Finite Group Databasebeta

← #14518837

Subgroups — #14518837

Order 1944.

1001 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 1001 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊#272C211yesmaximal, characteristic, complemented
2C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C211yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
4#10620157—31nomaximal
5#10620152—31nomaximal
6#10619904—33nomaximal
7#10619887—31nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊#272—21no—
10C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
11C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic, complemented
12C2×C3×C3⋊(C3⋊D3)—31no—
13C2×C32×C3⋊D3—31no—
14C2×C32×C3⋊D3—31no—
15C2×C32×C3⋊D3—61no—
16C3×C3⋊(C3⋊Dic3)D311yescharacteristic, complemented
17C32×C3⋊Dic3—31no—
18C2×C3⋊#272D311yescharacteristic, complemented
19C2×C3×#272—33no—
20C2×C3×#272—63no—
21C2×C3⋊((C3⋊D3)⋊C3)—31no—
22C2×C3⋊((C3⋊D3)⋊C3)—33no—
23C2×C3⋊((C3⋊D3)⋊C3)—63no—
24C2×C3⋊((C3⋊D3)⋊C3)—61no—
25C3⋊((C3⋊Dic3)⋊C3)D313yescomplemented
26C3×(C3⋊Dic3)⋊C3—31no—
27C3×(C3⋊Dic3)⋊C3—61no—
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29#6295—91no—
30#6295—93no—
31#6292—91no—
32#6292—93no—
33#6291—93no—
34#6291—91no—
35#6290—91no—
36#6200—93no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C2×D311yescharacteristic
40C3⋊(C3⋊(C3⋊D3))—21no—
41C3×C3⋊(C3⋊D3)—61no—
42C32×C3⋊D3—62no—
43C32×C3⋊D3—61no—
44C32×C3⋊D3—61no—
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)C2×D311yescharacteristic
52C2×C3×H(3,𝔽3)C2×D313yes—
53C3⋊#272—21no—
54C3×#272—66no—
55C3×#272—63no—
56C3⋊((C3⋊D3)⋊C3)—62no—
57C3⋊((C3⋊D3)⋊C3)—66no—
58C3⋊((C3⋊D3)⋊C3)—63no—
59C3⋊((C3⋊D3)⋊C3)—61no—
60C2×C3⋊(C3⋊D3)—31no—
61C2×C3⋊(C3⋊D3)—31no—
62C2×C3⋊(C3⋊D3)—33no—
63C2×C3⋊(C3⋊D3)—61no—
64C2×C3⋊(C3⋊D3)—63no—
65C2×C3⋊(C3⋊D3)—93no—
66C2×C3⋊(C3⋊D3)—183no—
67C2×C3×C3⋊D3—33no—
68C2×C3×C3⋊D3—33no—
69C2×C3×C3⋊D3—31no—
70C2×C3×C3⋊D3—31no—
71C2×C3×C3⋊D3—61no—
72C2×C3×C3⋊D3—63no—
73C2×C3×C3⋊D3—93no—
74C2×C3×C3⋊D3—91no—
75C2×C3×C3⋊D3—91no—
76C2×C3×C3⋊D3—181no—
77C2×C3×C3⋊D3—183no—
78C2×C32×D3—93no—
79C2×C32×D3—91no—
80C2×C32×D3—91no—
81C2×C32×D3—183no—
82C2×C32×D3—181no—
83C3⋊(C3⋊Dic3)C3⋊D311yescharacteristic, complemented
84C3×C3⋊Dic3—33no—
85C3×C3⋊Dic3—31no—
86C3×C3⋊Dic3—31no—
87C3×C3⋊Dic3—61no—
88C3×C3⋊Dic3—93no—
89C32×Dic3—93no—
90C32×Dic3—91no—
91C2×#272—33no—
92C2×#272—63no—
93C2×(C3⋊D3)⋊C3—93no—
94C2×(C3⋊D3)⋊C3—183no—
95(C3⋊Dic3)⋊C3—33no—
96(C3⋊Dic3)⋊C3—63no—
97C34—21no—
98C34D1211yescharacteristic, complemented
99C34#6711yescharacteristic, 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)D1213yescomplemented
107C3×H(3,𝔽3)#6711yescharacteristic, complemented
108#638—271no—
109C4⋊(C3⋊D3)—271no—
110#626—273no—
111#626—273no—
112#626—271no—
113#626—279no—
114#626—271no—
115#625—271no—
116#625—273no—
117C2×C33—23no—
118C2×C33—21no—
119C2×C33—21no—
120C2×C33—21no—
121C2×C33—23no—
122C2×C33—21no—
123C2×C33—21no—
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—123no—
133C2×C33D3211yescharacteristic
