Finite Group Databasebeta

← C3×#74980 #11808030

Subgroups — C3×#74980 #11808030

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#898C211yesmaximal, characteristic
2C32×#387C211yesmaximal, characteristic, complemented
3C3×#4989C211yesmaximal, characteristic
4C3×#4984C211yesmaximal, characteristic, complemented
5C3×#4975C211yesmaximal, characteristic, complemented
6C3×#4940C211yesmaximal, characteristic
7C3×#4928C211yesmaximal, characteristic, complemented
8C3×#4670C211yesmaximal, characteristic
9C3×#4669C211yesmaximal, characteristic
10C3×#4668C211yesmaximal, characteristic
11C3×#4668C211yesmaximal, characteristic
12C3×#4654C211yesmaximal, characteristic, complemented
13C3×#4652C211yesmaximal, characteristic, complemented
14C3×#4651C211yesmaximal, characteristic, complemented
15C3×#4647C211yesmaximal, characteristic, complemented
16C3×#2383—31nomaximal
17#74980C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#898C418yescomplemented
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C32×#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×#126—31no—
55C2×#898C2×C311yescharacteristic
56C3×#389—31no—
57C3×#389—31no—
58C3×#389—31no—
59C3×#388—31no—
60C3×#388—31no—
61C3×#388—31no—
62C3×#387—21no—
63C3×#387—31no—
64C3×#387—31no—
65C3×#387D311yescharacteristic, complemented
66C3×#387C2×C311yescharacteristic, complemented
67C3×#385—31no—
68C3×#385—31no—
69C3×#385—31no—
70C3×#384—31no—
71C3×#383—31no—
72#4989C2×C311yescharacteristic
73#4984C2×C311yescharacteristic, complemented
74#4975C2×C311yescharacteristic, complemented
75#4940C2×C311yescharacteristic
76#4928C2×C311yescharacteristic, complemented
77#4670C2×C311yescharacteristic
78#4669C2×C311yescharacteristic
79#4668C2×C311yescharacteristic
80#4668C2×C311yescharacteristic
81#4654C2×C311yescharacteristic, complemented
82#4652C2×C311yescharacteristic, complemented
83#4651C2×C311yescharacteristic, complemented
84#4647C2×C311yescharacteristic, complemented
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—41no—
101C2×C3×C4×D3—41no—
102C2×C3×C4×D3—41no—
103C32×C4⋊C4—41no—
104C32×C4⋊C4C2×C414yescomplemented
105C32×C42—41no—
106C3×(C2×D3)⋊C4—41no—
107C3×(C2×D3)⋊C4—41no—
108C3×(C2×D3)⋊C4—41no—
109C3×(C2×D3)⋊C4C2×C414yes—
110C3×(C2×D3)⋊C4C2×C414yes—
111C3×(C2×D3)⋊C4C2×C414yes—
112C3×C4⋊Dic3—41no—
113C3×C4⋊Dic3—41no—
114C3×C4⋊Dic3—41no—
115C3×C4⋊Dic3C2×C414yescomplemented
116C3×Dic3⋊C4—41no—
117C3×Dic3⋊C4—41no—
118C3×Dic3⋊C4—41no—
119C3×Dic3⋊C4—41no—
120C3×Dic3⋊C4—41no—
121C3×Dic3⋊C4C2×C414yescomplemented
122C3×C4×Dic3—41no—
123C3×C4×Dic3—41no—
124C3×C4×Dic3C2×C414yescomplemented
125#2383—31noSylow
126C23×C3×C4—31no—
127C22×C4×D3C22×C311yescharacteristic
128C3×#126—38no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4C2×D311yescharacteristic
142C2×C3×C4⋊C4C2×D311yescharacteristic
143C2×C3×C4⋊C4C22×C311yescharacteristic
144C2×C3×C4⋊C4C22×C311yescharacteristic
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C42—21no—
152C2×C3×C42—31no—
153C2×C3×C42—31no—
154C2×C3×C42—31no—
155C2×C3×C42C2×D311yescharacteristic
156C2×C3×C42C22×C311yescharacteristic
157C2×(C2×D3)⋊C4C22×C311yescharacteristic
