Finite Group Databasebeta

← C2×#13091651 #72244447

Subgroups — C2×#13091651 #72244447

Order 2916.

1261 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091651C212yesmaximal, direct product factor
2C2×#10624931C211yesmaximal, characteristic, complemented
3C2×#92404C311yesmaximal, characteristic
4C2×C3⋊#4208—31nomaximal
5C2×C3⋊#4176—31nomaximal
6C2×C3⋊#4176—31nomaximal
7C2×C3⋊#4176—31nomaximal
8C2×C3⋊#4176—31nomaximal
9C2×C3⋊#4176—31nomaximal
10C2×C3⋊#4176—31nomaximal
11C2×C3⋊#4176—31nomaximal
12C2×C3⋊#4176—31nomaximal
13C2×C3⋊#4176—31nomaximal
14C2×C3⋊#4176—31nomaximal
15C2×C3⋊#4176—31nomaximal
16C2×C3⋊#4176—31nomaximal
17#10624931C2211yescharacteristic, complemented, Sylow
18C2×3−1+4—21no—
19C2×H(5,𝔽3)C2×C311yescharacteristic
20C2×C3×#737D311yescharacteristic, complemented
21#92404C2×C312yes—
22C3⋊#4208—32no—
23C2×#6910—21no—
24C2×#6910—21no—
25C2×#6910—21no—
26C2×#6910—21no—
27C2×#6910—21no—
28C2×#6910—21no—
29C2×#6910—21no—
30C2×#6910—21no—
31C2×#6910—21no—
32C2×#6910—21no—
33C2×#6910—21no—
34C2×#6910—21no—
35C2×C3×#731D311yescharacteristic, complemented
36C2×C3×#731D311yescharacteristic, complemented
37C2×C3×#731D311yescharacteristic, complemented
38C2×C3×#731D311yescharacteristic, complemented
39C2×C3×#731D311yescharacteristic, complemented
40C2×C3×#731D311yescharacteristic, complemented
41C2×C3×#731D311yescharacteristic, complemented
42C2×C3×#731D311yescharacteristic, complemented
43C2×C3×#731D311yescharacteristic, complemented
44C2×C3×#731D311yescharacteristic, complemented
45C2×C3×#731D311yescharacteristic, complemented
46C2×C3×#731D311yescharacteristic, complemented
47C3⋊#4176—32no—
48C3⋊#4176—32no—
49C3⋊#4176—32no—
50C3⋊#4176—32no—
51C3⋊#4176—32no—
52C3⋊#4176—32no—
53C3⋊#4176—32no—
54C3⋊#4176—32no—
55C3⋊#4176—32no—
56C3⋊#4176—32no—
57C3⋊#4176—32no—
58C3⋊#4176—32no—
59C2×C3⋊#272—31no—
60C2×C3⋊#272—31no—
61C2×C3⋊#272—31no—
62C2×C3⋊#272—31no—
63C2×C3⋊#272—31no—
64C2×C3⋊#272—31no—
65C2×C3⋊#272—31no—
66C2×C3⋊#272—31no—
67C2×C3⋊#272—31no—
68C2×C3⋊#272—31no—
69C2×C3⋊#272—31no—
70C2×C3⋊#272—31no—
71C2×C3⋊#272—31no—
72C2×C3⋊#272—91no—
73C2×C3⋊#272—91no—
74C2×C3⋊#272—91no—
75C2×C3⋊#272—91no—
76C2×C3⋊#272—91no—
77C2×C3⋊#272—91no—
78C2×C3⋊#272—91no—
79C2×C3⋊#272—91no—
80C2×C3⋊#272—91no—
81C2×#4208—91no—
82C2×#4208—91no—
83C2×#4208—91no—
84C2×#4208—91no—
85C2×#4208—91no—
86C2×#4208—91no—
87C2×#4208—91no—
88C2×#4208—91no—
89C2×#4208—91no—
90C2×C9×C3⋊D3—91no—
91C2×C9×C3⋊D3—91no—
92C2×C9×C3⋊D3—91no—
93C2×C9×C3⋊D3—91no—
94C2×#4176—91no—
95C2×#4176—91no—
96C2×#4176—91no—
97C2×#4176—91no—
98C2×#4176—91no—
99C2×#4176—91no—
100C2×#4176—91no—
101C2×#4176—91no—
102C2×#4176—91no—
1033−1+4—21no—
104H(5,𝔽3)C22×C311yescharacteristic
105C3×#737C2×D311yescharacteristic, complemented
106#6910—21no—
107#6910—21no—
108#6910—21no—
109#6910—21no—
110#6910—21no—
111#6910—21no—
112#6910—21no—
113#6910—21no—
114#6910—21no—
115#6910—21no—
116#6910—21no—
117#6910—21no—
118C3×#731C2×D311yescharacteristic, complemented
119C3×#731C2×D311yescharacteristic, complemented
120C3×#731C2×D311yescharacteristic, complemented
