Finite Group Databasebeta

← #14518830

Subgroups — #14518830

Order 1944.

929 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 929 conjugacy classes of subgroups — too many to draw. Only its 79 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
2C3×C3⋊#1084C211yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
4#10620154—31nomaximal
5#10620150—31nomaximal
6#10619901—33nomaximal
7#10619883—31nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3⋊(C3⋊((C3⋊D3)⋊C3))C412yescomplemented
10C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic
11C2×C3×C3⋊(C3⋊D3)—31no—
12C3×C3⋊(C3⋊Dic3)D311yescharacteristic, complemented
13C32×C3⋊Dic3—31no—
14C32×C3⋊Dic3—31no—
15C32×C3⋊Dic3—31no—
16C32×C3⋊Dic3—61no—
17C2×C3⋊((C3⋊D3)⋊C3)—31no—
18C2×C3⋊((C3⋊D3)⋊C3)—33no—
19C2×C3⋊((C3⋊D3)⋊C3)—63no—
20C2×C3⋊((C3⋊D3)⋊C3)—61no—
21C3⋊#1084D311yescharacteristic, complemented
22C3×#1084—33no—
23C3×#1084—63no—
24C3⋊((C3⋊Dic3)⋊C3)D313yescomplemented
25C3×(C3⋊Dic3)⋊C3—31no—
26C3×(C3⋊Dic3)⋊C3—61no—
27C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
28#6294—91no—
29#6294—93no—
30#6289—91no—
31#6289—91no—
32#6289—93no—
33#6289—93no—
34Dic3×C3⋊D3—91no—
35((C3⋊D3)⋊C3)⋊C4—93no—
36C2×C34—21no—
37C2×C34C2×D311yescharacteristic
38C2×C34C2×D311yescharacteristic
39C3⋊(C3⋊(C3⋊D3))Dic312yescomplemented
40C3×C3⋊(C3⋊D3)—32no—
41C2×C3×H(3,𝔽3)—21no—
42C2×C3×H(3,𝔽3)—21no—
43C2×C3×H(3,𝔽3)—23no—
44C2×C3×H(3,𝔽3)—23no—
45C2×C3×H(3,𝔽3)—43no—
46C2×C3×H(3,𝔽3)—41no—
47C2×C3×H(3,𝔽3)C2×D311yescharacteristic
48C2×C3×H(3,𝔽3)C2×D313yes—
49C3⋊((C3⋊D3)⋊C3)—32no—
50C3⋊((C3⋊D3)⋊C3)—36no—
51C3⋊((C3⋊D3)⋊C3)—66no—
52C3⋊((C3⋊D3)⋊C3)—62no—
53C2×C3⋊(C3⋊D3)—31no—
54C2×C3⋊(C3⋊D3)—31no—
55C2×C3⋊(C3⋊D3)—33no—
56C2×C3⋊(C3⋊D3)—61no—
57C2×C3⋊(C3⋊D3)—63no—
58C2×C3⋊(C3⋊D3)—93no—
59C2×C3⋊(C3⋊D3)—183no—
60C2×C3×C3⋊D3—93no—
61C2×C3×C3⋊D3—91no—
62C2×C3×C3⋊D3—91no—
63C2×C3×C3⋊D3—181no—
64C2×C3×C3⋊D3—183no—
65C3⋊(C3⋊Dic3)C3⋊D311yescharacteristic, complemented
66C3×C3⋊Dic3—33no—
67C3×C3⋊Dic3—33no—
68C3×C3⋊Dic3—33no—
69C3×C3⋊Dic3—31no—
70C3×C3⋊Dic3—31no—
71C3×C3⋊Dic3—31no—
72C3×C3⋊Dic3—31no—
73C3×C3⋊Dic3—61no—
74C3×C3⋊Dic3—61no—
75C3×C3⋊Dic3—63no—
76C3×C3⋊Dic3—93no—
77C32×Dic3—93no—
78C32×Dic3—91no—
79C32×Dic3—93no—
80C32×Dic3—91no—
81C32×Dic3—91no—
82C32×Dic3—183no—
83C32×Dic3—181no—
84C2×(C3⋊D3)⋊C3—93no—
85C2×(C3⋊D3)⋊C3—183no—
86#1084—33no—
87#1084—63no—
88(C3⋊Dic3)⋊C3—33no—
89(C3⋊Dic3)⋊C3—63no—
90C34—21no—
91C34C4×D311yescharacteristic, complemented
92C34C2×Dic311yescharacteristic, complemented
93C3×H(3,𝔽3)—21no—
94C3×H(3,𝔽3)—21no—
95C3×H(3,𝔽3)—23no—
96C3×H(3,𝔽3)—23no—
97C3×H(3,𝔽3)—43no—
98C3×H(3,𝔽3)—41no—
99C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
100C3×H(3,𝔽3)C4×D313yescomplemented
101C4×C3⋊D3—271no—
102C4×C3⋊D3—271no—
103#624—273no—
104#624—273no—
105#624—271no—
106#624—279no—
107D3×Dic3—271no—
108D3×Dic3—273no—
109D3×Dic3—271no—
110C2×C33—23no—
111C2×C33—21no—
