Finite Group Databasebeta

← C2×#13091524 #72243946

Subgroups — C2×#13091524 #72243946

Order 2916.

889 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091524C212yesmaximal, direct product factor
2C2×#10624900C211yesmaximal, characteristic, complemented
3C2×C3⋊#4208—31nomaximal
4C2×C9⋊#272C311yesmaximal, characteristic
5C2×#6895⋊C2—31nomaximal
6C2×#6895⋊C2—31nomaximal
7C2×#6895⋊C2—31nomaximal
8C2×#6895⋊C2—31nomaximal
9C2×#6895⋊C2—31nomaximal
10C2×#6895⋊C2—31nomaximal
11C2×#6895⋊C2—31nomaximal
12C2×#6895⋊C2—31nomaximal
13C2×C3⋊(D9⋊C9)—31nomaximal
14C2×C3⋊(D9⋊C9)—31nomaximal
15C2×C3⋊(D9⋊C9)—31nomaximal
16C2×C3⋊(D9⋊C9)—31nomaximal
17#10624900C2211yescharacteristic, complemented, Sylow
18C2×C3×#737D311yescharacteristic
19C3⋊#4208—32no—
20C2×#6895D311yescharacteristic, complemented
21C2×#6895D311yescharacteristic, complemented
22C2×#6895D311yescharacteristic, complemented
23C2×#6895D311yescharacteristic, complemented
24C2×#6895D311yescharacteristic, complemented
25C2×#6895D311yescharacteristic, complemented
26C2×#6895D311yescharacteristic, complemented
27C2×#6895D311yescharacteristic, complemented
28C2×#6894—21no—
29C2×#6894—21no—
30C2×#6894—21no—
31C2×#6894—21no—
32C2×#6894—21no—
33C2×#6894—21no—
34C2×#6894—21no—
35C2×#6894—21no—
36C2×#6894—21no—
37C2×#6894—21no—
38C2×#6894—21no—
39C2×#6894—21no—
40C2×C9×H(3,𝔽3)—21no—
41C2×C9×H(3,𝔽3)C2×C311yescharacteristic
42C2×C3×C9⋊C9D311yescharacteristic, complemented
43C2×C3×C9⋊C9D311yescharacteristic, complemented
44C2×C3×C9⋊C9D311yescharacteristic, complemented
45C2×C3×C9⋊C9D311yescharacteristic, complemented
46C9⋊#272C2×C312yes—
47#6895⋊C2—32no—
48#6895⋊C2—32no—
49#6895⋊C2—32no—
50#6895⋊C2—32no—
51#6895⋊C2—32no—
52#6895⋊C2—32no—
53#6895⋊C2—32no—
54#6895⋊C2—32no—
55C3⋊(D9⋊C9)—32no—
56C3⋊(D9⋊C9)—32no—
57C3⋊(D9⋊C9)—32no—
58C3⋊(D9⋊C9)—32no—
59C2×C3⋊#272—31no—
60C2×#4208—91no—
61C2×#4208—91no—
62C2×#4208—91no—
63C2×#4208—91no—
64C2×#4208—91no—
65C2×#4208—91no—
66C2×#4208—91no—
67C2×#4208—91no—
68C2×#4208—91no—
69C2×C9×C3⋊D3—91no—
70C2×C9×C3⋊D3—91no—
71C2×C9×C3⋊D3—91no—
72C2×C9×C3⋊D3—91no—
73C2×C3×C3⋊D9—31no—
74C2×C3×C3⋊D9—31no—
75C2×C3×C3⋊D9—31no—
76C2×C3×C3⋊D9—31no—
77C2×#4181—31no—
78C2×#4181—31no—
79C2×#4181—31no—
80C2×#4181—31no—
81C2×#4181—31no—
82C2×#4181—31no—
83C2×#4181—31no—
84C2×#4181—31no—
85C2×D9⋊C9—91no—
86C2×D9⋊C9—91no—
87C2×D9⋊C9—91no—
88C2×D9⋊C9—91no—
89C2×D9⋊C9—91no—
90C2×D9⋊C9—91no—
91C2×D9⋊C9—91no—
92C2×D9⋊C9—91no—
93C2×D9⋊C9—91no—
94C3×#737C2×D311yescharacteristic
95#6895C2×D311yescharacteristic, complemented
96#6895C2×D311yescharacteristic, complemented
97#6895C2×D311yescharacteristic, complemented