121C3×#731C2×D311yescharacteristic, complemented
122C3×#731C2×D311yescharacteristic, complemented
123C3×#731C2×D311yescharacteristic, complemented
124C3×#731C2×D311yescharacteristic, complemented
125C3×#731C2×D311yescharacteristic, complemented
126C3×#731C2×D311yescharacteristic, complemented
127C3×#731C2×D311yescharacteristic, complemented
128C3×#731C2×D311yescharacteristic, complemented
129C3×#731C2×D311yescharacteristic, complemented
130C2×#737—31no—
131C2×#737—31no—
132C2×#737—31no—
133C2×#737—31no—
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×#737—61no—
145C2×#737—61no—
146C2×#737—61no—
147C2×#737—61no—
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+2—21no—
154C2×C3×3−1+2—21no—
155C2×C3×3−1+2—21no—
156C2×C3×3−1+2—21no—
157C2×C3×3−1+2—21no—
158C2×C3×3−1+2—21no—
159C2×C3×3−1+2—21no—
160C2×C3×3−1+2—21no—
161C2×C3×3−1+2—21no—
162C2×C3×3−1+2—21no—
163C2×C3×3−1+2—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)—31no—
169C2×C3×H(3,𝔽3)—31no—
170C2×C3×H(3,𝔽3)—31no—
171C2×C3×H(3,𝔽3)—31no—
172C2×C3×H(3,𝔽3)—31no—
173C2×C3×H(3,𝔽3)C3×D311yescharacteristic
174C2×C3×H(3,𝔽3)C3×D311yescharacteristic
175C2×C3×H(3,𝔽3)C3×D311yescharacteristic
176C2×C3×H(3,𝔽3)C3×D311yescharacteristic
177C2×C3×H(3,𝔽3)C3×D311yescharacteristic
178C2×C3×H(3,𝔽3)C3×D311yescharacteristic
179C2×C3×H(3,𝔽3)C3×D311yescharacteristic
180C2×C3×H(3,𝔽3)C3×D311yescharacteristic
181C2×C3×H(3,𝔽3)C3×D311yescharacteristic
182C2×C3×H(3,𝔽3)C3×D311yescharacteristic
183C2×C3×H(3,𝔽3)C3×D311yescharacteristic
184C2×C3×H(3,𝔽3)C3×D311yescharacteristic
185C2×C3×H(3,𝔽3)C3×D311yescharacteristic
186C2×C32×C9C3⋊D311yescharacteristic, complemented
187C2×C32×C9C3⋊D311yescharacteristic, complemented
188C2×C32×C9C3⋊D311yescharacteristic, complemented
189C2×C32×C9C3⋊D311yescharacteristic, complemented
190C3⋊#272—32no—
191C3⋊#272—32no—
192C3⋊#272—32no—
193C3⋊#272—32no—
194C3⋊#272—32no—
195C3⋊#272—32no—
196C3⋊#272—32no—
197C3⋊#272—32no—
198C3⋊#272—32no—
199C3⋊#272—32no—
200C3⋊#272—32no—
201C3⋊#272—32no—
202C3⋊#272—32no—
203C3⋊#272—92no—
204C3⋊#272—92no—
205C3⋊#272—92no—
206C3⋊#272—92no—
207C3⋊#272—92no—
208C3⋊#272—92no—
209C3⋊#272—92no—
210C3⋊#272—92no—
211C3⋊#272—92no—
212#4208—92no—
213#4208—92no—
214#4208—92no—
215#4208—92no—
216#4208—92no—
217#4208—92no—
218#4208—92no—
219#4208—92no—
220#4208—92no—
221C9×C3⋊D3—92no—
222C9×C3⋊D3—92no—
223C9×C3⋊D3—92no—
224C9×C3⋊D3—92no—
225C2×#731—21no—
226C2×#731—21no—
227C2×#731—21no—
228C2×#731—21no—
229C2×#731—21no—
230C2×#731—21no—
231C2×#731—21no—
232C2×#731—21no—
233C2×#731—21no—
234C2×#731—21no—
235C2×#731—21no—
236C2×#731—21no—
237C2×#731—21no—
238C2×#731—21no—
239C2×#731—21no—
240C2×#731—21no—
241C2×#731—21no—
242C2×#731—21no—
243C2×#731—21no—
244C2×#731—21no—
245C2×#731—21no—
246C2×#731—21no—
247C2×#731—21no—
248C2×#731—21no—
249C2×#731—21no—
250C2×#731—21no—
251C2×#731—21no—
252C2×#731—21no—
253C2×#731—21no—
254C2×#731—21no—
255C2×#731—21no—
256C2×#731—21no—
257C2×#731—21no—
258C2×#731—21no—
259C2×#731—21no—
260C2×#731—21no—
261C2×#731C3⋊D311yescharacteristic, complemented