158C2×(C2×D3)⋊C4C22×C311yescharacteristic
159C2×(C2×D3)⋊C4C22×C311yescharacteristic
160C2×(C2×D3)⋊C4C22×C311yescharacteristic
161C2×(C2×D3)⋊C4C22×C311yescharacteristic
162C2×(C2×D3)⋊C4C22×C311yescharacteristic
163C2×C4⋊Dic3C22×C311yescharacteristic
164C2×C4⋊Dic3C22×C311yescharacteristic
165C2×C4⋊Dic3C22×C311yescharacteristic
166C2×C4⋊Dic3C22×C311yescharacteristic
167C2×Dic3⋊C4C22×C311yescharacteristic
168C2×Dic3⋊C4C22×C311yescharacteristic
169C2×Dic3⋊C4C22×C311yescharacteristic
170C2×Dic3⋊C4C22×C311yescharacteristic
171C2×Dic3⋊C4C22×C311yescharacteristic
172C2×Dic3⋊C4C22×C311yescharacteristic
173C2×C4×Dic3C22×C311yescharacteristic
174C2×C4×Dic3C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176#898C3×C418yescomplemented
177C3×#95—21no—
178C3×#95—21no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95C2×D311yescharacteristic
190C3×#95C2×D311yescharacteristic
191C3×#95C2×D311yescharacteristic
192C3×#95C2×D311yescharacteristic
193C3×#95C22×C311yescharacteristic
194C3×#95C22×C311yescharacteristic
195C3×#95C22×C311yescharacteristic
196C3×#95C22×C311yescharacteristic
197C3⋊#95C22×C311yescharacteristic
198C3⋊#95C22×C311yescharacteristic
199C3⋊#95C22×C311yescharacteristic
200C3⋊#95C22×C311yescharacteristic
201C3⋊#95C22×C311yescharacteristic
202C3⋊#95C22×C311yescharacteristic
203C3⋊#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4C22×C412yes—
232C2×C32×C4C22×C412yes—
233C2×C32×C4C22×C412yes—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C3×C4×D3—44no—
256C2×#126—31no—
257#389—31no—
258#389—31no—
259#389—31no—
260#388—31no—
261#388—31no—
262#388—31no—
263#387—31no—
264#387—31no—
265#387C3×D311yescharacteristic, complemented
266#385—31no—
267#385—31no—
268#385—31no—
269#384—31no—
270#383—31no—
271C24×C3—31no—
272C23×D3C23×C311yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—121no—
288C22×C3×C4—121no—
289C22×C3×C4—121no—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C23×C311yescharacteristic
298C22×C3×C4C23×C311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C311yescharacteristic
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C311yescharacteristic
310C22×Dic3C23×C311yescharacteristic
311C2×C4×D3—41no—
312C2×C4×D3—41no—
313C2×C4×D3—41no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—34no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—41no—
318C3×C4⋊C4—41no—
319C3×C4⋊C4—42no—
320C3×C4⋊C4—121no—
321C3×C4⋊C4—121no—
322C3×C4⋊C4—121no—
323C3×C4⋊C4—121no—
324C3×C4⋊C4—121no—
325C3×C4⋊C4—121no—
326C3×C4⋊C4—121no—
327C3×C4⋊C4—121no—
328C3×C4⋊C4C4×D314yescomplemented
329C3×C4⋊C4C2×C3×C414yescomplemented
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—121no—
334C3×C22⋊C4—121no—
335C3×C22⋊C4—121no—
336C3×C42—34no—
337C3×C42—41no—
338C3×C42—41no—
339C3×C42—42no—
340C3×C42—121no—
341C3×C42—121no—
342(C2×D3)⋊C4—41no—
343(C2×D3)⋊C4—41no—
344(C2×D3)⋊C4—41no—
345(C2×D3)⋊C4C2×C3×C414yes—
346(C2×D3)⋊C4C2×C3×C414yes—
347(C2×D3)⋊C4C2×C3×C414yes—
348C4⋊Dic3—41no—
349C4⋊Dic3—41no—
350C4⋊Dic3—41no—
351C4⋊Dic3C2×C3×C414yescomplemented
352Dic3⋊C4—41no—
353Dic3⋊C4—41no—
354Dic3⋊C4—41no—
355Dic3⋊C4—41no—
356Dic3⋊C4—41no—
357Dic3⋊C4C2×C3×C414yescomplemented
358C4×Dic3—41no—
