Finite Group Databasebeta

← C3×#75836 #11806092

Subgroups — C3×#75836 #11806092

Order 1152.

1951 conjugacy classes of subgroups.

The subgroup lattice has 1107 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic
3C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×C4×D12C211yesmaximal, characteristic, complemented
6C32×#388C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8C3×#4957C211yesmaximal, characteristic, complemented
9C3×#4956C211yesmaximal, characteristic, complemented
10C3×#4951C211yesmaximal, characteristic, complemented
11C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12C3×#4668C211yesmaximal, characteristic, complemented
13C3×#4666C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2358—31nomaximal
17#75836C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C42C2211yescharacteristic, complemented
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×C4×Dic3C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#893—24no—
48C3×#882C418yescomplemented
49C3×D3×C22⋊C4—24no—
50C3×D3×C22⋊C4—24no—
51C3×C4×D12—24no—
52C32×#95C2211yescharacteristic, complemented
53C32×#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C3×C3⋊#95C2211yescharacteristic, complemented
58C2×C3×#120—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C22×C3×C22⋊C4—31no—
62C22×C3×C22⋊C4—31no—
63C2×#893C2×C311yescharacteristic, complemented
64C2×#882C2×C311yescharacteristic
65C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
66C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
67C2×C4×D12C2×C311yescharacteristic, complemented
68C3×#390—31no—
69C3×#388—21no—
70C3×#388—31no—
71C3×#388D311yescharacteristic, complemented
72C3×#388C2×C311yescharacteristic, complemented
73C3×#386—31no—
74C3×#386—31no—
75C3×#386—31no—
76C3×#385—31no—
77C3×#385—31no—
78C3×C4×C22⋊C4—31no—
79C3×C4×C22⋊C4—31no—
80#4989C2×C311yescharacteristic, complemented
81#4957C2×C311yescharacteristic, complemented
82#4956C2×C311yescharacteristic, complemented
83#4951C2×C311yescharacteristic, complemented
84C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
85#4668C2×C311yescharacteristic, complemented
86#4666C2×C311yescharacteristic, complemented
87#4665C2×C311yescharacteristic, complemented
88#4665C2×C311yescharacteristic, complemented
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2×C414yescomplemented
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C23×C3×D3C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C2×C3×#67—41no—
107C2×C3×#67—41no—
108C2×C3×#67C2×C414yescomplemented
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×D12—22no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×D12C2×C414yescomplemented
119C2×C3×D12C2×C414yescomplemented
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—22no—
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—41no—
131C2×C3×C4×D3—41no—
132C2×C3×C4×D3—41no—
133C2×C3×C4×D3—41no—
134C2×C3×C4×D3—41no—
135C32×C4⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4—22no—
138C32×C22⋊C4C2×C414yescomplemented
139C32×C42—22no—
140C3×#217—22no—
141C3×#217—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—41no—
147C3×(C2×D3)⋊C4C2×C414yescomplemented
148C3×(C2×D3)⋊C4C2×C414yescomplemented
149C3×(C2×D3)⋊C4D414yescomplemented
150C3×(C2×D3)⋊C4D414yescomplemented
151C3×C4⋊Dic3—22no—
152C3×Dic3⋊C4—41no—
153C3×C4×Dic3—22no—
154C3×C4×Dic3—41no—
155#2358—31noSylow
156C25×C3—31no—