262C2×#731C3⋊D311yescharacteristic, complemented
263C2×#731C3⋊D311yescharacteristic, complemented
264C2×#731C3⋊D311yescharacteristic, complemented
265C2×#731C3⋊D311yescharacteristic, complemented
266C2×#731C3⋊D311yescharacteristic, complemented
267C2×#731C3⋊D311yescharacteristic, complemented
268C2×#731C3⋊D311yescharacteristic, complemented
269C2×#731C3⋊D311yescharacteristic, complemented
270#4176—92no—
271#4176—92no—
272#4176—92no—
273#4176—92no—
274#4176—92no—
275#4176—92no—
276#4176—92no—
277#4176—92no—
278#4176—92no—
279C2×C3×C3⋊D3—91no—
280C2×C3×C3⋊D3—91no—
281C2×C3×C3⋊D3—91no—
282C2×C3×C3⋊D3—91no—
283C2×C3×C3⋊D3—271no—
284C2×C3×C3⋊D3—271no—
285C2×C3×C3⋊D3—271no—
286C2×C3×C3⋊D3—271no—
287C2×C3×C3⋊D3—271no—
288C2×C3×C3⋊D3—271no—
289C2×C3×C3⋊D3—271no—
290C2×C3×C3⋊D3—271no—
291C2×C3×C3⋊D3—271no—
292C2×C3×C3⋊D3—271no—
293C2×C3×C3⋊D3—271no—
294C2×C3×C3⋊D3—271no—
295C2×#272—91no—
296C2×#272—91no—
297C2×#272—91no—
298C2×#272—91no—
299C2×#272—91no—
300C2×#272—91no—
301C2×#272—91no—
302C2×#272—91no—
303C2×#272—91no—
304C2×#272—91no—
305C2×#272—91no—
306C2×#272—91no—
307C2×#272—91no—
308C2×#272—91no—
309C2×#272—91no—
310C2×#272—91no—
311C2×#272—91no—
312C2×#272—91no—
313C2×#272—271no—
314C2×#272—271no—
315C2×#272—271no—
316C2×#272—271no—
317C2×#272—271no—
318C2×#272—271no—
319C2×#272—271no—
320C2×#272—271no—
321C2×#272—271no—
322C2×#272—271no—
323C2×#272—271no—
324C2×#272—271no—
325C2×#272—271no—
326C2×#272—271no—
327C2×#272—271no—
328C2×#272—271no—
329C2×#272—271no—
330C2×#272—271no—
331C2×#272—271no—
332C2×#272—271no—
333C2×#272—271no—
334C2×#272—271no—
335C2×#272—271no—
336C2×#272—271no—
337C2×D3×C9—271no—
338C2×D3×C9—271no—
339C2×D3×C9—271no—
340C2×D3×C9—271no—
341C2×D3×C9—271no—
342C2×D3×C9—271no—
343C2×D3×C9—271no—
344C2×D3×C9—271no—
345C2×D3×C9—271no—
346C2×D3×C9—271no—
347C2×D3×C9—271no—
348C2×D3×C9—271no—
349C2×D3×C9—271no—
350#737—31no—
351#737—31no—
352#737—31no—
353#737—31no—
354#737—61no—
355#737—61no—
356#737—61no—
357#737—61no—
358#737—61no—
359#737—61no—
360#737—61no—
361#737—61no—
362#737—61no—
363#737—61no—
364#737—61no—
365#737—61no—
366#737—61no—
367#737—61no—
368C3×3−1+2—21no—
369C3×3−1+2—21no—
370C3×3−1+2—21no—
371C3×3−1+2—21no—
372C3×3−1+2—21no—
373C3×3−1+2—21no—
374C3×3−1+2—21no—
375C3×3−1+2—21no—
376C3×3−1+2—21no—
377C3×3−1+2—21no—
378C3×3−1+2—21no—
379C3×3−1+2—21no—
380C3×3−1+2—21no—
381C3×3−1+2—21no—
382C3×3−1+2—21no—
383C3×3−1+2—21no—
384C3×H(3,𝔽3)—31no—
385C3×H(3,𝔽3)—31no—
386C3×H(3,𝔽3)—31no—
387C3×H(3,𝔽3)—31no—
388C3×H(3,𝔽3)—31no—
389C3×H(3,𝔽3)—31no—
390C3×H(3,𝔽3)—31no—
391C3×H(3,𝔽3)—31no—
392C3×H(3,𝔽3)—31no—
393C3×H(3,𝔽3)C2×C3×D311yescharacteristic
394C3×H(3,𝔽3)C2×C3×D311yescharacteristic
395C3×H(3,𝔽3)C2×C3×D311yescharacteristic
396C3×H(3,𝔽3)C2×C3×D311yescharacteristic
397C3×H(3,𝔽3)C2×C3×D311yescharacteristic
398C3×H(3,𝔽3)C2×C3×D311yescharacteristic
399C3×H(3,𝔽3)C2×C3×D311yescharacteristic
400C3×H(3,𝔽3)C2×C3×D311yescharacteristic
401C3×H(3,𝔽3)C2×C3×D311yescharacteristic
402C3×H(3,𝔽3)C2×C3×D311yescharacteristic
403C3×H(3,𝔽3)C2×C3×D311yescharacteristic
