Finite Group Databasebeta

← #72229124

Subgroups — #72229124

Order 5832.

1564 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 106 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
1H(3,𝔽3)×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
2C2×H(3,𝔽3)×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C2×#13091503C211yesmaximal, characteristic, complemented
4#14518683C311yesmaximal, characteristic, complemented
5#14518675C311yesmaximal, characteristic, complemented
6C3×#6291⋊C3—31nomaximal
7C3×#6292⋊C3—31nomaximal
8#14516803C312yesmaximal, complemented
9#13091503—21no—
10H(3,𝔽3)×(C3⋊D3)⋊C3—21no—
11C2×H(3,𝔽3)2C2211yescharacteristic
12C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2×C311yescharacteristic, complemented
13C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2×C311yescharacteristic, complemented
14C2×C3⋊D3×H(3,𝔽3)C2×C311yescharacteristic, complemented
15C2×C3×C3⋊((C3⋊D3)⋊C3)—31no—
16C2×C3×C3⋊((C3⋊D3)⋊C3)—31no—
17C2×C3×D3×H(3,𝔽3)—31no—
18C2×C32×(C3⋊D3)⋊C3—21no—
19C2×C32×(C3⋊D3)⋊C3D311yescharacteristic, complemented
20C2×C32×(C3⋊D3)⋊C3C2×C311yescharacteristic, complemented
21H(3,𝔽3)×C3⋊Dic3C2×C311yescharacteristic, complemented
22C3×Dic3×H(3,𝔽3)—31no—
23C32×(C3⋊Dic3)⋊C3—21no—
24C32×(C3⋊Dic3)⋊C3D311yescharacteristic, complemented
25C32×(C3⋊Dic3)⋊C3C2×C311yescharacteristic, complemented
26C2×#92301C2×C312yescomplemented
27C2×#92258—61no—
28C2×(C3⋊D3)⋊H(3,𝔽3)—21no—
29C2×(C3⋊D3)⋊H(3,𝔽3)—22no—
30C2×(C3⋊D3)⋊H(3,𝔽3)C2×C312yescomplemented
31(C3⋊Dic3)⋊H(3,𝔽3)—21no—
32(C3⋊Dic3)⋊H(3,𝔽3)—22no—
33(C3⋊Dic3)⋊H(3,𝔽3)C2×C312yescomplemented
34H(3,𝔽3)2D411yescharacteristic, complemented, Sylow
35#10620152C3211yescharacteristic, complemented
36C3×#6292—31no—
37C3×#6291—31no—
38C32×#626—91no—
39C3×#638⋊C3—91no—
40C3×C4⋊((C3⋊D3)⋊C3)—91no—
41#6291⋊C3—31no—
42#6291⋊C3—32no—
43#6291⋊C3—91no—
44#6292⋊C3—31no—
45#6292⋊C3—32no—
46#6292⋊C3—91no—
47C2×C32×H(3,𝔽3)—21no—
48C2×C32×H(3,𝔽3)—21no—
49C2×C32×H(3,𝔽3)C2×D311yescharacteristic
50C2×C32×H(3,𝔽3)C2×D311yescharacteristic
51C2×C32×H(3,𝔽3)C22×C311yescharacteristic
52C2×C32×H(3,𝔽3)C22×C311yescharacteristic
53C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
54C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
55C3⋊D3×H(3,𝔽3)—21no—
56C3×C3⋊((C3⋊D3)⋊C3)—61no—
57C3×C3⋊((C3⋊D3)⋊C3)—61no—
58C3×D3×H(3,𝔽3)—61no—
59C32×(C3⋊D3)⋊C3—22no—
60C32×(C3⋊D3)⋊C3—21no—
61C32×(C3⋊D3)⋊C3—21no—
62C2×C32⋊H(3,𝔽3)—21no—
63C2×C32⋊H(3,𝔽3)—21no—
64C2×C32⋊H(3,𝔽3)—21no—
65C2×C32⋊H(3,𝔽3)—22no—
66C2×C32⋊H(3,𝔽3)—22no—
67C2×C32⋊H(3,𝔽3)—42no—
68C2×C32⋊H(3,𝔽3)—41no—
69C2×C32⋊H(3,𝔽3)—41no—
70C2×C32⋊H(3,𝔽3)C22×C312yes—
71#92301—22no—
72#92258—62no—
73(C3⋊D3)⋊H(3,𝔽3)—22no—
74(C3⋊D3)⋊H(3,𝔽3)—24no—
75(C3⋊D3)⋊H(3,𝔽3)—22no—
76C2×C3⋊(C3⋊(C3⋊D3))C2×C3211yescharacteristic, complemented
77C2×C3×C3⋊(C3⋊D3)—31no—
78C2×C3×C3⋊(C3⋊D3)—31no—
79C2×C32×C3⋊D3—21no—
80C2×C32×C3⋊D3—91no—
81C2×C32×C3⋊D3C3×D311yescharacteristic, complemented
82C2×C32×C3⋊D3C2×C3211yescharacteristic, complemented
83C2×C33×D3—31no—
84C2×C33×D3—31no—
85C2×C33×D3—61no—
86C32×C3⋊Dic3—21no—
87C32×C3⋊Dic3C3×D311yescharacteristic, complemented
88C32×C3⋊Dic3C2×C3211yescharacteristic, complemented
89C33×Dic3—31no—
90C33×Dic3—31no—
91C33×Dic3—61no—
92C22×C3×H(3,𝔽3)—91no—
93C2×C3⋊((C3⋊D3)⋊C3)—31no—
94C2×C3⋊((C3⋊D3)⋊C3)—31no—
