Finite Group Databasebeta

← C2×#13091424 #72243905

Subgroups — C2×#13091424 #72243905

Order 2916.

1227 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091424C212yesmaximal, direct product factor
2C2×#10624869C211yesmaximal, characteristic, complemented
3C2×C3×#4207—31nomaximal
4C2×C3×#4207—31nomaximal
5C2×C3×#4207—31nomaximal
6C2×C32×C3⋊D9—31nomaximal
7C2×C9⋊#272C311yesmaximal, characteristic, complemented
8C2×#92304—31nomaximal
9C2×#92304—31nomaximal
10C2×#92304—31nomaximal
11C2×#92304—31nomaximal
12C2×#92304—31nomaximal
13C2×#92304—31nomaximal
14C2×#92302—31nomaximal
15C2×#92302—31nomaximal
16C2×#92300—31nomaximal
17#10624869C2211yescharacteristic, complemented, Sylow
18C2×C3×#737D311yescharacteristic, complemented
19C2×C3×#737D311yescharacteristic, complemented
20C2×C3×#737D311yescharacteristic, complemented
21C2×C33×C9D311yescharacteristic, complemented
22C3×#4207—32no—
23C3×#4207—32no—
24C3×#4207—32no—
25C32×C3⋊D9—32no—
26C2×#6893D311yescharacteristic, complemented
27C2×#6893D311yescharacteristic, complemented
28C2×#6893D311yescharacteristic, complemented
29C2×#6893D311yescharacteristic, complemented
30C2×#6893D311yescharacteristic, complemented
31C2×#6893D311yescharacteristic, complemented
32C2×C9⋊H(3,𝔽3)—21no—
33C2×C9⋊H(3,𝔽3)—21no—
34C2×C9⋊H(3,𝔽3)—21no—
35C2×C9⋊H(3,𝔽3)—21no—
36C2×C9⋊H(3,𝔽3)—21no—
37C2×C9⋊H(3,𝔽3)—21no—
38C2×C9⋊H(3,𝔽3)—21no—
39C2×C9⋊H(3,𝔽3)—21no—
40C2×C9⋊H(3,𝔽3)—21no—
41C2×#6891D311yescharacteristic, complemented
42C2×#6891D311yescharacteristic, complemented
43C2×C32⋊H(3,𝔽3)D311yescharacteristic
44C2×C9×H(3,𝔽3)—21no—
45C2×C9×H(3,𝔽3)—21no—
46C2×C9×H(3,𝔽3)—21no—
47C2×C9×H(3,𝔽3)—21no—
48C2×C9×H(3,𝔽3)C2×C311yescharacteristic, complemented
49C9⋊#272C2×C312yescomplemented
50#92304—32no—
51#92304—32no—
52#92304—32no—
53#92304—32no—
54#92304—32no—
55#92304—32no—
56#92302—32no—
57#92302—32no—
58#92300—32no—
59C2×C32×C3⋊D3—91no—
60C2×C3⋊#272—31no—
61C2×#4207—31no—
62C2×#4207—31no—
63C2×#4207—31no—
64C2×#4207—31no—
65C2×#4207—31no—
66C2×#4207—31no—
67C2×#4207—31no—
68C2×#4207—31no—
69C2×#4207—31no—
70C2×C3×C3⋊D9—31no—
71C2×C3×C3⋊D9—31no—
72C2×C3×C3⋊D9—31no—
73C2×C3×C3⋊D9—31no—
74C2×C3×C3⋊D9—31no—
75C2×C3×C3⋊D9—31no—
76C2×C3×C3⋊D9—31no—
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×AGL(1,ℤ/9)—91no—
83C2×C3×(C3⋊D3)⋊C3—91no—
84C2×C3×(C3⋊D3)⋊C3—91no—
85C2×C3×(C3⋊D3)⋊C3—91no—
86C2×C32×D9—91no—
87C2×C32×D9—91no—
88C2×C32×D9—91no—
89C2×#4181—31no—
90C2×#4181—31no—
91C2×#4181—31no—
92C2×#4181—31no—
93C2×#4181—31no—
94C2×#4181—31no—
95C2×#4181—31no—
96C2×#4181—31no—
97C3×#737C2×D311yescharacteristic, complemented
98C3×#737C2×D311yescharacteristic, complemented
99C3×#737C2×D311yescharacteristic, complemented