359C4×Dic3—41no—
360C4×Dic3C2×C3×C414yescomplemented
361C22×C32C23×C411yescharacteristic
362C22×C32H(5,𝔽2)11yescharacteristic
363C22×C32H(5,𝔽2)11yescharacteristic
364C22×C32H(5,𝔽2)11yescharacteristic
365C22×C322−1+411yescharacteristic
366C22×C322−1+411yescharacteristic
367C22×C322−1+411yescharacteristic
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—41no—
372C2×C3×D3—41no—
373C2×C3×D3—41no—
374C2×C3×D3—41no—
375C32×C4—22no—
376C32×C4—22no—
377C32×C4—22no—
378C32×C4—41no—
379C32×C4—41no—
380C32×C4—41no—
381C32×C4—41no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—41no—
386C3×Dic3—41no—
387C3×Dic3—41no—
388C3×Dic3—41no—
389C23×C4—31no—
390#126—38no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4C2×C3×D311yescharacteristic
402C2×C4⋊C4C2×C3×D311yescharacteristic
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42C2×C3×D311yescharacteristic
413#95—31no—
414#95—31no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95C2×C3×D311yescharacteristic
422#95C2×C3×D311yescharacteristic
423#95C2×C3×D311yescharacteristic
424#95C2×C3×D311yescharacteristic
425C23×C3—21no—
426C23×C3—32no—
427C23×C3—61no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3C23×D311yescharacteristic
434C23×C3C24×C311yescharacteristic
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3C22×C3×C412yes—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—124no—
521C2×C3×C4C2×C4×D312yes—
522C2×C3×C4C2×C4×D312yes—
523C2×C3×C4C2×C4×D312yes—
524C2×C3×C4C22×C3×C412yes—
525C2×C3×C4C22×C3×C412yes—
526C2×C3×C4C22×C3×C412yes—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3C22×C3×C412yes—
546C2×Dic3C22×C3×C412yes—
547C2×Dic3C22×C3×C412yes—
548C4×D3—44no—
549C2×C32#52011yescharacteristic
550C2×C32#52011yescharacteristic
551C2×C32#52011yescharacteristic
552C2×C32#56011yescharacteristic
553C2×C32#56311yescharacteristic
554C2×C32#56311yescharacteristic
555C2×C32#56311yescharacteristic
556C3×D3—42no—
557C24—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—121no—
566C22×C4—121no—
567C22×C4—121no—
568C22×C4C22×C3×D311yescharacteristic
569C22×C4C22×C3×D311yescharacteristic
570C22×C4C22×C3×D311yescharacteristic
571C22×C4C22×C3×D311yescharacteristic
572C22×C4C22×C3×D311yescharacteristic
573C22×C4C22×C3×D311yescharacteristic
574C22×C4C22×C3×D311yescharacteristic
575C4⋊C4—34no—
576C4⋊C4—34no—
577C4⋊C4—41no—
578C4⋊C4—121no—
579C4⋊C4—121no—
580C4⋊C4—121no—
581C4⋊C4—121no—
582C4⋊C4—121no—
583C4⋊C4—121no—
584C4⋊C4—121no—
585C4⋊C4—121no—
586C4⋊C4C3×C4×D314yescomplemented
587C22⋊C4—34no—
588C22⋊C4—34no—
589C22⋊C4—34no—
590C22⋊C4—121no—
591C22⋊C4—121no—
592C22⋊C4—121no—
593C42—34no—
594C42—41no—
595C42—121no—
596C42—121no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3C22×C4×D311yescharacteristic
612C22×C3#100411yescharacteristic
613C22×C3#100711yescharacteristic
614C22×C3#100911yescharacteristic
615C22×C3#100911yescharacteristic
616C22×C3#101011yescharacteristic
617C22×C3#101011yescharacteristic
618C22×C3C23×C3×C411yescharacteristic
619C22×C3C3×H(5,𝔽2)11yescharacteristic
620C22×C3C3×H(5,𝔽2)11yescharacteristic
621C22×C3C3×H(5,𝔽2)11yescharacteristic
622C22×C3C3×2−1+411yescharacteristic