157C24×D3C22×C311yescharacteristic
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C22×#67C22×C311yescharacteristic
167C22×D12C22×C311yescharacteristic
168C22×D12C22×C311yescharacteristic
169C22×C4×D3C22×C311yescharacteristic
170C22×C4×D3C22×C311yescharacteristic
171C22×C4×D3C22×C311yescharacteristic
172C22×C4×D3C22×C311yescharacteristic
173C22×C4×D3C22×C311yescharacteristic, complemented
174C3×#120—38no—
175C3×C4×D4—64no—
176C3×C4×D4—64no—
177C2×C3×C4⋊C4—21no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
181C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
182C2×C3×C22⋊C4—21no—
183C2×C3×C22⋊C4—21no—
184C2×C3×C22⋊C4—21no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—64no—
197C2×C3×C22⋊C4—64no—
198C2×C3×C22⋊C4C2×D311yescharacteristic
199C2×C3×C22⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4C2×D311yescharacteristic
201C2×C3×C22⋊C4C22×C311yescharacteristic
202C2×C3×C22⋊C4C22×C311yescharacteristic
203C2×C3×C22⋊C4C22×C311yescharacteristic
204C2×C3×C42—21no—
205C2×C3×C42—31no—
206C2×C3×C42—31no—
207C2×C3×C42C2×D311yescharacteristic, complemented
208C2×C3×C42C22×C311yescharacteristic, complemented
209C2×#217C22×C311yescharacteristic
210C2×#217C22×C311yescharacteristic
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×(C2×D3)⋊C4C22×C311yescharacteristic
216C2×(C2×D3)⋊C4C22×C311yescharacteristic
217C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
218C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
219C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
220C2×C4⋊Dic3C22×C311yescharacteristic, complemented
221C2×Dic3⋊C4C22×C311yescharacteristic, complemented
222C2×C4×Dic3C22×C311yescharacteristic, complemented
223C2×C4×Dic3C22×C311yescharacteristic, complemented
224#893—24no—
225#882C3×C418yescomplemented
226D3×C22⋊C4—24no—
227D3×C22⋊C4—24no—
228C4×D12—24no—
229C3×#95—21no—
230C3×#95—21no—
231C3×#95—31no—
232C3×#95—31no—
233C3×#95—31no—
234C3×#95—31no—
235C3×#95C2×D311yescharacteristic, complemented
236C3×#95C2×D311yescharacteristic, complemented
237C3×#95C22×C311yescharacteristic, complemented
238C3×#95C22×C311yescharacteristic, complemented
239C3⋊#95C22×C311yescharacteristic, complemented
240C3⋊#95C22×C311yescharacteristic, complemented
241C3⋊#95C22×C311yescharacteristic, complemented
242C3⋊#95C22×C311yescharacteristic, complemented
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C22×C412yes—
250C23×C32C2411yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—28no—
266C22×C3×D3—28no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3—44no—
270C22×C3×D3—44no—
271C22×C3×D3—44no—
272C22×C3×D3C22×C412yes—
273C22×C3×D3C22×C412yes—
274C22×C3×D3C22×C412yes—
275C22×C3×D3C2×D412yes—
276C22×C3×D3C2×D412yes—
277C22×C3×D3#4112yes—
278C22×C3×D3#4112yes—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C22×C412yes—
294C2×C32×C4C22×C412yes—
295C2×C32×C4C2×D412yes—
296C2×C32×C4C2×D412yes—
297C3×#67—44no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C22×C412yes—
311C2×C3×Dic3C2×D412yes—
312C2×C3×Dic3C2×D412yes—
313C3×D12—28no—
314C3×D12—28no—
315C3×C4×D3—44no—
316C3×C4×D3—44no—
317C3×C4×D3—44no—
318C3×C4×D3—44no—
319C3×C4×D3—44no—
320C2×#120—31no—
321C2×C4×D4—31no—
322C2×C4×D4—31no—
323C22×C22⋊C4—31no—
324C22×C22⋊C4—31no—
325#390—31no—
326#388—31no—
327#388C3×D311yescharacteristic, complemented
328#386—31no—
329#386—31no—
330#386—31no—
331#385—31no—
332#385—31no—
