Finite Group Databasebeta

← C3×#75306 #11805739

Subgroups — C3×#75306 #11805739

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C32×#387C211yesmaximal, characteristic, complemented
3C3×#4990C211yesmaximal, characteristic, complemented
4C3×#4987C211yesmaximal, characteristic, complemented
5C3×#4980C211yesmaximal, characteristic, complemented
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8C3×#4670C211yesmaximal, characteristic, complemented
9C3×#4666C211yesmaximal, characteristic, complemented
10C3×#4665C211yesmaximal, characteristic
11C3×#4665C211yesmaximal, characteristic
12C3×#4664C211yesmaximal, characteristic, complemented
13C3×D3×#95C211yesmaximal, characteristic, complemented
14C3×#4651C211yesmaximal, characteristic, complemented
15C3×#4648C211yesmaximal, characteristic, complemented
16C3×#2353—31nomaximal
17#75306C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#893C418yescomplemented
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C2×C3×C4×D4—31no—
55C2×#893C2×C311yescharacteristic
56C3×#388—31no—
57C3×#388—31no—
58C3×#387—21no—
59C3×#387—31no—
60C3×#387D311yescharacteristic, complemented
61C3×#387C2×C311yescharacteristic, complemented
62C3×#386—31no—
63C3×#386—31no—
64C3×#383—31no—
65C3×#381—31no—
66C3×#380—31no—
67C3×C4×C22⋊C4—31no—
68C3×C4×C22⋊C4—31no—
69C3×C4×C22⋊C4—31no—
70C3×#376—31no—
71C2×C3×#95—31no—
72#4990C2×C311yescharacteristic, complemented
73#4987C2×C311yescharacteristic, complemented
74#4980C2×C311yescharacteristic, complemented
75C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
76C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
77#4670C2×C311yescharacteristic, complemented
78#4666C2×C311yescharacteristic, complemented
79#4665C2×C311yescharacteristic
80#4665C2×C311yescharacteristic
81#4664C2×C311yescharacteristic, complemented
82D3×#95C2×C311yescharacteristic, complemented
83#4651C2×C311yescharacteristic, complemented
84#4648C2×C311yescharacteristic, complemented
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×D12—22no—
101C2×C3×D12—22no—
102C2×C3×D12C2×C414yes—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—41no—
108C2×C3×C4×D3—41no—
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3C2×C414yes—
114C2×C3×C4×D3C2×C414yescomplemented
115C32×C4⋊C4—41no—
116C32×C4⋊C4C2×C414yescomplemented
117C32×C42—41no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—22no—
122C3×(C2×D3)⋊C4—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4C2×C414yes—
125C3×(C2×D3)⋊C4C2×C414yescomplemented
126C3×C4⋊Dic3—41no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—22no—
129C3×C4×Dic3—41no—
130C3×C4×Dic3C2×C414yescomplemented
131#2353—31noSylow
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C23×C3×C4—31no—
137C22×D12C22×C311yescharacteristic
138C22×C4×D3C22×C311yescharacteristic
139C22×C4×D3C22×C311yescharacteristic
140C22×C4×D3C22×C311yescharacteristic
141C22×C4×D3C22×C311yescharacteristic
142C3×C4×D4—38no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C4⋊C4C2×D311yescharacteristic
148C2×C3×C4⋊C4C22×C311yescharacteristic
149C2×C3×C4⋊C4C22×C311yescharacteristic
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C42—21no—
159C2×C3×C42—31no—
160C2×C3×C42—31no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42C2×D311yescharacteristic
164C2×C3×C42C22×C311yescharacteristic
165C2×(C2×D3)⋊C4C22×C311yescharacteristic
166C2×(C2×D3)⋊C4C22×C311yescharacteristic
167C2×(C2×D3)⋊C4C22×C311yescharacteristic
168C2×(C2×D3)⋊C4C22×C311yescharacteristic
169C2×(C2×D3)⋊C4C22×C311yescharacteristic
170C2×(C2×D3)⋊C4C22×C311yescharacteristic