98#6895C2×D311yescharacteristic, complemented
99#6895C2×D311yescharacteristic, complemented
100#6895C2×D311yescharacteristic, complemented
101#6895C2×D311yescharacteristic, complemented
102#6895C2×D311yescharacteristic, complemented
103#6894—21no—
104#6894—21no—
105#6894—21no—
106#6894—21no—
107#6894—21no—
108#6894—21no—
109#6894—21no—
110#6894—21no—
111#6894—21no—
112#6894—21no—
113#6894—21no—
114#6894—21no—
115C9×H(3,𝔽3)—21no—
116C9×H(3,𝔽3)C22×C311yescharacteristic
117C3×C9⋊C9C2×D311yescharacteristic, complemented
118C3×C9⋊C9C2×D311yescharacteristic, complemented
119C3×C9⋊C9C2×D311yescharacteristic, complemented
120C3×C9⋊C9C2×D311yescharacteristic, complemented
121C2×#737—31no—
122C2×#737—31no—
123C2×#737—31no—
124C2×#737—31no—
125C2×#737—31no—
126C2×#737—61no—
127C2×#737—61no—
128C2×#737—61no—
129C2×#737—61no—
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×H(3,𝔽3)C3×D311yescharacteristic
135C2×C32×C9—21no—
136C2×C32×C9—21no—
137C2×C32×C9—21no—
138C2×C32×C9—21no—
139C2×C32×C9C3×D311yescharacteristic
140C2×C32×C9C3×D311yescharacteristic
141C2×C32×C9C3×D311yescharacteristic
142C2×C32×C9C3×D311yescharacteristic
143C2×C32×C9C3⋊D311yescharacteristic
144C2×C32×C9C3⋊D311yescharacteristic
145C2×C32×C9C3⋊D311yescharacteristic
146C2×C32×C9C3⋊D311yescharacteristic
147C3⋊#272—32no—
148#4208—92no—
149#4208—92no—
150#4208—92no—
151#4208—92no—
152#4208—92no—
153#4208—92no—
154#4208—92no—
155#4208—92no—
156#4208—92no—
157C9×C3⋊D3—92no—
158C9×C3⋊D3—92no—
159C9×C3⋊D3—92no—
160C9×C3⋊D3—92no—
161C3×C3⋊D9—32no—
162C3×C3⋊D9—32no—
163C3×C3⋊D9—32no—
164C3×C3⋊D9—32no—
165C2×C9⋊C9—21no—
166C2×C9⋊C9—21no—
167C2×C9⋊C9—21no—
168C2×C9⋊C9—21no—
169C2×C9⋊C9—21no—
170C2×C9⋊C9—21no—
171C2×C9⋊C9—21no—
172C2×C9⋊C9—21no—
173C2×C9⋊C9—21no—
174C2×C9⋊C9—21no—
175C2×C9⋊C9—21no—
176C2×C9⋊C9—21no—
177C2×C9⋊C9—21no—
178C2×C9⋊C9—21no—
179C2×C9⋊C9—21no—
180C2×C9⋊C9—21no—
181C2×C9⋊C9—21no—
182C2×C9⋊C9—21no—
183C2×C9⋊C9—21no—
184C2×C9⋊C9—21no—
185C2×C9⋊C9—21no—
186C2×C9⋊C9—21no—
187C2×C9⋊C9—21no—
188C2×C9⋊C9—21no—
189C2×C9⋊C9—21no—
190C2×C9⋊C9—21no—
191C2×C9⋊C9—21no—
192C2×C9⋊C9—21no—
193C2×C9⋊C9—21no—
194C2×C9⋊C9—21no—
195C2×C9⋊C9—21no—
196C2×C9⋊C9—21no—
197C2×C9⋊C9—21no—
198C2×C9⋊C9—21no—
199C2×C9⋊C9—21no—
200C2×C9⋊C9—21no—
201C2×C9⋊C9C3⋊D311yescharacteristic
202C2×C9⋊C9C3⋊D311yescharacteristic
203C2×C9⋊C9C3⋊D311yescharacteristic
204C2×C9⋊C9C3⋊D311yescharacteristic
205C2×C9⋊C9C3⋊D311yescharacteristic
206C2×C9⋊C9C3⋊D311yescharacteristic
207C2×C9⋊C9C3⋊D311yescharacteristic
208C2×C9⋊C9C3⋊D311yescharacteristic
209C2×C9⋊C9C3⋊D311yescharacteristic
210C2×C32⋊C9—21no—
211C2×C32⋊C9—21no—
212C2×C32⋊C9—21no—
213C2×C32⋊C9—21no—
