Finite Group Databasebeta

← C2×#13091647 #72243826

Subgroups — C2×#13091647 #72243826

Order 2916.

1243 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091647C212yesmaximal, direct product factor
2C2×#10624930C211yesmaximal, characteristic, complemented
3C2×#4207⋊C3—31nomaximal
4C2×#4207⋊C3—31nomaximal
5C2×#92391—31nomaximal
6C2×C3×C3⋊((C3⋊D3)⋊C3)—31nomaximal
7C2×C3⋊#4183C311yesmaximal, characteristic, complemented
8C2×#4183⋊C3—31nomaximal
9C2×#4183⋊C3—31nomaximal
10C2×#4183⋊C3—31nomaximal
11C2×#4183⋊C3—31nomaximal
12C2×#4183⋊C3—31nomaximal
13C2×#4183⋊C3—31nomaximal
14C2×C3×#4183—31nomaximal
15C2×C3×#4183—31nomaximal
16C2×C3×#4183—31nomaximal
17#10624930C2211yescharacteristic, complemented, Sylow
18C2×3−1+4D311yescharacteristic, complemented
19C2×3−1+4D311yescharacteristic, complemented
20C2×H(5,𝔽3)D311yescharacteristic, complemented
21C2×C32×H(3,𝔽3)D311yescharacteristic, complemented
22#4207⋊C3—32no—
23#4207⋊C3—32no—
24#92391—32no—
25C3×C3⋊((C3⋊D3)⋊C3)—32no—
26C2×#6909—21no—
27C2×#6909—21no—
28C2×#6909—21no—
29C2×#6909—21no—
30C2×#6909—21no—
31C2×#6909—21no—
32C2×#6909—21no—
33C2×#6909—21no—
34C2×#6909—21no—
35C2×#6909D311yescharacteristic, complemented
36C2×#6909D311yescharacteristic, complemented
37C2×#6909D311yescharacteristic, complemented
38C2×#6909D311yescharacteristic, complemented
39C2×#6909D311yescharacteristic, complemented
40C2×#6909D311yescharacteristic, complemented
41C2×C3×AΣL(1,𝔽27)—21no—
42C2×C3×AΣL(1,𝔽27)—21no—
43C2×C3×AΣL(1,𝔽27)—21no—
44C2×C3×AΣL(1,𝔽27)—21no—
45C2×C3×AΣL(1,𝔽27)D311yescharacteristic, complemented
46C2×C3×AΣL(1,𝔽27)D311yescharacteristic, complemented
47C2×C3×AΣL(1,𝔽27)D311yescharacteristic, complemented
48C2×C3×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
49C3⋊#4183C2×C312yescomplemented
50#4183⋊C3—32no—
51#4183⋊C3—32no—
52#4183⋊C3—32no—
53#4183⋊C3—32no—
54#4183⋊C3—32no—
55#4183⋊C3—32no—
56C3×#4183—32no—
57C3×#4183—32no—
58C3×#4183—32no—
59C2×C3×C3⋊(C3⋊D3)—31no—
60C2×C32×C3⋊D3—91no—
61C2×#4207—31no—
62C2×#4207—31no—
63C2×#4207—31no—
64C2×#4207—31no—
65C2×#4207—31no—
66C2×#4207—31no—
67C2×C3⋊AGL(1,ℤ/9)—31no—
68C2×C3⋊AGL(1,ℤ/9)—31no—
69C2×C3⋊((C3⋊D3)⋊C3)—31no—
70C2×C3⋊((C3⋊D3)⋊C3)—31no—
71C2×C3⋊((C3⋊D3)⋊C3)—31no—
72C2×C3⋊((C3⋊D3)⋊C3)—31no—
73C2×C3⋊((C3⋊D3)⋊C3)—31no—
74C2×C3⋊((C3⋊D3)⋊C3)—31no—
75C2×C3⋊((C3⋊D3)⋊C3)—31no—
76C2×C3×AGL(1,ℤ/9)—91no—
77C2×C3×AGL(1,ℤ/9)—91no—
78C2×C3×AGL(1,ℤ/9)—91no—
79C2×C3×AGL(1,ℤ/9)—91no—
80C2×C3×AGL(1,ℤ/9)—91no—
81C2×C3×AGL(1,ℤ/9)—91no—
82C2×C3×(C3⋊D3)⋊C3—91no—
83C2×C3×(C3⋊D3)⋊C3—91no—
84C2×C3×(C3⋊D3)⋊C3—91no—
85C2×C3×(C3⋊D3)⋊C3—91no—
86C2×C3×(C3⋊D3)⋊C3—91no—
87C2×C3×(C3⋊D3)⋊C3—91no—
88C2×#4183—31no—
89C2×#4183—31no—
90C2×#4183—31no—
91C2×#4183—31no—
92C2×#4183—31no—
93C2×#4183—31no—
94C2×#4183—31no—
95C2×#4183—31no—
96C2×#4183—31no—
973−1+4C2×D311yescharacteristic, complemented
983−1+4C2×D311yescharacteristic, complemented
99H(5,𝔽3)C2×D311yescharacteristic, complemented
100C32×H(3,𝔽3)C2×D311yescharacteristic, complemented
101#6909—21no—
102#6909—21no—
103#6909—21no—
104#6909—21no—
105#6909—21no—
106#6909—21no—
107#6909—21no—
108#6909—21no—
109#6909—21no—
110#6909C2×D311yescharacteristic, complemented
111#6909C2×D311yescharacteristic, complemented
112#6909C2×D311yescharacteristic, complemented
113#6909C2×D311yescharacteristic, complemented
114#6909C2×D311yescharacteristic, complemented