134C2×C33D3213yes—
135C2×C33D3211yescharacteristic
136C2×C33D3211yescharacteristic
137C2×C33C2×C3⋊D311yescharacteristic
138C3⋊(C3⋊D3)—61no—
139C3⋊(C3⋊D3)—66no—
140C3⋊(C3⋊D3)—62no—
141C3⋊(C3⋊D3)—61no—
142C3⋊(C3⋊D3)—63no—
143C3⋊(C3⋊D3)—183no—
144C3⋊(C3⋊D3)—186no—
145C3×C3⋊D3—62no—
146C3×C3⋊D3—63no—
147C3×C3⋊D3—63no—
148C3×C3⋊D3—66no—
149C3×C3⋊D3—61no—
150C3×C3⋊D3—61no—
151C3×C3⋊D3—182no—
152C3×C3⋊D3—183no—
153C3×C3⋊D3—186no—
154C3×C3⋊D3—181no—
155C3×C3⋊D3—181no—
156C32×D3—182no—
157C32×D3—186no—
158C32×D3—181no—
159C32×D3—183no—
160C32×D3—181no—
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)D3213yes—
169#272—66no—
170#272—63no—
171(C3⋊D3)⋊C3—186no—
172(C3⋊D3)⋊C3—183no—
173C22×C32—271no—
174C2×C3⋊D3—31no—
175C2×C3⋊D3—31no—
176C2×C3⋊D3—61no—
177C2×C3⋊D3—91no—
178C2×C3⋊D3—93no—
179C2×C3⋊D3—91no—
180C2×C3⋊D3—93no—
181C2×C3⋊D3—181no—
182C2×C3⋊D3—183no—
183C2×C3⋊D3—183no—
184C2×C3⋊D3—271no—
185C2×C3⋊D3—279no—
186C2×C3⋊D3—541no—
187C2×C3⋊D3—541no—
188C2×C3⋊D3—549no—
189C2×C3⋊D3—542no—
190C2×C3×D3—93no—
191C2×C3×D3—99no—
192C2×C3×D3—93no—
193C2×C3×D3—91no—
194C2×C3×D3—93no—
195C2×C3×D3—91no—
196C2×C3×D3—183no—
197C2×C3×D3—181no—
198C2×C3×D3—183no—
199C2×C3×D3—189no—
200C2×C3×D3—271no—
201C2×C3×D3—273no—
202C2×C3×D3—271no—
203C2×C3×D3—541no—
204C2×C3×D3—543no—
205C32×C4—271no—
206C3⋊Dic3—31no—
207C3⋊Dic3—31no—
208C3⋊Dic3—61no—
209C3⋊Dic3—93no—
210C3×Dic3—99no—
211C3×Dic3—93no—
212C3×Dic3—93no—
213C3×Dic3—91no—
214C3×Dic3—271no—
215C3×Dic3—541no—
216C33—21no—
217C33—23no—
218C33—21no—
219C33—21no—
220C33—23no—
221C33—21no—
222C33—21no—
223C33—33no—
224C33—33no—
225C33—41no—
226C33—43no—
227C33—41no—
228C33—63no—
229C33—63no—
230C33—63no—
231C33—123no—
232C33#62511yescharacteristic, complemented
233C33#62611yescharacteristic
234C33#62613yescomplemented
235C33#62611yescharacteristic, complemented
236C33C4⋊(C3⋊D3)11yescharacteristic, complemented
237H(3,𝔽3)—23no—
238H(3,𝔽3)—23no—
239H(3,𝔽3)—23no—
240H(3,𝔽3)—43no—
241H(3,𝔽3)—43no—
242H(3,𝔽3)—46no—
243H(3,𝔽3)—43no—
244H(3,𝔽3)#62613yescomplemented
245#67—813no—
246#67—811no—
247#67—811no—
248D12—811no—
249D12—813no—
250C2×C32—23no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—23no—
255C2×C32—23no—
256C2×C32—31no—
257C2×C32—39no—
258C2×C32—33no—
259C2×C32—31no—
260C2×C32—43no—
261C2×C32—41no—
262C2×C32—61no—
263C2×C32—69no—
264C2×C32—61no—
265C2×C32—63no—
266C2×C32—62no—
267C2×C32—61no—
268C2×C32—61no—
269C2×C32—63no—
270C2×C32—69no—
271C2×C32—61no—
272C2×C32—121no—
273C2×C32—123no—
274C2×C32—129no—
275C2×C32—121no—
276C2×C32—122no—
277C2×C32—121no—
278C2×C32—541no—
279C2×C32((C3⋊D3)⋊C3)⋊C213yes—
280C2×C32D3×C3⋊D311yescharacteristic
281C2×C32D3×C3⋊D311yescharacteristic
282C2×C32#111311yescharacteristic
283C2×C32#111313yes—
284C3⋊D3—61no—
285C3⋊D3—61no—
286C3⋊D3—62no—
287C3⋊D3—182no—
288C3⋊D3—186no—
289C3⋊D3—183no—
290C3⋊D3—181no—
291C3⋊D3—181no—
292C3⋊D3—186no—
293C3⋊D3—183no—
294C3⋊D3—541no—
295C3⋊D3—549no—
296C3⋊D3—542no—
297C3⋊D3—5418no—
298C3⋊D3—544no—
299C3⋊D3—542no—