171C2×(C2×D3)⋊C4C22×C311yescharacteristic
172C2×(C2×D3)⋊C4C22×C311yescharacteristic
173C2×C4⋊Dic3C22×C311yescharacteristic
174C2×C4×Dic3C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176C2×C4×Dic3C22×C311yescharacteristic
177C2×C4×Dic3C22×C311yescharacteristic
178#893C3×C418yescomplemented
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C3×#95—21no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95C2×D311yescharacteristic
194C3×#95C2×D311yescharacteristic
195C3×#95C2×D311yescharacteristic
196C3×#95C2×D311yescharacteristic
197C3×#95C22×C311yescharacteristic
198C3×#95C22×C311yescharacteristic
199C3×#95C22×C311yescharacteristic
200C3×#95C22×C311yescharacteristic
201C3⋊#95C22×C311yescharacteristic
202C3⋊#95C22×C311yescharacteristic
203C3⋊#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C3⋊#95C22×C311yescharacteristic
206C3⋊#95C22×C311yescharacteristic
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C23×C32C2411yescharacteristic
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3C22×C412yes—
223C22×C3×D3C22×C412yes—
224C22×C3×D3#4112yes—
225C22×C3×D3#4112yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C22×C412yes—
244C2×C32×C4C22×C412yes—
245C2×C32×C4C22×C412yes—
246C2×C32×C4#4112yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3#4112yes—
265C3×D12—28no—
266C3×C4×D3—44no—
267C3×C4×D3—44no—
268C3×C4×D3—44no—
269C3×C4×D3—44no—
270C2×C4×D4—31no—
271#388—31no—
272#388—31no—
273#387—31no—
274#387C3×D311yescharacteristic, complemented
275#386—31no—
276#386—31no—
277#383—31no—
278#381—31no—
279#380—31no—
280C4×C22⋊C4—31no—
281C4×C22⋊C4—31no—
282C4×C22⋊C4—31no—
283#376—31no—
284C2×#95—31no—
285C24×C3—31no—
286C24×C3—31no—
287C23×D3C23×C311yescharacteristic
288C23×D3C23×C311yescharacteristic
289C2×C3×D4—34no—
290C2×C3×D4—62no—
291C2×C3×D4—62no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—34no—
303C22×C3×C4—34no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—62no—
308C22×C3×C4—62no—
309C22×C3×C4—62no—
310C22×C3×C4—62no—
311C22×C3×C4—121no—
312C22×C3×C4—121no—
313C22×C3×C4—121no—
314C22×C3×C4—121no—
315C22×C3×C4—121no—
316C22×C3×C4—121no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C23×C311yescharacteristic
325C22×C3×C4C23×C311yescharacteristic
326C22×C3×C4C23×C311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C22×C3×C4C23×C311yescharacteristic
329C22×C3×C4C23×C311yescharacteristic
330C22×C3×C4C23×C311yescharacteristic
331C22×Dic3C23×C311yescharacteristic
332C22×Dic3C23×C311yescharacteristic
333C22×Dic3C23×C311yescharacteristic
334C22×Dic3C23×C311yescharacteristic
335C22×Dic3C23×C311yescharacteristic
336C22×Dic3C23×C311yescharacteristic
337C2×D12—22no—
338C2×D12—22no—
339C2×D12C2×C3×C414yes—
340C2×C4×D3—22no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—41no—
345C2×C4×D3—41no—
346C2×C4×D3—41no—
347C2×C4×D3—41no—
348C2×C4×D3—41no—
349C2×C4×D3—41no—
350C2×C4×D3C2×C3×C414yes—
351C2×C4×D3C2×C3×C414yescomplemented
352C3×C4⋊C4—24no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—42no—
356C3×C4⋊C4—121no—
357C3×C4⋊C4C4×D314yescomplemented
358C3×C4⋊C4C2×C3×C414yescomplemented
359C3×C22⋊C4—34no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—62no—
362C3×C22⋊C4—62no—
363C3×C22⋊C4—62no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—121no—
366C3×C22⋊C4—121no—
367C3×C42—34no—
368C3×C42—41no—
369C3×C42—41no—
370C3×C42—42no—
371C3×C42—62no—
372C3×C42—62no—
373C3×C42—121no—
374(C2×D3)⋊C4—22no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—22no—
378(C2×D3)⋊C4—41no—
379(C2×D3)⋊C4—41no—
380(C2×D3)⋊C4C2×C3×C414yes—
381(C2×D3)⋊C4C2×C3×C414yescomplemented