112C2×C33—21no—
113C2×C33—21no—
114C2×C33—23no—
115C2×C33—21no—
116C2×C33—21no—
117C2×C33—33no—
118C2×C33—33no—
119C2×C33—41no—
120C2×C33—43no—
121C2×C33—41no—
122C2×C33—63no—
123C2×C33—63no—
124C2×C33—63no—
125C2×C33—123no—
126C2×C33D3211yescharacteristic
127C2×C33D3213yes—
128C2×C33D3211yescharacteristic
129C2×C33D3211yescharacteristic
130C2×C33C2×C3⋊D311yescharacteristic
131C3⋊(C3⋊D3)—32no—
132C3⋊(C3⋊D3)—32no—
133C3⋊(C3⋊D3)—36no—
134C3⋊(C3⋊D3)—62no—
135C3⋊(C3⋊D3)—66no—
136C3⋊(C3⋊D3)—96no—
137C3⋊(C3⋊D3)—186no—
138C3×C3⋊D3—92no—
139C3×C3⋊D3—96no—
140C3×C3⋊D3—92no—
141C3×C3⋊D3—182no—
142C3×C3⋊D3—186no—
143C2×H(3,𝔽3)—23no—
144C2×H(3,𝔽3)—23no—
145C2×H(3,𝔽3)—23no—
146C2×H(3,𝔽3)—43no—
147C2×H(3,𝔽3)—43no—
148C2×H(3,𝔽3)—46no—
149C2×H(3,𝔽3)—43no—
150C2×H(3,𝔽3)D3213yes—
151(C3⋊D3)⋊C3—96no—
152(C3⋊D3)⋊C3—186no—
153C2×C3⋊D3—91no—
154C2×C3⋊D3—93no—
155C2×C3⋊D3—91no—
156C2×C3⋊D3—93no—
157C2×C3⋊D3—181no—
158C2×C3⋊D3—183no—
159C2×C3⋊D3—183no—
160C2×C3⋊D3—271no—
161C2×C3⋊D3—279no—
162C2×C3⋊D3—541no—
163C2×C3⋊D3—541no—
164C2×C3⋊D3—549no—
165C2×C3⋊D3—542no—
166C2×C3×D3—271no—
167C2×C3×D3—273no—
168C2×C3×D3—271no—
169C2×C3×D3—541no—
170C2×C3×D3—543no—
171C32×C4—271no—
172C32×C4—271no—
173C3⋊Dic3—31no—
174C3⋊Dic3—31no—
175C3⋊Dic3—31no—
176C3⋊Dic3—31no—
177C3⋊Dic3—61no—
178C3⋊Dic3—61no—
179C3⋊Dic3—93no—
180C3×Dic3—93no—
181C3×Dic3—99no—
182C3×Dic3—99no—
183C3×Dic3—93no—
184C3×Dic3—93no—
185C3×Dic3—91no—
186C3×Dic3—93no—
187C3×Dic3—93no—
188C3×Dic3—91no—
189C3×Dic3—91no—
190C3×Dic3—183no—
191C3×Dic3—181no—
192C3×Dic3—183no—
193C3×Dic3—189no—
194C3×Dic3—271no—
195C3×Dic3—541no—
196C33—21no—
197C33—23no—
198C33—21no—
199C33—21no—
200C33—23no—
201C33—21no—
202C33—21no—
203C33—33no—
204C33—33no—
205C33—41no—
206C33—43no—
207C33—41no—
208C33—63no—
209C33—63no—
210C33—63no—
211C33—123no—
212C33D3×Dic311yescharacteristic
213C33D3×Dic313yescomplemented
214C33D3×Dic311yescharacteristic, complemented
215C33#62411yescharacteristic, complemented
216C33C4×C3⋊D311yescharacteristic, complemented
217H(3,𝔽3)—23no—
218H(3,𝔽3)—23no—
219H(3,𝔽3)—23no—
220H(3,𝔽3)—43no—
221H(3,𝔽3)—43no—
222H(3,𝔽3)—46no—
223H(3,𝔽3)—43no—
224H(3,𝔽3)#62413yescomplemented
225C2×Dic3—811no—
226C4×D3—813no—
227C4×D3—811no—
228C4×D3—811no—
229C4×D3—813no—
230C2×C32—23no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32—23no—
235C2×C32—23no—
236C2×C32—31no—
237C2×C32—39no—
238C2×C32—33no—
239C2×C32—31no—
240C2×C32—43no—
241C2×C32—41no—
242C2×C32—61no—
243C2×C32—69no—
244C2×C32—61no—
245C2×C32—63no—
246C2×C32—62no—
247C2×C32—61no—
248C2×C32—61no—
249C2×C32—63no—
250C2×C32—69no—
251C2×C32—61no—
252C2×C32—121no—
253C2×C32—123no—
254C2×C32—129no—
255C2×C32—121no—
256C2×C32—122no—
257C2×C32—121no—
258C2×C32((C3⋊D3)⋊C3)⋊C213yes—
259C2×C32D3×C3⋊D311yescharacteristic
260C2×C32D3×C3⋊D311yescharacteristic
261C2×C32#111311yescharacteristic
262C2×C32#111313yes—
263C3⋊D3—92no—
264C3⋊D3—96no—
