Finite Group Databasebeta

← C2×C3×#92281 #72254005

Subgroups — C2×C3×#92281 #72254005

Order 2916.

1270 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#92281C212yesmaximal, direct product factor
2C2×C3×#6909C211yesmaximal, characteristic, complemented
3C2×C32×#272C311yesmaximal, characteristic, complemented
4C2×C3×D3×H(3,𝔽3)—31nomaximal
5C2×#92281C311yesmaximal, characteristic, direct product factor
6C2×#92281C311yesmaximal, characteristic, direct product factor
7C2×#92281C311yesmaximal, characteristic, direct product factor
8C2×#92281C311yesmaximal, characteristic, direct product factor
9C2×#92281C311yesmaximal, characteristic, direct product factor
10C2×#92281C311yesmaximal, characteristic, direct product factor
11C2×#92281C311yesmaximal, characteristic, direct product factor
12C2×#92281C311yesmaximal, characteristic, direct product factor
13C2×#92281C311yesmaximal, characteristic, direct product factor
14C2×C3×#4174C311yesmaximal, characteristic, complemented
15C2×C3×#4174C311yesmaximal, characteristic, complemented
16C2×C3×#4174C311yesmaximal, characteristic, complemented
17C3×#6909C2211yescharacteristic, complemented, Sylow
18C2×C32×3−1+2—21no—
19C2×C32×H(3,𝔽3)D311yescharacteristic, complemented
20C2×C32×H(3,𝔽3)C2×C311yescharacteristic, complemented
21C32×#272C2×C312yescomplemented
22C3×D3×H(3,𝔽3)—32no—
23C2×#6909—21no—
24C2×#6909—21no—
25C2×#6909—21no—
26C2×#6909—21no—
27C2×#6909—21no—
28C2×#6909—21no—
29C2×#6909—21no—
30C2×#6909—21no—
31C2×#6909—21no—
32C2×#6909C2×C311yescharacteristic, complemented
33C2×#6909C2×C311yescharacteristic, complemented
34C2×#6909C2×C311yescharacteristic, complemented
35C2×#6909C2×C311yescharacteristic, complemented
36C2×#6909C2×C311yescharacteristic, complemented
37C2×#6909C2×C311yescharacteristic, complemented
38C2×#6909C2×C311yescharacteristic, complemented
39C2×#6909C2×C311yescharacteristic, complemented
40C2×#6909C2×C311yescharacteristic, complemented
41C2×C3×AΣL(1,𝔽27)—21no—
42C2×C3×AΣL(1,𝔽27)—21no—
43C2×C3×AΣL(1,𝔽27)—21no—
44C2×C3×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
45C2×C3×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
46C2×C3×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
47#92281C2×C312yesdirect product factor
48#92281C2×C312yesdirect product factor
49#92281C2×C312yesdirect product factor
50#92281C2×C312yesdirect product factor
51#92281C2×C312yesdirect product factor
52#92281C2×C312yesdirect product factor
53#92281C2×C312yesdirect product factor
54#92281C2×C312yesdirect product factor
55#92281C2×C312yesdirect product factor
56C3×#4174C2×C312yescomplemented
57C3×#4174C2×C312yescomplemented
58C3×#4174C2×C312yescomplemented
59C2×C33×D3—31no—
60C2×C33×D3—31no—
61C2×C33×D3—31no—
62C2×C33×D3—31no—
63C2×C33×D3—91no—
64C22×C3×H(3,𝔽3)—91no—
65C2×C3×#272C3211yescharacteristic
66C2×C3×#272C3211yescharacteristic, complemented
67C2×C3×#272C3211yescharacteristic, complemented
68C2×C3×#272C3211yescharacteristic, complemented
69C2×D3×H(3,𝔽3)—31no—
70C2×D3×H(3,𝔽3)—31no—
71C2×D3×H(3,𝔽3)—31no—
72C2×D3×H(3,𝔽3)—31no—
73C2×D3×H(3,𝔽3)—31no—
74C2×D3×H(3,𝔽3)—31no—
75C2×D3×H(3,𝔽3)—31no—
76C2×D3×H(3,𝔽3)—31no—
77C2×D3×H(3,𝔽3)—31no—
78C2×#4174C3211yescharacteristic, complemented
79C2×#4174C3211yescharacteristic, complemented
80C2×#4174C3211yescharacteristic, complemented
81C2×#4174C3211yescharacteristic, complemented
82C2×#4174C3211yescharacteristic, complemented
83C2×#4174C3211yescharacteristic, complemented
84C2×#4174C3211yescharacteristic, complemented
85C2×#4174C3211yescharacteristic, complemented
86C2×#4174C3211yescharacteristic, complemented
