Finite Group Databasebeta

← #14518682

Subgroups — #14518682

Order 1944.

959 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 959 conjugacy classes of subgroups — too many to draw. Only its 88 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×C3⋊(C3⋊((C3⋊D3)⋊C3))C211yesmaximal, characteristic, complemented
2C2×C3×D3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
4#10620146C311yesmaximal, characteristic, complemented
5C3×#6291—31nomaximal
6#10619977—31nomaximal
7#6291⋊C3—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
10C3×D3×H(3,𝔽3)—21no—
11C2×C3⋊(C3⋊(C3⋊D3))C2×C311yescharacteristic, complemented
12C2×C3×C3⋊(C3⋊D3)—31no—
13C2×C33×D3—21no—
14C2×C33×D3D311yescharacteristic, complemented
15C2×C33×D3C2×C311yescharacteristic, complemented
16C3×C3⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
17C32×C3⋊Dic3—31no—
18C22×C3×H(3,𝔽3)—31no—
19C2×C3⋊((C3⋊D3)⋊C3)—31no—
20C2×C3⋊((C3⋊D3)⋊C3)—33no—
21C2×C3⋊((C3⋊D3)⋊C3)—63no—
22C2×C3⋊((C3⋊D3)⋊C3)—61no—
23C2×D3×H(3,𝔽3)—23no—
24C2×D3×H(3,𝔽3)D313yescomplemented
25C3⋊((C3⋊Dic3)⋊C3)—21no—
26C3⋊((C3⋊Dic3)⋊C3)D311yescharacteristic, complemented
27C3×(C3⋊Dic3)⋊C3—33no—
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29#6312—31no—
30C3×#638—91no—
31#6291—31no—
32#6291—33no—
33#6291—93no—
34C3×#626—93no—
35C3×#626—91no—
36#638⋊C3—93no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C22×C311yescharacteristic
40C3⋊(C3⋊(C3⋊D3))—21no—
41C3×C3⋊(C3⋊D3)—61no—
42C33×D3—22no—
43C33×D3—21no—
44C33×D3—21no—
45C2×C3×H(3,𝔽3)—21no—
46C2×C3×H(3,𝔽3)—21no—
47C2×C3×H(3,𝔽3)—23no—
48C2×C3×H(3,𝔽3)—23no—
49C2×C3×H(3,𝔽3)—43no—
50C2×C3×H(3,𝔽3)—41no—
51C2×C3×H(3,𝔽3)—61no—
52C2×C3×H(3,𝔽3)C2×D311yescharacteristic
53C2×C3×H(3,𝔽3)C2×D313yes—
54C3⋊((C3⋊D3)⋊C3)—62no—
55C3⋊((C3⋊D3)⋊C3)—66no—
56C3⋊((C3⋊D3)⋊C3)—61no—
57C3⋊((C3⋊D3)⋊C3)—63no—
58D3×H(3,𝔽3)—26no—
59D3×H(3,𝔽3)—23no—
60C22×C33—31no—
61C22×C33—31no—
62C22×C33—61no—
63C2×C3⋊(C3⋊D3)—31no—
64C2×C3⋊(C3⋊D3)—31no—
65C2×C3⋊(C3⋊D3)—33no—
66C2×C3⋊(C3⋊D3)—61no—
67C2×C3⋊(C3⋊D3)—63no—
68C2×C3⋊(C3⋊D3)—93no—
69C2×C3⋊(C3⋊D3)—183no—
70C2×C3×C3⋊D3—93no—
71C2×C3×C3⋊D3—91no—
72C2×C3×C3⋊D3—91no—
73C2×C3×C3⋊D3—181no—
74C2×C3×C3⋊D3—183no—
75C2×C32×D3—21no—
76C2×C32×D3—23no—
77C2×C32×D3—33no—
78C2×C32×D3—33no—
79C2×C32×D3—63no—
80C2×C32×D3C3×D311yescharacteristic
81C2×C32×D3C3×D313yescomplemented
82C2×C32×D3C3⋊D311yescharacteristic, complemented
83C3⋊(C3⋊Dic3)C3×D311yescharacteristic, complemented