404C3×H(3,𝔽3)C2×C3×D311yescharacteristic
405C3×H(3,𝔽3)C2×C3×D311yescharacteristic
406C32×C9C2×C3⋊D311yescharacteristic, complemented
407C32×C9C2×C3⋊D311yescharacteristic, complemented
408C32×C9C2×C3⋊D311yescharacteristic, complemented
409C32×C9C2×C3⋊D311yescharacteristic, complemented
410#731—21no—
411#731—21no—
412#731—21no—
413#731—21no—
414#731—21no—
415#731—21no—
416#731—21no—
417#731—21no—
418#731—21no—
419#731—21no—
420#731—21no—
421#731—21no—
422#731—21no—
423#731—21no—
424#731—21no—
425#731—21no—
426#731—21no—
427#731—21no—
428#731—21no—
429#731—21no—
430#731—21no—
431#731—21no—
432#731—21no—
433#731—21no—
434#731—21no—
435#731—21no—
436#731—21no—
437#731—21no—
438#731—21no—
439#731—21no—
440#731—21no—
441#731—21no—
442#731—21no—
443#731—21no—
444#731—21no—
445#731—21no—
446#731C2×C3⋊D311yescharacteristic, complemented
447#731C2×C3⋊D311yescharacteristic, complemented
448#731C2×C3⋊D311yescharacteristic, complemented
449#731C2×C3⋊D311yescharacteristic, complemented
450#731C2×C3⋊D311yescharacteristic, complemented
451#731C2×C3⋊D311yescharacteristic, complemented
452#731C2×C3⋊D311yescharacteristic, complemented
453#731C2×C3⋊D311yescharacteristic, complemented
454#731C2×C3⋊D311yescharacteristic, complemented
455C2×C33—31no—
456C2×C33—31no—
457C2×C33—31no—
458C2×C33—31no—
459C2×C33—31no—
460C2×C33—31no—
461C2×C33—31no—
462C2×C33—31no—
463C2×C33—31no—
464C2×C33—31no—
465C2×C33—31no—
466C2×C33—31no—
467C2×C33C3×C3⋊D311yescharacteristic
468C2×C33C3×C3⋊D311yescharacteristic
469C2×C33C3×C3⋊D311yescharacteristic
470C2×C33C3×C3⋊D311yescharacteristic
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—
478C3×C3⋊D3—272no—
479C3×C3⋊D3—272no—
480C3×C3⋊D3—272no—
481C3×C3⋊D3—272no—
482C3×C3⋊D3—272no—
483C3×C3⋊D3—272no—
484C3×C3⋊D3—272no—
485C3×C3⋊D3—272no—
486C3×C3⋊D3—272no—
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—21no—
493C2×3−1+2—21no—
494C2×3−1+2—21no—
495C2×3−1+2—21no—
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+2—61no—
519C2×3−1+2—61no—
520C2×3−1+2—61no—
521C2×3−1+2—61no—
522C2×3−1+2—61no—
523C2×3−1+2—61no—
524C2×3−1+2—61no—
525C2×3−1+2—61no—
526C2×3−1+2—61no—
527C2×3−1+2—61no—
528C2×3−1+2—61no—
529C2×3−1+2—61no—
530C2×3−1+2—61no—
531C2×3−1+2—61no—
532C2×H(3,𝔽3)—31no—
533C2×H(3,𝔽3)—31no—
534C2×H(3,𝔽3)—31no—
535C2×H(3,𝔽3)—31no—
536C2×H(3,𝔽3)—31no—
537C2×H(3,𝔽3)—31no—
538C2×H(3,𝔽3)—31no—
539C2×H(3,𝔽3)—31no—
540C2×H(3,𝔽3)—31no—
541C2×H(3,𝔽3)—31no—
542C2×H(3,𝔽3)—31no—
543C2×H(3,𝔽3)—31no—
544C2×H(3,𝔽3)—31no—
545C2×H(3,𝔽3)—31no—
546C2×H(3,𝔽3)—31no—
547C2×H(3,𝔽3)—31no—
548C2×H(3,𝔽3)—31no—
549C2×H(3,𝔽3)—31no—
550C2×H(3,𝔽3)—31no—
551C2×H(3,𝔽3)—31no—
552C2×H(3,𝔽3)—31no—
553C2×H(3,𝔽3)—31no—
554C2×H(3,𝔽3)—31no—
555C2×H(3,𝔽3)—31no—
556C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
557C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
558C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
559C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
560C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
561C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