100C33×C9C2×D311yescharacteristic, complemented
101#6893C2×D311yescharacteristic, complemented
102#6893C2×D311yescharacteristic, complemented
103#6893C2×D311yescharacteristic, complemented
104#6893C2×D311yescharacteristic, complemented
105#6893C2×D311yescharacteristic, complemented
106#6893C2×D311yescharacteristic, complemented
107C9⋊H(3,𝔽3)—21no—
108C9⋊H(3,𝔽3)—21no—
109C9⋊H(3,𝔽3)—21no—
110C9⋊H(3,𝔽3)—21no—
111C9⋊H(3,𝔽3)—21no—
112C9⋊H(3,𝔽3)—21no—
113C9⋊H(3,𝔽3)—21no—
114C9⋊H(3,𝔽3)—21no—
115C9⋊H(3,𝔽3)—21no—
116#6891C2×D311yescharacteristic, complemented
117#6891C2×D311yescharacteristic, complemented
118C32⋊H(3,𝔽3)C2×D311yescharacteristic
119C9×H(3,𝔽3)—21no—
120C9×H(3,𝔽3)—21no—
121C9×H(3,𝔽3)—21no—
122C9×H(3,𝔽3)—21no—
123C9×H(3,𝔽3)C22×C311yescharacteristic, complemented
124C2×C34C3⋊D311yescharacteristic
125C32×C3⋊D3—92no—
126C2×#737—31no—
127C2×#737—31no—
128C2×#737—31no—
129C2×#737—61no—
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×#737—61no—
142C2×#737—61no—
143C2×#737—61no—
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+2—21no—
150C2×C3×3−1+2—21no—
151C2×C3×3−1+2—21no—
152C2×C3×3−1+2—21no—
153C2×C3×3−1+2C3⋊D311yescharacteristic
154C2×C3×3−1+2C3⋊D311yescharacteristic
155C2×C3×3−1+2C3⋊D311yescharacteristic
156C2×C3×3−1+2C3⋊D311yescharacteristic
157C2×C3×3−1+2C3⋊D311yescharacteristic
158C2×C3×3−1+2C3⋊D311yescharacteristic
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)C3×D311yescharacteristic
164C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
165C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
166C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
167C2×C32×C9—21no—
168C2×C32×C9—21no—
169C2×C32×C9—21no—
170C2×C32×C9—21no—
171C2×C32×C9—21no—
172C2×C32×C9—21no—
173C2×C32×C9—21no—
174C2×C32×C9—31no—
175C2×C32×C9—31no—
176C2×C32×C9—31no—
177C2×C32×C9—61no—
178C2×C32×C9—61no—
179C2×C32×C9—61no—
180C2×C32×C9C3×D311yescharacteristic
181C2×C32×C9C3×D311yescharacteristic, complemented
182C2×C32×C9C3×D311yescharacteristic, complemented
183C2×C32×C9C3×D311yescharacteristic, complemented
184C2×C32×C9C3⋊D311yescharacteristic
185C2×C32×C9C3⋊D311yescharacteristic
186C2×C32×C9C3⋊D311yescharacteristic
187C3⋊#272—32no—
188#4207—32no—
189#4207—32no—
190#4207—32no—
191#4207—32no—
192#4207—32no—
193#4207—32no—
194#4207—32no—
195#4207—32no—
196#4207—32no—
197C3×C3⋊D9—32no—
198C3×C3⋊D9—32no—
199C3×C3⋊D9—32no—
200C3×C3⋊D9—32no—
201C3×C3⋊D9—32no—
202C3×C3⋊D9—32no—
203C3×C3⋊D9—32no—
204C3×AGL(1,ℤ/9)—92no—
205C3×AGL(1,ℤ/9)—92no—
206C3×AGL(1,ℤ/9)—92no—
207C3×AGL(1,ℤ/9)—92no—
208C3×AGL(1,ℤ/9)—92no—
209C3×AGL(1,ℤ/9)—92no—
210C3×(C3⋊D3)⋊C3—92no—
211C3×(C3⋊D3)⋊C3—92no—
212C3×(C3⋊D3)⋊C3—92no—