84C3×C3⋊Dic3—31no—
85C3×C3⋊Dic3—31no—
86C3×C3⋊Dic3—33no—
87C3×C3⋊Dic3—61no—
88C3×C3⋊Dic3—93no—
89C32×Dic3—93no—
90C32×Dic3—91no—
91C22×H(3,𝔽3)—33no—
92C22×H(3,𝔽3)—63no—
93C2×(C3⋊D3)⋊C3—93no—
94C2×(C3⋊D3)⋊C3—183no—
95(C3⋊Dic3)⋊C3—33no—
96(C3⋊Dic3)⋊C3—63no—
97C34—21no—
98C34#6711yescharacteristic, complemented
99C34C3×D411yescharacteristic, complemented
100C3×H(3,𝔽3)—21no—
101C3×H(3,𝔽3)—21no—
102C3×H(3,𝔽3)—23no—
103C3×H(3,𝔽3)—23no—
104C3×H(3,𝔽3)—43no—
105C3×H(3,𝔽3)—41no—
106C3×H(3,𝔽3)D1211yescharacteristic, complemented
107C3×H(3,𝔽3)#6713yescomplemented
108#638—91no—
109#638—93no—
110#638—273no—
111C3×#67—271no—
112C3×#67—273no—
113C3×D12—271no—
114#626—93no—
115#626—91no—
116#626—273no—
117C2×C33—23no—
118C2×C33—21no—
119C2×C33—21no—
120C2×C33—21no—
121C2×C33—21no—
122C2×C33—21no—
123C2×C33—23no—
124C2×C33—33no—
125C2×C33—33no—
126C2×C33—41no—
127C2×C33—43no—
128C2×C33—41no—
129C2×C33—63no—
130C2×C33—63no—
131C2×C33—63no—
132C2×C33—62no—
133C2×C33—61no—
134C2×C33—61no—
135C2×C33—123no—
136C2×C33D3211yescharacteristic
137C2×C33C2×C3×D311yescharacteristic
138C2×C33C2×C3×D313yes—
139C2×C33C2×C3×D311yescharacteristic
140C2×C33C2×C3⋊D311yescharacteristic
141C3⋊(C3⋊D3)—61no—
142C3⋊(C3⋊D3)—66no—
143C3⋊(C3⋊D3)—62no—
144C3⋊(C3⋊D3)—61no—
145C3⋊(C3⋊D3)—63no—
146C3⋊(C3⋊D3)—183no—
147C3⋊(C3⋊D3)—186no—
148C3×C3⋊D3—182no—
149C3×C3⋊D3—183no—
150C3×C3⋊D3—186no—
151C3×C3⋊D3—181no—
152C3×C3⋊D3—181no—
153C32×D3—21no—
154C32×D3—22no—
155C32×D3—26no—
156C32×D3—23no—
157C32×D3—21no—
158C32×D3—63no—
159C32×D3—63no—
160C32×D3—66no—
161C2×H(3,𝔽3)—23no—
162C2×H(3,𝔽3)—23no—
163C2×H(3,𝔽3)—23no—
164C2×H(3,𝔽3)—43no—
165C2×H(3,𝔽3)—43no—
166C2×H(3,𝔽3)—46no—
167C2×H(3,𝔽3)—43no—
168C2×H(3,𝔽3)—66no—
169C2×H(3,𝔽3)—63no—
170C2×H(3,𝔽3)D3213yes—
171(C3⋊D3)⋊C3—186no—
172(C3⋊D3)⋊C3—183no—
173C22×C32—31no—
174C22×C32—33no—
175C22×C32—31no—
176C22×C32—63no—
177C22×C32—61no—
178C22×C32—93no—
179C22×C32—93no—
180C22×C32—183no—
181C2×C3⋊D3—91no—
182C2×C3⋊D3—93no—
183C2×C3⋊D3—91no—
184C2×C3⋊D3—93no—
185C2×C3⋊D3—181no—
186C2×C3⋊D3—183no—
187C2×C3⋊D3—183no—
188C2×C3⋊D3—273no—
189C2×C3⋊D3—273no—
190C2×C3⋊D3—543no—
191C2×C3⋊D3—549no—
192C2×C3⋊D3—543no—
193C2×C3×D3—33no—
194C2×C3×D3—31no—
195C2×C3×D3—61no—
196C2×C3×D3—63no—
197C2×C3×D3—271no—
198C2×C3×D3—273no—
199C2×C3×D3—271no—
200C2×C3×D3—541no—
201C2×C3×D3—543no—
202C2×C3×D3(C3⋊D3)⋊C313yescomplemented
203C2×C3×D3C3×C3⋊D311yescharacteristic
204C32×C4—271no—
205C3⋊Dic3—31no—