214C2×C32⋊C9—21no—
215C2×C32⋊C9—21no—
216C2×C32⋊C9—21no—
217C2×C32⋊C9—21no—
218C2×C32⋊C9C3×D311yescharacteristic
219C2×C32⋊C9C3×D311yescharacteristic
220C2×C32⋊C9C3×D311yescharacteristic
221C2×C32⋊C9C3×D311yescharacteristic
222C2×C32⋊C9C3×D311yescharacteristic
223C2×C32⋊C9C3×D311yescharacteristic
224C2×C32⋊C9C3×D311yescharacteristic
225C2×C32⋊C9C3×D311yescharacteristic
226#4181—32no—
227#4181—32no—
228#4181—32no—
229#4181—32no—
230#4181—32no—
231#4181—32no—
232#4181—32no—
233#4181—32no—
234D9⋊C9—92no—
235D9⋊C9—92no—
236D9⋊C9—92no—
237D9⋊C9—92no—
238D9⋊C9—92no—
239D9⋊C9—92no—
240D9⋊C9—92no—
241D9⋊C9—92no—
242D9⋊C9—92no—
243C2×C3×C3⋊D3—91no—
244C2×C3×C3⋊D3—91no—
245C2×C3×C3⋊D3—91no—
246C2×C3×C3⋊D3—91no—
247C2×#272—91no—
248C2×#272—91no—
249C2×#272—91no—
250C2×#272—91no—
251C2×#272—91no—
252C2×#272—91no—
253C2×#272—91no—
254C2×#272—91no—
255C2×#272—91no—
256C2×C3⋊D9—31no—
257C2×C3⋊D9—31no—
258C2×C3⋊D9—31no—
259C2×C3⋊D9—31no—
260C2×D3×C9—271no—
261C2×D3×C9—271no—
262C2×D3×C9—271no—
263C2×D3×C9—271no—
264C2×D3×C9—271no—
265C2×D3×C9—271no—
266C2×D3×C9—271no—
267C2×D3×C9—271no—
268C2×D3×C9—271no—
269C2×D3×C9—271no—
270C2×D3×C9—271no—
271C2×D3×C9—271no—
272C2×D3×C9—271no—
273C2×C3×D9—91no—
274C2×C3×D9—91no—
275C2×C3×D9—91no—
276C2×C3×D9—91no—
277C2×C3×D9—91no—
278C2×C3×D9—91no—
279C2×C3×D9—91no—
280C2×C3×D9—91no—
281C2×C3×D9—91no—
282#737—31no—
283#737—31no—
284#737—31no—
285#737—31no—
286#737—31no—
287#737—61no—
288#737—61no—
289#737—61no—
290#737—61no—
291C3×3−1+2—21no—
292C3×3−1+2—21no—
293C3×3−1+2—21no—
294C3×3−1+2—21no—
295C3×H(3,𝔽3)C2×C3×D311yescharacteristic
296C32×C9—21no—
297C32×C9—21no—
298C32×C9—21no—
299C32×C9—21no—
300C32×C9C2×C3×D311yescharacteristic
301C32×C9C2×C3×D311yescharacteristic
302C32×C9C2×C3×D311yescharacteristic
303C32×C9C2×C3×D311yescharacteristic
304C32×C9C2×C3⋊D311yescharacteristic
305C32×C9C2×C3⋊D311yescharacteristic
306C32×C9C2×C3⋊D311yescharacteristic
307C32×C9C2×C3⋊D311yescharacteristic
308C9⋊C9—21no—
309C9⋊C9—21no—
310C9⋊C9—21no—
311C9⋊C9—21no—
312C9⋊C9—21no—
313C9⋊C9—21no—
314C9⋊C9—21no—
315C9⋊C9—21no—
316C9⋊C9—21no—
317C9⋊C9—21no—
318C9⋊C9—21no—
319C9⋊C9—21no—
320C9⋊C9—21no—
321C9⋊C9—21no—
322C9⋊C9—21no—
323C9⋊C9—21no—
324C9⋊C9—21no—
325C9⋊C9—21no—
326C9⋊C9—21no—
327C9⋊C9—21no—
328C9⋊C9—21no—
329C9⋊C9—21no—
330C9⋊C9—21no—
331C9⋊C9—21no—
332C9⋊C9—21no—
333C9⋊C9—21no—
334C9⋊C9—21no—
335C9⋊C9—21no—
336C9⋊C9—21no—
337C9⋊C9—21no—
338C9⋊C9—21no—
339C9⋊C9—21no—
340C9⋊C9—21no—
341C9⋊C9—21no—
342C9⋊C9—21no—
343C9⋊C9—21no—
344C9⋊C9C2×C3⋊D311yescharacteristic
345C9⋊C9C2×C3⋊D311yescharacteristic
346C9⋊C9C2×C3⋊D311yescharacteristic
347C9⋊C9C2×C3⋊D311yescharacteristic