95C2×C3⋊((C3⋊D3)⋊C3)—32no—
96C2×C3⋊((C3⋊D3)⋊C3)—32no—
97C2×C3⋊((C3⋊D3)⋊C3)—61no—
98C2×C3⋊((C3⋊D3)⋊C3)—61no—
99C2×C3⋊((C3⋊D3)⋊C3)—62no—
100C2×C3⋊((C3⋊D3)⋊C3)—91no—
101C2×C3⋊((C3⋊D3)⋊C3)—91no—
102C2×C3⋊((C3⋊D3)⋊C3)—181no—
103C2×C3⋊((C3⋊D3)⋊C3)—181no—
104C2×D3×H(3,𝔽3)—31no—
105C2×D3×H(3,𝔽3)—32no—
106C2×D3×H(3,𝔽3)—62no—
107C2×D3×H(3,𝔽3)—61no—
108C2×D3×H(3,𝔽3)—91no—
109C2×C3×(C3⋊D3)⋊C3—22no—
110C2×C3×(C3⋊D3)⋊C3—21no—
111C2×C3×(C3⋊D3)⋊C3—31no—
112C2×C3×(C3⋊D3)⋊C3—31no—
113C2×C3×(C3⋊D3)⋊C3—61no—
114C2×C3×(C3⋊D3)⋊C3—62no—
115C2×C3×(C3⋊D3)⋊C3—61no—
116C2×C3×(C3⋊D3)⋊C3—61no—
117C2×C3×(C3⋊D3)⋊C3—91no—
118C2×C3×(C3⋊D3)⋊C3—91no—
119C2×C3×(C3⋊D3)⋊C3—181no—
120C2×C3×(C3⋊D3)⋊C3—181no—
121C2×C3×(C3⋊D3)⋊C3C3×D311yescharacteristic
122C2×C3×(C3⋊D3)⋊C3C3×D312yescomplemented
123C3×C4×H(3,𝔽3)—91no—
124Dic3×H(3,𝔽3)—31no—
125Dic3×H(3,𝔽3)—32no—
126Dic3×H(3,𝔽3)—62no—
127Dic3×H(3,𝔽3)—61no—
128Dic3×H(3,𝔽3)—91no—
129C3×(C3⋊Dic3)⋊C3—22no—
130C3×(C3⋊Dic3)⋊C3—21no—
131C3×(C3⋊Dic3)⋊C3—31no—
132C3×(C3⋊Dic3)⋊C3—31no—
133C3×(C3⋊Dic3)⋊C3—61no—
134C3×(C3⋊Dic3)⋊C3—62no—
135C3×(C3⋊Dic3)⋊C3—61no—
136C3×(C3⋊Dic3)⋊C3—61no—
137C3×(C3⋊Dic3)⋊C3C3×D311yescharacteristic
138C3×(C3⋊Dic3)⋊C3C3×D312yescomplemented
139C32×H(3,𝔽3)—21no—
140C32×H(3,𝔽3)—21no—
141C32×H(3,𝔽3)D1211yescharacteristic, complemented
142C32×H(3,𝔽3)#6711yescharacteristic, complemented
143C32×H(3,𝔽3)C3×D411yescharacteristic, complemented
144C32×H(3,𝔽3)C3×D411yescharacteristic, complemented
145C32⋊H(3,𝔽3)—21no—
146C32⋊H(3,𝔽3)—21no—
147C32⋊H(3,𝔽3)—21no—
148C32⋊H(3,𝔽3)—22no—
149C32⋊H(3,𝔽3)—22no—
150C32⋊H(3,𝔽3)—42no—
151C32⋊H(3,𝔽3)—41no—
152C32⋊H(3,𝔽3)—41no—
153C32⋊H(3,𝔽3)C3×D412yescomplemented
154C3×#638—91no—
155C3×C4⋊(C3⋊D3)—91no—
156C32×#67—271no—
157C32×D12—271no—
158#6292—31no—
159#6292—91no—
160#6291—31no—
161#6291—91no—
162C3×#626—92no—
163C3×#626—91no—
164C3×#626—91no—
165C3×#626—271no—
166C3×#626—271no—
167#638⋊C3—92no—
168#638⋊C3—91no—
169C4⋊((C3⋊D3)⋊C3)—92no—
170C4⋊((C3⋊D3)⋊C3)—91no—
171C2×C34—21no—
172C2×C34—21no—
173C2×C34—21no—
174C2×C34—21no—
175C2×C34—41no—
176C2×C34D3211yescharacteristic
177C2×C34C2×C3×D311yescharacteristic
178C2×C34C2×C3×D311yescharacteristic
179C2×C34C22×C3211yescharacteristic
180C3⋊(C3⋊(C3⋊D3))—21no—
181C3×C3⋊(C3⋊D3)—61no—
182C3×C3⋊(C3⋊D3)—61no—
183C32×C3⋊D3—22no—
184C32×C3⋊D3—21no—
185C32×C3⋊D3—21no—
186C32×C3⋊D3—181no—
187C33×D3—62no—
188C33×D3—61no—
189C33×D3—61no—
190C2×C3×H(3,𝔽3)—22no—
191C2×C3×H(3,𝔽3)—21no—
192C2×C3×H(3,𝔽3)—22no—
193C2×C3×H(3,𝔽3)—21no—
194C2×C3×H(3,𝔽3)—21no—
195C2×C3×H(3,𝔽3)—21no—
196C2×C3×H(3,𝔽3)—21no—
197C2×C3×H(3,𝔽3)—22no—
198C2×C3×H(3,𝔽3)—21no—
199C2×C3×H(3,𝔽3)—22no—
200C2×C3×H(3,𝔽3)—22no—
201C2×C3×H(3,𝔽3)—31no—
202C2×C3×H(3,𝔽3)—31no—
203C2×C3×H(3,𝔽3)—31no—
204C2×C3×H(3,𝔽3)—31no—
205C2×C3×H(3,𝔽3)—41no—
206C2×C3×H(3,𝔽3)—41no—
207C2×C3×H(3,𝔽3)—42no—
208C2×C3×H(3,𝔽3)—42no—
209C2×C3×H(3,𝔽3)—41no—
210C2×C3×H(3,𝔽3)—41no—
211C2×C3×H(3,𝔽3)—42no—
212C2×C3×H(3,𝔽3)—41no—
213C2×C3×H(3,𝔽3)—42no—
214C2×C3×H(3,𝔽3)—42no—
215C2×C3×H(3,𝔽3)—42no—
216C2×C3×H(3,𝔽3)—42no—
217C2×C3×H(3,𝔽3)—61no—
218C2×C3×H(3,𝔽3)—61no—
219C2×C3×H(3,𝔽3)—61no—
220C2×C3×H(3,𝔽3)—61no—
221C2×C3×H(3,𝔽3)—62no—
222C2×C3×H(3,𝔽3)—62no—
223C2×C3×H(3,𝔽3)—61no—
224C2×C3×H(3,𝔽3)—61no—
225C2×C3×H(3,𝔽3)—61no—
226C2×C3×H(3,𝔽3)—61no—
227C2×C3×H(3,𝔽3)—61no—
228C2×C3×H(3,𝔽3)—61no—
