Finite Group Databasebeta

← C3×#75455 #11802418

Subgroups — C3×#75455 #11802418

Order 1152.

1127 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#879C211yesmaximal, characteristic
2C32×#388C211yesmaximal, characteristic
3C3×#4978C211yesmaximal, characteristic, complemented
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#4945C211yesmaximal, characteristic
6C3×#4944C211yesmaximal, characteristic
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic
8C3×Dic3×C22⋊C4C211yesmaximal, characteristic
9C3×Dic3×C22⋊C4C211yesmaximal, characteristic
10C3×#4933C211yesmaximal, characteristic, complemented
11C3×C42×Dic3C211yesmaximal, characteristic, complemented
12C3×#4654C211yesmaximal, characteristic, complemented
13C3×#4651C211yesmaximal, characteristic, complemented
14C3×#4649C211yesmaximal, characteristic, complemented
15C3×#4649C211yesmaximal, characteristic, complemented
16C3×C4×#126—31nomaximal
17#75455C311yesmaximal, characteristic, direct product factor
18C23×C3×Dic3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#879C418yescomplemented
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×#126—31no—
55C2×#879C2×C311yescharacteristic
56C3×#388—21no—
57C3×#388—31no—
58C3×#388—31no—
59C3×#388D311yescharacteristic
60C3×#388C2×C311yescharacteristic
61C3×#387—31no—
62C3×#387—31no—
63C3×#387—31no—
64C3×#383—31no—
65C3×C4×C4⋊C4—31no—
66C3×C4×C4⋊C4—31no—
67C3×C4×C4⋊C4—31no—
68C3×C4×C22⋊C4—31no—
69C3×C4×C22⋊C4—31no—
70C3×C4×C22⋊C4—31no—
71C3×C43—31no—
72#4978C2×C311yescharacteristic, complemented
73Dic3×C4⋊C4C2×C311yescharacteristic, complemented
74#4945C2×C311yescharacteristic
75#4944C2×C311yescharacteristic
76Dic3×C22⋊C4C2×C311yescharacteristic
77Dic3×C22⋊C4C2×C311yescharacteristic
78Dic3×C22⋊C4C2×C311yescharacteristic
79#4933C2×C311yescharacteristic, complemented
80C42×Dic3C2×C311yescharacteristic, complemented
81#4654C2×C311yescharacteristic, complemented
82#4651C2×C311yescharacteristic, complemented
83#4649C2×C311yescharacteristic, complemented
84#4649C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3×Dic3—22no—
93C22×C3×Dic3—22no—
94C22×C3×Dic3—22no—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C32×C4⋊C4—22no—
104C32×C22⋊C4—22no—
105C32×C22⋊C4—22no—
106C32×C22⋊C4C2×C414yes—
107C32×C42—22no—
108C3×#217—22no—
109C3×#217C2×C414yes—
110C3×#217C2×C414yes—
111C3×C4⋊Dic3C2×C414yescomplemented
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4C2×C414yescomplemented
115C3×Dic3⋊C4C2×C414yescomplemented
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3—22no—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124C3×C4×Dic3C2×C414yescomplemented
125C4×#126—31noSylow
126C23×C3×C4—31no—
127C23×Dic3C22×C311yescharacteristic
128C3×#126—38no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C4⋊C4C22×C311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4C2×D311yescharacteristic
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C22×C311yescharacteristic
147C2×C3×C22⋊C4C22×C311yescharacteristic
148C2×C3×C22⋊C4C22×C311yescharacteristic
149C2×C3×C42—21no—
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×C3×C42—31no—
154C2×C3×C42—31no—
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42C2×D311yescharacteristic
160C2×C3×C42C22×C311yescharacteristic
161C2×#217C22×C311yescharacteristic
162C2×#217C22×C311yescharacteristic
163C2×#217C22×C311yescharacteristic
164C2×C4⋊Dic3C22×C311yescharacteristic
165C2×Dic3⋊C4C22×C311yescharacteristic
166C2×Dic3⋊C4C22×C311yescharacteristic
167C2×Dic3⋊C4C22×C311yescharacteristic
168C2×Dic3⋊C4C22×C311yescharacteristic
169C2×C4×Dic3C22×C311yescharacteristic
170C2×C4×Dic3C22×C311yescharacteristic
171C2×C4×Dic3C22×C311yescharacteristic
172C2×C4×Dic3C22×C311yescharacteristic
173C2×C4×Dic3C22×C311yescharacteristic
174C2×C4×Dic3C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176C2×C4×Dic3C22×C311yescharacteristic
177C2×C4×Dic3C22×C311yescharacteristic
178#879C3×C418yescomplemented
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×#95—31no—
190C3×#95—31no—
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×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32C22×C412yes—
212C23×C32C2411yescharacteristic
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×C4C22×C412yes—
228C2×C32×C4C22×C412yes—
229C2×C32×C4#4112yes—