348C9⋊C9C2×C3⋊D311yescharacteristic
349C9⋊C9C2×C3⋊D311yescharacteristic
350C9⋊C9C2×C3⋊D311yescharacteristic
351C9⋊C9C2×C3⋊D311yescharacteristic
352C9⋊C9C2×C3⋊D311yescharacteristic
353C32⋊C9—21no—
354C32⋊C9—21no—
355C32⋊C9—21no—
356C32⋊C9—21no—
357C32⋊C9—21no—
358C32⋊C9—21no—
359C32⋊C9—21no—
360C32⋊C9—21no—
361C32⋊C9C2×C3×D311yescharacteristic
362C32⋊C9C2×C3×D311yescharacteristic
363C32⋊C9C2×C3×D311yescharacteristic
364C32⋊C9C2×C3×D311yescharacteristic
365C32⋊C9C2×C3×D311yescharacteristic
366C32⋊C9C2×C3×D311yescharacteristic
367C32⋊C9C2×C3×D311yescharacteristic
368C32⋊C9C2×C3×D311yescharacteristic
369C2×C33C3×C3⋊D311yescharacteristic
370C2×C33C3×C3⋊D311yescharacteristic
371C2×C33C3×C3⋊D311yescharacteristic
372C2×C33C3×C3⋊D311yescharacteristic
373C3×C3⋊D3—92no—
374C3×C3⋊D3—92no—
375C3×C3⋊D3—92no—
376C3×C3⋊D3—92no—
377C2×3−1+2—61no—
378C2×3−1+2—61no—
379C2×3−1+2—61no—
380C2×3−1+2—61no—
381C2×3−1+2—61no—
382C2×3−1+2—61no—
383C2×3−1+2—61no—
384C2×3−1+2—61no—
385C2×3−1+2—61no—
386C2×3−1+2—61no—
387C2×3−1+2—61no—
388C2×3−1+2—61no—
389C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
390C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
391C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
392C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
393C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
394C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
395C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
396C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
397C2×H(3,𝔽3)AGL(1,ℤ/9)11yescharacteristic
398C2×C3×C9—21no—
399C2×C3×C9—21no—
400C2×C3×C9—21no—
401C2×C3×C9—21no—
402C2×C3×C9—21no—
403C2×C3×C9—21no—
404C2×C3×C9—21no—
405C2×C3×C9—21no—
406C2×C3×C9—21no—
407C2×C3×C9—21no—
408C2×C3×C9—21no—
409C2×C3×C9—21no—
410C2×C3×C9—21no—
411C2×C3×C9—31no—
412C2×C3×C9—31no—
413C2×C3×C9—31no—
414C2×C3×C9—31no—
415C2×C3×C9—31no—
416C2×C3×C9—31no—
417C2×C3×C9—31no—
418C2×C3×C9—61no—
419C2×C3×C9—61no—
420C2×C3×C9—61no—
421C2×C3×C9—61no—
422C2×C3×C9—61no—
423C2×C3×C9—61no—
424C2×C3×C9—61no—
425C2×C3×C9—61no—
426C2×C3×C9—61no—
427C2×C3×C9—61no—
428C2×C3×C9—61no—
429C2×C3×C9—61no—
430C2×C3×C9—61no—
431C2×C3×C9—181no—
432C2×C3×C9—181no—
433C2×C3×C9—181no—
434C2×C3×C9—181no—
435C2×C3×C9C3×C3⋊D311yescharacteristic
436C2×C3×C9C3×C3⋊D311yescharacteristic
437C2×C3×C9C3×C3⋊D311yescharacteristic
438C2×C3×C9C3×C3⋊D311yescharacteristic
439C2×C3×C9C3×C3⋊D311yescharacteristic
440C2×C3×C9C3×C3⋊D311yescharacteristic
441C2×C3×C9C3×C3⋊D311yescharacteristic
442C2×C3×C9C3×C3⋊D311yescharacteristic
443C2×C3×C9C3×C3⋊D311yescharacteristic
444C2×C3×C9C3⋊(C3⋊D3)11yescharacteristic