562C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
563C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
564C2×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
565C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
566C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
567C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
568C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
569C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
570C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
571C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
572C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
573C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
574C2×C3×C9—21no—
575C2×C3×C9—21no—
576C2×C3×C9—21no—
577C2×C3×C9—21no—
578C2×C3×C9—31no—
579C2×C3×C9—31no—
580C2×C3×C9—61no—
581C2×C3×C9—61no—
582C2×C3×C9—61no—
583C2×C3×C9—61no—
584C2×C3×C9—61no—
585C2×C3×C9—61no—
586C2×C3×C9—61no—
587C2×C3×C9—61no—
588C2×C3×C9—61no—
589C2×C3×C9—61no—
590C2×C3×C9—61no—
591C2×C3×C9—61no—
592C2×C3×C9—61no—
593C2×C3×C9—61no—
594C2×C3×C9—61no—
595C2×C3×C9—61no—
596C2×C3×C9—61no—
597C2×C3×C9—61no—
598C2×C3×C9—61no—
599C2×C3×C9—61no—
600C2×C3×C9—61no—
601C2×C3×C9—61no—
602C2×C3×C9C3⋊(C3⋊D3)11yescharacteristic
603#272—92no—
604#272—92no—
605#272—92no—
606#272—92no—
607#272—92no—
608#272—92no—
609#272—92no—
610#272—92no—
611#272—92no—
612#272—92no—
613#272—92no—
614#272—92no—
615#272—92no—
616#272—92no—
617#272—92no—
618#272—92no—
619#272—92no—
620#272—92no—
621#272—272no—
622#272—272no—
623#272—272no—
624#272—272no—
625#272—272no—
626#272—272no—
627#272—272no—
628#272—272no—
629#272—272no—
630#272—272no—
631#272—272no—
632#272—272no—
633#272—272no—
634#272—272no—
635#272—272no—
636#272—272no—
637#272—272no—
638#272—272no—
639#272—272no—
640#272—272no—
641#272—272no—
642#272—272no—
643#272—272no—
644#272—272no—
645D3×C9—272no—
646D3×C9—272no—
647D3×C9—272no—
648D3×C9—272no—
649D3×C9—272no—
650D3×C9—272no—
651D3×C9—272no—
652D3×C9—272no—
653D3×C9—272no—
654D3×C9—272no—
655D3×C9—272no—
656D3×C9—272no—
657D3×C9—272no—
658C2×C3⋊D3—91no—
659C2×C3⋊D3—91no—
660C2×C3⋊D3—91no—
661C2×C3⋊D3—91no—
662C2×C3⋊D3—271no—
663C2×C3⋊D3—271no—
664C2×C3⋊D3—271no—
665C2×C3⋊D3—271no—
666C2×C3⋊D3—271no—
667C2×C3⋊D3—271no—
668C2×C3⋊D3—271no—
669C2×C3⋊D3—271no—
670C2×C3⋊D3—271no—
671C2×C3⋊D3—271no—
672C2×C3⋊D3—271no—
673C2×C3⋊D3—271no—
674C2×C3×D3—271no—
675C2×C3×D3—271no—
676C2×C3×D3—271no—
677C2×C3×D3—271no—
678C2×C3×D3—271no—
679C2×C3×D3—271no—
680C2×C3×D3—271no—
681C2×C3×D3—271no—
682C2×C3×D3—271no—
683C2×C3×D3—271no—
684C2×C3×D3—271no—
685C2×C3×D3—271no—
686C2×C3×D3—271no—
687C2×C3×D3—811no—
688C2×C3×D3—811no—
689C2×C3×D3—811no—
690C2×C3×D3—811no—
691C2×C3×D3—811no—
692C2×C3×D3—811no—
693C2×C3×D3—811no—
694C2×C3×D3—811no—
695C2×C3×D3—811no—
696C22×C9—811no—
697C33—31no—
698C33—31no—
699C33—31no—
700C33—31no—
701C33—31no—
702C33—31no—
703C33—31no—
704C33—31no—
705C33—31no—
706C33—31no—
707C33—31no—
708C33—31no—
709C33C2×C3×C3⋊D311yescharacteristic