87C32×3−1+2—21no—
88C32×H(3,𝔽3)C2×D311yescharacteristic, complemented
89C32×H(3,𝔽3)C22×C311yescharacteristic, complemented
90#6909—21no—
91#6909—21no—
92#6909—21no—
93#6909—21no—
94#6909—21no—
95#6909—21no—
96#6909—21no—
97#6909—21no—
98#6909—21no—
99#6909C22×C311yescharacteristic, complemented
100#6909C22×C311yescharacteristic, complemented
101#6909C22×C311yescharacteristic, complemented
102#6909C22×C311yescharacteristic, complemented
103#6909C22×C311yescharacteristic, complemented
104#6909C22×C311yescharacteristic, complemented
105#6909C22×C311yescharacteristic, complemented
106#6909C22×C311yescharacteristic, complemented
107#6909C22×C311yescharacteristic, complemented
108C3×AΣL(1,𝔽27)—21no—
109C3×AΣL(1,𝔽27)—21no—
110C3×AΣL(1,𝔽27)—21no—
111C3×AΣL(1,𝔽27)C22×C311yescharacteristic, complemented
112C3×AΣL(1,𝔽27)C22×C311yescharacteristic, complemented
113C3×AΣL(1,𝔽27)C22×C311yescharacteristic, complemented
114C2×C34—31no—
115C2×C34C3×D311yescharacteristic
116C2×C34C3×D311yescharacteristic, complemented
117C2×C34C3×D311yescharacteristic, complemented
118C2×C34C3×D311yescharacteristic, complemented
119C33×D3—32no—
120C33×D3—32no—
121C33×D3—32no—
122C33×D3—32no—
123C33×D3—92no—
124C2×C3×3−1+2—21no—
125C2×C3×3−1+2—21no—
126C2×C3×3−1+2—21no—
127C2×C3×3−1+2—21no—
128C2×C3×3−1+2—21no—
129C2×C3×3−1+2—21no—
130C2×C3×3−1+2—21no—
131C2×C3×3−1+2—21no—
132C2×C3×3−1+2—21no—
133C2×C3×3−1+2—21no—
134C2×C3×3−1+2—21no—
135C2×C3×3−1+2—21no—
136C2×C3×3−1+2—61no—
137C2×C3×3−1+2—61no—
138C2×C3×3−1+2—61no—
139C2×C3×3−1+2—61no—
140C2×C3×3−1+2—61no—
141C2×C3×3−1+2—61no—
142C2×C3×3−1+2—61no—
143C2×C3×3−1+2—61no—
144C2×C3×H(3,𝔽3)—21no—
145C2×C3×H(3,𝔽3)—21no—
146C2×C3×H(3,𝔽3)—21no—
147C2×C3×H(3,𝔽3)—21no—
148C2×C3×H(3,𝔽3)—61no—
149C2×C3×H(3,𝔽3)—61no—
150C2×C3×H(3,𝔽3)—61no—
151C2×C3×H(3,𝔽3)—61no—
152C2×C3×H(3,𝔽3)—61no—
153C2×C3×H(3,𝔽3)—61no—
154C2×C3×H(3,𝔽3)—61no—
155C2×C3×H(3,𝔽3)—61no—
156C2×C3×H(3,𝔽3)—61no—
157C2×C3×H(3,𝔽3)—92no—
158C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
159C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
160C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
161C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
162C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
163C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
164C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
165C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
166C2×C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
167C2×C3×H(3,𝔽3)C2×C3211yescharacteristic
168C2×C3×H(3,𝔽3)C2×C3211yescharacteristic, complemented
169C2×C3×H(3,𝔽3)C2×C3211yescharacteristic, complemented
170C2×C3×H(3,𝔽3)C2×C3211yescharacteristic, complemented
171C2×C32×C9—61no—
172C3×#272C2×C3212yes—
173C3×#272C2×C3212yescomplemented
174C3×#272C2×C3212yescomplemented
175C3×#272C2×C3212yescomplemented
176D3×H(3,𝔽3)—32no—
177D3×H(3,𝔽3)—32no—
178D3×H(3,𝔽3)—32no—
179D3×H(3,𝔽3)—32no—
180D3×H(3,𝔽3)—32no—
181D3×H(3,𝔽3)—32no—
182D3×H(3,𝔽3)—32no—
183D3×H(3,𝔽3)—32no—
184D3×H(3,𝔽3)—32no—
185C2×AΣL(1,𝔽27)—21no—
186C2×AΣL(1,𝔽27)—21no—
187C2×AΣL(1,𝔽27)—21no—
188C2×AΣL(1,𝔽27)—21no—
189C2×AΣL(1,𝔽27)—21no—
190C2×AΣL(1,𝔽27)—21no—
191C2×AΣL(1,𝔽27)—21no—
192C2×AΣL(1,𝔽27)—21no—
193C2×AΣL(1,𝔽27)—21no—
194C2×AΣL(1,𝔽27)—21no—
195C2×AΣL(1,𝔽27)—21no—
196C2×AΣL(1,𝔽27)—21no—
197C2×AΣL(1,𝔽27)—21no—
198C2×AΣL(1,𝔽27)—21no—
199C2×AΣL(1,𝔽27)—21no—
200C2×AΣL(1,𝔽27)—21no—
201C2×AΣL(1,𝔽27)—21no—
202C2×AΣL(1,𝔽27)—21no—
203C2×AΣL(1,𝔽27)—21no—
204C2×AΣL(1,𝔽27)—21no—
205C2×AΣL(1,𝔽27)—21no—
206C2×AΣL(1,𝔽27)—21no—
207C2×AΣL(1,𝔽27)—21no—
208C2×AΣL(1,𝔽27)—21no—