445#272—92no—
446#272—92no—
447#272—92no—
448#272—92no—
449#272—92no—
450#272—92no—
451#272—92no—
452#272—92no—
453#272—92no—
454C3⋊D9—32no—
455C3⋊D9—32no—
456C3⋊D9—32no—
457C3⋊D9—32no—
458D3×C9—272no—
459D3×C9—272no—
460D3×C9—272no—
461D3×C9—272no—
462D3×C9—272no—
463D3×C9—272no—
464D3×C9—272no—
465D3×C9—272no—
466D3×C9—272no—
467D3×C9—272no—
468D3×C9—272no—
469D3×C9—272no—
470D3×C9—272no—
471C3×D9—92no—
472C3×D9—92no—
473C3×D9—92no—
474C3×D9—92no—
475C3×D9—92no—
476C3×D9—92no—
477C3×D9—92no—
478C3×D9—92no—
479C3×D9—92no—
480C2×C3⋊D3—91no—
481C2×C3⋊D3—91no—
482C2×C3⋊D3—91no—
483C2×C3⋊D3—91no—
484C2×C3×D3—271no—
485C2×C3×D3—271no—
486C2×C3×D3—271no—
487C2×C3×D3—271no—
488C2×C3×D3—271no—
489C2×C3×D3—271no—
490C2×C3×D3—271no—
491C2×C3×D3—271no—
492C2×C3×D3—271no—
493C2×C3×D3—271no—
494C2×C3×D3—271no—
495C2×C3×D3—271no—
496C2×C3×D3—271no—
497C22×C9—811no—
498C2×D9—91no—
499C2×D9—91no—
500C2×D9—91no—
501C2×D9—91no—
502C2×D9—91no—
503C2×D9—91no—
504C2×D9—91no—
505C2×D9—91no—
506C2×D9—91no—
507C33C2×C3×C3⋊D311yescharacteristic
508C33C2×C3×C3⋊D311yescharacteristic
509C33C2×C3×C3⋊D311yescharacteristic
510C33C2×C3×C3⋊D311yescharacteristic
5113−1+2—61no—
5123−1+2—61no—
5133−1+2—61no—
5143−1+2—61no—
5153−1+2—61no—
5163−1+2—61no—
5173−1+2—61no—
5183−1+2—61no—
5193−1+2—61no—
5203−1+2—61no—
5213−1+2—61no—
5223−1+2—61no—
523H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
524H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
525H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
526H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
527H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
528H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
529H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
530H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
531H(3,𝔽3)C2×AGL(1,ℤ/9)11yescharacteristic
532C3×C9—21no—
533C3×C9—21no—
534C3×C9—21no—
535C3×C9—21no—
536C3×C9—21no—
537C3×C9—21no—
538C3×C9—21no—
539C3×C9—21no—
540C3×C9—21no—
541C3×C9—21no—
542C3×C9—21no—
543C3×C9—21no—
544C3×C9—21no—
545C3×C9—31no—
546C3×C9—31no—
547C3×C9—31no—
548C3×C9—31no—
549C3×C9—31no—
550C3×C9—31no—
551C3×C9—31no—
552C3×C9—61no—
553C3×C9—61no—
554C3×C9—61no—
555C3×C9—61no—
556C3×C9—61no—
557C3×C9—61no—
558C3×C9—61no—
559C3×C9—61no—
560C3×C9—61no—
561C3×C9—61no—
562C3×C9—61no—
563C3×C9—61no—
564C3×C9—61no—
565C3×C9—181no—
566C3×C9—181no—
567C3×C9—181no—
568C3×C9—181no—
569C3×C9C2×C3×C3⋊D311yescharacteristic
570C3×C9C2×C3×C3⋊D311yescharacteristic
571C3×C9C2×C3×C3⋊D311yescharacteristic
572C3×C9C2×C3×C3⋊D311yescharacteristic
573C3×C9C2×C3×C3⋊D311yescharacteristic
574C3×C9C2×C3×C3⋊D311yescharacteristic
