Finite Group Databasebeta

← #11722965

Subgroups — #11722965

Order 864.

506 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 78 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×#6294C211yesmaximal, characteristic, complemented
2C2×#6290C211yesmaximal, characteristic, complemented
3C2×C3×#626C211yesmaximal, characteristic, complemented
4C2×C3×#625C211yesmaximal, characteristic, complemented
5#88807C211yesmaximal, characteristic, complemented
6(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#63970—31nomaximal
9#63958—31nomaximal
10#63885—31nomaximal
11C22×C3×C3⋊D3C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C22×C32×D3C2211yescharacteristic
14C2×C3⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C3⋊Dic3C2211yescharacteristic
16C2×C3×C3⋊Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18#6294—22no—
19#6290—22no—
20C3×#626—22no—
21C3×#625—22no—
22C2×#638—31no—
23C2×C3×#67—31no—
24C2×C3×#67—31no—
25C2×C3×#67—31no—
26C2×C3×D12—31no—
27C2×#626D311yescharacteristic, complemented
28C2×#625—31no—
29C2×#625—31no—
30C2×#625—61no—
31C2×#625D311yescharacteristic, complemented
32C2×#624—31no—
33C2×D3×Dic3—31no—
34C2×D3×Dic3—31no—
35#3757—31no—
36#3750—31no—
37C3×#217—31no—
38C3×(C2×D3)⋊C4—31no—
39Dic3⋊Dic3—31no—
40Dic3⋊Dic3—31no—
41Dic3⋊Dic3—61no—
42(C2×D3)⋊Dic3—31no—
43(C2×D3)⋊Dic3—31no—
44(C2×D3)⋊Dic3—61no—
45(C2×D3)⋊Dic3D311yescharacteristic, complemented
46C22×C33C2311yescharacteristic
47C2×C3×C3⋊D3—21no—
48C2×C3×C3⋊D3—21no—
49C2×C3×C3⋊D3D412yescomplemented
50C2×C32×D3—21no—
51C2×C32×D3—21no—
52C2×C32×D3—21no—
53C2×C32×D3—21no—
54C2×C32×D3—21no—
55C2×C32×D3—21no—
56C3⋊(C3⋊Dic3)—21no—
57C3×C3⋊Dic3—21no—
58C3×C3⋊Dic3D412yescomplemented
59C32×Dic3—21no—
60#939—91no—
61#938—91no—
62#884—91no—
63C23×C32—31no—
64C23×C32—31no—
65C22×C3⋊D3C2×D311yescharacteristic
66C22×C3×D3—21no—
67C22×C3×D3—21no—
68C22×C3×D3—31no—
69C22×C3×D3—31no—
70C22×C3×D3—61no—
71C22×C3×D3C2×D311yescharacteristic
72C22×C3×D3C2×D311yescharacteristic
73C22×C3×D3C2×D311yescharacteristic
74C22×C3×D3C2×D311yescharacteristic
75C2×C32×C4—31no—
76#638—62no—
77C2×C3⋊Dic3—31no—
78C2×C3⋊Dic3—31no—
79C2×C3⋊Dic3—31no—
80C2×C3⋊Dic3—61no—
81C2×C3⋊Dic3—61no—
82C2×C3⋊Dic3—61no—
83C2×C3⋊Dic3—121no—
84C2×C3⋊Dic3C2×D311yescharacteristic
85C2×C3⋊Dic3C2×D311yescharacteristic
86C3×#67—62no—
87C3×#67—62no—
88C3×#67—62no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—31no—
91C2×C3×Dic3—31no—
92C2×C3×Dic3—31no—
93C2×C3×Dic3—31no—
94C2×C3×Dic3—61no—
95C2×C3×Dic3—61no—
96C2×C3×Dic3C2×D311yescharacteristic
97C2×C3×Dic3C2×D311yescharacteristic
98C3×D12—62no—
99#626—22no—
100#625—22no—
101#625—62no—
102#625—62no—
103#625—64no—
104#624—62no—
105D3×Dic3—62no—
106D3×Dic3—62no—
107C2×C33C2×D411yescharacteristic
108C2×C33C2×D411yescharacteristic
109C2×C33#4111yescharacteristic
110C3×C3⋊D3—22no—
111C32×D3—41no—
112C32×D3—41no—
113C2×C3×D4—91no—
114C2×C3×D4—91no—
115C2×#67—31no—
116C2×#67—31no—
117C2×#67—31no—
118C2×#67—91no—
119C2×#67—91no—
120C2×#67—91no—
121C2×#67—181no—
122C22×Dic3—91no—
123C2×D12—31no—
124C2×C4×D3—91no—
125C2×C4×D3—91no—
126C3×C22⋊C4—91no—