382C4⋊Dic3—41no—
383C4×Dic3—22no—
384C4×Dic3—22no—
385C4×Dic3—41no—
386C4×Dic3C2×C3×C414yescomplemented
387C22×C32C23×C411yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3#11714yes—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4—41no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C4×D4—38no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4C2×C3×D311yescharacteristic
429C2×C4⋊C4C2×C3×D311yescharacteristic
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C42—31no—
439C2×C42—31no—
440C2×C42—31no—
441C2×C42—31no—
442C2×C42C2×C3×D311yescharacteristic
443#95—31no—
444#95—31no—
445#95—31no—
446#95—31no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95C2×C3×D311yescharacteristic
454#95C2×C3×D311yescharacteristic
455#95C2×C3×D311yescharacteristic
456#95C2×C3×D311yescharacteristic
457C23×C3—21no—
458C23×C3—32no—
459C23×C3—32no—
460C23×C3—32no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3C23×D311yescharacteristic
473C23×C3C24×C311yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3C22×C3×C412yes—
485C22×D3C22×C3×C412yes—
486C22×D3C3×#4112yes—
487C22×D3C3×#4112yes—
488C3×D4—68no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—32no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—124no—
563C2×C3×C4—124no—
564C2×C3×C4—124no—
565C2×C3×C4—124no—
566C2×C3×C4C2×C4×D312yes—
567C2×C3×C4C2×C4×D312yes—
568C2×C3×C4C2×C4×D312yes—
569C2×C3×C4#23912yes—
570C2×C3×C4C22×C3×C412yes—
571C2×C3×C4C22×C3×C412yes—
572C2×C3×C4C22×C3×C412yes—
573C2×C3×C4C3×#4112yes—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3C22×C3×C412yes—
590C2×Dic3C22×C3×C412yes—
591C2×Dic3C3×#4112yes—
592D12—28no—
593C4×D3—44no—
594C4×D3—44no—
595C4×D3—44no—
596C4×D3—44no—
597C2×C32C2×#11711yescharacteristic
598C2×C32C4×#4111yescharacteristic
599C2×C32#51811yescharacteristic
600C2×C32#55111yescharacteristic
601C2×C32#55111yescharacteristic
602C2×C32#55311yescharacteristic
603C2×C32#55311yescharacteristic
604C3×D3—24no—
605C3×D3—42no—
606C24—31no—
607C24—31no—
608C2×D4—34no—
609C2×D4—62no—
610C2×D4—62no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—34no—
615C22×C4—34no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—121no—
624C22×C4—121no—
625C22×C4—121no—
626C22×C4—121no—
627C22×C4—121no—
628C22×C4—121no—
629C22×C4C22×C3×D311yescharacteristic
630C22×C4C22×C3×D311yescharacteristic
631C22×C4C22×C3×D311yescharacteristic
632C22×C4C22×C3×D311yescharacteristic
633C22×C4C22×C3×D311yescharacteristic
634C22×C4C22×C3×D311yescharacteristic
635C22×C4C22×C3×D311yescharacteristic
636C4⋊C4—41no—
637C4⋊C4—121no—
638C4⋊C4C3×C4×D314yescomplemented
639C22⋊C4—34no—
640C22⋊C4—34no—
641C22⋊C4—62no—
642C22⋊C4—62no—
643C22⋊C4—62no—
644C22⋊C4—62no—
645C22⋊C4—121no—
646C22⋊C4—121no—
647C42—34no—
648C42—41no—
649C42—62no—
650C42—62no—
651C42—121no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—34no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C22×C4×D311yescharacteristic
674C22×C3#100411yescharacteristic
675C22×C3C2×#23911yescharacteristic
676C22×C3D3×#4111yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3#100911yescharacteristic
680C22×C3C23×C3×C411yescharacteristic
681C22×C3C2×C3×#4111yescharacteristic
682C22×C3C2×C3×#4111yescharacteristic
683C22×C3C2×C3×#4111yescharacteristic
684C22×C3C2×C3×#4111yescharacteristic
685C22×C3C3×H(5,𝔽2)11yescharacteristic
686C22×C3C3×H(5,𝔽2)11yescharacteristic
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3C3×#11714yes—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—22no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—42no—
712C3×C4—42no—