575C3×C9C2×C3×C3⋊D311yescharacteristic
576C3×C9C2×C3×C3⋊D311yescharacteristic
577C3×C9C2×C3×C3⋊D311yescharacteristic
578C3×C9C2×C3⋊(C3⋊D3)11yescharacteristic
579C2×C32—31no—
580C2×C32—31no—
581C2×C32—61no—
582C2×C32—61no—
583C2×C32—61no—
584C2×C32—61no—
585C2×C32—61no—
586C2×C32—61no—
587C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
588C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
589C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
590C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
591C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
592C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
593C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
594C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
595C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
596C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
597C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
598C2×C32C3⋊AGL(1,ℤ/9)11yescharacteristic
599C2×C32C3×C3⋊(C3⋊D3)11yescharacteristic
600C3⋊D3—92no—
601C3⋊D3—92no—
602C3⋊D3—92no—
603C3⋊D3—92no—
604C3×D3—272no—
605C3×D3—272no—
606C3×D3—272no—
607C3×D3—272no—
608C3×D3—272no—
609C3×D3—272no—
610C3×D3—272no—
611C3×D3—272no—
612C3×D3—272no—
613C3×D3—272no—
614C3×D3—272no—
615C3×D3—272no—
616C3×D3—272no—
617C2×C9—21no—
618C2×C9—31no—
619C2×C9—31no—
620C2×C9—61no—
621C2×C9—61no—
622C2×C9—61no—
623C2×C9—61no—
624C2×C9—61no—
625C2×C9—61no—
626C2×C9—61no—
627C2×C9—61no—
628C2×C9—61no—
629C2×C9—61no—
630C2×C9—61no—
631C2×C9—61no—
632C2×C9—61no—
633C2×C9—61no—
634C2×C9—61no—
635C2×C9—61no—
636C2×C9—61no—
637C2×C9—61no—
638C2×C9—61no—
639C2×C9—61no—
640C2×C9—812no—
641C2×C9#420811yescharacteristic, complemented
642D9—92no—
643D9—92no—
644D9—92no—
645D9—92no—
646D9—92no—
647D9—92no—
648D9—92no—
649D9—92no—
650D9—92no—
651C22×C3—811no—
652C2×D3—271no—
653C2×D3—271no—
654C2×D3—271no—
655C2×D3—271no—
656C2×D3—271no—
657C2×D3—271no—
658C2×D3—271no—
659C2×D3—271no—
660C2×D3—271no—
661C2×D3—271no—
662C2×D3—271no—
663C2×D3—271no—
664C2×D3—271no—
665C32—31no—
666C32—31no—
667C32—61no—
668C32—61no—
669C32—61no—
670C32—61no—
671C32—61no—
672C32—61no—
673C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
674C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
675C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
676C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
677C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
678C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
679C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
680C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
