×D3)⋊C4—91no—
136(C2×D3)⋊C4—91no—
137C4⋊Dic3—31no—
138Dic3⋊C4—31no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—41no—
143C22×C32—61no—
144C22×C32—61no—
145C22×C32—61no—
146C22×C32C22×D311yescharacteristic
147C22×C32C22×D311yescharacteristic
148C22×C32C22×D311yescharacteristic
149C2×C3⋊D3—21no—
150C2×C3⋊D3—21no—
151C2×C3⋊D3—21no—
152C2×C3⋊D3—32no—
153C2×C3⋊D3—32no—
154C2×C3⋊D3—32no—
155C2×C3⋊D3—62no—
156C2×C3⋊D3—62no—
157C2×C3⋊D3—62no—
158C2×C3⋊D3—61no—
159C2×C3⋊D3—61no—
160C2×C3⋊D3—62no—
161C2×C3⋊D3—62no—
162C2×C3⋊D3—61no—
163C2×C3⋊D3—61no—
164C2×C3⋊D3—61no—
165C2×C3⋊D3—61no—
166C2×C3⋊D3—122no—
167C2×C3⋊D3—121no—
168C2×C3⋊D3—121no—
169C2×C3⋊D3—121no—
170C2×C3⋊D3—121no—
171C2×C3⋊D3—122no—
172C2×C3⋊D3—122no—
173C2×C3×D3—22no—
174C2×C3×D3—21no—
175C2×C3×D3—21no—
176C2×C3×D3—21no—
177C2×C3×D3—21no—
178C2×C3×D3—21no—
179C2×C3×D3—21no—
180C2×C3×D3—41no—
181C2×C3×D3—41no—
182C2×C3×D3—62no—
183C2×C3×D3—61no—
184C2×C3×D3—61no—
185C2×C3×D3—61no—
186C2×C3×D3—61no—
187C2×C3×D3—61no—
188C2×C3×D3—61no—
189C2×C3×D3—121no—
190C2×C3×D3—121no—
191C32×C4—32no—
192C32×C4—61no—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3×Dic3—22no—
196C3×Dic3—21no—
197C3×Dic3—21no—
198C3×Dic3—22no—
199C3×Dic3—62no—
200C3×Dic3—62no—
201C3×Dic3—61no—
202C3×Dic3—61no—
203C3×Dic3—61no—
204C3×Dic3—61no—
205C3×Dic3D1212yescomplemented
206C3×Dic3#6712yescomplemented
207#121—271noSylow
208C33#12111yescharacteristic, complemented, Sylow
209C23×C3—31no—
210C23×C3—31no—
211C23×C3—61no—
212C23×C3—91no—
213C22×D3—31no—
214C22×D3—31no—
215C22×D3—61no—
216C22×D3—91no—
217C22×D3—91no—
218C22×D3—91no—
219C22×D3—181no—
220C22×D3—181no—
221C22×D3—181no—
222C22×D3—361no—
223C22×D3D3211yescharacteristic
224C3×D4—182no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—91no—
232C2×C3×C4—91no—
233#67—62no—
234#67—182no—
235#67—182no—
236#67—182no—
237#67—184no—
238C2×Dic3—31no—
239C2×Dic3—31no—
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3D3211yescharacteristic
245C2×Dic3D3211yescharacteristic
246D12—62no—
247D12—182no—
248D12—182no—
249D12—184no—
250D12—182no—
251C4×D3—182no—
252C4×D3—182no—
253C4×D3—184no—
254C4×D3—182no—
255C2×C32—21no—
256C2×C32—21no—
257C2×C32—21no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32—41no—
265C2×C32—41no—
266C2×C32—41no—
267C2×C32—121no—
268C2×C32C2×D1211yescharacteristic
269C2×C32#23511yescharacteristic
270C2×C32D3×D411yescharacteristic
271C2×C32D3×D411yescharacteristic
272C2×C32D3×D411yescharacteristic
273C2×C32D3×D411yescharacteristic
274C2×C32#23711yescharacteristic
275C2×C32#23911yescharacteristic
276C2×C32C2×#6711yescharacteristic
277C3⋊D3—41no—
278C3⋊D3—62no—
279C3⋊D3—64no—
280C3⋊D3—62no—
281C3⋊D3—62no—
282C3⋊D3—122no—
283C3⋊D3—122no—
284C3⋊D3—124no—
285C3×D3—42no—
286C3×D3—41no—
287C3×D3—41no—
288C3×D3—122no—
289C3×D3—121no—
290C3×D3—121no—
291C2×D4—91no—
292C2×D4—271no—
293C2×D4—271no—
294C22×C4—271no—
295C4⋊C4—91no—
296C22⋊C4—91no—
297C22⋊C4—271no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—41no—
302C22×C3—62no—
303C22×C3—61no—
304C22×C3—61no—
305C22×C3—61no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3—61no—
309C22×C3—121no—
310C22×C3—121no—
311C22×C3—181no—
312C22×C3—181no—
313C22×C3—181no—