127#217—31no—
128#217—91no—
129#217—91no—
130#217—181no—
131(C2×D3)⋊C4—31no—
132(C2×D3)⋊C4—91no—
133C4⋊Dic3—91no—
134Dic3⋊C4—91no—
135Dic3⋊C4—91no—
136Dic3⋊C4—181no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—41no—
141C22×C32—61no—
142C22×C32—61no—
143C22×C32—61no—
144C22×C32—61no—
145C22×C32—61no—
146C22×C32—61no—
147C22×C32C22×D311yescharacteristic
148C22×C32C22×D311yescharacteristic
149C22×C32C22×D311yescharacteristic
150C2×C3⋊D3—21no—
151C2×C3⋊D3—21no—
152C2×C3⋊D3#6712yescomplemented
153C2×C3×D3—22no—
154C2×C3×D3—22no—
155C2×C3×D3—21no—
156C2×C3×D3—21no—
157C2×C3×D3—21no—
158C2×C3×D3—21no—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C2×C3×D3—21no—
162C2×C3×D3—21no—
163C2×C3×D3—21no—
164C2×C3×D3—21no—
165C2×C3×D3—21no—
166C2×C3×D3—21no—
167C2×C3×D3—32no—
168C2×C3×D3—32no—
169C2×C3×D3—41no—
170C2×C3×D3—41no—
171C2×C3×D3—41no—
172C2×C3×D3—41no—
173C2×C3×D3—62no—
174C2×C3×D3—61no—
175C2×C3×D3—61no—
176C2×C3×D3—61no—
177C2×C3×D3—61no—
178C2×C3×D3—121no—
179C2×C3×D3—121no—
180C32×C4—61no—
181C3⋊Dic3—21no—
182C3⋊Dic3—61no—
183C3⋊Dic3—62no—
184C3⋊Dic3—61no—
185C3⋊Dic3—61no—
186C3⋊Dic3—121no—
187C3⋊Dic3—121no—
188C3⋊Dic3—122no—
189C3⋊Dic3#6712yescomplemented
190C3×Dic3—21no—
191C3×Dic3—21no—
192C3×Dic3—32no—
193C3×Dic3—32no—
194C3×Dic3—41no—
195C3×Dic3—62no—
196C3×Dic3—61no—
197C3×Dic3—61no—
198C3×Dic3—121no—
199#121—271noSylow
200C33#12111yescharacteristic, complemented, Sylow
201C23×C3—31no—
202C23×C3—31no—
203C23×C3—31no—
204C23×C3—31no—
205C23×C3—61no—
206C23×C3—61no—
207C23×C3—91no—
208C22×D3—31no—
209C22×D3—31no—
210C22×D3—61no—
211C22×D3D3211yescharacteristic
212C22×D3D3211yescharacteristic
213C3×D4—182no—
214C3×D4—182no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—61no—
218C2×C3×C4—91no—
219C2×C3×C4—91no—
220#67—62no—
221#67—62no—
222#67—62no—
223#67—182no—
224#67—182no—
225#67—182no—
226#67—184no—
227C2×Dic3—31no—
228C2×Dic3—31no—
229C2×Dic3—31no—
230C2×Dic3—31no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—91no—
234C2×Dic3—91no—
235C2×Dic3—91no—
236C2×Dic3—181no—
237C2×Dic3—181no—
238C2×Dic3—181no—
239C2×Dic3—182no—
240C2×Dic3—361no—
241C2×Dic3D3211yescharacteristic
242D12—62no—
243C4×D3—182no—
244C4×D3—182no—
245C2×C32—21no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—41no—
255C2×C32—41no—
256C2×C32—41no—
257C2×C32—121no—
258C2×C32—121no—
259C2×C32#23511yescharacteristic
260C2×C32D3×D411yescharacteristic
261C2×C32D3×D411yescharacteristic
262C2×C32D3×D411yescharacteristic
263C2×C32D3×D411yescharacteristic
264C2×C32#23711yescharacteristic
265C2×C32#23711yescharacteristic
266C2×C32C2×#6711yescharacteristic
267C2×C32C2×#6711yescharacteristic
268C3⋊D3—22no—
269C3×D3—42no—
270C3×D3—42no—
271C3×D3—41no—
272C3×D3—41no—
273C3×D3—41no—
274C3×D3—41no—
275C3×D3—62no—
276C3×D3—62no—
277C3×D3—122no—
278C2×D4—91no—
279C2×D4—91no—
280C2×D4—271no—
281C22×C4—271no—
282C4⋊C4—271no—
283C22⋊C4—91no—
284C22⋊C4—271no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—41no—
289C22×C3—62no—
290C22×C3—62no—
291C22×C3—61no—
292C22×C3—61no—
293C22×C3—61no—
294C22×C3—61no—
295C22×C3—61no—