681C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
682C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
683C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
684C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
685C32C2×C3×C3⋊(C3⋊D3)11yescharacteristic
686C9—21no—
687C9—31no—
688C9—31no—
689C9—61no—
690C9—61no—
691C9—61no—
692C9—61no—
693C9—61no—
694C9—61no—
695C9—61no—
696C9—61no—
697C9—61no—
698C9—61no—
699C9—61no—
700C9—61no—
701C9—61no—
702C9—61no—
703C9—61no—
704C9—61no—
705C9—61no—
706C9—61no—
707C9—61no—
708C9—61no—
709C9C2×#420811yescharacteristic, complemented
710C2×C3—21no—
711C2×C3—31no—
712C2×C3—31no—
713C2×C3—31no—
714C2×C3—31no—
715C2×C3—31no—
716C2×C3—31no—
717C2×C3—61no—
718C2×C3—61no—
719C2×C3—61no—
720C2×C3—61no—
721C2×C3—61no—
722C2×C3—61no—
723C2×C3—812no—
724C2×C3C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic
725C2×C3C3⋊#420811yescharacteristic
726D3—272no—
727D3—272no—
728D3—272no—
729D3—272no—
730D3—272no—
731D3—272no—
732D3—272no—
733D3—272no—
734D3—272no—
735D3—272no—
736D3—272no—
737D3—272no—
738D3—272no—
739C22—811noSylow
740C3—21no—
741C3—31no—
742C3—31no—
743C3—31no—
744C3—31no—
745C3—31no—
746C3—31no—
747C3—61no—
748C3—61no—
749C3—61no—
750C3—61no—
751C3—61no—
752C3—61no—
753C3C2×C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic
754C3C2×C3⋊#420811yescharacteristic
755C2—812no—
756C2#1309152411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C3⋊(C3⋊AGL(1,ℤ/9))
commutator, cosocle, hypocenterC9×H(3,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624900C2
socleC2×C32C3×C3⋊(C3⋊D3)
prime radicalC2×C9⋊#272C3
LCSG ▷ C9×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #13091524C2direct (N × H)
2. C2×#10624900C2semidirect
17. #10624900C22semidirect
20. C2×#6895D3semidirect
21. C2×#6895D3semidirect
22. C2×#6895D3semidirect
23. C2×#6895D3semidirect
24. C2×#6895D3semidirect
25. C2×#6895D3semidirect
26. C2×#6895D3semidirect
27. C2×#6895D3semidirect
42. C2×C3×C9⋊C9D3semidirect
43. C2×C3×C9⋊C9D3semidirect
44. C2×C3×C9⋊C9D3semidirect
45. C2×C3×C9⋊C9D3semidirect
95. #6895C2×D3semidirect
96. #6895C2×D3semidirect
97. #6895C2×D3semidirect
98. #6895C2×D3semidirect
99. #6895C2×D3semidirect
100. #6895C2×D3semidirect
101. #6895C2×D3semidirect
102. #6895C2×D3semidirect
117. C3×C9⋊C9C2×D3semidirect
118. C3×C9⋊C9C2×D3semidirect
119. C3×C9⋊C9C2×D3semidirect
120. C3×C9⋊C9C2×D3semidirect
641. C2×C9#4208semidirect
709. C9C2×#4208semidirect
756. C2#13091524direct (N × H)

Maximal subgroups

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

subgroupindex
#130915242
C2×#106249002
C2×C3⋊#42083
C2×C9⋊#2723
C2×#6895⋊C23
C2×C3⋊(D9⋊C9)3