314C22×C3C2×D3211yescharacteristic
315C22×C3C2×D3211yescharacteristic
316C22×C3C2×D3211yescharacteristic
317C2×D3—21no—
318C2×D3—21no—
319C2×D3—21no—
320C2×D3—62no—
321C2×D3—61no—
322C2×D3—61no—
323C2×D3—61no—
324C2×D3—61no—
325C2×D3—61no—
326C2×D3—61no—
327C2×D3—92no—
328C2×D3—92no—
329C2×D3—92no—
330C2×D3—121no—
331C2×D3—121no—
332C2×D3—182no—
333C2×D3—182no—
334C2×D3—182no—
335C2×D3—182no—
336C2×D3—182no—
337C2×D3—181no—
338C2×D3—181no—
339C2×D3—181no—
340C2×D3—181no—
341C2×D3—181no—
342C2×D3—181no—
343C2×D3—362no—
344C2×D3—361no—
345C2×D3—361no—
346C2×D3—361no—
347C2×D3—361no—
348C2×D3—362no—
349C2×D3—362no—
350C3×C4—32no—
351C3×C4—32no—
352C3×C4—62no—
353C3×C4—62no—
354C3×C4—61no—
355C3×C4—61no—
356C3×C4—181no—
357C3×C4—181no—
358Dic3—21no—
359Dic3—62no—
360Dic3—62no—
361Dic3—61no—
362Dic3—61no—
363Dic3—61no—
364Dic3—61no—
365Dic3#62612yescomplemented
366C32—21no—
367C32—21no—
368C32—21no—
369C32—41no—
370C32#88411yescharacteristic, complemented
371C32#89511yescharacteristic, complemented
372C32#93811yescharacteristic, complemented
373C23—31no—
374C23—91no—
375C23—271no—
376D4—182no—
377D4—542no—
378D4—542no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—91no—
382C2×C4—91no—
383C2×C4—542no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—41no—
396C2×C3—122no—
397C2×C3—121no—
398C2×C3—121no—
399C2×C3—361no—
400C2×C3#379611yescharacteristic
401C2×C3#379911yescharacteristic
402C2×C3D3×D1211yescharacteristic
403C2×C3#380211yescharacteristic
404C2×C3#380411yescharacteristic
405C2×C3C2×#62611yescharacteristic
406C2×C3D3×#6711yescharacteristic
407C2×C3#381111yescharacteristic
408C2×C3#381111yescharacteristic
409D3—41no—
410D3—122no—
411D3—121no—
412D3—121no—
413D3—184no—
414D3—182no—
415D3—182no—
416D3—182no—
417D3—362no—
418D3—362no—
419D3—364no—
420C22—61no—
421C22—61no—
422C22—61no—
423C22—181no—
424C22—181no—
425C22—181no—
426C22—272no—
427C22—541no—
428C22—541no—
429C22D3311yescharacteristic
430C4—32no—
431C4—61no—
432C4—181no—
433C4—181no—
434C3—21no—
435C3—21no—
436C3—21no—
437C3—41no—
438C3#6391011yescharacteristic, complemented
439C3#6391611yescharacteristic, complemented
440C3#6395811yescharacteristic, complemented
441C2—121no—
442C2—361no—
443C2—542no—
444C2D3×#62611yescharacteristic
445C2#8895411yescharacteristic
446C2#8896211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D33
commutator, Fitting, socle, cosocleC22×C33C23
hypocenterC33#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#6292C2semidirect
2. C2×#6291C2semidirect
3. C2×#6289C2semidirect
4. C2×C3×#626C2semidirect
5. #88814C2semidirect
6. C3×Dic3⋊Dic3C2semidirect
7. C3×(C2×D3)⋊Dic3C2semidirect
33. C2×#626D3semidirect
41. Dic3⋊Dic3D3semidirect
45. (C2×D3)⋊Dic3D3semidirect
49. C2×C3⋊(C3⋊D3)D4semidirect
59. C32×Dic3D4semidirect
205. C3×Dic3D12semidirect
206. C3×Dic3#67semidirect
208. C33#121semidirect
365. Dic3#626semidirect
370. C32#884semidirect
371. C32#895semidirect
372. C32#938semidirect
438. C3#63910semidirect
439. C3#63916semidirect
440. C3#63958semidirect

Maximal subgroups

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

subgroupindex
C2×#62922
C2×#62912
C2×#62892
C2×C3×#6262
#888142
C3×Dic3⋊Dic32
C3×(C2×D3)⋊Dic32
#639583
#639163
#639103