229C2×C3×H(3,𝔽3)—121no—
230C2×C3×H(3,𝔽3)—121no—
231C2×C3×H(3,𝔽3)—121no—
232C2×C3×H(3,𝔽3)—121no—
233C2×C3×H(3,𝔽3)—122no—
234C2×C3×H(3,𝔽3)—122no—
235C2×C3×H(3,𝔽3)—121no—
236C2×C3×H(3,𝔽3)—121no—
237C2×C3×H(3,𝔽3)—181no—
238C2×C3×H(3,𝔽3)C2×C3×D311yescharacteristic
239C2×C3×H(3,𝔽3)C2×C3×D311yescharacteristic
240C2×C3×H(3,𝔽3)C2×C3×D312yes—
241C2×C3×H(3,𝔽3)C2×C3×D312yes—
242C3⋊((C3⋊D3)⋊C3)—61no—
243C3⋊((C3⋊D3)⋊C3)—62no—
244C3⋊((C3⋊D3)⋊C3)—61no—
245C3⋊((C3⋊D3)⋊C3)—62no—
246C3⋊((C3⋊D3)⋊C3)—64no—
247C3⋊((C3⋊D3)⋊C3)—62no—
248C3⋊((C3⋊D3)⋊C3)—62no—
249C3⋊((C3⋊D3)⋊C3)—181no—
250C3⋊((C3⋊D3)⋊C3)—181no—
251C3⋊((C3⋊D3)⋊C3)—182no—
252C3⋊((C3⋊D3)⋊C3)—182no—
253D3×H(3,𝔽3)—62no—
254D3×H(3,𝔽3)—64no—
255D3×H(3,𝔽3)—61no—
256D3×H(3,𝔽3)—62no—
257D3×H(3,𝔽3)—181no—
258C3×(C3⋊D3)⋊C3—21no—
259C3×(C3⋊D3)⋊C3—24no—
260C3×(C3⋊D3)⋊C3—22no—
261C3×(C3⋊D3)⋊C3—22no—
262C3×(C3⋊D3)⋊C3—61no—
263C3×(C3⋊D3)⋊C3—61no—
264C3×(C3⋊D3)⋊C3—62no—
265C3×(C3⋊D3)⋊C3—62no—
266C3×(C3⋊D3)⋊C3—64no—
267C3×(C3⋊D3)⋊C3—62no—
268C3×(C3⋊D3)⋊C3—181no—
269C3×(C3⋊D3)⋊C3—181no—
270C3×(C3⋊D3)⋊C3—182no—
271C3×(C3⋊D3)⋊C3—182no—
272C22×C33—91no—
273C22×C33—91no—
274C22×C33—181no—
275C2×C3⋊(C3⋊D3)—31no—
276C2×C3⋊(C3⋊D3)—31no—
277C2×C3⋊(C3⋊D3)—61no—
278C2×C3⋊(C3⋊D3)—91no—
279C2×C3⋊(C3⋊D3)—91no—
280C2×C3⋊(C3⋊D3)—181no—
281C2×C3⋊(C3⋊D3)—181no—
282C2×C3⋊(C3⋊D3)—541no—
283C2×C3×C3⋊D3—31no—
284C2×C3×C3⋊D3—31no—
285C2×C3×C3⋊D3—61no—
286C2×C3×C3⋊D3—91no—
287C2×C3×C3⋊D3—91no—
288C2×C3×C3⋊D3—92no—
289C2×C3×C3⋊D3—91no—
290C2×C3×C3⋊D3—91no—
291C2×C3×C3⋊D3—181no—
292C2×C3×C3⋊D3—181no—
293C2×C3×C3⋊D3—271no—
294C2×C3×C3⋊D3—271no—
295C2×C3×C3⋊D3—541no—
296C2×C3×C3⋊D3—541no—
297C2×C3×C3⋊D3C32×D311yescharacteristic
298C2×C32×D3—31no—
299C2×C32×D3—32no—
300C2×C32×D3—31no—
301C2×C32×D3—31no—
302C2×C32×D3—62no—
303C2×C32×D3—61no—
304C2×C32×D3—61no—
305C2×C32×D3—91no—
306C2×C32×D3—91no—
307C2×C32×D3—91no—
308C2×C32×D3—91no—
309C2×C32×D3—181no—
310C2×C32×D3—181no—
311C2×C32×D3—181no—
312C2×C32×D3—182no—
313C2×C32×D3—181no—
314C2×C32×D3—271no—
315C2×C32×D3—271no—
316C2×C32×D3—541no—
317C33×C4—91no—
318C33×C4—91no—
319C33×C4—181no—
320C3×C3⋊Dic3—31no—
321C3×C3⋊Dic3—31no—
322C3×C3⋊Dic3—61no—
323C3×C3⋊Dic3C32×D311yescharacteristic
324C32×Dic3—31no—
325C32×Dic3—32no—
326C32×Dic3—31no—
327C32×Dic3—31no—
328C32×Dic3—62no—
329C32×Dic3—61no—
330C32×Dic3—61no—
331C32×Dic3—91no—
332C32×Dic3—91no—
333C32×Dic3—91no—
334C32×Dic3—91no—
335C32×Dic3—181no—
336C32×Dic3—181no—
337C32×Dic3—181no—
338C32×Dic3—182no—
339C32×Dic3—181no—
340C22×H(3,𝔽3)—92no—
341C22×H(3,𝔽3)—91no—
342C22×H(3,𝔽3)—182no—
343C22×H(3,𝔽3)—181no—
344C2×(C3⋊D3)⋊C3—21no—
345C2×(C3⋊D3)⋊C3—32no—
346C2×(C3⋊D3)⋊C3—61no—
347C2×(C3⋊D3)⋊C3—62no—
348C2×(C3⋊D3)⋊C3—92no—
349C2×(C3⋊D3)⋊C3—92no—
350C2×(C3⋊D3)⋊C3—91no—
351C2×(C3⋊D3)⋊C3—91no—
352C2×(C3⋊D3)⋊C3—181no—
353C2×(C3⋊D3)⋊C3—181no—
354C2×(C3⋊D3)⋊C3—182no—
355C2×(C3⋊D3)⋊C3—182no—
356C2×(C3⋊D3)⋊C3—541no—
357C2×(C3⋊D3)⋊C3—541no—
358C2×(C3⋊D3)⋊C3—542no—
359C2×(C3⋊D3)⋊C3(C3⋊D3)⋊C311yescharacteristic, complemented
360C4×H(3,𝔽3)—92no—
361C4×H(3,𝔽3)—91no—
362C4×H(3,𝔽3)—182no—
363C4×H(3,𝔽3)—181no—
364(C3⋊Dic3)⋊C3—21no—
365(C3⋊Dic3)⋊C3—32no—
366(C3⋊Dic3)⋊C3—61no—
367(C3⋊Dic3)⋊C3—62no—
368(C3⋊Dic3)⋊C3(C3⋊D3)⋊C311yescharacteristic, complemented
369C34—21no—
370C34—21no—
371C34—21no—
372C34—21no—
373C34—41no—