213C32×D9—92no—
214C32×D9—92no—
215C32×D9—92no—
216C2×C32⋊C9—21no—
217C2×C32⋊C9—21no—
218C2×C32⋊C9—21no—
219C2×C32⋊C9—21no—
220C2×C32⋊C9—21no—
221C2×C32⋊C9—21no—
222C2×C32⋊C9—21no—
223C2×C32⋊C9—21no—
224C2×C32⋊C9—21no—
225C2×C32⋊C9—21no—
226C2×C32⋊C9—21no—
227C2×C32⋊C9—21no—
228C2×C32⋊C9—21no—
229C2×C32⋊C9—21no—
230C2×C32⋊C9—21no—
231C2×C32⋊C9—21no—
232C2×C32⋊C9—21no—
233C2×C32⋊C9—21no—
234C2×C32⋊C9—21no—
235C2×C32⋊C9—21no—
236C2×C32⋊C9—21no—
237C2×C32⋊C9—21no—
238C2×C32⋊C9—21no—
239C2×C32⋊C9—21no—
240C2×C32⋊C9—21no—
241C2×C32⋊C9—21no—
242C2×C32⋊C9—21no—
243C2×C32⋊C9—21no—
244C2×C32⋊C9—21no—
245C2×C32⋊C9—21no—
246C2×C32⋊C9—21no—
247C2×C32⋊C9—21no—
248C2×C32⋊C9C3×D311yescharacteristic
249C2×C32⋊C9C3×D311yescharacteristic
250C2×C32⋊C9C3×D311yescharacteristic, complemented
251C2×C32⋊C9C3×D311yescharacteristic, complemented
252C2×C32⋊C9C3×D311yescharacteristic, complemented
253C2×C32⋊C9C3×D311yescharacteristic, complemented
254C2×C32⋊C9C3×D311yescharacteristic, complemented
255C2×C32⋊C9C3×D311yescharacteristic, complemented
256#4181—32no—
257#4181—32no—
258#4181—32no—
259#4181—32no—
260#4181—32no—
261#4181—32no—
262#4181—32no—
263#4181—32no—
264C2×C3×C3⋊D3—91no—
265C2×C3×C3⋊D3—91no—
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×C32×D3—271no—
272C2×C32×D3—271no—
273C2×C32×D3—271no—
274C2×C32×D3—271no—
275C2×#272—271no—
276C2×#272—271no—
277C2×#272—271no—
278C2×C3⋊D9—31no—
279C2×C3⋊D9—31no—
280C2×C3⋊D9—31no—
281C2×C3⋊D9—31no—
282C2×AGL(1,ℤ/9)—91no—
283C2×AGL(1,ℤ/9)—91no—
284C2×AGL(1,ℤ/9)—91no—
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×(C3⋊D3)⋊C3—91no—
301C2×(C3⋊D3)⋊C3—91no—
302C2×(C3⋊D3)⋊C3—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×D9—91no—
310C2×C3×D9—91no—
311C2×C3×D9—91no—
312C2×C3×D9—91no—
313C2×C3×D9—91no—
314C2×C3×D9—91no—
315C2×C3×D9—91no—
316C2×C3×D9—91no—
317C2×C3×D9—91no—
318C2×C3×D9—91no—
319C2×C3×D9—91no—
320C2×C3×D9—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—
327C34C2×C3⋊D311yescharacteristic
328#737—31no—
329#737—31no—
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—
342#737—61no—
343#737—61no—
344#737—61no—
345#737—61no—
346C3×3−1+2—21no—
347C3×3−1+2—21no—
348C3×3−1+2—21no—
349C3×3−1+2—21no—
350C3×3−1+2—21no—
351C3×3−1+2—21no—
352C3×3−1+2—21no—
353C3×3−1+2—21no—
354C3×3−1+2—21no—
355C3×3−1+2C2×C3⋊D311yescharacteristic
356C3×3−1+2C2×C3⋊D311yescharacteristic
357C3×3−1+2C2×C3⋊D311yescharacteristic
358C3×3−1+2C2×C3⋊D311yescharacteristic
359C3×3−1+2C2×C3⋊D311yescharacteristic
360C3×3−1+2C2×C3⋊D311yescharacteristic
361C3×H(3,𝔽3)—21no—
362C3×H(3,𝔽3)—21no—
363C3×H(3,𝔽3)—21no—
364C3×H(3,𝔽3)—21no—
365C3×H(3,𝔽3)C2×C3×D311yescharacteristic
366C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