333C4×C22⋊C4—31no—
334C4×C22⋊C4—31no—
335C24×C3—21no—
336C24×C3—31no—
337C24×C3—31no—
338C24×C3—31no—
339C24×C3—34no—
340C24×C3—62no—
341C24×C3—62no—
342C24×C3—62no—
343C24×C3—62no—
344C24×C3—121no—
345C24×C3—121no—
346C24×C3C22×D311yescharacteristic
347C24×C3C23×C311yescharacteristic
348C23×D3—22no—
349C23×D3—22no—
350C23×D3—22no—
351C23×D3—22no—
352C23×D3—41no—
353C23×D3—41no—
354C23×D3C2×C3×C414yescomplemented
355C23×D3C23×C311yescharacteristic
356C23×D3C23×C311yescharacteristic
357C23×D3C23×C311yescharacteristic
358C2×C3×D4—34no—
359C2×C3×D4—34no—
360C2×C3×D4—34no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—121no—
366C2×C3×D4—121no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—62no—
382C22×C3×C4—62no—
383C22×C3×C4—62no—
384C22×C3×C4—62no—
385C22×C3×C4—62no—
386C22×C3×C4—62no—
387C22×C3×C4—62no—
388C22×C3×C4—121no—
389C22×C3×C4—121no—
390C22×C3×C4—121no—
391C22×C3×C4—121no—
392C22×C3×C4—121no—
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C23×C311yescharacteristic
400C22×C3×C4C23×C311yescharacteristic
401C22×C3×C4C23×C311yescharacteristic
402C22×C3×C4C23×C311yescharacteristic
403C22×C3×C4C23×C311yescharacteristic
404C22×C3×C4C23×C311yescharacteristic
405C2×#67—41no—
406C2×#67—41no—
407C2×#67C2×C3×C414yescomplemented
408C22×Dic3C23×C311yescharacteristic
409C22×Dic3C23×C311yescharacteristic
410C22×Dic3C23×C311yescharacteristic
411C22×Dic3C23×C311yescharacteristic
412C22×Dic3C23×C311yescharacteristic
413C2×D12—22no—
414C2×D12—22no—
415C2×D12—22no—
416C2×D12—22no—
417C2×D12C2×C3×C414yescomplemented
418C2×D12C2×C3×C414yescomplemented
419C2×C4×D3—22no—
420C2×C4×D3—22no—
421C2×C4×D3—22no—
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—22no—
428C2×C4×D3—22no—
429C2×C4×D3—41no—
430C2×C4×D3—41no—
431C2×C4×D3—41no—
432C2×C4×D3—41no—
433C2×C4×D3—41no—
434C3×C4⋊C4—22no—
435C3×C4⋊C4—22no—
436C3×C4⋊C4—42no—
437C3×C4⋊C4—62no—
438C3×C4⋊C4—121no—
439C3×C22⋊C4—22no—
440C3×C22⋊C4—22no—
441C3×C22⋊C4—22no—
442C3×C22⋊C4—22no—
443C3×C22⋊C4—24no—
444C3×C22⋊C4—34no—
445C3×C22⋊C4—34no—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—42no—
449C3×C22⋊C4—42no—
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—121no—
457C3×C22⋊C4C4×D314yescomplemented
458C3×C22⋊C4C2×C3×C414yescomplemented
459C3×C42—22no—
460C3×C42—22no—
461C3×C42—42no—
462C3×C42—62no—
463C3×C42—121no—
464#217—22no—
465#217—22no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—41no—
471(C2×D3)⋊C4C2×C3×C414yescomplemented
472(C2×D3)⋊C4C2×C3×C414yescomplemented
473(C2×D3)⋊C4C3×D414yescomplemented
474(C2×D3)⋊C4C3×D414yescomplemented
475C4⋊Dic3—22no—
476Dic3⋊C4—41no—
477C4×Dic3—22no—
478C4×Dic3—41no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32C23×C411yescharacteristic
487C22×C32C22×D411yescharacteristic
488C22×C32C22×D411yescharacteristic
489C22×C32C2×#4111yescharacteristic
490C22×C32C2×#4111yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C22×C32H(5,𝔽2)11yescharacteristic
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—416no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C2×C3×D3C4×D414yescomplemented
514C2×C3×D3C4×D414yescomplemented
515C32×C4—22no—
516C32×C4—22no—
517C32×C4—22no—
518C32×C4—22no—
519C32×C4—41no—
520C32×C4—41no—
521C3×Dic3—22no—
522C3×Dic3—22no—
523C3×Dic3—22no—
524C3×Dic3—41no—
525C3×Dic3—41no—
526C25—31no—
527C22×D4—31no—
528C22×D4—31no—
529C22×D4—31no—
530C23×C4—31no—
531C23×C4—31no—