115#6909C2×D311yescharacteristic, complemented
116C3×AΣL(1,𝔽27)—21no—
117C3×AΣL(1,𝔽27)—21no—
118C3×AΣL(1,𝔽27)—21no—
119C3×AΣL(1,𝔽27)—21no—
120C3×AΣL(1,𝔽27)C2×D311yescharacteristic, complemented
121C3×AΣL(1,𝔽27)C2×D311yescharacteristic, complemented
122C3×AΣL(1,𝔽27)C2×D311yescharacteristic, complemented
123C3×AΣL(1,𝔽27)C22×C311yescharacteristic, complemented
124C2×C34—21no—
125C2×C34C3×D311yescharacteristic, complemented
126C2×C34C3⋊D311yescharacteristic, complemented
127C3×C3⋊(C3⋊D3)—32no—
128C32×C3⋊D3—92no—
129C2×#737—31no—
130C2×#737—61no—
131C2×#737—61no—
132C2×#737—61no—
133C2×#737—61no—
134C2×#737—61no—
135C2×#737—61no—
136C2×#737—61no—
137C2×#737—61no—
138C2×#737—61no—
139C2×#737—61no—
140C2×#737—61no—
141C2×C3×3−1+2—21no—
142C2×C3×3−1+2—21no—
143C2×C3×3−1+2—21no—
144C2×C3×3−1+2—21no—
145C2×C3×3−1+2—21no—
146C2×C3×3−1+2—21no—
147C2×C3×3−1+2—21no—
148C2×C3×3−1+2—21no—
149C2×C3×3−1+2C3×D311yescharacteristic, complemented
150C2×C3×3−1+2C3×D311yescharacteristic, complemented
151C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
152C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
153C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
154C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
155C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
156C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
157C2×C3×H(3,𝔽3)—21no—
158C2×C3×H(3,𝔽3)—21no—
159C2×C3×H(3,𝔽3)—21no—
160C2×C3×H(3,𝔽3)—21no—
161C2×C3×H(3,𝔽3)—21no—
162C2×C3×H(3,𝔽3)—21no—
163C2×C3×H(3,𝔽3)—21no—
164C2×C3×H(3,𝔽3)—31no—
165C2×C3×H(3,𝔽3)—31no—
166C2×C3×H(3,𝔽3)—31no—
167C2×C3×H(3,𝔽3)—31no—
168C2×C3×H(3,𝔽3)—61no—
169C2×C3×H(3,𝔽3)—61no—
170C2×C3×H(3,𝔽3)—61no—
171C2×C3×H(3,𝔽3)—61no—
172C2×C3×H(3,𝔽3)—61no—
173C2×C3×H(3,𝔽3)—61no—
174C2×C3×H(3,𝔽3)—61no—
175C2×C3×H(3,𝔽3)—61no—
176C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
177C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
178C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic, complemented
179C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic, complemented
180C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic, complemented
181C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic, complemented
182C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic, complemented
183#4207—32no—
184#4207—32no—
185#4207—32no—
186#4207—32no—
187#4207—32no—
188#4207—32no—
189C3⋊AGL(1,ℤ/9)—32no—
190C3⋊AGL(1,ℤ/9)—32no—
191C3⋊((C3⋊D3)⋊C3)—32no—
192C3⋊((C3⋊D3)⋊C3)—32no—
193C3⋊((C3⋊D3)⋊C3)—32no—
194C3⋊((C3⋊D3)⋊C3)—32no—
195C3⋊((C3⋊D3)⋊C3)—32no—
196C3⋊((C3⋊D3)⋊C3)—32no—
197C3⋊((C3⋊D3)⋊C3)—32no—
198C3×AGL(1,ℤ/9)—92no—
199C3×AGL(1,ℤ/9)—92no—
200C3×AGL(1,ℤ/9)—92no—
201C3×AGL(1,ℤ/9)—92no—
202C3×AGL(1,ℤ/9)—92no—
203C3×AGL(1,ℤ/9)—92no—
204C3×(C3⋊D3)⋊C3—92no—
205C3×(C3⋊D3)⋊C3—92no—
206C3×(C3⋊D3)⋊C3—92no—
207C3×(C3⋊D3)⋊C3—92no—
208C3×(C3⋊D3)⋊C3—92no—
209C3×(C3⋊D3)⋊C3—92no—
210C2×AΣL(1,𝔽27)—21no—
211C2×AΣL(1,𝔽27)—21no—
212C2×AΣL(1,𝔽27)—21no—
213C2×AΣL(1,𝔽27)—21no—
214C2×AΣL(1,𝔽27)—21no—
215C2×AΣL(1,𝔽27)—21no—
216C2×AΣL(1,𝔽27)—21no—
217C2×AΣL(1,𝔽27)—21no—
218C2×AΣL(1,𝔽27)—21no—
219C2×AΣL(1,𝔽27)—21no—
220C2×AΣL(1,𝔽27)—21no—
221C2×AΣL(1,𝔽27)—21no—
222C2×AΣL(1,𝔽27)—21no—
223C2×AΣL(1,𝔽27)—21no—
224C2×AΣL(1,𝔽27)—21no—
225C2×AΣL(1,𝔽27)—21no—
226C2×AΣL(1,𝔽27)—21no—
227C2×AΣL(1,𝔽27)—21no—
228C2×AΣL(1,𝔽27)—21no—
229C2×AΣL(1,𝔽27)—21no—