713C3×C4—42no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4—81no—
724C3×C4—81no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—121no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734C32#235311yescharacteristic, complemented, Sylow
735C23—32no—
736C23—32no—
737C23—32no—
738C23—32no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23C23×C3×D311yescharacteristic
750D4—68no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—124no—
787C2×C4—124no—
788C2×C4—124no—
789C2×C4—124no—
790C2×C4C2×C3×C4×D312yes—
791C2×C4C2×C3×C4×D312yes—
792C2×C4C2×C3×C4×D312yes—
793C2×C4C3×#23912yes—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—64no—
802C2×C3—122no—
803C2×C3D3×#11711yescharacteristic
804C2×C3#554511yescharacteristic
805C2×C3C4×#23911yescharacteristic
806C2×C3#563711yescharacteristic
807C2×C3#566111yescharacteristic
808C2×C3#569511yescharacteristic
809C2×C3#570511yescharacteristic
810C2×C3C2×C3×#11711yescharacteristic
811C2×C3C3×C4×#4111yescharacteristic
812C2×C3C3×#51811yescharacteristic
813C2×C3C3×#55111yescharacteristic
814C2×C3C3×#55111yescharacteristic
815C2×C3C3×#55311yescharacteristic
816C2×C3C3×#55311yescharacteristic
817D3—24no—
818D3—42no—
819C22—34no—
820C22—62no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—62no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22C22×C3×C4×D311yescharacteristic
834C22C3×#100411yescharacteristic
835C22C2×C3×#23911yescharacteristic
836C22C3×D3×#4111yescharacteristic
837C22C3×D3×#4111yescharacteristic
838C22C3×D3×#4111yescharacteristic
839C22C3×#100911yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—62no—
848C4—62no—
849C4—62no—
850C4—121no—
851C4—121no—
852C4—121no—
853C3—21no—
854C3#7530611yescharacteristic, direct product factor
855C3C3×#235311yescharacteristic, complemented
856C2—64no—
857C2—122no—
858C2C3×D3×#11711yescharacteristic
859C2C3×#554511yescharacteristic
860C2C3×C4×#23911yescharacteristic
861C2C3×#563711yescharacteristic
862C2C3×#566111yescharacteristic
863C2C3×#569511yescharacteristic
864C2C3×#570511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#387C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC3×#387D3
hypocenterC3C3×#2353
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C32×#387C2semidirect
3. C3×#4990C2semidirect
4. C3×#4987C2semidirect
5. C3×#4980C2semidirect
6. C3×C4×(C2×D3)⋊C4C2semidirect
7. C3×C4×(C2×D3)⋊C4C2semidirect
8. C3×#4670C2semidirect
9. C3×#4666C2semidirect
12. C3×#4664C2semidirect
13. C3×D3×#95C2semidirect
14. C3×#4651C2semidirect
15. C3×#4648C2semidirect
17. #75306C3direct (N × H)
39. C3×#893C4semidirect
60. C3×#387D3semidirect
61. C3×#387C2×C3semidirect
72. #4990C2×C3semidirect
73. #4987C2×C3semidirect
74. #4980C2×C3semidirect
75. C4×(C2×D3)⋊C4C2×C3semidirect
76. C4×(C2×D3)⋊C4C2×C3semidirect
77. #4670C2×C3semidirect
78. #4666C2×C3semidirect
81. #4664C2×C3semidirect
82. D3×#95C2×C3semidirect
83. #4651C2×C3semidirect
84. #4648C2×C3semidirect
114. C2×C3×C4×D3C2×C4semidirect
116. C32×C4⋊C4C2×C4semidirect
125. C3×(C2×D3)⋊C4C2×C4semidirect
130. C3×C4×Dic3C2×C4semidirect
178. #893C3×C4semidirect
274. #387C3×D3semidirect
351. C2×C4×D3C2×C3×C4semidirect
357. C3×C4⋊C4C4×D3semidirect
358. C3×C4⋊C4C2×C3×C4semidirect
381. (C2×D3)⋊C4C2×C3×C4semidirect
386. C4×Dic3C2×C3×C4semidirect
638. C4⋊C4C3×C4×D3semidirect
734. C32#2353semidirect
854. C3#75306direct (N × H)
855. C3C3×#2353semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C32×#3872
C3×#49902
C3×#49872
C3×#49802
C3×C4×(C2×D3)⋊C42
C3×#46702
C3×#46662
C3×#46652
C3×#46642
C3×D3×#952
C3×#46512
C3×#46482
C3×#23533
#753063