374C34#62611yescharacteristic, complemented
375C34C3×D1211yescharacteristic, complemented
376C34C3×#6711yescharacteristic, complemented
377C34C32×D411yescharacteristic, complemented
378C3×H(3,𝔽3)—22no—
379C3×H(3,𝔽3)—21no—
380C3×H(3,𝔽3)—22no—
381C3×H(3,𝔽3)—21no—
382C3×H(3,𝔽3)—21no—
383C3×H(3,𝔽3)—21no—
384C3×H(3,𝔽3)—22no—
385C3×H(3,𝔽3)—21no—
386C3×H(3,𝔽3)—22no—
387C3×H(3,𝔽3)—21no—
388C3×H(3,𝔽3)—22no—
389C3×H(3,𝔽3)—31no—
390C3×H(3,𝔽3)—31no—
391C3×H(3,𝔽3)—31no—
392C3×H(3,𝔽3)—31no—
393C3×H(3,𝔽3)—41no—
394C3×H(3,𝔽3)—41no—
395C3×H(3,𝔽3)—42no—
396C3×H(3,𝔽3)—42no—
397C3×H(3,𝔽3)—41no—
398C3×H(3,𝔽3)—41no—
399C3×H(3,𝔽3)—42no—
400C3×H(3,𝔽3)—41no—
401C3×H(3,𝔽3)—42no—
402C3×H(3,𝔽3)—42no—
403C3×H(3,𝔽3)—42no—
404C3×H(3,𝔽3)—42no—
405C3×H(3,𝔽3)—61no—
406C3×H(3,𝔽3)—61no—
407C3×H(3,𝔽3)—61no—
408C3×H(3,𝔽3)—61no—
409C3×H(3,𝔽3)—62no—
410C3×H(3,𝔽3)—62no—
411C3×H(3,𝔽3)—61no—
412C3×H(3,𝔽3)—61no—
413C3×H(3,𝔽3)—61no—
414C3×H(3,𝔽3)—61no—
415C3×H(3,𝔽3)—61no—
416C3×H(3,𝔽3)—61no—
417C3×H(3,𝔽3)—121no—
418C3×H(3,𝔽3)—121no—
419C3×H(3,𝔽3)—121no—
420C3×H(3,𝔽3)—121no—
421C3×H(3,𝔽3)—122no—
422C3×H(3,𝔽3)—122no—
423C3×H(3,𝔽3)—121no—
424C3×H(3,𝔽3)—121no—
425C3×H(3,𝔽3)C3×D1211yescharacteristic
426C3×H(3,𝔽3)C3×D1212yescomplemented
427C3×H(3,𝔽3)C3×#6711yescharacteristic
428C3×H(3,𝔽3)C3×#6712yescomplemented
429C32×D4—811no—
430#638—91no—
431C4⋊(C3⋊D3)—91no—
432C3×#67—271no—
433C3×#67—272no—
434C3×#67—271no—
435C3×#67—811no—
436C3×D12—271no—
437C3×D12—272no—
438C3×D12—271no—
439C3×D12—811no—
440#626—91no—
441#626—271no—
442#626—271no—
443#626—811no—
444C2×C33—21no—
445C2×C33—21no—
446C2×C33—21no—
447C2×C33—21no—
448C2×C33—22no—
449C2×C33—21no—
450C2×C33—22no—
451C2×C33—31no—
452C2×C33—31no—
453C2×C33—31no—
454C2×C33—31no—
455C2×C33—31no—
456C2×C33—31no—
457C2×C33—31no—
458C2×C33—31no—
459C2×C33—42no—
460C2×C33—41no—
461C2×C33—41no—
462C2×C33—61no—
463C2×C33—61no—
464C2×C33—61no—
465C2×C33—61no—
466C2×C33—61no—
467C2×C33—61no—
468C2×C33—61no—
469C2×C33—61no—
470C2×C33—61no—
471C2×C33—61no—
472C2×C33—61no—
473C2×C33—61no—
474C2×C33—62no—
475C2×C33—62no—
476C2×C33—61no—
477C2×C33—61no—
478C2×C33—61no—
479C2×C33—61no—
480C2×C33—121no—
481C2×C33—121no—
482C2×C33—121no—
483C2×C33—121no—
484C2×C33—121no—
485C2×C33—121no—
486C2×C33—121no—
487C2×C33—121no—
488C2×C33—122no—
489C2×C33—122no—
490C2×C33—181no—
491C2×C33—181no—
492C2×C33—181no—
493C2×C33—181no—
494C2×C33—181no—
495C2×C33—181no—
496C2×C33—182no—
497C2×C33—361no—
498C2×C33—361no—
499C2×C33—361no—
500C2×C33—361no—
501C2×C33—361no—
502C2×C33—361no—
503C2×C33C3×D3211yescharacteristic
504C2×C33C3×D3211yescharacteristic
505C2×C33C3×D3212yes—
506C2×C33C2×C32×D311yescharacteristic
507C2×C33C2×C32×D311yescharacteristic
508C3⋊(C3⋊D3)—61no—
509C3⋊(C3⋊D3)—61no—
510C3⋊(C3⋊D3)—62no—
511C3⋊(C3⋊D3)—181no—
512C3⋊(C3⋊D3)—181no—
513C3⋊(C3⋊D3)—182no—
514C3⋊(C3⋊D3)—182no—
515C3⋊(C3⋊D3)—542no—
516C3×C3⋊D3—21no—
517C3×C3⋊D3—61no—
518C3×C3⋊D3—61no—
519C3×C3⋊D3—62no—
520C3×C3⋊D3—182no—
521C3×C3⋊D3—181no—
522C3×C3⋊D3—181no—
523C3×C3⋊D3—181no—
524C3×C3⋊D3—181no—
525C3×C3⋊D3—182no—
526C3×C3⋊D3—182no—
527C3×C3⋊D3—541no—
528C3×C3⋊D3—541no—
529C3×C3⋊D3—542no—
530C3×C3⋊D3—542no—
531C32×D3—61no—
532C32×D3—62no—
533C32×D3—64no—
534C32×D3—62no—
535C32×D3—62no—
536C32×D3—61no—
537C32×D3—61no—
538C32×D3—181no—
539C32×D3—181no—
540C32×D3—182no—