230C2×AΣL(1,𝔽27)—21no—
231C2×AΣL(1,𝔽27)—21no—
232C2×AΣL(1,𝔽27)—21no—
233C2×AΣL(1,𝔽27)—21no—
234C2×AΣL(1,𝔽27)—21no—
235C2×AΣL(1,𝔽27)—21no—
236C2×AΣL(1,𝔽27)—21no—
237C2×AΣL(1,𝔽27)—21no—
238C2×AΣL(1,𝔽27)—21no—
239C2×AΣL(1,𝔽27)—21no—
240C2×AΣL(1,𝔽27)—21no—
241C2×AΣL(1,𝔽27)—21no—
242C2×AΣL(1,𝔽27)—21no—
243C2×AΣL(1,𝔽27)—21no—
244C2×AΣL(1,𝔽27)—21no—
245C2×AΣL(1,𝔽27)—21no—
246C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
247C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
248C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
249C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
250C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
251C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
252C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
253C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
254C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
255#4183—32no—
256#4183—32no—
257#4183—32no—
258#4183—32no—
259#4183—32no—
260#4183—32no—
261#4183—32no—
262#4183—32no—
263#4183—32no—
264C2×C3⋊(C3⋊D3)—31no—
265C2×C3⋊(C3⋊D3)—31no—
266C2×C3×C3⋊D3—91no—
267C2×C3×C3⋊D3—91no—
268C2×C3×C3⋊D3—91no—
269C2×C3×C3⋊D3—91no—
270C2×C3×C3⋊D3—91no—
271C2×C3×C3⋊D3—91no—
272C2×C3×C3⋊D3—91no—
273C2×C3×C3⋊D3—91no—
274C2×C3×C3⋊D3—91no—
275C2×C3×C3⋊D3—91no—
276C2×C3×C3⋊D3—271no—
277C2×C3×C3⋊D3—271no—
278C2×C3×C3⋊D3—271no—
279C2×C32×D3—271no—
280C2×C32×D3—271no—
281C2×C32×D3—271no—
282C2×C32×D3—271no—
283C2×C3⋊D9—31no—
284C2×C3⋊D9—31no—
285C2×AGL(1,ℤ/9)—91no—
286C2×AGL(1,ℤ/9)—91no—
287C2×AGL(1,ℤ/9)—91no—
288C2×AGL(1,ℤ/9)—91no—
289C2×AGL(1,ℤ/9)—91no—
290C2×AGL(1,ℤ/9)—91no—
291C2×AGL(1,ℤ/9)—91no—
292C2×AGL(1,ℤ/9)—91no—
293C2×AGL(1,ℤ/9)—91no—
294C2×AGL(1,ℤ/9)—91no—
295C2×AGL(1,ℤ/9)—91no—
296C2×AGL(1,ℤ/9)—91no—
297C2×AGL(1,ℤ/9)—91no—
298C2×AGL(1,ℤ/9)—91no—
299C2×AGL(1,ℤ/9)—91no—
300C2×AGL(1,ℤ/9)—91no—
301C2×AGL(1,ℤ/9)—91no—
302C2×AGL(1,ℤ/9)—91no—
303C2×(C3⋊D3)⋊C3—91no—
304C2×(C3⋊D3)⋊C3—91no—
305C2×(C3⋊D3)⋊C3—91no—
306C2×(C3⋊D3)⋊C3—91no—
307C2×(C3⋊D3)⋊C3—91no—
308C2×(C3⋊D3)⋊C3—91no—
309C2×(C3⋊D3)⋊C3—91no—
310C2×(C3⋊D3)⋊C3—91no—
311C2×(C3⋊D3)⋊C3—91no—
312C2×(C3⋊D3)⋊C3—91no—
313C2×(C3⋊D3)⋊C3—91no—
314C2×(C3⋊D3)⋊C3—91no—
315C2×(C3⋊D3)⋊C3—91no—
316C2×(C3⋊D3)⋊C3—91no—
317C2×(C3⋊D3)⋊C3—91no—
318C2×(C3⋊D3)⋊C3—91no—
319C2×(C3⋊D3)⋊C3—91no—
320C2×(C3⋊D3)⋊C3—91no—
321C2×C3×D9—91no—
322C2×C3×D9—91no—
323C2×C3×D9—91no—
324C2×C3×D9—91no—
325C2×C3×D9—91no—
326C2×C3×D9—91no—
327C34—21no—
328C34C2×C3×D311yescharacteristic, complemented
329C34C2×C3⋊D311yescharacteristic, complemented
330#737—31no—
331#737—61no—
332#737—61no—
333#737—61no—
334#737—61no—
335#737—61no—
336#737—61no—
337#737—61no—
338#737—61no—
339#737—61no—
340#737—61no—
341#737—61no—
342C3×3−1+2—21no—
343C3×3−1+2—21no—
344C3×3−1+2—21no—
345C3×3−1+2—21no—
346C3×3−1+2—21no—
347C3×3−1+2—21no—
348C3×3−1+2—21no—
349C3×3−1+2—21no—
350C3×3−1+2C2×C3×D311yescharacteristic, complemented
351C3×3−1+2C2×C3×D311yescharacteristic, complemented
352C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
353C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
354C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
355C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
356C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
357C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
358C3×H(3,𝔽3)—21no—
359C3×H(3,𝔽3)—21no—
360C3×H(3,𝔽3)—21no—