230C2×C32×C4#4112yes—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
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—44no—
248C2×C3×Dic3C22×C412yes—
249C2×C3×Dic3C22×C412yes—
250C2×C3×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3#4112yes—
253C2×C3×Dic3#4112yes—
254C2×C3×Dic3#4112yes—
255C2×C3×Dic3#4112yes—
256C2×#126—31no—
257#388—31no—
258#388—31no—
259#388C3×D311yescharacteristic
260#387—31no—
261#387—31no—
262#387—31no—
263#383—31no—
264C4×C4⋊C4—31no—
265C4×C4⋊C4—31no—
266C4×C4⋊C4—31no—
267C4×C22⋊C4—31no—
268C4×C22⋊C4—31no—
269C4×C22⋊C4—31no—
270C43—31no—
271C24×C3—21no—
272C24×C3C22×D311yescharacteristic
273C24×C3C23×C311yescharacteristic
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—31no—
288C22×C3×C4—62no—
289C22×C3×C4—62no—
290C22×C3×C4—62no—
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×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C311yescharacteristic
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C311yescharacteristic
310C22×Dic3C23×C311yescharacteristic
311C22×Dic3C23×C311yescharacteristic
312C22×Dic3C23×C311yescharacteristic
313C22×Dic3C23×C311yescharacteristic
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—34no—
318C3×C4⋊C4—34no—
319C3×C4⋊C4—42no—
320C3×C4⋊C4—62no—
321C3×C4⋊C4—62no—
322C3×C22⋊C4—22no—
323C3×C22⋊C4—22no—
324C3×C22⋊C4—22no—
325C3×C22⋊C4—22no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—34no—
328C3×C22⋊C4—34no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C22⋊C4—62no—
332C3×C22⋊C4C4×D314yes—
333C3×C22⋊C4C2×C3×C414yes—
334C3×C42—22no—
335C3×C42—22no—
336C3×C42—34no—
337C3×C42—42no—
338C3×C42—62no—
339C3×C42—62no—
340C3×C42—62no—
341C3×C42—62no—
342C3×C42—62no—
343C3×C42—62no—
344C3×C42—62no—
345C3×C42—62no—
346#217—22no—
347#217C2×C3×C414yes—
348#217C2×C3×C414yes—
349C4⋊Dic3C2×C3×C414yescomplemented
350Dic3⋊C4—22no—
351Dic3⋊C4—22no—
352Dic3⋊C4C2×C3×C414yescomplemented
353Dic3⋊C4C2×C3×C414yescomplemented
354C4×Dic3—22no—
355C4×Dic3—22no—
356C4×Dic3—22no—
357C4×Dic3—22no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—22no—
362C4×Dic3C2×C3×C414yescomplemented
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32C23×C411yescharacteristic
371C22×C32C2×#4111yescharacteristic
372C22×C32C2×#4111yescharacteristic
373C22×C32C2×#4111yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C32×C4—22no—
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—22no—
381C32×C4—41no—
382C32×C4—41no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3#12614yescomplemented
391C23×C4—31no—
392#126—38no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4C2×C3×D311yescharacteristic
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4C2×C3×D311yescharacteristic
403C2×C22⋊C4C2×C3×D311yescharacteristic
404C2×C22⋊C4C2×C3×D311yescharacteristic
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42C2×C3×D311yescharacteristic
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—31no—
425#95C2×C3×D311yescharacteristic
426#95C2×C3×D311yescharacteristic
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—22no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3C2×C4×D312yes—
448C23×C3C22×C3×C412yes—
449C23×C3C23×D311yescharacteristic
450C23×C3C24×C311yescharacteristic
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
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—22no—
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—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
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—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
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—61no—
521C2×C3×C4—124no—
522C2×C3×C4C2×C4×D312yes—
523C2×C3×C4C2×C4×D312yes—
524C2×C3×C4#23712yes—
525C2×C3×C4#23712yes—
526C2×C3×C4C22×C3×C412yes—
527C2×C3×C4C22×C3×C412yes—
528C2×C3×C4C3×#4112yes—
529C2×C3×C4C3×#4112yes—
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×Dic3—21no—
546C2×Dic3—44no—
547C2×Dic3C22×C3×C412yes—
548C2×Dic3C22×C3×C412yes—
549C2×Dic3C22×C3×C412yes—
550C2×Dic3C22×C3×C412yes—
551C2×Dic3C3×#4112yes—
552C2×Dic3C3×#4112yes—
553C2×Dic3C3×#4112yes—
554C2×Dic3C3×#4112yes—
555C2×C32—42no—
556C2×C32C4×#4111yescharacteristic
557C2×C32C4×#4111yescharacteristic
558C2×C32C4×#4111yescharacteristic
559C2×C32C2×#12611yescharacteristic
560C2×C32#52911yescharacteristic
561C2×C32#52911yescharacteristic