541C32×D3—182no—
542C32×D3—184no—
543C32×D3—182no—
544C32×D3—181no—
545C32×D3—181no—
546C32×D3—182no—
547C32×D3—541no—
548C32×D3—541no—
549C32×D3—542no—
550C2×H(3,𝔽3)—21no—
551C2×H(3,𝔽3)—21no—
552C2×H(3,𝔽3)—21no—
553C2×H(3,𝔽3)—21no—
554C2×H(3,𝔽3)—32no—
555C2×H(3,𝔽3)—32no—
556C2×H(3,𝔽3)—41no—
557C2×H(3,𝔽3)—41no—
558C2×H(3,𝔽3)—62no—
559C2×H(3,𝔽3)—62no—
560C2×H(3,𝔽3)—62no—
561C2×H(3,𝔽3)—62no—
562C2×H(3,𝔽3)—61no—
563C2×H(3,𝔽3)—61no—
564C2×H(3,𝔽3)—61no—
565C2×H(3,𝔽3)—61no—
566C2×H(3,𝔽3)—61no—
567C2×H(3,𝔽3)—62no—
568C2×H(3,𝔽3)—61no—
569C2×H(3,𝔽3)—62no—
570C2×H(3,𝔽3)—121no—
571C2×H(3,𝔽3)—121no—
572C2×H(3,𝔽3)—121no—
573C2×H(3,𝔽3)—121no—
574C2×H(3,𝔽3)—122no—
575C2×H(3,𝔽3)—122no—
576C2×H(3,𝔽3)—121no—
577C2×H(3,𝔽3)—121no—
578C2×H(3,𝔽3)—121no—
579C2×H(3,𝔽3)—121no—
580C2×H(3,𝔽3)—122no—
581C2×H(3,𝔽3)—122no—
582C2×H(3,𝔽3)—122no—
583C2×H(3,𝔽3)—122no—
584C2×H(3,𝔽3)—122no—
585C2×H(3,𝔽3)—122no—
586C2×H(3,𝔽3)—122no—
587C2×H(3,𝔽3)—122no—
588C2×H(3,𝔽3)—124no—
589C2×H(3,𝔽3)—124no—
590C2×H(3,𝔽3)—121no—
591C2×H(3,𝔽3)—121no—
592C2×H(3,𝔽3)—182no—
593C2×H(3,𝔽3)—182no—
594C2×H(3,𝔽3)—184no—
595C2×H(3,𝔽3)—182no—
596C2×H(3,𝔽3)—181no—
597C2×H(3,𝔽3)—362no—
598C2×H(3,𝔽3)—362no—
599C2×H(3,𝔽3)—361no—
600C2×H(3,𝔽3)—362no—
601C2×H(3,𝔽3)—362no—
602C2×H(3,𝔽3)—362no—
603C2×H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
604C2×H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
605(C3⋊D3)⋊C3—22no—
606(C3⋊D3)⋊C3—21no—
607(C3⋊D3)⋊C3—62no—
608(C3⋊D3)⋊C3—62no—
609(C3⋊D3)⋊C3—64no—
610(C3⋊D3)⋊C3—182no—
611(C3⋊D3)⋊C3—182no—
612(C3⋊D3)⋊C3—182no—
613(C3⋊D3)⋊C3—182no—
614(C3⋊D3)⋊C3—184no—
615(C3⋊D3)⋊C3—184no—
616(C3⋊D3)⋊C3—181no—
617(C3⋊D3)⋊C3—181no—
618(C3⋊D3)⋊C3—542no—
619(C3⋊D3)⋊C3—542no—
620(C3⋊D3)⋊C3—544no—
621C22×C32—91no—
622C22×C32—92no—
623C22×C32—91no—
624C22×C32—91no—
625C22×C32—181no—
626C22×C32—182no—
627C22×C32—181no—
628C22×C32—271no—
629C22×C32—271no—
630C22×C32—541no—
631C22×C32—541no—
632C22×C32—541no—
633C22×C32—542no—
634C22×C32—811no—
635C2×C3⋊D3—91no—
636C2×C3⋊D3—91no—
637C2×C3⋊D3—91no—
638C2×C3⋊D3—181no—
639C2×C3⋊D3—181no—
640C2×C3⋊D3—271no—
641C2×C3⋊D3—271no—
642C2×C3⋊D3—541no—
643C2×C3⋊D3—541no—
644C2×C3⋊D3—541no—
645C2×C3⋊D3—541no—
646C2×C3⋊D3—542no—
647C2×C3⋊D3—811no—
648C2×C3⋊D3—1621no—
649C2×C3⋊D3—1621no—
650C2×C3⋊D3—1622no—
651C2×C3⋊D3C3×(C3⋊D3)⋊C311yescharacteristic, complemented
652C2×C3×D3—31no—
653C2×C3×D3—31no—
654C2×C3×D3—61no—
655C2×C3×D3—92no—
656C2×C3×D3—91no—
657C2×C3×D3—91no—
658C2×C3×D3—91no—
659C2×C3×D3—181no—
660C2×C3×D3—182no—
661C2×C3×D3—181no—
662C2×C3×D3—271no—
663C2×C3×D3—271no—
664C2×C3×D3—272no—
665C2×C3×D3—272no—
666C2×C3×D3—271no—
667C2×C3×D3—271no—
668C2×C3×D3—271no—
669C2×C3×D3—271no—
670C2×C3×D3—541no—
671C2×C3×D3—542no—
672C2×C3×D3—541no—
673C2×C3×D3—541no—
674C2×C3×D3—811no—
675C2×C3×D3—811no—
676C2×C3×D3—1621no—
677C2×C3×D3—1621no—
678C32×C4—91no—
679C32×C4—92no—
680C32×C4—91no—
681C32×C4—91no—
682C32×C4—181no—
683C32×C4—182no—
684C32×C4—181no—
685C32×C4—271no—
686C32×C4—271no—
687C32×C4—541no—
688C32×C4—541no—
689C32×C4—541no—
690C32×C4—542no—
691C3⋊Dic3C3×(C3⋊D3)⋊C311yescharacteristic, complemented
692C3×Dic3—31no—
693C3×Dic3—31no—
694C3×Dic3—61no—
695C3×Dic3—92no—
696C3×Dic3—91no—
697C3×Dic3—91no—
698C3×Dic3—91no—
699C3×Dic3—181no—
700C3×Dic3—182no—
701C3×Dic3—181no—
702C3×Dic3—271no—
