Finite Group Databasebeta

← #14518681

Subgroups — #14518681

Order 1944.

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

normal subgroups only

This group has 877 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#10620145C311yesmaximal, characteristic, complemented
5C3×#6290—31nomaximal
6#10619977—31nomaximal
7#6290⋊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×C32×C3⋊D3—31no—
13C2×C33×D3—21no—
14C2×C33×D3D311yescharacteristic, complemented
15C2×C33×D3C2×C311yescharacteristic, complemented
16C3⋊(C3⋊(C3⋊Dic3))C2×C311yescharacteristic, complemented
17C3×C3⋊(C3⋊Dic3)—31no—
18C22×C3×H(3,𝔽3)—31no—
19C2×C3⋊((C3⋊D3)⋊C3)—21no—
20C2×C3⋊((C3⋊D3)⋊C3)D311yescharacteristic, complemented
21C2×D3×H(3,𝔽3)—23no—
22C2×D3×H(3,𝔽3)D313yescomplemented
23C2×C3×(C3⋊D3)⋊C3—33no—
24C3⋊((C3⋊Dic3)⋊C3)—31no—
25C3⋊((C3⋊Dic3)⋊C3)—33no—
26C3⋊((C3⋊Dic3)⋊C3)—63no—
27C3⋊((C3⋊Dic3)⋊C3)—61no—
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29#6312—31no—
30C3×#638—91no—
31#6290—31no—
32#6290—33no—
33#6290—93no—
34C3×#625—93no—
35C3×#625—91no—
36#638⋊C3—93no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C22×C311yescharacteristic
40C3×C3⋊(C3⋊D3)—21no—
41C32×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)—22no—
55C3⋊((C3⋊D3)⋊C3)—21no—
56D3×H(3,𝔽3)—26no—
57D3×H(3,𝔽3)—23no—
58C3×(C3⋊D3)⋊C3—63no—
59C22×C33—31no—
60C22×C33—31no—
61C22×C33—61no—
62C2×C3⋊(C3⋊D3)C3×D311yescharacteristic, complemented
63C2×C3×C3⋊D3—31no—
64C2×C3×C3⋊D3—31no—
65C2×C3×C3⋊D3—33no—
66C2×C3×C3⋊D3—61no—
67C2×C3×C3⋊D3—93no—
68C2×C32×D3—21no—
69C2×C32×D3—23no—
70C2×C32×D3—33no—
71C2×C32×D3—33no—
72C2×C32×D3—63no—
73C2×C32×D3—93no—
74C2×C32×D3—91no—
75C2×C32×D3C3×D311yescharacteristic
76C2×C32×D3C3×D313yescomplemented
77C2×C32×D3C3⋊D311yescharacteristic, complemented
78C3⋊(C3⋊Dic3)—31no—
79C3⋊(C3⋊Dic3)—31no—
80C3⋊(C3⋊Dic3)—33no—
81C3⋊(C3⋊Dic3)—61no—
82C3⋊(C3⋊Dic3)—63no—
83C3⋊(C3⋊Dic3)—93no—
84C3⋊(C3⋊Dic3)—183no—
85C3×C3⋊Dic3—93no—
86C3×C3⋊Dic3—91no—
87C3×C3⋊Dic3—91no—
88C3×C3⋊Dic3—181no—
89C3×C3⋊Dic3—183no—
90C22×H(3,𝔽3)—33no—
91C22×H(3,𝔽3)—63no—
92C2×(C3⋊D3)⋊C3—33no—
93C2×(C3⋊D3)⋊C3—63no—
94(C3⋊Dic3)⋊C3—93no—
95(C3⋊Dic3)⋊C3—183no—
96C34—21no—
97C34#6711yescharacteristic, complemented
98C34C3×D411yescharacteristic, complemented
99C3×H(3,𝔽3)—21no—
100C3×H(3,𝔽3)—21no—
101C3×H(3,𝔽3)—23no—
102C3×H(3,𝔽3)—23no—
103C3×H(3,𝔽3)—43no—
104C3×H(3,𝔽3)—41no—
105C3×H(3,𝔽3)#6711yescharacteristic, complemented
106C3×H(3,𝔽3)#6713yescomplemented
107#638—91no—
108#638—93no—
109#638—273no—
110C3×#67—271no—
111C3×#67—271no—
112C3×#67—273no—
113#625—93no—
114#625—91no—
115#625—273no—
116C2×C33—23no—
117C2×C33—21no—
118C2×C33—21no—
119C2×C33—21no—
120C2×C33—21no—
121C2×C33—21no—
122C2×C33—23no—
123C2×C33—33no—
124C2×C33—33no—
125C2×C33—41no—
126C2×C33—43no—
127C2×C33—41no—
128C2×C33—63no—
129C2×C33—63no—
130C2×C33—63no—
131C2×C33—62no—
132C2×C33—61no—