367C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
368C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
369C32×C9—21no—
370C32×C9—21no—
371C32×C9—21no—
372C32×C9—21no—
373C32×C9—21no—
374C32×C9—21no—
375C32×C9—21no—
376C32×C9—31no—
377C32×C9—31no—
378C32×C9—31no—
379C32×C9—61no—
380C32×C9—61no—
381C32×C9—61no—
382C32×C9C2×C3×D311yescharacteristic
383C32×C9C2×C3×D311yescharacteristic, complemented
384C32×C9C2×C3×D311yescharacteristic, complemented
385C32×C9C2×C3×D311yescharacteristic, complemented
386C32×C9C2×C3⋊D311yescharacteristic
387C32×C9C2×C3⋊D311yescharacteristic
388C32×C9C2×C3⋊D311yescharacteristic
389C32⋊C9—21no—
390C32⋊C9—21no—
391C32⋊C9—21no—
392C32⋊C9—21no—
393C32⋊C9—21no—
394C32⋊C9—21no—
395C32⋊C9—21no—
396C32⋊C9—21no—
397C32⋊C9—21no—
398C32⋊C9—21no—
399C32⋊C9—21no—
400C32⋊C9—21no—
401C32⋊C9—21no—
402C32⋊C9—21no—
403C32⋊C9—21no—
404C32⋊C9—21no—
405C32⋊C9—21no—
406C32⋊C9—21no—
407C32⋊C9—21no—
408C32⋊C9—21no—
409C32⋊C9—21no—
410C32⋊C9—21no—
411C32⋊C9—21no—
412C32⋊C9—21no—
413C32⋊C9—21no—
414C32⋊C9—21no—
415C32⋊C9—21no—
416C32⋊C9—21no—
417C32⋊C9—21no—
418C32⋊C9—21no—
419C32⋊C9—21no—
420C32⋊C9—21no—
421C32⋊C9C2×C3×D311yescharacteristic
422C32⋊C9C2×C3×D311yescharacteristic
423C32⋊C9C2×C3×D311yescharacteristic, complemented
424C32⋊C9C2×C3×D311yescharacteristic, complemented
425C32⋊C9C2×C3×D311yescharacteristic, complemented
426C32⋊C9C2×C3×D311yescharacteristic, complemented
427C32⋊C9C2×C3×D311yescharacteristic, complemented
428C32⋊C9C2×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×C33C3×C3⋊D311yescharacteristic
443C2×C33C3×C3⋊D311yescharacteristic
444C2×C33C3×C3⋊D311yescharacteristic
445C2×C33C3×C3⋊D311yescharacteristic
446C2×C33C3⋊(C3⋊D3)11yescharacteristic
447C3×C3⋊D3—92no—
448C3×C3⋊D3—92no—
449C3×C3⋊D3—92no—
450C3×C3⋊D3—92no—
451C3×C3⋊D3—92no—
452C3×C3⋊D3—92no—
453C3×C3⋊D3—92no—
454C32×D3—272no—
455C32×D3—272no—
456C32×D3—272no—
457C32×D3—272no—
458C2×3−1+2—31no—
459C2×3−1+2—31no—
460C2×3−1+2—31no—
461C2×3−1+2—31no—
462C2×3−1+2—31no—
463C2×3−1+2—31no—
464C2×3−1+2—31no—
465C2×3−1+2—61no—
466C2×3−1+2—61no—
467C2×3−1+2—61no—
468C2×3−1+2—61no—
469C2×3−1+2—61no—
470C2×3−1+2—61no—
471C2×3−1+2—61no—
472C2×3−1+2—61no—
473C2×3−1+2—61no—
474C2×3−1+2—61no—
475C2×3−1+2—61no—
476C2×3−1+2—61no—
477C2×3−1+2—61no—
478C2×3−1+2—61no—
479C2×3−1+2—61no—
480C2×3−1+2—61no—
481C2×3−1+2—61no—
482C2×3−1+2—61no—
483C2×3−1+2—61no—
484C2×3−1+2—61no—
485C2×3−1+2—61no—
486C2×3−1+2—61no—
487C2×3−1+2—61no—
488C2×3−1+2—61no—
489C2×3−1+2—61no—
490C2×3−1+2—61no—
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×H(3,𝔽3)—31no—
504C2×H(3,𝔽3)—31no—
505C2×H(3,𝔽3)—31no—
506C2×H(3,𝔽3)—31no—