710C33C2×C3×C3⋊D311yescharacteristic
711C33C2×C3×C3⋊D311yescharacteristic
712C33C2×C3×C3⋊D311yescharacteristic
7133−1+2—21no—
7143−1+2—21no—
7153−1+2—21no—
7163−1+2—21no—
7173−1+2—21no—
7183−1+2—21no—
7193−1+2—21no—
7203−1+2—21no—
7213−1+2—21no—
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+2—61no—
7363−1+2—61no—
7373−1+2—61no—
7383−1+2—61no—
7393−1+2—61no—
7403−1+2—61no—
7413−1+2—61no—
7423−1+2—61no—
7433−1+2—61no—
7443−1+2—61no—
7453−1+2—61no—
7463−1+2—61no—
7473−1+2—61no—
7483−1+2—61no—
7493−1+2—61no—
7503−1+2—61no—
7513−1+2—61no—
7523−1+2—61no—
7533−1+2—61no—
7543−1+2—61no—
7553−1+2—61no—
7563−1+2—61no—
7573−1+2—61no—
758H(3,𝔽3)—31no—
759H(3,𝔽3)—31no—
760H(3,𝔽3)—31no—
761H(3,𝔽3)—31no—
762H(3,𝔽3)—31no—
763H(3,𝔽3)—31no—
764H(3,𝔽3)—31no—
765H(3,𝔽3)—31no—
766H(3,𝔽3)—31no—
767H(3,𝔽3)—31no—
768H(3,𝔽3)—31no—
769H(3,𝔽3)—31no—
770H(3,𝔽3)—31no—
771H(3,𝔽3)—31no—
772H(3,𝔽3)—31no—
773H(3,𝔽3)—31no—
774H(3,𝔽3)—31no—
775H(3,𝔽3)—31no—
776H(3,𝔽3)—31no—
777H(3,𝔽3)—31no—
778H(3,𝔽3)—31no—
779H(3,𝔽3)—31no—
780H(3,𝔽3)—31no—
781H(3,𝔽3)—31no—
782H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
783H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
784H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
785H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
786H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
787H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
788H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
789H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
790H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic
791H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
792H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
793H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
794H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
795H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
796H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
797H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
798H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
799H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
800C3×C9—21no—
801C3×C9—21no—
802C3×C9—21no—
803C3×C9—21no—
804C3×C9—31no—
805C3×C9—31no—
806C3×C9—61no—
807C3×C9—61no—
808C3×C9—61no—
809C3×C9—61no—
810C3×C9—61no—
811C3×C9—61no—
812C3×C9—61no—
813C3×C9—61no—
814C3×C9—61no—
815C3×C9—61no—
816C3×C9—61no—
817C3×C9—61no—
818C3×C9—61no—
819C3×C9—61no—
820C3×C9—61no—
821C3×C9—61no—
822C3×C9—61no—
823C3×C9—61no—
824C3×C9—61no—
825C3×C9—61no—
826C3×C9—61no—
827C3×C9—61no—
828C3×C9C2×C3⋊(C3⋊D3)11yescharacteristic
829C2×C32—31no—
830C2×C32—31no—
831C2×C32—31no—
832C2×C32—31no—
833C2×C32—31no—
834C2×C32—31no—
835C2×C32—31no—
836C2×C32—31no—
837C2×C32—31no—
838C2×C32—181no—
839C2×C32—181no—
840C2×C32—181no—
841C2×C32—181no—
842C2×C32—271no—
843C2×C32—271no—
844C2×C32—541no—
845C2×C32—541no—
846C2×C32—541no—
847C2×C32—541no—
848C2×C32—541no—
849C2×C32—541no—
850C2×C32—541no—
851C2×C32—541no—
852C2×C32—541no—
853C2×C32—541no—
854C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