703C3×Dic3—271no—
704C3×Dic3—541no—
705C33—21no—
706C33—21no—
707C33—21no—
708C33—21no—
709C33—22no—
710C33—21no—
711C33—22no—
712C33—31no—
713C33—31no—
714C33—31no—
715C33—31no—
716C33—31no—
717C33—31no—
718C33—31no—
719C33—31no—
720C33—42no—
721C33—41no—
722C33—41no—
723C33—61no—
724C33—61no—
725C33—61no—
726C33—61no—
727C33—61no—
728C33—61no—
729C33—61no—
730C33—61no—
731C33—61no—
732C33—61no—
733C33—61no—
734C33—61no—
735C33—62no—
736C33—62no—
737C33—61no—
738C33—61no—
739C33—61no—
740C33—61no—
741C33—121no—
742C33—121no—
743C33—121no—
744C33—121no—
745C33—121no—
746C33—121no—
747C33—121no—
748C33—121no—
749C33—122no—
750C33—122no—
751C33—181no—
752C33—181no—
753C33—181no—
754C33—181no—
755C33—361no—
756C33—361no—
757C33—361no—
758C33—361no—
759C33—361no—
760C33—361no—
761C33C3×#62611yescharacteristic
762C33C3×#62611yescharacteristic
763C33C3×#62612yes—
764C33C32×D1211yescharacteristic
765C33C32×#6711yescharacteristic
766H(3,𝔽3)—21no—
767H(3,𝔽3)—21no—
768H(3,𝔽3)—21no—
769H(3,𝔽3)—21no—
770H(3,𝔽3)—32no—
771H(3,𝔽3)—32no—
772H(3,𝔽3)—41no—
773H(3,𝔽3)—41no—
774H(3,𝔽3)—62no—
775H(3,𝔽3)—62no—
776H(3,𝔽3)—62no—
777H(3,𝔽3)—62no—
778H(3,𝔽3)—61no—
779H(3,𝔽3)—61no—
780H(3,𝔽3)—61no—
781H(3,𝔽3)—62no—
782H(3,𝔽3)—61no—
783H(3,𝔽3)—62no—
784H(3,𝔽3)—61no—
785H(3,𝔽3)—61no—
786H(3,𝔽3)—121no—
787H(3,𝔽3)—121no—
788H(3,𝔽3)—121no—
789H(3,𝔽3)—121no—
790H(3,𝔽3)—121no—
791H(3,𝔽3)—121no—
792H(3,𝔽3)—121no—
793H(3,𝔽3)—121no—
794H(3,𝔽3)—122no—
795H(3,𝔽3)—122no—
796H(3,𝔽3)—122no—
797H(3,𝔽3)—122no—
798H(3,𝔽3)—122no—
799H(3,𝔽3)—122no—
800H(3,𝔽3)—122no—
801H(3,𝔽3)—122no—
802H(3,𝔽3)—122no—
803H(3,𝔽3)—122no—
804H(3,𝔽3)—124no—
805H(3,𝔽3)—124no—
806H(3,𝔽3)—121no—
807H(3,𝔽3)—121no—
808H(3,𝔽3)—182no—
809H(3,𝔽3)—362no—
810H(3,𝔽3)—362no—
811H(3,𝔽3)—361no—
812H(3,𝔽3)—362no—
813H(3,𝔽3)—362no—
814H(3,𝔽3)—362no—
815H(3,𝔽3)C4⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
816H(3,𝔽3)#638⋊C311yescharacteristic, complemented
817C3×D4—811no—
818C3×D4—811no—
819C3×D4—812no—
820#67—271no—
821#67—811no—
822D12—271no—
823D12—811no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—31no—
831C2×C32—31no—
832C2×C32—31no—
833C2×C32—31no—
834C2×C32—32no—
835C2×C32—32no—
836C2×C32—41no—
837C2×C32—41no—
838C2×C32—61no—
839C2×C32—61no—
840C2×C32—61no—
841C2×C32—61no—
842C2×C32—62no—
843C2×C32—62no—
844C2×C32—61no—
845C2×C32—61no—
846C2×C32—62no—
847C2×C32—62no—
848C2×C32—61no—
849C2×C32—61no—
850C2×C32—61no—
851C2×C32—61no—
852C2×C32—61no—
853C2×C32—61no—
854C2×C32—62no—
855C2×C32—62no—
856C2×C32—91no—
857C2×C32—91no—
858C2×C32—91no—
859C2×C32—91no—
860C2×C32—121no—
861C2×C32—121no—
862C2×C32—121no—
863C2×C32—121no—
864C2×C32—122no—
865C2×C32—122no—
866C2×C32—122no—
867C2×C32—122no—
868C2×C32—122no—
869C2×C32—122no—
870C2×C32—121no—
871C2×C32—121no—
872C2×C32—122no—
873C2×C32—122no—
874C2×C32—121no—
875C2×C32—121no—
876C2×C32—181no—
877C2×C32—181no—
878C2×C32—181no—
879C2×C32—181no—
880C2×C32—181no—
881C2×C32—181no—
882C2×C32—181no—
883C2×C32—181no—
884C2×C32—181no—
885C2×C32—181no—
886C2×C32—181no—
887C2×C32—181no—
888C2×C32—182no—
889C2×C32—182no—
890C2×C32—182no—
891C2×C32—181no—
892C2×C32—182no—
893C2×C32—182no—
894C2×C32—184no—
895C2×C32—182no—
896C2×C32—181no—
897C2×C32—181no—
898C2×C32—361no—
899C2×C32—361no—
900C2×C32—361no—
901C2×C32—361no—