209C2×AΣL(1,𝔽27)—21no—
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)C2×C3211yescharacteristic, complemented
222C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
223C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
224C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
225C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
226C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
227C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
228C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
229C2×AΣL(1,𝔽27)C2×C3211yescharacteristic, complemented
230#4174C2×C3212yescomplemented
231#4174C2×C3212yescomplemented
232#4174C2×C3212yescomplemented
233#4174C2×C3212yescomplemented
234#4174C2×C3212yescomplemented
235#4174C2×C3212yescomplemented
236#4174C2×C3212yescomplemented
237#4174C2×C3212yescomplemented
238#4174C2×C3212yescomplemented
239C22×C33—91no—
240C22×C33—91no—
241C22×C33—91no—
242C22×C33—91no—
243C2×C32×D3—31no—
244C2×C32×D3—31no—
245C2×C32×D3—31no—
246C2×C32×D3—31no—
247C2×C32×D3—31no—
248C2×C32×D3—31no—
249C2×C32×D3—31no—
250C2×C32×D3—31no—
251C2×C32×D3—31no—
252C2×C32×D3—31no—
253C2×C32×D3—31no—
254C2×C32×D3—31no—
255C2×C32×D3—31no—
256C2×C32×D3—91no—
257C2×C32×D3—91no—
258C2×C32×D3—91no—
259C2×C32×D3—91no—
260C2×C32×D3—91no—
261C2×C32×D3—91no—
262C2×C32×D3—91no—
263C2×C32×D3—91no—
264C2×C32×D3—91no—
265C2×C32×D3—91no—
266C2×C32×D3—91no—
267C2×C32×D3—91no—
268C2×C32×D3—91no—
269C2×C32×D3—91no—
270C2×C32×D3—91no—
271C2×C32×D3—91no—
272C2×C32×D3—91no—
273C2×C32×D3—91no—
274C2×C32×D3—91no—
275C2×C32×D3—91no—
276C2×C32×D3—91no—
277C2×C32×D3—91no—
278C2×C32×D3—91no—
279C2×C32×D3—91no—
280C2×C32×D3—91no—
281C22×H(3,𝔽3)—91no—
282C22×H(3,𝔽3)—91no—
283C22×H(3,𝔽3)—91no—
284C22×H(3,𝔽3)—91no—
285C22×H(3,𝔽3)—91no—
286C22×H(3,𝔽3)—91no—
287C22×H(3,𝔽3)—91no—
288C22×H(3,𝔽3)—91no—
289C22×H(3,𝔽3)—91no—
290C2×#272C3311yescharacteristic
291C34—31no—
292C34C2×C3×D311yescharacteristic
293C34C2×C3×D311yescharacteristic, complemented
294C34C2×C3×D311yescharacteristic, complemented
295C34C2×C3×D311yescharacteristic, complemented
296C3×3−1+2—21no—
297C3×3−1+2—21no—
298C3×3−1+2—21no—
299C3×3−1+2—21no—
300C3×3−1+2—21no—
301C3×3−1+2—21no—
302C3×3−1+2—21no—
303C3×3−1+2—21no—
304C3×3−1+2—21no—
305C3×3−1+2—21no—
306C3×3−1+2—21no—
307C3×3−1+2—21no—
308C3×3−1+2—61no—
309C3×3−1+2—61no—
310C3×3−1+2—61no—
311C3×3−1+2—61no—
312C3×3−1+2—61no—
313C3×3−1+2—61no—
314C3×3−1+2—61no—
315C3×3−1+2—61no—
316C3×H(3,𝔽3)—21no—
317C3×H(3,𝔽3)—21no—
318C3×H(3,𝔽3)—21no—
319C3×H(3,𝔽3)—21no—
320C3×H(3,𝔽3)—61no—
321C3×H(3,𝔽3)—61no—
322C3×H(3,𝔽3)—61no—
323C3×H(3,𝔽3)—61no—
324C3×H(3,𝔽3)—61no—
325C3×H(3,𝔽3)—61no—
326C3×H(3,𝔽3)—61no—
327C3×H(3,𝔽3)—61no—
328C3×H(3,𝔽3)—61no—
329C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
330C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
331C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
332C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
333C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
334C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
335C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
336C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
337C3×H(3,𝔽3)C2×C3×D311yescharacteristic, complemented
338C3×H(3,𝔽3)C22×C3211yescharacteristic
339C3×H(3,𝔽3)C22×C3211yescharacteristic, complemented
340C3×H(3,𝔽3)C22×C3211yescharacteristic, complemented
341C3×H(3,𝔽3)C22×C3211yescharacteristic, complemented
342C32×C9—61no—
343AΣL(1,𝔽27)—21no—
344AΣL(1,𝔽27)—21no—
345AΣL(1,𝔽27)—21no—
346AΣL(1,𝔽27)—21no—
347AΣL(1,𝔽27)—21no—
348AΣL(1,𝔽27)—21no—