265C3⋊D3—92no—
266C3⋊D3—96no—
267C3⋊D3—182no—
268C3⋊D3—186no—
269C3⋊D3—186no—
270C3⋊D3—272no—
271C3⋊D3—2718no—
272C3⋊D3—542no—
273C3⋊D3—542no—
274C3⋊D3—5418no—
275C3⋊D3—544no—
276C3×D3—272no—
277C3×D3—276no—
278C3×D3—272no—
279C3×D3—542no—
280C3×D3—546no—
281C22×C3—811no—
282C2×D3—273no—
283C2×D3—271no—
284C2×D3—271no—
285C2×D3—543no—
286C2×D3—541no—
287C2×D3—813no—
288C2×D3—1623no—
289C3×C4—273no—
290C3×C4—273no—
291C3×C4—271no—
292C3×C4—271no—
293Dic3—93no—
294Dic3—91no—
295Dic3—93no—
296Dic3—91no—
297Dic3—91no—
298Dic3—181no—
299Dic3—183no—
300Dic3—271no—
301Dic3—541no—
302C32—23no—
303C32—21no—
304C32—23no—
305C32—21no—
306C32—21no—
307C32—23no—
308C32—31no—
309C32—33no—
310C32—39no—
311C32—31no—
312C32—43no—
313C32—41no—
314C32—61no—
315C32—61no—
316C32—69no—
317C32—63no—
318C32—62no—
319C32—61no—
320C32—61no—
321C32—63no—
322C32—69no—
323C32—61no—
324C32—121no—
325C32—123no—
326C32—121no—
327C32—129no—
328C32—122no—
329C32—121no—
330C32((C3⋊D3)⋊C3)⋊C413yescomplemented
331C32Dic3×C3⋊D311yescharacteristic
332C32#628911yescharacteristic, complemented
333C32#629411yescharacteristic
334C32#629413yescomplemented
335C2×C4—2431noSylow
336C2×C3—23no—
337C2×C3—21no—
338C2×C3—31no—
339C2×C3—33no—
340C2×C3—61no—
341C2×C3—63no—
342C2×C3—61no—
343C2×C3—63no—
344C2×C3—121no—
345C2×C3—123no—
346C2×C3—812no—
347C2×C3((C3⋊D3)⋊C3)⋊D313yes—
348C2×C3#6643211yescharacteristic
349C2×C3C3⋊#111311yescharacteristic
350D3—276no—
351D3—272no—
352D3—272no—
353D3—546no—
354D3—542no—
355D3—816no—
356D3—1626no—
357C22—811no—
358C4—271no—
359C4—271no—
360C3—23no—
361C3—21no—
362C3—33no—
363C3—31no—
364C3—63no—
365C3—61no—
366C3—61no—
367C3—63no—
368C3—121no—
369C3—123no—
370C3#1061988313yescomplemented
371C3#1061990111yescharacteristic, complemented
372C3#1062015411yescharacteristic
373C2—812no—
374C2#1175809011yescharacteristic
subgroupG/H
center, hypercenterC2#11758090
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C3⋊#1113
Fitting, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33D32
prime radicalC2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊#1084C2semidirect
3. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
9. C3⋊(C3⋊((C3⋊D3)⋊C3))C4semidirect
12. C3×C3⋊(C3⋊Dic3)D3semidirect
21. C3⋊#1084D3semidirect
24. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
39. C3⋊(C3⋊(C3⋊D3))Dic3semidirect
65. C3⋊(C3⋊Dic3)C3⋊D3semidirect
91. C34C4×D3semidirect
92. C34C2×Dic3semidirect
99. C3×H(3,𝔽3)C4×D3semidirect
100. C3×H(3,𝔽3)C4×D3semidirect
213. C33D3×Dic3semidirect
214. C33D3×Dic3semidirect
215. C33#624semidirect
216. C33C4×C3⋊D3semidirect
224. H(3,𝔽3)#624semidirect
330. C32((C3⋊D3)⋊C3)⋊C4semidirect
332. C32#6289semidirect
334. C32#6294semidirect
370. C3#10619883semidirect
371. C3#10619901semidirect

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
C3×C3⋊#10842
C3×C3⋊((C3⋊Dic3)⋊C3)2
#106201543
#106201503
#106199013
#106198833