296C22×C3—61no—
297C22×C3—61no—
298C22×C3—61no—
299C22×C3—61no—
300C22×C3—61no—
301C22×C3—61no—
302C22×C3—61no—
303C22×C3—92no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3—121no—
307C22×C3—121no—
308C22×C3—181no—
309C22×C3—181no—
310C22×C3C2×D3211yescharacteristic
311C22×C3C2×D3211yescharacteristic
312C22×C3C2×D3211yescharacteristic
313C2×D3—21no—
314C2×D3—21no—
315C2×D3—21no—
316C2×D3—21no—
317C2×D3—21no—
318C2×D3—21no—
319C2×D3—32no—
320C2×D3—32no—
321C2×D3—62no—
322C2×D3—61no—
323C2×D3—61no—
324C2×D3—61no—
325C2×D3—61no—
326C2×D3—121no—
327C2×D3—121no—
328C3×C4—61no—
329C3×C4—61no—
330C3×C4—92no—
331C3×C4—121no—
332C3×C4—181no—
333Dic3—21no—
334Dic3—32no—
335Dic3—32no—
336Dic3—62no—
337Dic3—61no—
338Dic3—61no—
339Dic3—121no—
340Dic3—182no—
341Dic3—181no—
342Dic3—181no—
343Dic3—181no—
344Dic3—361no—
345Dic3—361no—
346Dic3—362no—
347C32—21no—
348C32—21no—
349C32—21no—
350C32—41no—
351C32#88411yescharacteristic, complemented
352C32#93811yescharacteristic, complemented
353C32#93911yescharacteristic, complemented
354C23—31no—
355C23—31no—
356C23—91no—
357D4—182no—
358D4—182no—
359D4—542no—
360C2×C4—31no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—271no—
364C2×C4—542no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—41no—
375C2×C3—41no—
376C2×C3—41no—
377C2×C3—122no—
378C2×C3—122no—
379C2×C3—121no—
380C2×C3—121no—
381C2×C3—121no—
382C2×C3—121no—
383C2×C3—182no—
384C2×C3#379511yescharacteristic
385C2×C3#380211yescharacteristic
386C2×C3#380411yescharacteristic
387C2×C3#380511yescharacteristic
388C2×C3D3×#6711yescharacteristic
389C2×C3D3×#6711yescharacteristic
390C2×C3D3×#6711yescharacteristic
391C2×C3D3×#6711yescharacteristic
392C2×C3#381111yescharacteristic
393D3—41no—
394D3—41no—
395D3—62no—
396D3—62no—
397D3—122no—
398C22—61no—
399C22—61no—
400C22—61no—
401C22—61no—
402C22—61no—
403C22—61no—
404C22—92no—
405C22—181no—
406C22—181no—
407C22D3311yescharacteristic
408C4—61no—
409C4—92no—
410C4—181no—
411C4—541no—
412C3—21no—
413C3—21no—
414C3—21no—
415C3—41no—
416C3#6388511yescharacteristic, complemented
417C3#6395811yescharacteristic, complemented
418C3#6397011yescharacteristic, complemented
419C2—121no—
420C2—121no—
421C2—182no—
422C2#8895211yescharacteristic
423C2#8895311yescharacteristic
424C2#8896111yescharacteristic
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×#6294C2semidirect
2. C2×#6290C2semidirect
3. C2×C3×#626C2semidirect
4. C2×C3×#625C2semidirect
5. #88807C2semidirect
6. (C2×D3)⋊(C3⋊Dic3)C2semidirect
7. C3×(C2×D3)⋊Dic3C2semidirect
27. C2×#626D3semidirect
31. C2×#625D3semidirect
45. (C2×D3)⋊Dic3D3semidirect
49. C2×C3×C3⋊D3D4semidirect
58. C3×C3⋊Dic3D4semidirect
152. C2×C3⋊D3#67semidirect
189. C3⋊Dic3#67semidirect
200. C33#121semidirect
351. C32#884semidirect
352. C32#938semidirect
353. C32#939semidirect
416. C3#63885semidirect
417. C3#63958semidirect
418. C3#63970semidirect

Maximal subgroups

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

subgroupindex
C2×#62942
C2×#62902
C2×C3×#6262
C2×C3×#6252
#888072
(C2×D3)⋊(C3⋊Dic3)2
C3×(C2×D3)⋊Dic32
#639703
#639583
#638853