349AΣL(1,𝔽27)—21no—
350AΣL(1,𝔽27)—21no—
351AΣL(1,𝔽27)—21no—
352AΣL(1,𝔽27)—21no—
353AΣL(1,𝔽27)—21no—
354AΣL(1,𝔽27)—21no—
355AΣL(1,𝔽27)—21no—
356AΣL(1,𝔽27)—21no—
357AΣL(1,𝔽27)—21no—
358AΣL(1,𝔽27)—21no—
359AΣL(1,𝔽27)—21no—
360AΣL(1,𝔽27)—21no—
361AΣL(1,𝔽27)—21no—
362AΣL(1,𝔽27)—21no—
363AΣL(1,𝔽27)—21no—
364AΣL(1,𝔽27)—21no—
365AΣL(1,𝔽27)—21no—
366AΣL(1,𝔽27)—21no—
367AΣL(1,𝔽27)—21no—
368AΣL(1,𝔽27)—21no—
369AΣL(1,𝔽27)—21no—
370AΣL(1,𝔽27)—21no—
371AΣL(1,𝔽27)—21no—
372AΣL(1,𝔽27)—21no—
373AΣL(1,𝔽27)—21no—
374AΣL(1,𝔽27)—21no—
375AΣL(1,𝔽27)—21no—
376AΣL(1,𝔽27)—21no—
377AΣL(1,𝔽27)—21no—
378AΣL(1,𝔽27)—21no—
379AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
380AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
381AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
382AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
383AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
384AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
385AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
386AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
387AΣL(1,𝔽27)C22×C3211yescharacteristic, complemented
388C2×C33—21no—
389C2×C33—21no—
390C2×C33—21no—
391C2×C33—21no—
392C2×C33—31no—
393C2×C33—31no—
394C2×C33—31no—
395C2×C33—31no—
396C2×C33—31no—
397C2×C33—31no—
398C2×C33—61no—
399C2×C33—61no—
400C2×C33—61no—
401C2×C33—61no—
402C2×C33—61no—
403C2×C33—61no—
404C2×C33—61no—
405C2×C33—61no—
406C2×C33—91no—
407C2×C33—91no—
408C2×C33—92no—
409C2×C33—92no—
410C2×C33—92no—
411C2×C33—92no—
412C2×C33—181no—
413C2×C33—181no—
414C2×C33—181no—
415C2×C33—181no—
416C2×C33—181no—
417C2×C33—181no—
418C2×C33—181no—
419C2×C33—181no—
420C2×C33—181no—
421C2×C33—181no—
422C2×C33—181no—
423C2×C33—181no—
424C2×C33—181no—
425C2×C33—181no—
426C2×C33—181no—
427C2×C33—181no—
428C2×C33—181no—
429C2×C33—181no—
430C2×C33—181no—
431C2×C33(C3⋊D3)⋊C311yescharacteristic
432C2×C33C32×D311yescharacteristic
433C2×C33C32×D311yescharacteristic
434C2×C33C32×D311yescharacteristic
435C2×C33C32×D311yescharacteristic
436C2×C33C32×D311yescharacteristic, complemented
437C2×C33C32×D311yescharacteristic, complemented
438C2×C33C32×D311yescharacteristic, complemented
439C2×C33C32×D311yescharacteristic, complemented
440C2×C33C32×D311yescharacteristic, complemented
441C2×C33C32×D311yescharacteristic, complemented
442C2×C33C32×D311yescharacteristic, complemented
443C2×C33C32×D311yescharacteristic, complemented
444C2×C33C32×D311yescharacteristic, complemented
445C32×D3—32no—
446C32×D3—32no—
447C32×D3—32no—
448C32×D3—32no—
449C32×D3—32no—
450C32×D3—32no—
451C32×D3—32no—
452C32×D3—32no—
453C32×D3—32no—
454C32×D3—32no—
455C32×D3—32no—
456C32×D3—32no—
457C32×D3—32no—
458C32×D3—92no—
459C32×D3—92no—
460C32×D3—92no—
461C32×D3—92no—
462C32×D3—92no—
463C32×D3—92no—
464C32×D3—92no—
465C32×D3—92no—
466C32×D3—92no—
467C32×D3—92no—
468C32×D3—92no—
469C32×D3—92no—
470C32×D3—92no—
471C32×D3—92no—
472C32×D3—92no—
473C32×D3—92no—
474C32×D3—92no—
475C32×D3—92no—
476C32×D3—92no—
477C32×D3—92no—
478C32×D3—92no—
479C32×D3—92no—
480C32×D3—92no—
481C32×D3—92no—
482C32×D3—92no—
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—21no—
489C2×3−1+2—21no—
490C2×3−1+2—21no—
491C2×3−1+2—21no—
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×H(3,𝔽3)—21no—
517C2×H(3,𝔽3)—21no—
518C2×H(3,𝔽3)—21no—
519C2×H(3,𝔽3)—21no—
520C2×H(3,𝔽3)—31no—
521C2×H(3,𝔽3)—31no—
522C2×H(3,𝔽3)—31no—
523C2×H(3,𝔽3)—61no—
524C2×H(3,𝔽3)—61no—
525C2×H(3,𝔽3)—61no—
526C2×H(3,𝔽3)—61no—
527C2×H(3,𝔽3)—61no—
528C2×H(3,𝔽3)—61no—
529C2×H(3,𝔽3)—61no—
530C2×H(3,𝔽3)—61no—
531C2×H(3,𝔽3)—61no—
532C2×H(3,𝔽3)—61no—