532C23×C4—31no—
533C23×C4—31no—
534C23×C4—31no—
535#120—38no—
536C4×D4—64no—
537C4×D4—64no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—64no—
553C2×C22⋊C4—64no—
554C2×C22⋊C4C2×C3×D311yescharacteristic
555C2×C22⋊C4C2×C3×D311yescharacteristic
556C2×C22⋊C4C2×C3×D311yescharacteristic
557C2×C42—31no—
558C2×C42—31no—
559C2×C42C2×C3×D311yescharacteristic, complemented
560#95—31no—
561#95—31no—
562#95—31no—
563#95—31no—
564#95C2×C3×D311yescharacteristic, complemented
565#95C2×C3×D311yescharacteristic, complemented
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—22no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—68no—
594C23×C3—68no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—124no—
612C23×C3—124no—
613C23×C3—124no—
614C23×C3C2×C4×D312yes—
615C23×C3C22×C3×C412yes—
616C23×C3C23×D311yescharacteristic
617C23×C3C24×C311yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—28no—
633C22×D3—28no—
634C22×D3—44no—
635C22×D3—44no—
636C22×D3—44no—
637C22×D3—44no—
638C22×D3—44no—
639C22×D3C22×C3×C412yes—
640C22×D3C22×C3×C412yes—
641C22×D3C22×C3×C412yes—
642C22×D3C2×C3×D412yes—
643C22×D3C2×C3×D412yes—
644C22×D3C3×#4112yes—
645C22×D3C3×#4112yes—
646C3×D4—68no—
647C3×D4—68no—
648C3×D4—124no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—124no—
711C2×C3×C4—124no—
712C2×C3×C4—124no—
713C2×C3×C4—124no—
714C2×C3×C4—124no—
715C2×C3×C4C2×C4×D312yes—
716C2×C3×C4C2×C4×D312yes—
717C2×C3×C4D3×D412yes—
718C2×C3×C4D3×D412yes—
719C2×C3×C4C22×C3×C412yes—
720C2×C3×C4C22×C3×C412yes—
721C2×C3×C4C2×C3×D412yes—
722C2×C3×C4C2×C3×D412yes—
723#67—44no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3C22×C3×C412yes—
737C2×Dic3C2×C3×D412yes—
738C2×Dic3C2×C3×D412yes—
739D12—28no—
740D12—28no—
741C4×D3—44no—
742C4×D3—44no—
743C4×D3—44no—
744C4×D3—44no—
745C4×D3—44no—
746C2×C32—42no—
747C2×C32C2×C4×D411yescharacteristic
748C2×C32C2×C4×D411yescharacteristic
749C2×C32#51811yescharacteristic
750C2×C32D4211yescharacteristic
751C2×C32#54611yescharacteristic
752C2×C32#54611yescharacteristic
753C2×C32#55111yescharacteristic
754C3×D3—24no—
755C3×D3—24no—
756C3×D3—42no—
757C24—31no—
758C24—31no—
759C24—31no—
760C24—34no—
761C24—62no—
762C24—62no—
763C24—62no—
764C24—62no—
765C24—121no—
766C24—121no—
767C24C22×C3×D311yescharacteristic
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—121no—
776C2×D4—121no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—62no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—62no—
791C22×C4—62no—
792C22×C4—121no—
793C22×C4—121no—
794C22×C4—121no—
795C22×C4—121no—
796C22×C4—121no—
797C22×C4C22×C3×D311yescharacteristic
798C22×C4C22×C3×D311yescharacteristic
799C22×C4C22×C3×D311yescharacteristic
800C22×C4C22×C3×D311yescharacteristic
801C22×C4C22×C3×D311yescharacteristic
802C22×C4C22×C3×D311yescharacteristic
803C4⋊C4—22no—
804C4⋊C4—62no—
805C4⋊C4—121no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—34no—
809C22⋊C4—34no—
810C22⋊C4—34no—
811C22⋊C4—34no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—62no—
817C22⋊C4—62no—
818C22⋊C4—121no—
819C22⋊C4C3×C4×D314yescomplemented
820C42—22no—
821C42—62no—
822C42—121no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—34no—
837C22×C3—34no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—81no—
865C22×C3—81no—
866C22×C3—81no—
867C22×C3—81no—
868C22×C3—1216no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3C22×C4×D311yescharacteristic