855C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
856C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
857C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
858C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
859C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
860C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
861C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
862C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
863C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
864C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
865C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
866C2×C32C3×C3⋊(C3⋊D3)11yescharacteristic
867C3⋊D3—92no—
868C3⋊D3—92no—
869C3⋊D3—92no—
870C3⋊D3—92no—
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—272no—
887C3×D3—272no—
888C3×D3—272no—
889C3×D3—272no—
890C3×D3—272no—
891C3×D3—272no—
892C3×D3—272no—
893C3×D3—272no—
894C3×D3—272no—
895C3×D3—272no—
896C3×D3—812no—
897C3×D3—812no—
898C3×D3—812no—
899C3×D3—812no—
900C3×D3—812no—
901C3×D3—812no—
902C3×D3—812no—
903C3×D3—812no—
904C3×D3—812no—
905C2×C9—31no—
906C2×C9—61no—
907C2×C9—61no—
908C2×C9—61no—
909C2×C9—61no—
910C2×C9—61no—
911C2×C9—61no—
912C2×C9—61no—
913C2×C9—61no—
914C2×C9—61no—
915C2×C9—61no—
916C2×C9—61no—
917C2×C9—61no—
918C2×C9—61no—
919C2×C9—812no—
920C22×C3—811no—
921C2×D3—271no—
922C2×D3—271no—
923C2×D3—271no—
924C2×D3—271no—
925C2×D3—271no—
926C2×D3—271no—
927C2×D3—271no—
928C2×D3—271no—
929C2×D3—271no—
930C2×D3—271no—
931C2×D3—271no—
932C2×D3—271no—
933C2×D3—271no—
934C2×D3—811no—
935C2×D3—811no—
936C2×D3—811no—
937C2×D3—811no—
938C2×D3—811no—
939C2×D3—811no—
940C2×D3—811no—
941C2×D3—811no—
942C2×D3—811no—
943C32—31no—
944C32—31no—
945C32—31no—
946C32—31no—
947C32—31no—
948C32—31no—
949C32—31no—
950C32—31no—
951C32—31no—
952C32—181no—
953C32—181no—
954C32—181no—
955C32—181no—
956C32—271no—
957C32—271no—
958C32—541no—
959C32—541no—
960C32—541no—
961C32—541no—
962C32—541no—
963C32—541no—
964C32—541no—
965C32—541no—
966C32—541no—
967C32—541no—
968C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
969C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
970C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
971C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
972C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
973C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
974C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
975C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
976C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
977C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
978C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
979C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
980C32C2×C3×C3⋊(C3⋊D3)11yescharacteristic
981C9—31no—
982C9—61no—
983C9—61no—
984C9—61no—
985C9—61no—
986C9—61no—
987C9—61no—
988C9—61no—
989C9—61no—
990C9—61no—
991C9—61no—
992C9—61no—
993C9—61no—
994C9—61no—
995C2×C3—31no—
996C2×C3—31no—
997C2×C3—31no—
998C2×C3—31no—
999C2×C3—31no—
1000C2×C3—61no—
1001C2×C3—61no—