533C2×H(3,𝔽3)—61no—
534C2×H(3,𝔽3)—62no—
535C2×H(3,𝔽3)—62no—
536C2×H(3,𝔽3)—62no—
537C2×H(3,𝔽3)—62no—
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)—92no—
547C2×H(3,𝔽3)—92no—
548C2×H(3,𝔽3)—92no—
549C2×H(3,𝔽3)—92no—
550C2×H(3,𝔽3)—92no—
551C2×H(3,𝔽3)—92no—
552C2×H(3,𝔽3)—92no—
553C2×H(3,𝔽3)—92no—
554C2×H(3,𝔽3)—92no—
555C2×H(3,𝔽3)C2×C3311yescharacteristic
556C2×C3×C9—61no—
557C2×C3×C9—61no—
558C2×C3×C9—61no—
559C2×C3×C9—61no—
560C2×C3×C9—61no—
561C2×C3×C9—61no—
562C2×C3×C9—61no—
563C2×C3×C9—61no—
564C2×C3×C9—61no—
565C2×C3×C9—61no—
566C2×C3×C9—61no—
567C2×C3×C9—61no—
568#272C2×C3312yes—
569C22×C32—91no—
570C22×C32—91no—
571C22×C32—91no—
572C22×C32—91no—
573C22×C32—91no—
574C22×C32—91no—
575C22×C32—91no—
576C22×C32—91no—
577C22×C32—91no—
578C22×C32—91no—
579C22×C32—91no—
580C22×C32—91no—
581C22×C32—91no—
582C22×C32—271no—
583C22×C32—271no—
584C22×C32—271no—
585C22×C32—271no—
586C22×C32—271no—
587C22×C32—271no—
588C22×C32—271no—
589C22×C32—271no—
590C22×C32—271no—
591C22×C32—271no—
592C22×C32—271no—
593C22×C32—271no—
594C2×C3×D3—31no—
595C2×C3×D3—31no—
596C2×C3×D3—31no—
597C2×C3×D3—31no—
598C2×C3×D3—91no—
599C2×C3×D3—91no—
600C2×C3×D3—91no—
601C2×C3×D3—91no—
602C2×C3×D3—91no—
603C2×C3×D3—91no—
604C2×C3×D3—91no—
605C2×C3×D3—91no—
606C2×C3×D3—91no—
607C2×C3×D3—91no—
608C2×C3×D3—91no—
609C2×C3×D3—91no—
610C2×C3×D3—91no—
611C2×C3×D3—91no—
612C2×C3×D3—91no—
613C2×C3×D3—91no—
614C2×C3×D3—91no—
615C2×C3×D3—91no—
616C2×C3×D3—91no—
617C2×C3×D3—91no—
618C2×C3×D3—91no—
619C2×C3×D3—91no—
620C2×C3×D3—91no—
621C2×C3×D3—91no—
622C2×C3×D3—91no—
623C33—21no—
624C33—21no—
625C33—21no—
626C33—21no—
627C33—31no—
628C33—31no—
629C33—31no—
630C33—31no—
631C33—31no—
632C33—31no—
633C33—61no—
634C33—61no—
635C33—61no—
636C33—61no—
637C33—61no—
638C33—61no—
639C33—61no—
640C33—61no—
641C33—91no—
642C33—91no—
643C33—181no—
644C33—181no—
645C33—181no—
646C33—181no—
647C33—181no—
648C33—181no—
649C33—181no—
650C33—181no—
651C33—181no—
652C33—181no—
653C33—181no—
654C33—181no—
655C33—181no—
656C33—181no—
657C33—181no—
658C33—181no—
659C33—181no—
660C33—181no—
661C33—181no—
662C33C2×(C3⋊D3)⋊C311yescharacteristic
663C33C2×C32×D311yescharacteristic
664C33C2×C32×D311yescharacteristic
665C33C2×C32×D311yescharacteristic
666C33C2×C32×D311yescharacteristic
667C33C2×C32×D311yescharacteristic, complemented
668C33C2×C32×D311yescharacteristic, complemented
669C33C2×C32×D311yescharacteristic, complemented
670C33C2×C32×D311yescharacteristic, complemented
671C33C2×C32×D311yescharacteristic, complemented
672C33C2×C32×D311yescharacteristic, complemented
673C33C2×C32×D311yescharacteristic, complemented
674C33C2×C32×D311yescharacteristic, complemented
675C33C2×C32×D311yescharacteristic, complemented
6763−1+2—21no—
6773−1+2—21no—
6783−1+2—21no—
6793−1+2—21no—
6803−1+2—21no—
6813−1+2—21no—
6823−1+2—21no—
6833−1+2—21no—
6843−1+2—21no—
6853−1+2—61no—
6863−1+2—61no—
6873−1+2—61no—
6883−1+2—61no—
6893−1+2—61no—
6903−1+2—61no—
6913−1+2—61no—
6923−1+2—61no—
6933−1+2—61no—
6943−1+2—61no—
6953−1+2—61no—
6963−1+2—61no—
6973−1+2—61no—
6983−1+2—61no—
6993−1+2—61no—
7003−1+2—61no—
7013−1+2—61no—
7023−1+2—61no—
7033−1+2—61no—
7043−1+2—61no—
7053−1+2—61no—
7063−1+2—61no—
7073−1+2—61no—
7083−1+2—61no—
709H(3,𝔽3)—21no—
710H(3,𝔽3)—21no—
711H(3,𝔽3)—21no—
712H(3,𝔽3)—21no—
713H(3,𝔽3)—31no—
714H(3,𝔽3)—31no—
715H(3,𝔽3)—31no—
716H(3,𝔽3)—61no—
717H(3,𝔽3)—61no—
718H(3,𝔽3)—61no—
719H(3,𝔽3)—61no—
720H(3,𝔽3)—61no—
721H(3,𝔽3)—61no—
722H(3,𝔽3)—61no—
723H(3,𝔽3)—61no—
724H(3,𝔽3)—61no—
725H(3,𝔽3)—61no—
726H(3,𝔽3)—61no—
727H(3,𝔽3)—62no—
728H(3,𝔽3)—62no—
729H(3,𝔽3)—62no—