133C2×C33—61no—
134C2×C33—123no—
135C2×C33D3211yescharacteristic
136C2×C33C2×C3×D311yescharacteristic
137C2×C33C2×C3×D313yes—
138C2×C33C2×C3×D311yescharacteristic
139C2×C33C2×C3⋊D311yescharacteristic
140C3⋊(C3⋊D3)—21no—
141C3×C3⋊D3—62no—
142C3×C3⋊D3—61no—
143C3×C3⋊D3—61no—
144C3×C3⋊D3—63no—
145C3×C3⋊D3—183no—
146C32×D3—21no—
147C32×D3—22no—
148C32×D3—26no—
149C32×D3—23no—
150C32×D3—21no—
151C32×D3—63no—
152C32×D3—63no—
153C32×D3—66no—
154C32×D3—183no—
155C32×D3—181no—
156C2×H(3,𝔽3)—23no—
157C2×H(3,𝔽3)—23no—
158C2×H(3,𝔽3)—23no—
159C2×H(3,𝔽3)—43no—
160C2×H(3,𝔽3)—43no—
161C2×H(3,𝔽3)—46no—
162C2×H(3,𝔽3)—43no—
163C2×H(3,𝔽3)—66no—
164C2×H(3,𝔽3)—63no—
165C2×H(3,𝔽3)D3213yes—
166(C3⋊D3)⋊C3—66no—
167(C3⋊D3)⋊C3—63no—
168C22×C32—31no—
169C22×C32—33no—
170C22×C32—31no—
171C22×C32—63no—
172C22×C32—61no—
173C22×C32—93no—
174C22×C32—93no—
175C22×C32—183no—
176C22×C32—271no—
177C2×C3⋊D3—31no—
178C2×C3⋊D3—33no—
179C2×C3⋊D3—93no—
180C2×C3×D3—33no—
181C2×C3×D3—31no—
182C2×C3×D3—61no—
183C2×C3×D3—63no—
184C2×C3×D3—93no—
185C2×C3×D3—93no—
186C2×C3×D3—91no—
187C2×C3×D3—91no—
188C2×C3×D3—181no—
189C2×C3×D3—183no—
190C2×C3×D3—273no—
191C2×C3×D3(C3⋊D3)⋊C313yescomplemented
192C2×C3×D3C3×C3⋊D311yescharacteristic
193C3⋊Dic3—91no—
194C3⋊Dic3—93no—
195C3⋊Dic3—91no—
196C3⋊Dic3—93no—
197C3⋊Dic3—181no—
198C3⋊Dic3—183no—
199C3⋊Dic3—183no—
200C3⋊Dic3—273no—
201C3⋊Dic3—273no—
202C3⋊Dic3—543no—
203C3⋊Dic3—549no—
204C3⋊Dic3—543no—
205C3×Dic3—271no—
206C3×Dic3—273no—
207C3×Dic3—271no—
208C3×Dic3—541no—
209C3×Dic3—543no—
210C33—21no—
211C33—21no—
212C33—23no—
213C33—21no—
214C33—21no—
215C33—21no—
216C33—23no—
217C33—33no—
218C33—33no—
219C33—41no—
220C33—43no—
221C33—41no—
222C33—63no—
223C33—63no—
224C33—63no—
225C33—123no—
226C33#62511yescharacteristic, complemented
227C33C3×#6711yescharacteristic
228C33C3×#6713yescomplemented
229C33C3×#6711yescharacteristic, complemented
230C33#63811yescharacteristic, complemented
231H(3,𝔽3)—23no—
232H(3,𝔽3)—23no—
233H(3,𝔽3)—23no—
234H(3,𝔽3)—43no—
235H(3,𝔽3)—43no—
236H(3,𝔽3)—46no—
237H(3,𝔽3)—43no—
238H(3,𝔽3)#62513yescomplemented
239C3×D4—811no—
240#67—271no—
241#67—273no—
242#67—271no—
243#67—813no—
244C2×C32—23no—
245C2×C32—21no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32—23no—
249C2×C32—23no—
250C2×C32—33no—
251C2×C32—33no—
252C2×C32—33no—
253C2×C32—31no—
254C2×C32—43no—
255C2×C32—41no—
256C2×C32—69no—
257C2×C32—63no—
258C2×C32—61no—
259C2×C32—63no—
260C2×C32—61no—
261C2×C32—63no—
262C2×C32—63no—
263C2×C32—63no—
264C2×C32—61no—
265C2×C32—63no—
266C2×C32—62no—
267C2×C32—66no—
268C2×C32—63no—
269C2×C32—61no—
270C2×C32—123no—
271C2×C32—129no—
272C2×C32—121no—
273C2×C32—123no—
274C2×C32—123no—
275C2×C32—183no—
276C2×C32—183no—
277C2×C32—186no—
278C2×C32—541no—
279C2×C32C2×(C3⋊D3)⋊C313yes—
280C2×C32C3×D3213yes—
281C2×C32C3×D3211yescharacteristic
282C2×C32D3×C3⋊D311yescharacteristic