874C22×C3C2×D3×D411yescharacteristic
875C22×C3C2×D3×D411yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3#100911yescharacteristic
879C22×C3#100911yescharacteristic
880C22×C3C23×C3×C411yescharacteristic
881C22×C3C22×C3×D411yescharacteristic
882C22×C3C22×C3×D411yescharacteristic
883C22×C3C2×C3×#4111yescharacteristic
884C22×C3C2×C3×#4111yescharacteristic
885C22×C3C3×H(5,𝔽2)11yescharacteristic
886C22×C3C3×H(5,𝔽2)11yescharacteristic
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—22no—
897C2×D3—22no—
898C2×D3—22no—
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—22no—
902C2×D3—416no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C2×D3—41no—
907C2×D3C3×C4×D414yescomplemented
908C2×D3C3×C4×D414yescomplemented
909C3×C4—22no—
910C3×C4—22no—
911C3×C4—22no—
912C3×C4—22no—
913C3×C4—22no—
914C3×C4—22no—
915C3×C4—22no—
916C3×C4—22no—
917C3×C4—42no—
918C3×C4—42no—
919C3×C4—42no—
920C3×C4—42no—
921C3×C4—41no—
922C3×C4—41no—
923C3×C4—41no—
924C3×C4—41no—
925C3×C4—62no—
926C3×C4—62no—
927C3×C4—62no—
928C3×C4—81no—
929C3×C4—81no—
930C3×C4—121no—
931C3×C4—121no—
932Dic3—22no—
933Dic3—22no—
934Dic3—22no—
935Dic3—41no—
936Dic3—41no—
937C32#235811yescharacteristic, complemented, Sylow
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—32no—
945C23—32no—
946C23—32no—
947C23—32no—
948C23—32no—
949C23—32no—
950C23—32no—
951C23—68no—
952C23—68no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—61no—
966C23—61no—
967C23—124no—
968C23—124no—
969C23—124no—
970C23—124no—
971C23—124no—
972C23C2×C3×C4×D312yes—
973C23C23×C3×D311yescharacteristic
974D4—68no—
975D4—68no—
976D4—124no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—32no—
992C2×C4—32no—
993C2×C4—32no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—124no—
1007C2×C4—124no—
1008C2×C4—124no—
1009C2×C4—124no—
1010C2×C4—124no—
1011C2×C4C2×C3×C4×D312yes—
1012C2×C4C2×C3×C4×D312yes—
1013C2×C4C3×D3×D412yes—
1014C2×C4C3×D3×D412yes—
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—42no—
1023C2×C3—42no—
1024C2×C3—64no—
1025C2×C3—64no—
1026C2×C3—82no—
1027C2×C3—122no—
1028C2×C3#552111yescharacteristic
1029C2×C3C4×D3×D411yescharacteristic
1030C2×C3C4×D3×D411yescharacteristic
1031C2×C3#560911yescharacteristic
1032C2×C3#565411yescharacteristic
1033C2×C3#567611yescharacteristic
1034C2×C3#570511yescharacteristic
1035C2×C3C2×C3×C4×D411yescharacteristic
1036C2×C3C2×C3×C4×D411yescharacteristic
1037C2×C3C3×#51811yescharacteristic
1038C2×C3C3×D4211yescharacteristic
1039C2×C3C3×#54611yescharacteristic
1040C2×C3C3×#54611yescharacteristic
1041C2×C3C3×#55111yescharacteristic
1042D3—24no—
1043D3—24no—
1044D3—42no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—34no—
1049C22—34no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—62no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—62no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—1216no—
1070C22—121no—
1071C22—121no—
1072C22—121no—
1073C22—121no—
1074C22C22×C3×C4×D311yescharacteristic
1075C22C2×C3×D3×D411yescharacteristic
1076C22C2×C3×D3×D411yescharacteristic
1077C22C3×D3×#4111yescharacteristic
1078C22C3×D3×#4111yescharacteristic
1079C22C3×#100911yescharacteristic
1080C22C3×#100911yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—41no—
1086C4—41no—
1087C4—62no—
1088C4—62no—
1089C4—62no—
1090C4—121no—
1091C4—121no—
1092C3—21no—
1093C3#7583611yescharacteristic, direct product factor