730H(3,𝔽3)—62no—
731H(3,𝔽3)—61no—
732H(3,𝔽3)—61no—
733H(3,𝔽3)—61no—
734H(3,𝔽3)—61no—
735H(3,𝔽3)—61no—
736H(3,𝔽3)—61no—
737H(3,𝔽3)—61no—
738H(3,𝔽3)—61no—
739H(3,𝔽3)C22×C3311yescharacteristic
740C3×C9—61no—
741C3×C9—61no—
742C3×C9—61no—
743C3×C9—61no—
744C3×C9—61no—
745C3×C9—61no—
746C3×C9—61no—
747C3×C9—61no—
748C3×C9—61no—
749C3×C9—61no—
750C3×C9—61no—
751C3×C9—61no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—31no—
757C2×C32—31no—
758C2×C32—31no—
759C2×C32—31no—
760C2×C32—31no—
761C2×C32—31no—
762C2×C32—31no—
763C2×C32—61no—
764C2×C32—61no—
765C2×C32—61no—
766C2×C32—61no—
767C2×C32—61no—
768C2×C32—61no—
769C2×C32—61no—
770C2×C32—61no—
771C2×C32—61no—
772C2×C32—61no—
773C2×C32—61no—
774C2×C32—61no—
775C2×C32—61no—
776C2×C32—61no—
777C2×C32—61no—
778C2×C32—61no—
779C2×C32—91no—
780C2×C32—91no—
781C2×C32—91no—
782C2×C32—91no—
783C2×C32—92no—
784C2×C32—91no—
785C2×C32—91no—
786C2×C32—91no—
787C2×C32—91no—
788C2×C32—92no—
789C2×C32—92no—
790C2×C32—92no—
791C2×C32—92no—
792C2×C32—92no—
793C2×C32—92no—
794C2×C32—92no—
795C2×C32—92no—
796C2×C32—92no—
797C2×C32—92no—
798C2×C32—92no—
799C2×C32—92no—
800C2×C32—181no—
801C2×C32—181no—
802C2×C32—181no—
803C2×C32—181no—
804C2×C32—181no—
805C2×C32—181no—
806C2×C32—181no—
807C2×C32—181no—
808C2×C32—181no—
809C2×C32—181no—
810C2×C32—181no—
811C2×C32—181no—
812C2×C32—181no—
813C2×C32—181no—
814C2×C32—181no—
815C2×C32—181no—
816C2×C32—181no—
817C2×C32—181no—
818C2×C32—181no—
819C2×C32—181no—
820C2×C32—181no—
821C2×C32—183no—
822C2×C32—183no—
823C2×C32—181no—
824C2×C32—181no—
825C2×C32—183no—
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—272no—
844C2×C32—272no—
845C2×C32—272no—
846C2×C32—272no—
847C2×C32—272no—
848C2×C32—272no—
849C2×C32—272no—
850C2×C32—272no—
851C2×C32—272no—
852C2×C32—272no—
853C2×C32—272no—
854C2×C32—272no—
855C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
856C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
857C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
858C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
859C2×C32C33×D311yescharacteristic
860C3×D3—32no—
861C3×D3—32no—
862C3×D3—32no—
863C3×D3—32no—
864C3×D3—92no—
865C3×D3—92no—
866C3×D3—92no—
867C3×D3—92no—
868C3×D3—92no—
869C3×D3—92no—
870C3×D3—92no—
871C3×D3—92no—
872C3×D3—92no—
873C3×D3—92no—
874C3×D3—92no—
875C3×D3—92no—
876C3×D3—92no—
877C3×D3—92no—
878C3×D3—92no—
879C3×D3—92no—
880C3×D3—92no—
881C3×D3—92no—
882C3×D3—92no—
883C3×D3—92no—
884C3×D3—92no—
885C3×D3—92no—
886C3×D3—92no—
887C3×D3—92no—
888C3×D3—92no—
889C2×C9—61no—
890C2×C9—61no—
891C2×C9—61no—
892C2×C9—61no—
893C2×C9—61no—
894C2×C9—61no—
895C2×C9—61no—
896C2×C9—61no—
897C2×C9—61no—
898C22×C3—91no—
899C22×C3—91no—
900C22×C3—91no—
901C22×C3—91no—
902C22×C3—271no—
903C22×C3—271no—
904C22×C3—271no—
905C22×C3—271no—
906C22×C3—271no—
907C22×C3—271no—
908C22×C3—271no—
909C22×C3—271no—
910C22×C3—271no—
911C22×C3—271no—
912C22×C3—271no—
913C22×C3—271no—
914C2×D3—31no—
915C2×D3—91no—
916C32—21no—
917C32—21no—
918C32—21no—
919C32—21no—
920C32—31no—
921C32—31no—
922C32—31no—
923C32—31no—
924C32—31no—
925C32—31no—
926C32—31no—
927C32—61no—
928C32—61no—
929C32—61no—
930C32—61no—
931C32—61no—
932C32—61no—
933C32—61no—
934C32—61no—
935C32—61no—
936C32—61no—
937C32—61no—
938C32—61no—
939C32—61no—
940C32—61no—
941C32—61no—
942C32—61no—
943C32—91no—
944C32—91no—
945C32—91no—
946C32—91no—
947C32—91no—
948C32—91no—
949C32—91no—
950C32—91no—
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—183no—
975C32—183no—
976C32—181no—
977C32—181no—
978C32—181no—
979C32—181no—
980C32—181no—
981C32—181no—