283C2×C32C2×C3×C3⋊D311yescharacteristic
284C3⋊D3—61no—
285C3⋊D3—63no—
286C3⋊D3—183no—
287C3×D3—23no—
288C3×D3—21no—
289C3×D3—63no—
290C3×D3—61no—
291C3×D3—62no—
292C3×D3—66no—
293C3×D3—182no—
294C3×D3—183no—
295C3×D3—186no—
296C3×D3—183no—
297C3×D3—181no—
298C3×D3—181no—
299C3×D3—543no—
300C22×C3—33no—
301C22×C3—31no—
302C22×C3—93no—
303C22×C3—91no—
304C22×C3—181no—
305C22×C3—183no—
306C22×C3—271no—
307C22×C3—271no—
308C22×C3—541no—
309C2×D3—93no—
310C2×D3—91no—
311C2×D3—273no—
312C2×D3C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
313C3×C4—811no—
314Dic3—273no—
315Dic3—271no—
316Dic3—271no—
317Dic3—543no—
318Dic3—541no—
319Dic3—813no—
320Dic3—1623no—
321C32—23no—
322C32—21no—
323C32—21no—
324C32—21no—
325C32—23no—
326C32—23no—
327C32—33no—
328C32—33no—
329C32—31no—
330C32—33no—
331C32—43no—
332C32—41no—
333C32—63no—
334C32—61no—
335C32—69no—
336C32—63no—
337C32—63no—
338C32—63no—
339C32—61no—
340C32—63no—
341C32—63no—
342C32—123no—
343C32—121no—
344C32—123no—
345C32—129no—
346C32—123no—
347C32#638⋊C313yescomplemented
348C32C3×#62511yescharacteristic
349C32C3×#62513yescomplemented
350C32#629011yescharacteristic, complemented
351C32C3×#63811yescharacteristic
352D4—811noSylow
353C2×C3—23no—
354C2×C3—21no—
355C2×C3—33no—
356C2×C3—31no—
357C2×C3—63no—
358C2×C3—61no—
359C2×C3—63no—
360C2×C3—61no—
361C2×C3—63no—
362C2×C3—61no—
363C2×C3—121no—
364C2×C3—123no—
365C2×C3—183no—
366C2×C3—181no—
367C2×C3—182no—
368C2×C3—186no—
369C2×C3—541no—
370C2×C3—542no—
371C2×C3—541no—
372C2×C3D3×(C3⋊D3)⋊C313yes—
373C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
374C2×C3C3×D3×C3⋊D311yescharacteristic
375D3—21no—
376D3—183no—
377D3—181no—
378D3—543no—
379C22—31no—
380C22—271no—
381C4—811no—
382C3—23no—
383C3—21no—
384C3—33no—
385C3—31no—
386C3—61no—
387C3—63no—
388C3—61no—
389C3—63no—
390C3—121no—
391C3—123no—
392C3#6290⋊C313yescomplemented
393C3#1061997711yescharacteristic, complemented
394C3C3×#629011yescharacteristic
395C2—61no—
396C2—541no—
397C2D3×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. #10620145C3semidirect
11. C2×C3×C3⋊(C3⋊D3)C2×C3semidirect
14. C2×C33×D3D3semidirect
15. C2×C33×D3C2×C3semidirect
16. C3⋊(C3⋊(C3⋊Dic3))C2×C3semidirect
20. C2×C3⋊((C3⋊D3)⋊C3)D3semidirect
22. C2×D3×H(3,𝔽3)D3semidirect
28. C32×H(3,𝔽3)D4semidirect
62. C2×C3⋊(C3⋊D3)C3×D3semidirect
76. C2×C32×D3C3×D3semidirect
77. C2×C32×D3C3⋊D3semidirect
97. C34#67semidirect
98. C34C3×D4semidirect
105. C3×H(3,𝔽3)#67semidirect
106. C3×H(3,𝔽3)#67semidirect
191. C2×C3×D3(C3⋊D3)⋊C3semidirect
226. C33#625semidirect
228. C33C3×#67semidirect
229. C33C3×#67semidirect
230. C33#638semidirect
238. H(3,𝔽3)#625semidirect
312. C2×D3C3⋊((C3⋊D3)⋊C3)semidirect
347. C32#638⋊C3semidirect
349. C32C3×#625semidirect
350. C32#6290semidirect
392. C3#6290⋊C3semidirect
393. 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
#106201453
C3×#62903
#106199773
#6290⋊C33