507C2×H(3,𝔽3)—31no—
508C2×H(3,𝔽3)—31no—
509C2×H(3,𝔽3)—61no—
510C2×H(3,𝔽3)—61no—
511C2×H(3,𝔽3)—61no—
512C2×H(3,𝔽3)—61no—
513C2×H(3,𝔽3)—61no—
514C2×H(3,𝔽3)—61no—
515C2×H(3,𝔽3)—61no—
516C2×H(3,𝔽3)—61no—
517C2×H(3,𝔽3)—61no—
518C2×H(3,𝔽3)—61no—
519C2×H(3,𝔽3)—61no—
520C2×H(3,𝔽3)—61no—
521C2×H(3,𝔽3)—61no—
522C2×H(3,𝔽3)—61no—
523C2×H(3,𝔽3)—61no—
524C2×H(3,𝔽3)—61no—
525C2×H(3,𝔽3)—61no—
526C2×H(3,𝔽3)—61no—
527C2×C3×C9—21no—
528C2×C3×C9—21no—
529C2×C3×C9—21no—
530C2×C3×C9—21no—
531C2×C3×C9—21no—
532C2×C3×C9—21no—
533C2×C3×C9—21no—
534C2×C3×C9—21no—
535C2×C3×C9—21no—
536C2×C3×C9—21no—
537C2×C3×C9—21no—
538C2×C3×C9—21no—
539C2×C3×C9—31no—
540C2×C3×C9—31no—
541C2×C3×C9—31no—
542C2×C3×C9—31no—
543C2×C3×C9—31no—
544C2×C3×C9—61no—
545C2×C3×C9—61no—
546C2×C3×C9—61no—
547C2×C3×C9—61no—
548C2×C3×C9—61no—
549C2×C3×C9—61no—
550C2×C3×C9—61no—
551C2×C3×C9—61no—
552C2×C3×C9—61no—
553C2×C3×C9—61no—
554C2×C3×C9—61no—
555C2×C3×C9—61no—
556C2×C3×C9—62no—
557C2×C3×C9—62no—
558C2×C3×C9—62no—
559C2×C3×C9—62no—
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—
568C2×C3×C9—61no—
569C2×C3×C9—61no—
570C2×C3×C9#27211yescharacteristic, complemented
571C2×C3×C9#27211yescharacteristic, complemented
572C2×C3×C9#27211yescharacteristic, complemented
573C2×C3×C9C3×C3⋊D311yescharacteristic
574C2×C3×C9C3×C3⋊D311yescharacteristic
575C2×C3×C9C3×C3⋊D311yescharacteristic
576C2×C3×C9C3×C3⋊D311yescharacteristic
577C2×C3×C9C3×C3⋊D311yescharacteristic
578C2×C3×C9C3×C3⋊D311yescharacteristic
579C2×C3×C9C3×C3⋊D311yescharacteristic
580C2×C3×C9C3×C3⋊D311yescharacteristic
581C2×C3×C9C3×C3⋊D311yescharacteristic
582#272—272no—
583#272—272no—
584#272—272no—
585C3⋊D9—32no—
586C3⋊D9—32no—
587C3⋊D9—32no—
588C3⋊D9—32no—
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—
601AGL(1,ℤ/9)—92no—
602AGL(1,ℤ/9)—92no—
603AGL(1,ℤ/9)—92no—
604AGL(1,ℤ/9)—92no—
605AGL(1,ℤ/9)—92no—
606AGL(1,ℤ/9)—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—
616C3×D9—92no—
617C3×D9—92no—
618C3×D9—92no—
619C3×D9—92no—
620C3×D9—92no—
621C3×D9—92no—
622C3×D9—92no—
623C3×D9—92no—
624C3×D9—92no—
625C3×D9—92no—
626C3×D9—92no—
627C3×D9—92no—
628C3×D9—92no—
629C3×D9—92no—
630C3×D9—92no—
631C3×D9—92no—
632C3×D9—92no—
633C3×D9—92no—
634C22×C32—811no—
635C2×C3⋊D3—91no—
636C2×C3⋊D3—91no—
637C2×C3⋊D3—91no—
638C2×C3⋊D3—91no—
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—271no—
654C2×C3×D3—271no—
655C2×C3×D3—811no—
656C2×C3×D3—811no—
657C2×C3×D3—811no—
658C2×D9—91no—
659C2×D9—91no—
660C2×D9—91no—
661C2×D9—91no—
662C2×D9—91no—
663C2×D9—91no—
664C2×D9—91no—
665C2×D9—91no—
666C2×D9—91no—
667C33—21no—
668C33—21no—
669C33—21no—
670C33—21no—
671C33—31no—
672C33—31no—
673C33—31no—
674C33—61no—
675C33—61no—