206C3⋊Dic3—33no—
207C3⋊Dic3—93no—
208C3×Dic3—93no—
209C3×Dic3—93no—
210C3×Dic3—91no—
211C3×Dic3—91no—
212C3×Dic3—181no—
213C3×Dic3—183no—
214C3×Dic3—273no—
215C33—21no—
216C33—21no—
217C33—23no—
218C33—21no—
219C33—21no—
220C33—21no—
221C33—23no—
222C33—33no—
223C33—33no—
224C33—41no—
225C33—43no—
226C33—41no—
227C33—63no—
228C33—63no—
229C33—63no—
230C33—123no—
231C33#62611yescharacteristic, complemented
232C33C3×D1211yescharacteristic, complemented
233C33C3×#6711yescharacteristic
234C33C3×#6713yescomplemented
235C33#63811yescharacteristic, complemented
236H(3,𝔽3)—23no—
237H(3,𝔽3)—23no—
238H(3,𝔽3)—23no—
239H(3,𝔽3)—43no—
240H(3,𝔽3)—43no—
241H(3,𝔽3)—46no—
242H(3,𝔽3)—43no—
243H(3,𝔽3)#62613yescomplemented
244C3×D4—811no—
245#67—271no—
246#67—273no—
247#67—813no—
248D12—271no—
249C2×C32—23no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32—23no—
254C2×C32—23no—
255C2×C32—33no—
256C2×C32—33no—
257C2×C32—33no—
258C2×C32—31no—
259C2×C32—43no—
260C2×C32—41no—
261C2×C32—69no—
262C2×C32—63no—
263C2×C32—61no—
264C2×C32—63no—
265C2×C32—61no—
266C2×C32—63no—
267C2×C32—63no—
268C2×C32—63no—
269C2×C32—61no—
270C2×C32—63no—
271C2×C32—62no—
272C2×C32—66no—
273C2×C32—63no—
274C2×C32—61no—
275C2×C32—123no—
276C2×C32—129no—
277C2×C32—121no—
278C2×C32—123no—
279C2×C32—123no—
280C2×C32—183no—
281C2×C32—183no—
282C2×C32—186no—
283C2×C32C2×(C3⋊D3)⋊C313yes—
284C2×C32C3×D3213yes—
285C2×C32C3×D3211yescharacteristic
286C2×C32D3×C3⋊D311yescharacteristic
287C2×C32C2×C3×C3⋊D311yescharacteristic
288C3⋊D3—182no—
289C3⋊D3—186no—
290C3⋊D3—183no—
291C3⋊D3—181no—
292C3⋊D3—181no—
293C3⋊D3—186no—
294C3⋊D3—183no—
295C3⋊D3—543no—
296C3⋊D3—543no—
297C3⋊D3—546no—
298C3⋊D3—5418no—
299C3⋊D3—546no—
300C3×D3—23no—
301C3×D3—21no—
302C3×D3—61no—
303C3×D3—63no—
304C3×D3—62no—
305C3×D3—66no—
306C3×D3—541no—
307C3×D3—543no—
308C3×D3—542no—
309C3×D3—546no—
310C3×D3—541no—
311C22×C3—33no—
312C22×C3—31no—
313C22×C3—93no—
314C22×C3—91no—
315C22×C3—181no—
316C22×C3—183no—
317C22×C3—811no—
318C2×D3—273no—
319C2×D3—271no—
320C2×D3—271no—
321C2×D3—543no—
322C2×D3—541no—
323C2×D3—813no—
324C2×D3—1623no—
325C2×D3C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
326C3×C4—271no—
327C3×C4—271no—
328C3×C4—541no—
329Dic3—93no—
330Dic3—91no—
331Dic3—273no—
332C32—23no—
333C32—21no—
334C32—23no—
335C32—21no—
336C32—23no—
337C32—21no—
338C32—33no—
339C32—31no—
340C32—33no—
341C32—33no—
342C32—43no—
343C32—41no—
344C32—61no—
345C32—63no—