361C3×H(3,𝔽3)—21no—
362C3×H(3,𝔽3)—21no—
363C3×H(3,𝔽3)—21no—
364C3×H(3,𝔽3)—21no—
365C3×H(3,𝔽3)—31no—
366C3×H(3,𝔽3)—31no—
367C3×H(3,𝔽3)—31no—
368C3×H(3,𝔽3)—31no—
369C3×H(3,𝔽3)—61no—
370C3×H(3,𝔽3)—61no—
371C3×H(3,𝔽3)—61no—
372C3×H(3,𝔽3)—61no—
373C3×H(3,𝔽3)—61no—
374C3×H(3,𝔽3)—61no—
375C3×H(3,𝔽3)—61no—
376C3×H(3,𝔽3)—61no—
377C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
378C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
379C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic, complemented
380C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic, complemented
381C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic, complemented
382C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic, complemented
383C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic, complemented
384AΣL(1,𝔽27)—21no—
385AΣL(1,𝔽27)—21no—
386AΣL(1,𝔽27)—21no—
387AΣL(1,𝔽27)—21no—
388AΣL(1,𝔽27)—21no—
389AΣL(1,𝔽27)—21no—
390AΣL(1,𝔽27)—21no—
391AΣL(1,𝔽27)—21no—
392AΣL(1,𝔽27)—21no—
393AΣL(1,𝔽27)—21no—
394AΣL(1,𝔽27)—21no—
395AΣL(1,𝔽27)—21no—
396AΣL(1,𝔽27)—21no—
397AΣL(1,𝔽27)—21no—
398AΣL(1,𝔽27)—21no—
399AΣL(1,𝔽27)—21no—
400AΣL(1,𝔽27)—21no—
401AΣL(1,𝔽27)—21no—
402AΣL(1,𝔽27)—21no—
403AΣL(1,𝔽27)—21no—
404AΣL(1,𝔽27)—21no—
405AΣL(1,𝔽27)—21no—
406AΣL(1,𝔽27)—21no—
407AΣL(1,𝔽27)—21no—
408AΣL(1,𝔽27)—21no—
409AΣL(1,𝔽27)—21no—
410AΣL(1,𝔽27)—21no—
411AΣL(1,𝔽27)—21no—
412AΣL(1,𝔽27)—21no—
413AΣL(1,𝔽27)—21no—
414AΣL(1,𝔽27)—21no—
415AΣL(1,𝔽27)—21no—
416AΣL(1,𝔽27)—21no—
417AΣL(1,𝔽27)—21no—
418AΣL(1,𝔽27)—21no—
419AΣL(1,𝔽27)—21no—
420AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
421AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
422AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
423AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
424AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
425AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
426AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
427AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
428AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
429C2×C33—21no—
430C2×C33—21no—
431C2×C33—21no—
432C2×C33—21no—
433C2×C33—31no—
434C2×C33—31no—
435C2×C33—31no—
436C2×C33—61no—
437C2×C33—61no—
438C2×C33—61no—
439C2×C33—61no—
440C2×C33—61no—
441C2×C33—61no—
442C2×C33—61no—
443C2×C33—61no—
444C2×C33—61no—
445C2×C33—61no—
446C2×C33—61no—
447C2×C33—61no—
448C2×C33—61no—
449C2×C33—91no—
450C2×C33—91no—
451C2×C33—91no—
452C2×C33—181no—
453C2×C33—181no—
454C2×C33—181no—
455C2×C33—181no—
456C2×C33—181no—
457C2×C33—181no—
458C2×C33C3×C3⋊D311yescharacteristic
459C2×C33C3×C3⋊D311yescharacteristic
460C2×C33C3×C3⋊D311yescharacteristic
461C2×C33C3×C3⋊D311yescharacteristic
462C2×C33C3⋊(C3⋊D3)11yescharacteristic
463C3⋊(C3⋊D3)—32no—
464C3⋊(C3⋊D3)—32no—
465C3×C3⋊D3—92no—
466C3×C3⋊D3—92no—
467C3×C3⋊D3—92no—
468C3×C3⋊D3—92no—
469C3×C3⋊D3—92no—
470C3×C3⋊D3—92no—
471C3×C3⋊D3—92no—
472C3×C3⋊D3—92no—
473C3×C3⋊D3—92no—
474C3×C3⋊D3—92no—
475C3×C3⋊D3—272no—
476C3×C3⋊D3—272no—
477C3×C3⋊D3—272no—
478C32×D3—272no—
479C32×D3—272no—
480C32×D3—272no—
481C32×D3—272no—
482C2×3−1+2—21no—
483C2×3−1+2—21no—
484C2×3−1+2—21no—
485C2×3−1+2—21no—
486C2×3−1+2—21no—
487C2×3−1+2—21no—
488C2×3−1+2—31no—
489C2×3−1+2—31no—
490C2×3−1+2—31no—
491C2×3−1+2—61no—
492C2×3−1+2—61no—
493C2×3−1+2—61no—
494C2×3−1+2—61no—
495C2×3−1+2—61no—
496C2×3−1+2—61no—