676C33—61no—
677C33—61no—
678C33—61no—
679C33—61no—
680C33C2×C3×C3⋊D311yescharacteristic
681C33C2×C3×C3⋊D311yescharacteristic
682C33C2×C3×C3⋊D311yescharacteristic
683C33C2×C3×C3⋊D311yescharacteristic
684C33C2×C3⋊(C3⋊D3)11yescharacteristic
6853−1+2—31no—
6863−1+2—31no—
6873−1+2—31no—
6883−1+2—31no—
6893−1+2—31no—
6903−1+2—31no—
6913−1+2—31no—
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—
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—
730H(3,𝔽3)—31no—
731H(3,𝔽3)—31no—
732H(3,𝔽3)—31no—
733H(3,𝔽3)—31no—
734H(3,𝔽3)—31no—
735H(3,𝔽3)—31no—
736H(3,𝔽3)—61no—
737H(3,𝔽3)—61no—
738H(3,𝔽3)—61no—
739H(3,𝔽3)—61no—
740H(3,𝔽3)—61no—
741H(3,𝔽3)—61no—
742H(3,𝔽3)—61no—
743H(3,𝔽3)—61no—
744H(3,𝔽3)—61no—
745H(3,𝔽3)—61no—
746H(3,𝔽3)—61no—
747H(3,𝔽3)—61no—
748H(3,𝔽3)—61no—
749H(3,𝔽3)—61no—
750H(3,𝔽3)—61no—
751H(3,𝔽3)—61no—
752H(3,𝔽3)—61no—
753H(3,𝔽3)—61no—
754C3×C9—21no—
755C3×C9—21no—
756C3×C9—21no—
757C3×C9—21no—
758C3×C9—21no—
759C3×C9—21no—
760C3×C9—21no—
761C3×C9—21no—
762C3×C9—21no—
763C3×C9—21no—
764C3×C9—21no—
765C3×C9—21no—
766C3×C9—31no—
767C3×C9—31no—
768C3×C9—31no—
769C3×C9—31no—
770C3×C9—31no—
771C3×C9—61no—
772C3×C9—61no—
773C3×C9—61no—
774C3×C9—61no—
775C3×C9—61no—
776C3×C9—61no—
777C3×C9—61no—
778C3×C9—61no—
779C3×C9—61no—
780C3×C9—61no—
781C3×C9—61no—
782C3×C9—61no—
783C3×C9—62no—
784C3×C9—62no—
785C3×C9—62no—
786C3×C9—62no—
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×C9C2×#27211yescharacteristic, complemented
798C3×C9C2×#27211yescharacteristic, complemented
799C3×C9C2×#27211yescharacteristic, complemented
800C3×C9C2×C3×C3⋊D311yescharacteristic
801C3×C9C2×C3×C3⋊D311yescharacteristic
802C3×C9C2×C3×C3⋊D311yescharacteristic
803C3×C9C2×C3×C3⋊D311yescharacteristic
804C3×C9C2×C3×C3⋊D311yescharacteristic
805C3×C9C2×C3×C3⋊D311yescharacteristic
806C3×C9C2×C3×C3⋊D311yescharacteristic
807C3×C9C2×C3×C3⋊D311yescharacteristic
808C3×C9C2×C3×C3⋊D311yescharacteristic
809C2×C32—21no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—31no—
813C2×C32—31no—
814C2×C32—31no—
815C2×C32—31no—
816C2×C32—31no—
817C2×C32—31no—
818C2×C32—31no—
819C2×C32—61no—
820C2×C32—61no—
821C2×C32—61no—
822C2×C32—61no—
823C2×C32—61no—
824C2×C32—61no—
825C2×C32—61no—
826C2×C32—61no—
827C2×C32—61no—
828C2×C32—61no—
829C2×C32—61no—
830C2×C32—61no—
831C2×C32—61no—
832C2×C32—61no—
833C2×C32—61no—
834C2×C32—61no—
835C2×C32—61no—
836C2×C32—61no—
837C2×C32—61no—
838C2×C32—61no—
839C2×C32—61no—
840C2×C32—61no—
841C2×C32—61no—
842C2×C32—61no—
843C2×C32—61no—
844C2×C32—61no—
845C2×C32—61no—
846C2×C32—61no—
847C2×C32—61no—
848C2×C32—61no—
849C2×C32—61no—
850C2×C32—61no—
851C2×C32—61no—
852C2×C32—61no—
853C2×C32—61no—
854C2×C32—61no—
855C2×C32—61no—