346C32—69no—
347C32—63no—
348C32—63no—
349C32—63no—
350C32—61no—
351C32—63no—
352C32—63no—
353C32—123no—
354C32—121no—
355C32—123no—
356C32—129no—
357C32—123no—
358C32#638⋊C313yescomplemented
359C32C3×#62611yescharacteristic
360C32C3×#62613yescomplemented
361C32#629111yescharacteristic, complemented
362C32C3×#63811yescharacteristic
363D4—811noSylow
364C2×C3—23no—
365C2×C3—21no—
366C2×C3—33no—
367C2×C3—31no—
368C2×C3—63no—
369C2×C3—61no—
370C2×C3—61no—
371C2×C3—63no—
372C2×C3—61no—
373C2×C3—63no—
374C2×C3—121no—
375C2×C3—123no—
376C2×C3—183no—
377C2×C3—181no—
378C2×C3—182no—
379C2×C3—186no—
380C2×C3—1621no—
381C2×C3D3×(C3⋊D3)⋊C313yes—
382C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
383C2×C3C3×D3×C3⋊D311yescharacteristic
384D3—21no—
385D3—546no—
386D3—542no—
387D3—541no—
388D3—543no—
389D3—541no—
390D3—1623no—
391D3—1626no—
392C22—31no—
393C22—811no—
394C4—271no—
395C3—23no—
396C3—21no—
397C3—33no—
398C3—31no—
399C3—63no—
400C3—61no—
401C3—63no—
402C3—61no—
403C3—121no—
404C3—123no—
405C3#6291⋊C313yescomplemented
406C3#1061997711yescharacteristic, complemented
407C3C3×#629111yescharacteristic
408C2—61no—
409C2—1621no—
410C2D3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2D3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocleC2×C34C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
hypocenterC34C3×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2semidirect
2. C2×C3×D3×H(3,𝔽3)C2semidirect
3. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
4. #10620146C3semidirect
11. C2×C3⋊(C3⋊(C3⋊D3))C2×C3semidirect
14. C2×C33×D3D3semidirect
15. C2×C33×D3C2×C3semidirect
16. C3×C3⋊(C3⋊Dic3)C2×C3semidirect
24. C2×D3×H(3,𝔽3)D3semidirect
26. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
28. C32×H(3,𝔽3)D4semidirect
81. C2×C32×D3C3×D3semidirect
82. C2×C32×D3C3⋊D3semidirect
83. C3⋊(C3⋊Dic3)C3×D3semidirect
98. C34#67semidirect
99. C34C3×D4semidirect
106. C3×H(3,𝔽3)D12semidirect
107. C3×H(3,𝔽3)#67semidirect
202. C2×C3×D3(C3⋊D3)⋊C3semidirect
231. C33#626semidirect
232. C33C3×D12semidirect
234. C33C3×#67semidirect
235. C33#638semidirect
243. H(3,𝔽3)#626semidirect
325. C2×D3C3⋊((C3⋊D3)⋊C3)semidirect
358. C32#638⋊C3semidirect
360. C32C3×#626semidirect
361. C32#6291semidirect
405. C3#6291⋊C3semidirect
406. C3#10619977semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊((C3⋊D3)⋊C3))2
C2×C3×D3×H(3,𝔽3)2
C3×C3⋊((C3⋊Dic3)⋊C3)2
#106201463
C3×#62913
#106199773
#6291⋊C33