902C2×C32—361no—
903C2×C32—361no—
904C2×C32—361no—
905C2×C32—361no—
906C2×C32—361no—
907C2×C32—361no—
908C2×C32—362no—
909C2×C32—362no—
910C2×C32—362no—
911C2×C32—362no—
912C2×C32—362no—
913C2×C32—362no—
914C2×C32—364no—
915C2×C32—541no—
916C2×C32—541no—
917C2×C32—542no—
918C2×C32—542no—
919C2×C32—542no—
920C2×C32—544no—
921C2×C32—1621no—
922C2×C32D3×(C3⋊D3)⋊C311yescharacteristic
923C2×C32D3×(C3⋊D3)⋊C311yescharacteristic
924C2×C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
925C2×C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
926C2×C32C32×D3211yescharacteristic
927C3⋊D3—21no—
928C3⋊D3—181no—
929C3⋊D3—182no—
930C3⋊D3—182no—
931C3⋊D3—181no—
932C3⋊D3—181no—
933C3⋊D3—541no—
934C3⋊D3—541no—
935C3⋊D3—542no—
936C3⋊D3—542no—
937C3⋊D3—542no—
938C3⋊D3—542no—
939C3⋊D3—544no—
940C3⋊D3—1621no—
941C3⋊D3—1622no—
942C3⋊D3—1622no—
943C3⋊D3—1624no—
944C3×D3—62no—
945C3×D3—61no—
946C3×D3—61no—
947C3×D3—182no—
948C3×D3—181no—
949C3×D3—181no—
950C3×D3—182no—
951C3×D3—184no—
952C3×D3—182no—
953C3×D3—181no—
954C3×D3—541no—
955C3×D3—541no—
956C3×D3—542no—
957C3×D3—542no—
958C3×D3—542no—
959C3×D3—541no—
960C3×D3—541no—
961C3×D3—544no—
962C3×D3—542no—
963C3×D3—542no—
964C3×D3—541no—
965C3×D3—541no—
966C3×D3—1621no—
967C3×D3—1621no—
968C3×D3—1622no—
969C3×D3—1622no—
970C22×C3—91no—
971C22×C3—91no—
972C22×C3—181no—
973C22×C3—271no—
974C22×C3—271no—
975C22×C3—272no—
976C22×C3—541no—
977C22×C3—541no—
978C22×C3—542no—
979C22×C3—811no—
980C22×C3—811no—
981C22×C3—812no—
982C2×D3—31no—
983C2×D3—91no—
984C2×D3—271no—
985C2×D3—271no—
986C2×D3—541no—
987C2×D3—811no—
988C2×D3—811no—
989C2×D3—1621no—
990C2×D3—1621no—
991C2×D3—4861no—
992C3×C4—91no—
993C3×C4—91no—
994C3×C4—181no—
995C3×C4—271no—
996C3×C4—271no—
997C3×C4—272no—
998C3×C4—541no—
999C3×C4—541no—
1000C3×C4—542no—
1001Dic3—31no—
1002Dic3—91no—
1003C32—21no—
1004C32—21no—
1005C32—21no—
1006C32—21no—
1007C32—21no—
1008C32—21no—
1009C32—31no—
1010C32—31no—
1011C32—31no—
1012C32—31no—
1013C32—32no—
1014C32—32no—
1015C32—41no—
1016C32—41no—
1017C32—61no—
1018C32—61no—
1019C32—61no—
1020C32—61no—
1021C32—62no—
1022C32—62no—
1023C32—61no—
1024C32—61no—
1025C32—61no—
1026C32—62no—
1027C32—61no—
1028C32—61no—
1029C32—62no—
1030C32—61no—
1031C32—62no—
1032C32—61no—
1033C32—62no—
1034C32—61no—
1035C32—91no—
1036C32—91no—
1037C32—91no—
1038C32—91no—
1039C32—121no—
1040C32—121no—
1041C32—121no—
1042C32—121no—
1043C32—122no—
1044C32—122no—
1045C32—122no—
1046C32—122no—
1047C32—122no—
1048C32—122no—
1049C32—121no—
1050C32—122no—
1051C32—121no—
1052C32—121no—
1053C32—122no—
1054C32—121no—
1055C32—181no—
1056C32—181no—
1057C32—181no—
1058C32—181no—
1059C32—181no—
1060C32—181no—
1061C32—181no—
1062C32—181no—
1063C32—181no—
1064C32—181no—
1065C32—181no—
1066C32—181no—
1067C32—182no—
1068C32—182no—
1069C32—182no—
1070C32—361no—
1071C32—361no—
1072C32—361no—
1073C32—361no—
1074C32—361no—
1075C32—361no—
1076C32—361no—
1077C32—361no—
1078C32—361no—
1079C32—361no—
1080C32—362no—
1081C32—362no—
1082C32—362no—
1083C32—362no—
1084C32—362no—
1085C32—362no—
1086C32—364no—
1087C32#6292⋊C311yescharacteristic, complemented
1088C32#6291⋊C311yescharacteristic, complemented
1089C32C3×C4⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
1090C32C3×#638⋊C311yescharacteristic, complemented