623C22×C3C3×2−1+411yescharacteristic
624C22×C3C3×2−1+411yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660Dic3—22no—
661Dic3—22no—
662Dic3—22no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667C32#238311yescharacteristic, complemented, Sylow
668C23—32no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23C23×C3×D311yescharacteristic
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—124no—
716C2×C4C2×C3×C4×D312yes—
717C2×C4C2×C3×C4×D312yes—
718C2×C4C2×C3×C4×D312yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—122no—
727C2×C3#552311yescharacteristic
728C2×C3#554611yescharacteristic
729C2×C3#557411yescharacteristic
730C2×C3#564611yescharacteristic
731C2×C3#566611yescharacteristic
732C2×C3#569911yescharacteristic
733C2×C3#571211yescharacteristic
734C2×C3C3×#52011yescharacteristic
735C2×C3C3×#52011yescharacteristic
736C2×C3C3×#52011yescharacteristic
737C2×C3C3×#56011yescharacteristic
738C2×C3C3×#56311yescharacteristic
739C2×C3C3×#56311yescharacteristic
740C2×C3C3×#56311yescharacteristic
741D3—42no—
742C22—62no—
743C22—62no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22C22×C3×C4×D311yescharacteristic
750C22C3×#100411yescharacteristic
751C22C3×#100711yescharacteristic
752C22C3×#100911yescharacteristic
753C22C3×#100911yescharacteristic
754C22C3×#101011yescharacteristic
755C22C3×#101011yescharacteristic
756C4—22no—
757C4—22no—
758C4—22no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—62no—
764C4—62no—
765C4—62no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C3—21no—
771C3#7498011yescharacteristic, direct product factor
772C3C3×#238311yescharacteristic, complemented
773C2—122no—
774C2C3×#552311yescharacteristic
775C2C3×#554611yescharacteristic
776C2C3×#557411yescharacteristic
777C2C3×#564611yescharacteristic
778C2C3×#566611yescharacteristic
779C2C3×#569911yescharacteristic
780C2C3×#571211yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#387C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#387D3
hypocenterC3C3×#2383
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
4. C3×#4984C2semidirect
5. C3×#4975C2semidirect
7. C3×#4928C2semidirect
12. C3×#4654C2semidirect
13. C3×#4652C2semidirect
14. C3×#4651C2semidirect
15. C3×#4647C2semidirect
17. #74980C3direct (N × H)
41. C3×#898C4semidirect
65. C3×#387D3semidirect
66. C3×#387C2×C3semidirect
73. #4984C2×C3semidirect
74. #4975C2×C3semidirect
76. #4928C2×C3semidirect
81. #4654C2×C3semidirect
82. #4652C2×C3semidirect
83. #4651C2×C3semidirect
84. #4647C2×C3semidirect
104. C32×C4⋊C4C2×C4semidirect
115. C3×C4⋊Dic3C2×C4semidirect
121. C3×Dic3⋊C4C2×C4semidirect
124. C3×C4×Dic3C2×C4semidirect
176. #898C3×C4semidirect
265. #387C3×D3semidirect
328. C3×C4⋊C4C4×D3semidirect
329. C3×C4⋊C4C2×C3×C4semidirect
351. C4⋊Dic3C2×C3×C4semidirect
357. Dic3⋊C4C2×C3×C4semidirect
360. C4×Dic3C2×C3×C4semidirect
586. C4⋊C4C3×C4×D3semidirect
667. C32#2383semidirect
771. C3#74980direct (N × H)
772. C3C3×#2383semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8982
C32×#3872
C3×#49892
C3×#49842
C3×#49752
C3×#49402
C3×#49282
C3×#46702
C3×#46692
C3×#46682
C3×#46542
C3×#46522
C3×#46512
C3×#46472
C3×#23833
#749803