497C2×3−1+2—61no—
498C2×3−1+2—61no—
499C2×3−1+2—61no—
500C2×3−1+2—61no—
501C2×3−1+2—61no—
502C2×3−1+2—61no—
503C2×3−1+2—61no—
504C2×3−1+2—61no—
505C2×3−1+2—61no—
506C2×3−1+2—61no—
507C2×3−1+2—61no—
508C2×3−1+2—61no—
509C2×3−1+2—61no—
510C2×3−1+2—61no—
511C2×3−1+2—61no—
512C2×3−1+2—61no—
513C2×3−1+2—61no—
514C2×3−1+2—61no—
515C2×3−1+2—61no—
516C2×3−1+2—61no—
517C2×3−1+2—61no—
518C2×3−1+2C3×C3⋊D311yescharacteristic
519C2×3−1+2C3×C3⋊D311yescharacteristic
520C2×3−1+2C3×C3⋊D311yescharacteristic
521C2×3−1+2C3×C3⋊D311yescharacteristic
522C2×3−1+2C3×C3⋊D311yescharacteristic
523C2×3−1+2C3×C3⋊D311yescharacteristic
524C2×H(3,𝔽3)—21no—
525C2×H(3,𝔽3)—21no—
526C2×H(3,𝔽3)—21no—
527C2×H(3,𝔽3)—21no—
528C2×H(3,𝔽3)—21no—
529C2×H(3,𝔽3)—21no—
530C2×H(3,𝔽3)—31no—
531C2×H(3,𝔽3)—31no—
532C2×H(3,𝔽3)—31no—
533C2×H(3,𝔽3)—31no—
534C2×H(3,𝔽3)—31no—
535C2×H(3,𝔽3)—61no—
536C2×H(3,𝔽3)—61no—
537C2×H(3,𝔽3)—61no—
538C2×H(3,𝔽3)—61no—
539C2×H(3,𝔽3)—61no—
540C2×H(3,𝔽3)—61no—
541C2×H(3,𝔽3)—61no—
542C2×H(3,𝔽3)—61no—
543C2×H(3,𝔽3)—61no—
544C2×H(3,𝔽3)—61no—
545C2×H(3,𝔽3)—61no—
546C2×H(3,𝔽3)—61no—
547C2×H(3,𝔽3)—62no—
548C2×H(3,𝔽3)—61no—
549C2×H(3,𝔽3)—61no—
550C2×H(3,𝔽3)—61no—
551C2×H(3,𝔽3)—61no—
552C2×H(3,𝔽3)—61no—
553C2×H(3,𝔽3)—61no—
554C2×H(3,𝔽3)—61no—
555C2×H(3,𝔽3)—61no—
556C2×H(3,𝔽3)—61no—
557C2×H(3,𝔽3)—61no—
558C2×H(3,𝔽3)—61no—
559C2×H(3,𝔽3)#27211yescharacteristic
560C2×H(3,𝔽3)#27211yescharacteristic
561C2×H(3,𝔽3)#27211yescharacteristic
562C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
563C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
564C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
565C2×C3×C9—31no—
566C2×C3×C9—31no—
567C2×C3×C9—61no—
568C2×C3×C9—61no—
569C2×C3×C9—61no—
570C2×C3×C9—61no—
571C2×C3×C9—61no—
572C2×C3×C9—61no—
573C2×C3×C9—61no—
574C2×C3×C9—61no—
575C2×C3×C9—61no—
576C2×C3×C9—61no—
577C2×C3×C9—61no—
578C2×C3×C9—61no—
579C2×C3×C9—61no—
580C2×C3×C9—61no—
581C3⋊D9—32no—
582C3⋊D9—32no—
583AGL(1,ℤ/9)—92no—
584AGL(1,ℤ/9)—92no—
585AGL(1,ℤ/9)—92no—
586AGL(1,ℤ/9)—92no—
587AGL(1,ℤ/9)—92no—
588AGL(1,ℤ/9)—92no—
589AGL(1,ℤ/9)—92no—
590AGL(1,ℤ/9)—92no—
591AGL(1,ℤ/9)—92no—
592AGL(1,ℤ/9)—92no—
593AGL(1,ℤ/9)—92no—
594AGL(1,ℤ/9)—92no—
595AGL(1,ℤ/9)—92no—
596AGL(1,ℤ/9)—92no—
597AGL(1,ℤ/9)—92no—
598AGL(1,ℤ/9)—92no—
599AGL(1,ℤ/9)—92no—
600AGL(1,ℤ/9)—92no—
601(C3⋊D3)⋊C3—92no—
602(C3⋊D3)⋊C3—92no—
603(C3⋊D3)⋊C3—92no—
604(C3⋊D3)⋊C3—92no—
605(C3⋊D3)⋊C3—92no—
606(C3⋊D3)⋊C3—92no—
607(C3⋊D3)⋊C3—92no—
608(C3⋊D3)⋊C3—92no—
609(C3⋊D3)⋊C3—92no—
610(C3⋊D3)⋊C3—92no—
611(C3⋊D3)⋊C3—92no—
612(C3⋊D3)⋊C3—92no—
613(C3⋊D3)⋊C3—92no—
614(C3⋊D3)⋊C3—92no—
615(C3⋊D3)⋊C3—92no—
616(C3⋊D3)⋊C3—92no—
617(C3⋊D3)⋊C3—92no—
618(C3⋊D3)⋊C3—92no—
619C3×D9—92no—
620C3×D9—92no—
621C3×D9—92no—
622C3×D9—92no—
623C3×D9—92no—
624C3×D9—92no—
625C22×C32—811no—
626C2×C3⋊D3—91no—
627C2×C3⋊D3—91no—
628C2×C3⋊D3—91no—
629C2×C3⋊D3—91no—
630C2×C3⋊D3—91no—
631C2×C3⋊D3—91no—
632C2×C3⋊D3—91no—
633C2×C3⋊D3—271no—
634C2×C3⋊D3—271no—
635C2×C3⋊D3—271no—
636C2×C3⋊D3—811no—
637C2×C3×D3—271no—
638C2×C3×D3—271no—
639C2×C3×D3—271no—
640C2×C3×D3—271no—
641C2×C3×D3—271no—
642C2×C3×D3—271no—
643C2×C3×D3—271no—
644C2×C3×D3—271no—
645C2×C3×D3—271no—
646C2×C3×D3—271no—
647C2×C3×D3—271no—
648C2×C3×D3—271no—
649C2×C3×D3—271no—
650C2×C3×D3—271no—
651C2×C3×D3—271no—
652C2×C3×D3—271no—
653C2×C3×D3—811no—
654C2×C3×D3—811no—
655C2×C3×D3—811no—
656C2×C3×D3—811no—