1002C2×C3—61no—
1003C2×C3—61no—
1004C2×C3—61no—
1005C2×C3—61no—
1006C2×C3—61no—
1007C2×C3—61no—
1008C2×C3—91no—
1009C2×C3—91no—
1010C2×C3—91no—
1011C2×C3—181no—
1012C2×C3—181no—
1013C2×C3—181no—
1014C2×C3—181no—
1015C2×C3—181no—
1016C2×C3—181no—
1017C2×C3—812no—
1018C2×C3C3⋊(C3⋊((C3⋊D3)⋊C3))11yescharacteristic
1019D3—272no—
1020D3—272no—
1021D3—272no—
1022D3—272no—
1023D3—272no—
1024D3—272no—
1025D3—272no—
1026D3—272no—
1027D3—272no—
1028D3—272no—
1029D3—272no—
1030D3—272no—
1031D3—272no—
1032D3—812no—
1033D3—812no—
1034D3—812no—
1035D3—812no—
1036D3—812no—
1037D3—812no—
1038D3—812no—
1039D3—812no—
1040D3—812no—
1041C22—811noSylow
1042C3—31no—
1043C3—31no—
1044C3—31no—
1045C3—31no—
1046C3—31no—
1047C3—61no—
1048C3—61no—
1049C3—61no—
1050C3—61no—
1051C3—61no—
1052C3—61no—
1053C3—61no—
1054C3—61no—
1055C3—91no—
1056C3—91no—
1057C3—91no—
1058C3—181no—
1059C3—181no—
1060C3—181no—
1061C3—181no—
1062C3—181no—
1063C3—181no—
1064C3C2×C3⋊(C3⋊((C3⋊D3)⋊C3))11yescharacteristic
1065C2—812no—
1066C2#1309165111yescharacteristic, direct product factor
subgroupG/H
center, socle, hypercenterC2×C3C3⋊(C3⋊((C3⋊D3)⋊C3))
commutator, cosocle, hypocenterH(5,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624931C2
prime radicalC2×#92404C3
LCSG ▷ H(5,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #13091651C2direct (N × H)
2. C2×#10624931C2semidirect
17. #10624931C22semidirect
20. C2×C3×#737D3semidirect
35. C2×C3×#731D3semidirect
36. C2×C3×#731D3semidirect
37. C2×C3×#731D3semidirect
38. C2×C3×#731D3semidirect
39. C2×C3×#731D3semidirect
40. C2×C3×#731D3semidirect
41. C2×C3×#731D3semidirect
42. C2×C3×#731D3semidirect
43. C2×C3×#731D3semidirect
44. C2×C3×#731D3semidirect
45. C2×C3×#731D3semidirect
46. C2×C3×#731D3semidirect
105. C3×#737C2×D3semidirect
118. C3×#731C2×D3semidirect
119. C3×#731C2×D3semidirect
120. C3×#731C2×D3semidirect
121. C3×#731C2×D3semidirect
122. C3×#731C2×D3semidirect
123. C3×#731C2×D3semidirect
124. C3×#731C2×D3semidirect
125. C3×#731C2×D3semidirect
126. C3×#731C2×D3semidirect
127. C3×#731C2×D3semidirect
128. C3×#731C2×D3semidirect
129. C3×#731C2×D3semidirect
186. C2×C32×C9C3⋊D3semidirect
187. C2×C32×C9C3⋊D3semidirect
188. C2×C32×C9C3⋊D3semidirect
189. C2×C32×C9C3⋊D3semidirect
261. C2×#731C3⋊D3semidirect
262. C2×#731C3⋊D3semidirect
263. C2×#731C3⋊D3semidirect
264. C2×#731C3⋊D3semidirect
265. C2×#731C3⋊D3semidirect
266. C2×#731C3⋊D3semidirect
267. C2×#731C3⋊D3semidirect
268. C2×#731C3⋊D3semidirect
269. C2×#731C3⋊D3semidirect
406. C32×C9C2×C3⋊D3semidirect
407. C32×C9C2×C3⋊D3semidirect
408. C32×C9C2×C3⋊D3semidirect
409. C32×C9C2×C3⋊D3semidirect
446. #731C2×C3⋊D3semidirect
447. #731C2×C3⋊D3semidirect
448. #731C2×C3⋊D3semidirect
449. #731C2×C3⋊D3semidirect
450. #731C2×C3⋊D3semidirect
451. #731C2×C3⋊D3semidirect
452. #731C2×C3⋊D3semidirect
453. #731C2×C3⋊D3semidirect
454. #731C2×C3⋊D3semidirect
1066. C2#13091651direct (N × H)

Maximal subgroups

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

subgroupindex
#130916512
C2×#106249312
C2×#924043
C2×C3⋊#42083
C2×C3⋊#41763