1094C3C3×#235811yescharacteristic, complemented
1095C2—42no—
1096C2—64no—
1097C2—64no—
1098C2—122no—
1099C2C3×#552111yescharacteristic
1100C2C3×C4×D3×D411yescharacteristic
1101C2C3×C4×D3×D411yescharacteristic
1102C2C3×#560911yescharacteristic
1103C2C3×#565411yescharacteristic
1104C2C3×#567611yescharacteristic
1105C2C3×#570511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC2×C3×#882C2
cosocleC23×C3C24×C3
hypercenterC3×#388D3
hypocenterC3C3×#2358
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
3. C2×C3×D3×C22⋊C4C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C2×C3×C4×D12C2semidirect
6. C32×#388C2semidirect
7. C3×#4989C2semidirect
8. C3×#4957C2semidirect
9. C3×#4956C2semidirect
10. C3×#4951C2semidirect
11. C3×C4×(C2×D3)⋊C4C2semidirect
12. C3×#4668C2semidirect
13. C3×#4666C2semidirect
14. C3×#4665C2semidirect
15. C3×#4665C2semidirect
17. #75836C3direct (N × H)
26. C22×C3×C4×D3C22semidirect
27. C2×C32×C4⋊C4C22semidirect
31. C2×C32×C42C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×C4×Dic3C22semidirect
46. C2×C3×C4×Dic3C22semidirect
48. C3×#882C4semidirect
52. C32×#95C22semidirect
53. C32×#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
63. C2×#893C2×C3semidirect
65. C2×D3×C22⋊C4C2×C3semidirect
66. C2×D3×C22⋊C4C2×C3semidirect
67. C2×C4×D12C2×C3semidirect
71. C3×#388D3semidirect
72. C3×#388C2×C3semidirect
80. #4989C2×C3semidirect
81. #4957C2×C3semidirect
82. #4956C2×C3semidirect
83. #4951C2×C3semidirect
84. C4×(C2×D3)⋊C4C2×C3semidirect
85. #4668C2×C3semidirect
86. #4666C2×C3semidirect
87. #4665C2×C3semidirect
88. #4665C2×C3semidirect
96. C23×C3×D3C2×C4semidirect
108. C2×C3×#67C2×C4semidirect
118. C2×C3×D12C2×C4semidirect
119. C2×C3×D12C2×C4semidirect
138. C32×C22⋊C4C2×C4semidirect
147. C3×(C2×D3)⋊C4C2×C4semidirect
148. C3×(C2×D3)⋊C4C2×C4semidirect
149. C3×(C2×D3)⋊C4D4semidirect
150. C3×(C2×D3)⋊C4D4semidirect
173. C22×C4×D3C22×C3semidirect
180. C2×C3×C4⋊C4C2×D3semidirect
181. C2×C3×C4⋊C4C22×C3semidirect
207. C2×C3×C42C2×D3semidirect
208. C2×C3×C42C22×C3semidirect
217. C2×(C2×D3)⋊C4C22×C3semidirect
218. C2×(C2×D3)⋊C4C22×C3semidirect
219. C2×(C2×D3)⋊C4C22×C3semidirect
220. C2×C4⋊Dic3C22×C3semidirect
221. C2×Dic3⋊C4C22×C3semidirect
222. C2×C4×Dic3C22×C3semidirect
223. C2×C4×Dic3C22×C3semidirect
225. #882C3×C4semidirect
235. C3×#95C2×D3semidirect
236. C3×#95C2×D3semidirect
237. C3×#95C22×C3semidirect
238. C3×#95C22×C3semidirect
239. C3⋊#95C22×C3semidirect
240. C3⋊#95C22×C3semidirect
241. C3⋊#95C22×C3semidirect
242. C3⋊#95C22×C3semidirect
327. #388C3×D3semidirect
354. C23×D3C2×C3×C4semidirect
407. C2×#67C2×C3×C4semidirect
417. C2×D12C2×C3×C4semidirect
418. C2×D12C2×C3×C4semidirect
457. C3×C22⋊C4C4×D3semidirect
458. C3×C22⋊C4C2×C3×C4semidirect
471. (C2×D3)⋊C4C2×C3×C4semidirect
472. (C2×D3)⋊C4C2×C3×C4semidirect
473. (C2×D3)⋊C4C3×D4semidirect
474. (C2×D3)⋊C4C3×D4semidirect
513. C2×C3×D3C4×D4semidirect
514. C2×C3×D3C4×D4semidirect
540. C2×C4⋊C4C2×C3×D3semidirect
559. C2×C42C2×C3×D3semidirect
564. #95C2×C3×D3semidirect
565. #95C2×C3×D3semidirect
819. C22⋊C4C3×C4×D3semidirect
907. C2×D3C3×C4×D4semidirect
908. C2×D3C3×C4×D4semidirect
937. C32#2358semidirect
1093. C3#75836direct (N × H)
1094. C3C3×#2358semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#8822
C2×C3×D3×C22⋊C42
C2×C3×C4×D122
C32×#3882
C3×#49892
C3×#49572
C3×#49562
C3×#49512
C3×C4×(C2×D3)⋊C42
C3×#46682
C3×#46662
C3×#46652
C3×#23583
#758363