657C2×C3×D3—811no—
658C2×C3×D3—811no—
659C2×D9—91no—
660C2×D9—91no—
661C2×D9—91no—
662C2×D9—91no—
663C2×D9—91no—
664C2×D9—91no—
665C33—21no—
666C33—21no—
667C33—21no—
668C33—21no—
669C33—31no—
670C33—31no—
671C33—31no—
672C33—61no—
673C33—61no—
674C33—61no—
675C33—61no—
676C33—61no—
677C33—61no—
678C33—61no—
679C33—61no—
680C33—61no—
681C33—61no—
682C33—61no—
683C33—61no—
684C33—61no—
685C33—91no—
686C33—91no—
687C33—91no—
688C33—181no—
689C33—181no—
690C33—181no—
691C33—181no—
692C33—181no—
693C33—181no—
694C33C2×C3×C3⋊D311yescharacteristic
695C33C2×C3×C3⋊D311yescharacteristic
696C33C2×C3×C3⋊D311yescharacteristic
697C33C2×C3×C3⋊D311yescharacteristic
698C33C2×C3⋊(C3⋊D3)11yescharacteristic
6993−1+2—21no—
7003−1+2—21no—
7013−1+2—21no—
7023−1+2—21no—
7033−1+2—21no—
7043−1+2—21no—
7053−1+2—31no—
7063−1+2—31no—
7073−1+2—31no—
7083−1+2—61no—
7093−1+2—61no—
7103−1+2—61no—
7113−1+2—61no—
7123−1+2—61no—
7133−1+2—61no—
7143−1+2—61no—
7153−1+2—61no—
7163−1+2—61no—
7173−1+2—61no—
7183−1+2—61no—
7193−1+2—61no—
7203−1+2—61no—
7213−1+2—61no—
7223−1+2—61no—
7233−1+2—61no—
7243−1+2—61no—
7253−1+2—61no—
7263−1+2—61no—
7273−1+2—61no—
7283−1+2—61no—
7293−1+2—61no—
7303−1+2—61no—
7313−1+2—61no—
7323−1+2—61no—
7333−1+2—61no—
7343−1+2—61no—
7353−1+2C2×C3×C3⋊D311yescharacteristic
7363−1+2C2×C3×C3⋊D311yescharacteristic
7373−1+2C2×C3×C3⋊D311yescharacteristic
7383−1+2C2×C3×C3⋊D311yescharacteristic
7393−1+2C2×C3×C3⋊D311yescharacteristic
7403−1+2C2×C3×C3⋊D311yescharacteristic
741H(3,𝔽3)—21no—
742H(3,𝔽3)—21no—
743H(3,𝔽3)—21no—
744H(3,𝔽3)—21no—
745H(3,𝔽3)—21no—
746H(3,𝔽3)—21no—
747H(3,𝔽3)—31no—
748H(3,𝔽3)—31no—
749H(3,𝔽3)—31no—
750H(3,𝔽3)—31no—
751H(3,𝔽3)—31no—
752H(3,𝔽3)—61no—
753H(3,𝔽3)—61no—
754H(3,𝔽3)—61no—
755H(3,𝔽3)—61no—
756H(3,𝔽3)—61no—
757H(3,𝔽3)—61no—
758H(3,𝔽3)—61no—
759H(3,𝔽3)—61no—
760H(3,𝔽3)—61no—
761H(3,𝔽3)—61no—
762H(3,𝔽3)—61no—
763H(3,𝔽3)—61no—
764H(3,𝔽3)—62no—
765H(3,𝔽3)—61no—
766H(3,𝔽3)—61no—
767H(3,𝔽3)—61no—
768H(3,𝔽3)—61no—
769H(3,𝔽3)—61no—
770H(3,𝔽3)—61no—
771H(3,𝔽3)—61no—
772H(3,𝔽3)—61no—
773H(3,𝔽3)—61no—
774H(3,𝔽3)—61no—
775H(3,𝔽3)—61no—
776H(3,𝔽3)C2×#27211yescharacteristic
777H(3,𝔽3)C2×#27211yescharacteristic
778H(3,𝔽3)C2×#27211yescharacteristic
779H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
780H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
781H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
782C3×C9—31no—
783C3×C9—31no—
784C3×C9—61no—
785C3×C9—61no—
786C3×C9—61no—
787C3×C9—61no—
788C3×C9—61no—
789C3×C9—61no—
790C3×C9—61no—
791C3×C9—61no—
792C3×C9—61no—
793C3×C9—61no—
794C3×C9—61no—
795C3×C9—61no—
796C3×C9—61no—
797C3×C9—61no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—31no—
803C2×C32—31no—
804C2×C32—31no—
805C2×C32—31no—
806C2×C32—61no—
807C2×C32—61no—
808C2×C32—61no—
809C2×C32—61no—
810C2×C32—61no—
811C2×C32—61no—
812C2×C32—61no—
813C2×C32—61no—
814C2×C32—61no—
815C2×C32—61no—
816C2×C32—61no—
817C2×C32—91no—
818C2×C32—91no—
819C2×C32—91no—
820C2×C32—181no—
821C2×C32—181no—
822C2×C32—181no—
823C2×C32—181no—
824C2×C32—181no—
825C2×C32—181no—
826C2×C32—181no—
827C2×C32—181no—
828C2×C32—181no—
829C2×C32—181no—
830C2×C32—181no—
831C2×C32—181no—
832C2×C32—181no—
833C2×C32—181no—
834C2×C32—181no—
835C2×C32—181no—
836C2×C32—181no—
837C2×C32—181no—
838C2×C32—181no—
839C2×C32—181no—
840C2×C32—181no—
841C2×C32—181no—
842C2×C32—181no—