300C3×D3—182no—
301C3×D3—186no—
302C3×D3—183no—
303C3×D3—189no—
304C3×D3—186no—
305C3×D3—1818no—
306C3×D3—183no—
307C3×D3—181no—
308C3×D3—181no—
309C3×D3—183no—
310C3×D3—541no—
311C3×D3—543no—
312C3×D3—542no—
313C3×D3—546no—
314C3×D3—541no—
315C22×C3—273no—
316C22×C3—271no—
317C22×C3—811no—
318C2×D3—93no—
319C2×D3—91no—
320C2×D3—91no—
321C2×D3—181no—
322C2×D3—183no—
323C2×D3—273no—
324C2×D3—271no—
325C2×D3—271no—
326C2×D3—543no—
327C2×D3—541no—
328C2×D3—813no—
329C2×D3—1623no—
330C3×C4—273no—
331C3×C4—271no—
332Dic3—93no—
333Dic3—91no—
334Dic3—271no—
335Dic3—541no—
336C32—23no—
337C32—21no—
338C32—21no—
339C32—23no—
340C32—23no—
341C32—21no—
342C32—31no—
343C32—31no—
344C32—33no—
345C32—39no—
346C32—43no—
347C32—41no—
348C32—61no—
349C32—61no—
350C32—69no—
351C32—63no—
352C32—62no—
353C32—61no—
354C32—61no—
355C32—61no—
356C32—63no—
357C32—69no—
358C32—121no—
359C32—123no—
360C32—121no—
361C32—129no—
362C32—122no—
363C32—121no—
364C32#620013yescomplemented
365C32#629211yescharacteristic
366C32#629211yescharacteristic, complemented
367C32#629511yescharacteristic
368C32#629513yescomplemented
369D4—2431noSylow
370C2×C3—23no—
371C2×C3—21no—
372C2×C3—31no—
373C2×C3—33no—
374C2×C3—61no—
375C2×C3—61no—
376C2×C3—63no—
377C2×C3—63no—
378C2×C3—121no—
379C2×C3—123no—
380C2×C3—543no—
381C2×C3—541no—
382C2×C3—1621no—
383C2×C3((C3⋊D3)⋊C3)⋊D313yes—
384C2×C3#6643211yescharacteristic
385C2×C3C3⋊#111311yescharacteristic
386D3—183no—
387D3—181no—
388D3—182no—
389D3—186no—
390D3—181no—
391D3—546no—
392D3—542no—
393D3—541no—
394D3—543no—
395D3—541no—
396D3—1623no—
397D3—1626no—
398C22—271no—
399C22—811no—
400C4—271no—
401C3—23no—
402C3—21no—
403C3—33no—
404C3—31no—
405C3—61no—
406C3—63no—
407C3—63no—
408C3—61no—
409C3—121no—
410C3—123no—
411C3#1061988713yescomplemented
412C3#1061990411yescharacteristic, complemented
413C3#1062015611yescharacteristic
414C2—541no—
415C2—1621no—
416C2#1175809011yescharacteristic
subgroupG/H
center, hypercenterC2#11758090
commutator, Fitting, cosocleC2×C32×H(3,𝔽3)C22
FrattiniC2×C3C3⋊#1113
socleC2×C33D32
hypocenterC32×H(3,𝔽3)D4
LCSG ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊#272C2semidirect
2. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2semidirect
3. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
11. C2×C3⋊(C3⋊(C3⋊D3))D3semidirect
16. C3×C3⋊(C3⋊Dic3)D3semidirect
18. C2×C3⋊#272D3semidirect
25. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
28. C32×H(3,𝔽3)D4semidirect
83. C3⋊(C3⋊Dic3)C3⋊D3semidirect
98. C34D12semidirect
99. C34#67semidirect
106. C3×H(3,𝔽3)D12semidirect
107. C3×H(3,𝔽3)#67semidirect
232. C33#625semidirect
234. C33#626semidirect
235. C33#626semidirect
236. C33C4⋊(C3⋊D3)semidirect
244. H(3,𝔽3)#626semidirect
364. C32#6200semidirect
366. C32#6292semidirect
368. C32#6295semidirect
411. C3#10619887semidirect
412. C3#10619904semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊#2722
C2×C3⋊(C3⋊((C3⋊D3)⋊C3))2
C3×C3⋊((C3⋊Dic3)⋊C3)2
#106201573
#106201523
#106199043
#106198873