856C2×C32—61no—
857C2×C32—61no—
858C2×C32—812no—
859C2×C32#420711yescharacteristic, complemented
860C2×C32#420711yescharacteristic, complemented
861C2×C32#420711yescharacteristic, complemented
862C2×C32C3⋊#27211yescharacteristic
863C2×C32C3⋊#27211yescharacteristic
864C2×C32C3⋊#27211yescharacteristic
865C2×C32C3×C3⋊(C3⋊D3)11yescharacteristic
866C3⋊D3—92no—
867C3⋊D3—92no—
868C3⋊D3—92no—
869C3⋊D3—92no—
870C3×D3—272no—
871C3×D3—272no—
872C3×D3—272no—
873C3×D3—272no—
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—812no—
887C3×D3—812no—
888C3×D3—812no—
889C2×C9—21no—
890C2×C9—21no—
891C2×C9—21no—
892C2×C9—21no—
893C2×C9—31no—
894C2×C9—31no—
895C2×C9—31no—
896C2×C9—61no—
897C2×C9—61no—
898C2×C9—61no—
899C2×C9—61no—
900C2×C9—61no—
901C2×C9—61no—
902C2×C9—61no—
903C2×C9—61no—
904C2×C9—61no—
905C2×C9—61no—
906C2×C9—61no—
907C2×C9—61no—
908C2×C9—61no—
909C2×C9C3×#27211yescharacteristic
910D9—92no—
911D9—92no—
912D9—92no—
913D9—92no—
914D9—92no—
915D9—92no—
916D9—92no—
917D9—92no—
918D9—92no—
919C22×C3—811no—
920C22×C3—811no—
921C22×C3—811no—
922C22×C3—811no—
923C2×D3—271no—
924C2×D3—271no—
925C2×D3—271no—
926C2×D3—271no—
927C2×D3—811no—
928C2×D3—811no—
929C2×D3—811no—
930C32—21no—
931C32—21no—
932C32—21no—
933C32—31no—
934C32—31no—
935C32—31no—
936C32—31no—
937C32—31no—
938C32—31no—
939C32—31no—
940C32—61no—
941C32—61no—
942C32—61no—
943C32—61no—
944C32—61no—
945C32—61no—
946C32—61no—
947C32—61no—
948C32—61no—
949C32—61no—
950C32—61no—
951C32—61no—
952C32—61no—
953C32—61no—
954C32—61no—
955C32—61no—
956C32—61no—
957C32—61no—
958C32—61no—
959C32—61no—
960C32—61no—
961C32—61no—
962C32—61no—
963C32—61no—
964C32—61no—
965C32—61no—
966C32—61no—
967C32—61no—
968C32—61no—
969C32—61no—
970C32—61no—
971C32—61no—
972C32—61no—
973C32—61no—
974C32—61no—
975C32—61no—
976C32—61no—
977C32—61no—
978C32—61no—
979C32C2×#420711yescharacteristic, complemented
980C32C2×#420711yescharacteristic, complemented
981C32C2×#420711yescharacteristic, complemented
982C32C2×C3⋊#27211yescharacteristic
983C32C2×C3⋊#27211yescharacteristic
984C32C2×C3⋊#27211yescharacteristic
985C32C2×C3×C3⋊(C3⋊D3)11yescharacteristic
986C9—21no—
987C9—21no—
988C9—21no—
989C9—21no—
990C9—31no—
991C9—31no—
992C9—31no—
993C9—61no—
994C9—61no—
995C9—61no—
996C9—61no—
997C9—61no—
998C9—61no—
999C9—61no—
1000C9—61no—
1001C9—61no—
1002C9—61no—
1003C9—61no—
1004C9—61no—
1005C9—61no—
1006C9C2×C3×#27211yescharacteristic
1007C2×C3—21no—
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—61no—
1017C2×C3—91no—
1018C2×C3—91no—
1019C2×C3—181no—
1020C2×C3—181no—
1021C2×C3—181no—
1022C2×C3—181no—
1023C2×C3—812no—
1024C2×C3—812no—
1025C2×C3—812no—
1026C2×C3—812no—