982C32—183no—
983C32—181no—
984C32—181no—
985C32—181no—
986C32—181no—
987C32—181no—
988C32—181no—
989C32—181no—
990C32—181no—
991C32—181no—
992C32—181no—
993C32—181no—
994C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
995C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
996C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
997C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
998C32C2×C33×D311yescharacteristic
999C9—61no—
1000C9—61no—
1001C9—61no—
1002C9—61no—
1003C9—61no—
1004C9—61no—
1005C9—61no—
1006C9—61no—
1007C9—61no—
1008C2×C3—31no—
1009C2×C3—31no—
1010C2×C3—31no—
1011C2×C3—61no—
1012C2×C3—61no—
1013C2×C3—61no—
1014C2×C3—61no—
1015C2×C3—61no—
1016C2×C3—92no—
1017C2×C3—92no—
1018C2×C3—92no—
1019C2×C3—92no—
1020C2×C3—91no—
1021C2×C3—91no—
1022C2×C3—91no—
1023C2×C3—181no—
1024C2×C3—181no—
1025C2×C3—181no—
1026C2×C3—181no—
1027C2×C3—181no—
1028C2×C3—181no—
1029C2×C3—181no—
1030C2×C3—181no—
1031C2×C3—181no—
1032C2×C3—181no—
1033C2×C3—181no—
1034C2×C3—272no—
1035C2×C3—272no—
1036C2×C3—272no—
1037C2×C3—272no—
1038C2×C3—272no—
1039C2×C3—272no—
1040C2×C3—272no—
1041C2×C3—272no—
1042C2×C3—272no—
1043C2×C3—272no—
1044C2×C3—272no—
1045C2×C3—272no—
1046C2×C3#9228111yescharacteristic, direct product factor
1047C2×C3#9228111yescharacteristic, direct product factor
1048C2×C3#9228111yescharacteristic, direct product factor
1049C2×C3C32×(C3⋊D3)⋊C311yescharacteristic
1050D3—32no—
1051D3—92no—
1052C22—91noSylow
1053C3—31no—
1054C3—31no—
1055C3—31no—
1056C3—61no—
1057C3—61no—
1058C3—61no—
1059C3—61no—
1060C3—61no—
1061C3—91no—
1062C3—91no—
1063C3—91no—
1064C3—181no—
1065C3—181no—
1066C3—181no—
1067C3—181no—
1068C3—181no—
1069C3—181no—
1070C3—181no—
1071C3—181no—
1072C3—181no—
1073C3—181no—
1074C3—181no—
1075C3C2×#9228111yescharacteristic, direct product factor
1076C3C2×#9228111yescharacteristic, direct product factor
1077C3C2×#9228111yescharacteristic, direct product factor
1078C3C2×C32×(C3⋊D3)⋊C311yescharacteristic
1079C2—92no—
1080C2C3×#9228111yescharacteristic, direct product factor
subgroupG/H
center, socleC2×C32C3×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterH(3,𝔽3)C22×C33
FrattiniC32C2×C33×D3
FittingC2×C3×#6909C2
hypercenterC2×C33(C3⋊D3)⋊C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C32 ◁ C2×C33

Complements

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

NH ≅ G/Ntype
1. C3×#92281C2direct (N × H)
2. C2×C3×#6909C2semidirect
3. C2×C32×#272C3semidirect
5. C2×#92281C3direct (N × H)
6. C2×#92281C3direct (N × H)
7. C2×#92281C3direct (N × H)
8. C2×#92281C3direct (N × H)
9. C2×#92281C3direct (N × H)
10. C2×#92281C3direct (N × H)
11. C2×#92281C3direct (N × H)
12. C2×#92281C3direct (N × H)
13. C2×#92281C3direct (N × H)
14. C2×C3×#4174C3semidirect
15. C2×C3×#4174C3semidirect
16. C2×C3×#4174C3semidirect
17. C3×#6909C22semidirect
19. C2×C32×H(3,𝔽3)D3semidirect
20. C2×C32×H(3,𝔽3)C2×C3semidirect
21. C32×#272C2×C3semidirect
32. C2×#6909C2×C3semidirect
33. C2×#6909C2×C3semidirect
34. C2×#6909C2×C3semidirect
35. C2×#6909C2×C3semidirect
36. C2×#6909C2×C3semidirect
37. C2×#6909C2×C3semidirect
38. C2×#6909C2×C3semidirect
39. C2×#6909C2×C3semidirect
40. C2×#6909C2×C3semidirect
44. C2×C3×AΣL(1,𝔽27)C2×C3semidirect
45. C2×C3×AΣL(1,𝔽27)C2×C3semidirect
46. C2×C3×AΣL(1,𝔽27)C2×C3semidirect
47. #92281C2×C3direct (N × H)
48. #92281C2×C3direct (N × H)
49. #92281C2×C3direct (N × H)
50. #92281C2×C3direct (N × H)
51. #92281C2×C3direct (N × H)
52. #92281C2×C3direct (N × H)
53. #92281C2×C3direct (N × H)
54. #92281C2×C3direct (N × H)
55. #92281C2×C3direct (N × H)
56. C3×#4174C2×C3semidirect