843C2×C32—181no—
844C2×C32—181no—
845C2×C32—181no—
846C2×C32—181no—
847C2×C32—181no—
848C2×C32—181no—
849C2×C32—271no—
850C2×C32—541no—
851C2×C32—541no—
852C2×C32—541no—
853C2×C32—541no—
854C2×C32—541no—
855C2×C32—541no—
856C2×C32—541no—
857C2×C32—812no—
858C2×C32C3×#27211yescharacteristic
859C2×C32C3⋊#27211yescharacteristic
860C2×C32C3⋊#27211yescharacteristic
861C2×C32C3⋊#27211yescharacteristic
862C2×C32C3×C3⋊(C3⋊D3)11yescharacteristic
863C3⋊D3—92no—
864C3⋊D3—92no—
865C3⋊D3—92no—
866C3⋊D3—92no—
867C3⋊D3—92no—
868C3⋊D3—92no—
869C3⋊D3—92no—
870C3⋊D3—272no—
871C3⋊D3—272no—
872C3⋊D3—272no—
873C3⋊D3—812no—
874C3×D3—272no—
875C3×D3—272no—
876C3×D3—272no—
877C3×D3—272no—
878C3×D3—272no—
879C3×D3—272no—
880C3×D3—272no—
881C3×D3—272no—
882C3×D3—272no—
883C3×D3—272no—
884C3×D3—272no—
885C3×D3—272no—
886C3×D3—272no—
887C3×D3—272no—
888C3×D3—272no—
889C3×D3—272no—
890C3×D3—812no—
891C3×D3—812no—
892C3×D3—812no—
893C3×D3—812no—
894C3×D3—812no—
895C3×D3—812no—
896C2×C9—31no—
897C2×C9—31no—
898C2×C9—31no—
899C2×C9—31no—
900C2×C9—61no—
901C2×C9—61no—
902C2×C9—61no—
903C2×C9—61no—
904C2×C9—61no—
905C2×C9—61no—
906C2×C9—61no—
907C2×C9—61no—
908D9—92no—
909D9—92no—
910D9—92no—
911D9—92no—
912D9—92no—
913D9—92no—
914C22×C3—811no—
915C22×C3—811no—
916C22×C3—811no—
917C22×C3—811no—
918C2×D3—271no—
919C2×D3—271no—
920C2×D3—271no—
921C2×D3—271no—
922C2×D3—811no—
923C2×D3—811no—
924C2×D3—811no—
925C2×D3—811no—
926C2×D3—811no—
927C2×D3—811no—
928C32—21no—
929C32—21no—
930C32—21no—
931C32—21no—
932C32—31no—
933C32—31no—
934C32—31no—
935C32—31no—
936C32—61no—
937C32—61no—
938C32—61no—
939C32—61no—
940C32—61no—
941C32—61no—
942C32—61no—
943C32—61no—
944C32—61no—
945C32—61no—
946C32—61no—
947C32—91no—
948C32—91no—
949C32—91no—
950C32—181no—
951C32—181no—
952C32—181no—
953C32—181no—
954C32—181no—
955C32—181no—
956C32—181no—
957C32—181no—
958C32—181no—
959C32—181no—
960C32—181no—
961C32—181no—
962C32—181no—
963C32—181no—
964C32—181no—
965C32—181no—
966C32—181no—
967C32—181no—
968C32—181no—
969C32—181no—
970C32—181no—
971C32—181no—
972C32—181no—
973C32—181no—
974C32—181no—
975C32—181no—
976C32—181no—
977C32—181no—
978C32—181no—
979C32—271no—
980C32—541no—
981C32—541no—
982C32—541no—
983C32—541no—
984C32—541no—
985C32—541no—
986C32—541no—
987C32C2×C3×#27211yescharacteristic
988C32C2×C3⋊#27211yescharacteristic
989C32C2×C3⋊#27211yescharacteristic
990C32C2×C3⋊#27211yescharacteristic
991C32C2×C3×C3⋊(C3⋊D3)11yescharacteristic
992C9—31no—
993C9—31no—
994C9—31no—
995C9—31no—
996C9—61no—
997C9—61no—
998C9—61no—
999C9—61no—
1000C9—61no—
1001C9—61no—
1002C9—61no—
1003C9—61no—
1004C2×C3—31no—
1005C2×C3—31no—
1006C2×C3—31no—
1007C2×C3—61no—
1008C2×C3—61no—
1009C2×C3—61no—
1010C2×C3—61no—
1011C2×C3—61no—
1012C2×C3—61no—
1013C2×C3—61no—
1014C2×C3—61no—
1015C2×C3—61no—
1016C2×C3—91no—
1017C2×C3—181no—
1018C2×C3—181no—
1019C2×C3—181no—
1020C2×C3—181no—
1021C2×C3—181no—
1022C2×C3—181no—
1023C2×C3—181no—
1024C2×C3—181no—
1025C2×C3—181no—
1026C2×C3—181no—
1027C2×C3—812no—
1028C2×C3—812no—
1029C2×C3—812no—
1030C2×C3—812no—
1031C2×C3C3×C3⋊#27211yescharacteristic
1032D3—272no—
1033D3—272no—
1034D3—272no—
1035D3—272no—
1036D3—812no—
1037D3—812no—
1038D3—812no—
1039D3—812no—
1040D3—812no—
1041D3—812no—
1042C22—811noSylow
1043C3—31no—
1044C3—31no—
1045C3—31no—
1046C3—61no—
1047C3—61no—
1048C3—61no—
1049C3—61no—
1050C3—61no—