562C2×C32#52911yescharacteristic
563C24C22×C3×D311yescharacteristic
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4C22×C3×D311yescharacteristic
576C22×C4C22×C3×D311yescharacteristic
577C22×C4C22×C3×D311yescharacteristic
578C22×C4C22×C3×D311yescharacteristic
579C22×C4C22×C3×D311yescharacteristic
580C22×C4C22×C3×D311yescharacteristic
581C4⋊C4—22no—
582C4⋊C4—34no—
583C4⋊C4—34no—
584C4⋊C4—34no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—34no—
590C22⋊C4—34no—
591C22⋊C4—62no—
592C22⋊C4C3×C4×D314yes—
593C42—22no—
594C42—34no—
595C42—62no—
596C42—62no—
597C42—62no—
598C42—62no—
599C42—62no—
600C42—62no—
601C42—62no—
602C42—62no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3C22×C4×D311yescharacteristic
632C22×C3C2×#23711yescharacteristic
633C22×C3C2×#23711yescharacteristic
634C22×C3D3×#4111yescharacteristic
635C22×C3D3×#4111yescharacteristic
636C22×C3D3×#4111yescharacteristic
637C22×C3D3×#4111yescharacteristic
638C22×C3C23×C3×C411yescharacteristic
639C22×C3C2×C3×#4111yescharacteristic
640C22×C3C2×C3×#4111yescharacteristic
641C22×C3C2×C3×#4111yescharacteristic
642C22×C3C2×C3×#4111yescharacteristic
643C22×C3C2×C3×#4111yescharacteristic
644C22×C3C2×C3×#4111yescharacteristic
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—34no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671Dic3—22no—
672Dic3—22no—
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3C3×#12614yescomplemented
679C32C4×#12611yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23C2×C3×C4×D312yes—
687C23C23×C3×D311yescharacteristic
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—124no—
727C2×C4C2×C3×C4×D312yes—
728C2×C4C2×C3×C4×D312yes—
729C2×C4C3×#23712yes—
730C2×C4C3×#23712yes—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—82no—
741C2×C3#552211yescharacteristic
742C2×C3C4×#23711yescharacteristic
743C2×C3C4×#23711yescharacteristic
744C2×C3#560011yescharacteristic
745C2×C3#564911yescharacteristic
746C2×C3#568011yescharacteristic
747C2×C3D3×#12611yescharacteristic
748C2×C3C3×C4×#4111yescharacteristic
749C2×C3C3×C4×#4111yescharacteristic
750C2×C3C3×C4×#4111yescharacteristic
751C2×C3C2×C3×#12611yescharacteristic
752C2×C3C3×#52911yescharacteristic
753C2×C3C3×#52911yescharacteristic
754C2×C3C3×#52911yescharacteristic
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22C22×C3×C4×D311yescharacteristic
763C22C2×C3×#23711yescharacteristic
764C22C2×C3×#23711yescharacteristic
765C22C3×D3×#4111yescharacteristic
766C22C3×D3×#4111yescharacteristic
767C22C3×D3×#4111yescharacteristic
768C22C3×D3×#4111yescharacteristic
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—34no—
774C4—41no—
775C4—41no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—62no—
781C4—121no—
782C4—121no—
783C3—21no—
784C3#7545511yescharacteristic, direct product factor
785C3C3×C4×#12611yescharacteristic, complemented
786C2—42no—
787C2C3×#552211yescharacteristic
788C2C3×C4×#23711yescharacteristic
789C2C3×C4×#23711yescharacteristic
790C2C3×#560011yescharacteristic
791C2C3×#564911yescharacteristic
792C2C3×#568011yescharacteristic
793C2C3×D3×#12611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#388D3
hypocenterC3C3×C4×#126
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
3. C3×#4978C2semidirect
4. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4933C2semidirect
11. C3×C42×Dic3C2semidirect
12. C3×#4654C2semidirect
13. C3×#4651C2semidirect
14. C3×#4649C2semidirect
15. C3×#4649C2semidirect
17. #75455C3direct (N × H)
41. C3×#879C4semidirect
72. #4978C2×C3semidirect
73. Dic3×C4⋊C4C2×C3semidirect
79. #4933C2×C3semidirect
80. C42×Dic3C2×C3semidirect
81. #4654C2×C3semidirect
82. #4651C2×C3semidirect
83. #4649C2×C3semidirect
84. #4649C2×C3semidirect
111. C3×C4⋊Dic3C2×C4semidirect
114. C3×Dic3⋊C4C2×C4semidirect
115. C3×Dic3⋊C4C2×C4semidirect
124. C3×C4×Dic3C2×C4semidirect
178. #879C3×C4semidirect
349. C4⋊Dic3C2×C3×C4semidirect
352. Dic3⋊C4C2×C3×C4semidirect
353. Dic3⋊C4C2×C3×C4semidirect
362. C4×Dic3C2×C3×C4semidirect
390. C3×Dic3#126semidirect
678. Dic3C3×#126semidirect
679. C32C4×#126semidirect
784. C3#75455direct (N × H)
785. C3C3×C4×#126semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8792
C32×#3882
C3×#49782
C3×Dic3×C4⋊C42
C3×#49452
C3×#49442
C3×Dic3×C22⋊C42
C3×#49332
C3×C42×Dic32
C3×#46542
C3×#46512
C3×#46492
C3×C4×#1263
#754553