57. C3×#4174C2×C3semidirect
58. C3×#4174C2×C3semidirect
66. C2×C3×#272C32semidirect
67. C2×C3×#272C32semidirect
68. C2×C3×#272C32semidirect
78. C2×#4174C32semidirect
79. C2×#4174C32semidirect
80. C2×#4174C32semidirect
81. C2×#4174C32semidirect
82. C2×#4174C32semidirect
83. C2×#4174C32semidirect
84. C2×#4174C32semidirect
85. C2×#4174C32semidirect
86. C2×#4174C32semidirect
88. C32×H(3,𝔽3)C2×D3semidirect
89. C32×H(3,𝔽3)C22×C3semidirect
99. #6909C22×C3semidirect
100. #6909C22×C3semidirect
101. #6909C22×C3semidirect
102. #6909C22×C3semidirect
103. #6909C22×C3semidirect
104. #6909C22×C3semidirect
105. #6909C22×C3semidirect
106. #6909C22×C3semidirect
107. #6909C22×C3semidirect
111. C3×AΣL(1,𝔽27)C22×C3semidirect
112. C3×AΣL(1,𝔽27)C22×C3semidirect
113. C3×AΣL(1,𝔽27)C22×C3semidirect
116. C2×C34C3×D3semidirect
117. C2×C34C3×D3semidirect
118. C2×C34C3×D3semidirect
158. C2×C3×H(3,𝔽3)C3×D3semidirect
159. C2×C3×H(3,𝔽3)C3×D3semidirect
160. C2×C3×H(3,𝔽3)C3×D3semidirect
161. C2×C3×H(3,𝔽3)C3×D3semidirect
162. C2×C3×H(3,𝔽3)C3×D3semidirect
163. C2×C3×H(3,𝔽3)C3×D3semidirect
164. C2×C3×H(3,𝔽3)C3×D3semidirect
165. C2×C3×H(3,𝔽3)C3×D3semidirect
166. C2×C3×H(3,𝔽3)C3×D3semidirect
168. C2×C3×H(3,𝔽3)C2×C32semidirect
169. C2×C3×H(3,𝔽3)C2×C32semidirect
170. C2×C3×H(3,𝔽3)C2×C32semidirect
173. C3×#272C2×C32semidirect
174. C3×#272C2×C32semidirect
175. C3×#272C2×C32semidirect
221. C2×AΣL(1,𝔽27)C2×C32semidirect
222. C2×AΣL(1,𝔽27)C2×C32semidirect
223. C2×AΣL(1,𝔽27)C2×C32semidirect
224. C2×AΣL(1,𝔽27)C2×C32semidirect
225. C2×AΣL(1,𝔽27)C2×C32semidirect
226. C2×AΣL(1,𝔽27)C2×C32semidirect
227. C2×AΣL(1,𝔽27)C2×C32semidirect
228. C2×AΣL(1,𝔽27)C2×C32semidirect
229. C2×AΣL(1,𝔽27)C2×C32semidirect
230. #4174C2×C32semidirect
231. #4174C2×C32semidirect
232. #4174C2×C32semidirect
233. #4174C2×C32semidirect
234. #4174C2×C32semidirect
235. #4174C2×C32semidirect
236. #4174C2×C32semidirect
237. #4174C2×C32semidirect
238. #4174C2×C32semidirect
293. C34C2×C3×D3semidirect
294. C34C2×C3×D3semidirect
295. C34C2×C3×D3semidirect
329. C3×H(3,𝔽3)C2×C3×D3semidirect
330. C3×H(3,𝔽3)C2×C3×D3semidirect
331. C3×H(3,𝔽3)C2×C3×D3semidirect
332. C3×H(3,𝔽3)C2×C3×D3semidirect
333. C3×H(3,𝔽3)C2×C3×D3semidirect
334. C3×H(3,𝔽3)C2×C3×D3semidirect
335. C3×H(3,𝔽3)C2×C3×D3semidirect
336. C3×H(3,𝔽3)C2×C3×D3semidirect
337. C3×H(3,𝔽3)C2×C3×D3semidirect
339. C3×H(3,𝔽3)C22×C32semidirect
340. C3×H(3,𝔽3)C22×C32semidirect
341. C3×H(3,𝔽3)C22×C32semidirect
379. AΣL(1,𝔽27)C22×C32semidirect
380. AΣL(1,𝔽27)C22×C32semidirect
381. AΣL(1,𝔽27)C22×C32semidirect
382. AΣL(1,𝔽27)C22×C32semidirect
383. AΣL(1,𝔽27)C22×C32semidirect
384. AΣL(1,𝔽27)C22×C32semidirect
385. AΣL(1,𝔽27)C22×C32semidirect
386. AΣL(1,𝔽27)C22×C32semidirect
387. AΣL(1,𝔽27)C22×C32semidirect
436. C2×C33C32×D3semidirect
437. C2×C33C32×D3semidirect
438. C2×C33C32×D3semidirect
439. C2×C33C32×D3semidirect
440. C2×C33C32×D3semidirect
441. C2×C33C32×D3semidirect
442. C2×C33C32×D3semidirect
443. C2×C33C32×D3semidirect
444. C2×C33C32×D3semidirect
667. C33C2×C32×D3semidirect
668. C33C2×C32×D3semidirect
669. C33C2×C32×D3semidirect
670. C33C2×C32×D3semidirect
671. C33C2×C32×D3semidirect
672. C33C2×C32×D3semidirect
673. C33C2×C32×D3semidirect
674. C33C2×C32×D3semidirect
675. C33C2×C32×D3semidirect
1046. C2×C3#92281direct (N × H)
1047. C2×C3#92281direct (N × H)
1048. C2×C3#92281direct (N × H)
1075. C3C2×#92281direct (N × H)
1076. C3C2×#92281direct (N × H)
1077. C3C2×#92281direct (N × H)
1080. C2C3×#92281direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#922812
C2×C3×#69092
C2×C32×#2723
C2×C3×D3×H(3,𝔽3)3
C2×#922813
C2×C3×#41743