1091C32C32×#62611yescharacteristic
1092D4—811noSylow
1093C2×C3—21no—
1094C2×C3—31no—
1095C2×C3—31no—
1096C2×C3—31no—
1097C2×C3—31no—
1098C2×C3—61no—
1099C2×C3—61no—
1100C2×C3—61no—
1101C2×C3—61no—
1102C2×C3—61no—
1103C2×C3—61no—
1104C2×C3—92no—
1105C2×C3—121no—
1106C2×C3—121no—
1107C2×C3—181no—
1108C2×C3—182no—
1109C2×C3—181no—
1110C2×C3—181no—
1111C2×C3—182no—
1112C2×C3—181no—
1113C2×C3—181no—
1114C2×C3—182no—
1115C2×C3—361no—
1116C2×C3—361no—
1117C2×C3—362no—
1118C2×C3—541no—
1119C2×C3—541no—
1120C2×C3—542no—
1121C2×C3—542no—
1122C2×C3—542no—
1123C2×C3—544no—
1124C2×C3—1621no—
1125C2×C3—1621no—
1126C2×C3—1622no—
1127C2×C3C3×D3×(C3⋊D3)⋊C311yescharacteristic
1128C2×C3C3×D3×(C3⋊D3)⋊C311yescharacteristic
1129D3—61no—
1130D3—181no—
1131D3—542no—
1132D3—541no—
1133D3—541no—
1134D3—1621no—
1135D3—1621no—
1136D3—1622no—
1137D3—1622no—
1138D3—4862no—
1139C22—91no—
1140C22—811no—
1141C4—91no—
1142C3—21no—
1143C3—31no—
1144C3—31no—
1145C3—31no—
1146C3—31no—
1147C3—61no—
1148C3—61no—
1149C3—61no—
1150C3—61no—
1151C3—61no—
1152C3—61no—
1153C3—92no—
1154C3—121no—
1155C3—121no—
1156C3—181no—
1157C3—181no—
1158C3—182no—
1159C3—181no—
1160C3—182no—
1161C3—361no—
1162C3—361no—
1163C3—362no—
1164C3C3×#6292⋊C311yescharacteristic
1165C3C3×#6291⋊C311yescharacteristic
1166C2—181no—
1167C2—1621no—
1168C2(C3⋊D3)⋊C3211yescharacteristic
subgroupG/H
center, hypercenterC2(C3⋊D3)⋊C32
commutator, cosocleC2×C34C22×C32
Frattini, socleC2×C32C32×D32
FittingC2×H(3,𝔽3)2C22
hypocenterC34C32×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×(C3⋊Dic3)⋊C3C2semidirect
2. C2×H(3,𝔽3)×(C3⋊D3)⋊C3C2semidirect
3. C2×#13091503C2semidirect
4. #14518683C3semidirect
5. #14518675C3semidirect
8. #14516803C3semidirect
12. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2×C3semidirect
13. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2×C3semidirect
14. C2×C3⋊D3×H(3,𝔽3)C2×C3semidirect
19. C2×C32×(C3⋊D3)⋊C3D3semidirect
20. C2×C32×(C3⋊D3)⋊C3C2×C3semidirect
21. H(3,𝔽3)×C3⋊Dic3C2×C3semidirect
24. C32×(C3⋊Dic3)⋊C3D3semidirect
25. C32×(C3⋊Dic3)⋊C3C2×C3semidirect
26. C2×#92301C2×C3semidirect
30. C2×(C3⋊D3)⋊H(3,𝔽3)C2×C3semidirect
33. (C3⋊Dic3)⋊H(3,𝔽3)C2×C3semidirect
34. H(3,𝔽3)2D4semidirect
35. #10620152C32semidirect
76. C2×C3⋊(C3⋊(C3⋊D3))C2×C32semidirect
81. C2×C32×C3⋊D3C3×D3semidirect
82. C2×C32×C3⋊D3C2×C32semidirect
87. C32×C3⋊Dic3C3×D3semidirect
88. C32×C3⋊Dic3C2×C32semidirect
122. C2×C3×(C3⋊D3)⋊C3C3×D3semidirect
138. C3×(C3⋊Dic3)⋊C3C3×D3semidirect
141. C32×H(3,𝔽3)D12semidirect
142. C32×H(3,𝔽3)#67semidirect
143. C32×H(3,𝔽3)C3×D4semidirect
144. C32×H(3,𝔽3)C3×D4semidirect
153. C32⋊H(3,𝔽3)C3×D4semidirect
359. C2×(C3⋊D3)⋊C3(C3⋊D3)⋊C3semidirect
368. (C3⋊Dic3)⋊C3(C3⋊D3)⋊C3semidirect
374. C34#626semidirect
375. C34C3×D12semidirect
376. C34C3×#67semidirect
377. C34C32×D4semidirect
426. C3×H(3,𝔽3)C3×D12semidirect
428. C3×H(3,𝔽3)C3×#67semidirect
651. C2×C3⋊D3C3×(C3⋊D3)⋊C3semidirect
691. C3⋊Dic3C3×(C3⋊D3)⋊C3semidirect
815. H(3,𝔽3)C4⋊((C3⋊D3)⋊C3)semidirect
816. H(3,𝔽3)#638⋊C3semidirect
1087. C32#6292⋊C3semidirect
1088. C32#6291⋊C3semidirect
1089. C32C3×C4⋊((C3⋊D3)⋊C3)semidirect
1090. C32C3×#638⋊C3semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×(C3⋊Dic3)⋊C32
C2×H(3,𝔽3)×(C3⋊D3)⋊C32
C2×#130915032
#145186833
#145186753
C3×#6291⋊C33
C3×#6292⋊C33
#145168033