1027C2×C3C3×C3⋊#27211yescharacteristic
1028C2×C3C3⋊#420711yescharacteristic
1029D3—272no—
1030D3—272no—
1031D3—272no—
1032D3—272no—
1033D3—812no—
1034D3—812no—
1035D3—812no—
1036C22—811noSylow
1037C3—21no—
1038C3—31no—
1039C3—31no—
1040C3—31no—
1041C3—61no—
1042C3—61no—
1043C3—61no—
1044C3—61no—
1045C3—61no—
1046C3—61no—
1047C3—91no—
1048C3—91no—
1049C3—181no—
1050C3—181no—
1051C3—181no—
1052C3—181no—
1053C3C2×C3×C3⋊#27211yescharacteristic
1054C3C2×C3⋊#420711yescharacteristic
1055C2—812no—
1056C2#1309142411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C3⋊#4207
commutator, cosocle, hypocenterC9×H(3,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624869C2
socleC2×C32C3×C3⋊(C3⋊D3)
LCSG ▷ C9×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #13091424C2direct (N × H)
2. C2×#10624869C2semidirect
7. C2×C9⋊#272C3semidirect
17. #10624869C22semidirect
18. C2×C3×#737D3semidirect
19. C2×C3×#737D3semidirect
20. C2×C3×#737D3semidirect
21. C2×C33×C9D3semidirect
26. C2×#6893D3semidirect
27. C2×#6893D3semidirect
28. C2×#6893D3semidirect
29. C2×#6893D3semidirect
30. C2×#6893D3semidirect
31. C2×#6893D3semidirect
41. C2×#6891D3semidirect
42. C2×#6891D3semidirect
48. C2×C9×H(3,𝔽3)C2×C3semidirect
49. C9⋊#272C2×C3semidirect
97. C3×#737C2×D3semidirect
98. C3×#737C2×D3semidirect
99. C3×#737C2×D3semidirect
100. C33×C9C2×D3semidirect
101. #6893C2×D3semidirect
102. #6893C2×D3semidirect
103. #6893C2×D3semidirect
104. #6893C2×D3semidirect
105. #6893C2×D3semidirect
106. #6893C2×D3semidirect
116. #6891C2×D3semidirect
117. #6891C2×D3semidirect
123. C9×H(3,𝔽3)C22×C3semidirect
181. C2×C32×C9C3×D3semidirect
182. C2×C32×C9C3×D3semidirect
183. C2×C32×C9C3×D3semidirect
250. C2×C32⋊C9C3×D3semidirect
251. C2×C32⋊C9C3×D3semidirect
252. C2×C32⋊C9C3×D3semidirect
253. C2×C32⋊C9C3×D3semidirect
254. C2×C32⋊C9C3×D3semidirect
255. C2×C32⋊C9C3×D3semidirect
383. C32×C9C2×C3×D3semidirect
384. C32×C9C2×C3×D3semidirect
385. C32×C9C2×C3×D3semidirect
423. C32⋊C9C2×C3×D3semidirect
424. C32⋊C9C2×C3×D3semidirect
425. C32⋊C9C2×C3×D3semidirect
426. C32⋊C9C2×C3×D3semidirect
427. C32⋊C9C2×C3×D3semidirect
428. C32⋊C9C2×C3×D3semidirect
570. C2×C3×C9#272semidirect
571. C2×C3×C9#272semidirect
572. C2×C3×C9#272semidirect
797. C3×C9C2×#272semidirect
798. C3×C9C2×#272semidirect
799. C3×C9C2×#272semidirect
859. C2×C32#4207semidirect
860. C2×C32#4207semidirect
861. C2×C32#4207semidirect
979. C32C2×#4207semidirect
980. C32C2×#4207semidirect
981. C32C2×#4207semidirect
1056. C2#13091424direct (N × H)

Maximal subgroups

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

subgroupindex
#130914242
C2×#106248692
C2×C3×#42073
C2×C32×C3⋊D93
C2×C9⋊#2723
C2×#923043
C2×#923023
C2×#923003