1051C3—61no—
1052C3—61no—
1053C3—61no—
1054C3—61no—
1055C3—91no—
1056C3—181no—
1057C3—181no—
1058C3—181no—
1059C3—181no—
1060C3—181no—
1061C3—181no—
1062C3—181no—
1063C3—181no—
1064C3—181no—
1065C3—181no—
1066C3C2×C3×C3⋊#27211yescharacteristic
1067C2—812no—
1068C2#1309164711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#13091647
commutator, cosocle, hypocenterC3×AΣL(1,𝔽27)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624930C2
socleC2×C3C3×C3⋊#272
LCSG ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #13091647C2direct (N × H)
2. C2×#10624930C2semidirect
7. C2×C3⋊#4183C3semidirect
17. #10624930C22semidirect
18. C2×3−1+4D3semidirect
19. C2×3−1+4D3semidirect
20. C2×H(5,𝔽3)D3semidirect
21. C2×C32×H(3,𝔽3)D3semidirect
35. C2×#6909D3semidirect
36. C2×#6909D3semidirect
37. C2×#6909D3semidirect
38. C2×#6909D3semidirect
39. C2×#6909D3semidirect
40. C2×#6909D3semidirect
45. C2×C3×AΣL(1,𝔽27)D3semidirect
46. C2×C3×AΣL(1,𝔽27)D3semidirect
47. C2×C3×AΣL(1,𝔽27)D3semidirect
48. C2×C3×AΣL(1,𝔽27)C2×C3semidirect
49. C3⋊#4183C2×C3semidirect
97. 3−1+4C2×D3semidirect
98. 3−1+4C2×D3semidirect
99. H(5,𝔽3)C2×D3semidirect
100. C32×H(3,𝔽3)C2×D3semidirect
110. #6909C2×D3semidirect
111. #6909C2×D3semidirect
112. #6909C2×D3semidirect
113. #6909C2×D3semidirect
114. #6909C2×D3semidirect
115. #6909C2×D3semidirect
120. C3×AΣL(1,𝔽27)C2×D3semidirect
121. C3×AΣL(1,𝔽27)C2×D3semidirect
122. C3×AΣL(1,𝔽27)C2×D3semidirect
123. C3×AΣL(1,𝔽27)C22×C3semidirect
125. C2×C34C3×D3semidirect
126. C2×C34C3⋊D3semidirect
149. C2×C3×3−1+2C3×D3semidirect
150. C2×C3×3−1+2C3×D3semidirect
151. C2×C3×3−1+2C3⋊D3semidirect
152. C2×C3×3−1+2C3⋊D3semidirect
153. C2×C3×3−1+2C3⋊D3semidirect
154. C2×C3×3−1+2C3⋊D3semidirect
155. C2×C3×3−1+2C3⋊D3semidirect
156. C2×C3×3−1+2C3⋊D3semidirect
176. C2×C3×H(3,𝔽3)C3×D3semidirect
178. C2×C3×H(3,𝔽3)C3⋊D3semidirect
179. C2×C3×H(3,𝔽3)C3⋊D3semidirect
180. C2×C3×H(3,𝔽3)C3⋊D3semidirect
181. C2×C3×H(3,𝔽3)C3⋊D3semidirect
182. C2×C3×H(3,𝔽3)C3⋊D3semidirect
246. C2×AΣL(1,𝔽27)C3×D3semidirect
247. C2×AΣL(1,𝔽27)C3×D3semidirect
248. C2×AΣL(1,𝔽27)C3×D3semidirect
249. C2×AΣL(1,𝔽27)C3×D3semidirect
250. C2×AΣL(1,𝔽27)C3×D3semidirect
251. C2×AΣL(1,𝔽27)C3×D3semidirect
252. C2×AΣL(1,𝔽27)C3×D3semidirect
253. C2×AΣL(1,𝔽27)C3×D3semidirect
254. C2×AΣL(1,𝔽27)C3×D3semidirect
328. C34C2×C3×D3semidirect
329. C34C2×C3⋊D3semidirect
350. C3×3−1+2C2×C3×D3semidirect
351. C3×3−1+2C2×C3×D3semidirect
352. C3×3−1+2C2×C3⋊D3semidirect
353. C3×3−1+2C2×C3⋊D3semidirect
354. C3×3−1+2C2×C3⋊D3semidirect
355. C3×3−1+2C2×C3⋊D3semidirect
356. C3×3−1+2C2×C3⋊D3semidirect
357. C3×3−1+2C2×C3⋊D3semidirect
377. C3×H(3,𝔽3)C2×C3×D3semidirect
379. C3×H(3,𝔽3)C2×C3⋊D3semidirect
380. C3×H(3,𝔽3)C2×C3⋊D3semidirect
381. C3×H(3,𝔽3)C2×C3⋊D3semidirect
382. C3×H(3,𝔽3)C2×C3⋊D3semidirect
383. C3×H(3,𝔽3)C2×C3⋊D3semidirect
420. AΣL(1,𝔽27)C2×C3×D3semidirect
421. AΣL(1,𝔽27)C2×C3×D3semidirect
422. AΣL(1,𝔽27)C2×C3×D3semidirect
423. AΣL(1,𝔽27)C2×C3×D3semidirect
424. AΣL(1,𝔽27)C2×C3×D3semidirect
425. AΣL(1,𝔽27)C2×C3×D3semidirect
426. AΣL(1,𝔽27)C2×C3×D3semidirect
427. AΣL(1,𝔽27)C2×C3×D3semidirect
428. AΣL(1,𝔽27)C2×C3×D3semidirect
1068. C2#13091647direct (N × H)

Maximal subgroups

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

subgroupindex
#130916472
C2×#106249302
C2×#4207⋊C33
C2×#923913
C2×C3×C3⋊((C3⋊D3)⋊C3)3
C2×C3⋊#41833
C2×#4183⋊C33
C2×C3×#41833