Finite Group Databasebeta

← C3×#73482 #11808887

Subgroups — C3×#73482 #11808887

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C22⋊C4C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4C3×#4953C211yesmaximal, characteristic
5C3×#4952C211yesmaximal, characteristic
6C3×#4952C211yesmaximal, characteristic
7C3×#4948C211yesmaximal, characteristic
8C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C3×#4932C211yesmaximal, characteristic, complemented
10C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×C3⋊#401C211yesmaximal, characteristic, complemented
13C3×#4660C211yesmaximal, characteristic, complemented
14C3×#4659C211yesmaximal, characteristic, complemented
15C3×#4658C211yesmaximal, characteristic, complemented
16C3×#2401—31nomaximal
17#73482C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C32×#95C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#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×#401—31no—
54C3×#400—31no—
55C3×#400—31no—
56C3×#400—31no—
57C3×#397—31no—
58C3×#397—31no—
59C3×#397—31no—
60C3×#396—31no—
61C3×C4×C4⋊C4—31no—
62C3×C4×C4⋊C4—31no—
63C3×C4×C4⋊C4—31no—
64C3×C4×C22⋊C4—21no—
65C3×C4×C22⋊C4—31no—
66C3×C4×C22⋊C4—31no—
67C3×C4×C22⋊C4D311yescharacteristic
68C3×C4×C22⋊C4C2×C311yescharacteristic
69C3×#376—31no—
70C4×#217C2×C311yescharacteristic
71C4×#217C2×C311yescharacteristic
72#4953C2×C311yescharacteristic
73#4952C2×C311yescharacteristic
74#4952C2×C311yescharacteristic
75#4948C2×C311yescharacteristic
76C4×C4⋊Dic3C2×C311yescharacteristic, complemented
77#4932C2×C311yescharacteristic, complemented
78C4×Dic3⋊C4C2×C311yescharacteristic, complemented
79C4×Dic3⋊C4C2×C311yescharacteristic, complemented
80C3⋊#401C2×C311yescharacteristic, complemented
81#4660C2×C311yescharacteristic, complemented
82#4659C2×C311yescharacteristic, complemented
83#4658C2×C311yescharacteristic, complemented
84C24×C32C2311yescharacteristic
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—22no—
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
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C32×C22⋊C4—22no—
103C32×C22⋊C4—22no—
104C32×C42—22no—
105C32×C42—22no—
106C3×#217—22no—
107C3×#217—22no—
108C3×#217—22no—
109C3×#217—22no—
110C3×C4⋊Dic3—22no—
111C3×C4⋊Dic3—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—22no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120#2401—31noSylow
121C23×C3×C4—21no—
122C23×C3×C4C2×D311yescharacteristic
123C23×C3×C4C22×C311yescharacteristic
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—31no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4C2×D311yescharacteristic
137C2×C3×C22⋊C4C2×D311yescharacteristic
138C2×C3×C22⋊C4C22×C311yescharacteristic
139C2×C3×C22⋊C4C22×C311yescharacteristic
140C2×C3×C42—21no—
141C2×C3×C42—21no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42—31no—
146C2×C3×C42C2×D311yescharacteristic
147C2×C3×C42C2×D311yescharacteristic
148C2×C3×C42C22×C311yescharacteristic
149C2×C3×C42C22×C311yescharacteristic
150C2×#217C22×C311yescharacteristic
151C2×#217C22×C311yescharacteristic
152C2×#217C22×C311yescharacteristic
153C2×#217C22×C311yescharacteristic
154C2×C4⋊Dic3C22×C311yescharacteristic
155C2×C4⋊Dic3C22×C311yescharacteristic
156C2×Dic3⋊C4C22×C311yescharacteristic
157C2×Dic3⋊C4C22×C311yescharacteristic
158C2×Dic3⋊C4C22×C311yescharacteristic
159C2×Dic3⋊C4C22×C311yescharacteristic
160C2×C4×Dic3C22×C311yescharacteristic
161C2×C4×Dic3C22×C311yescharacteristic
162C2×C4×Dic3C22×C311yescharacteristic
163C2×C4×Dic3C22×C311yescharacteristic
164C3×#95—21no—
165C3×#95—21no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—31no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95—31no—
176C3×#95—31no—
177C3×#95—31no—
178C3×#95—31no—
179C3×#95—31no—
180C3×#95C2×D311yescharacteristic
181C3×#95C2×D311yescharacteristic
182C3×#95C22×C311yescharacteristic
183C3×#95C22×C311yescharacteristic
184C3⋊#95C22×C311yescharacteristic
185C3⋊#95C22×C311yescharacteristic
186C3⋊#95C22×C311yescharacteristic
187C3⋊#95C22×C311yescharacteristic
188C3⋊#95C22×C311yescharacteristic
189C3⋊#95C22×C311yescharacteristic
190C3⋊#95C22×C311yescharacteristic
191C3⋊#95C22×C311yescharacteristic
192C3⋊#95C22×C311yescharacteristic
193C3⋊#95C22×C311yescharacteristic
194C3⋊#95C22×C311yescharacteristic
195C3⋊#95C22×C311yescharacteristic
196C3⋊#95C22×C311yescharacteristic
197C3⋊#95C22×C311yescharacteristic
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32#4112yes—
205C23×C32C2411yescharacteristic
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
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—44no—
221C2×C32×C4#4112yes—
222C2×C32×C4#4112yes—
223C2×C32×C4#4112yes—
224C2×C32×C4#4112yes—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
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#4112yes—
248C2×C3×Dic3#4112yes—
249#401—31no—
250#400—31no—
251#400—31no—
252#400—31no—
253#397—31no—
254#397—31no—
255#397—31no—
256#396—31no—
257C4×C4⋊C4—31no—
258C4×C4⋊C4—31no—
259C4×C4⋊C4—31no—
260C4×C22⋊C4—31no—
261C4×C22⋊C4—31no—
262C4×C22⋊C4C3×D311yescharacteristic
263#376—31no—
264C24×C3—21no—
265C24×C3C22×D311yescharacteristic
266C24×C3C23×C311yescharacteristic
267C22×C3×C4—24no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
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—42no—
289C22×C3×C4—42no—
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×C4C23×C311yescharacteristic
297C22×C3×C4C23×C311yescharacteristic
298C22×C3×C4C23×C311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×Dic3C23×C311yescharacteristic
303C22×Dic3C23×C311yescharacteristic
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C311yescharacteristic
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C311yescharacteristic
310C3×C4⋊C4—62no—
311C3×C4⋊C4—62no—
312C3×C4⋊C4—62no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4—62no—
315C3×C4⋊C4—62no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—62no—
323C3×C22⋊C4—62no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—62no—
326C3×C42—22no—
327C3×C42—22no—
328C3×C42—22no—
329C3×C42—22no—
330C3×C42—42no—
331C3×C42—42no—
332C3×C42—62no—
333C3×C42—62no—
334C3×C42—62no—
335C3×C42—62no—
336#217—22no—
337#217—22no—
338#217—22no—
339#217—22no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342Dic3⋊C4—22no—
343Dic3⋊C4—22no—
344Dic3⋊C4—22no—
345Dic3⋊C4—22no—
346C4×Dic3—22no—
347C4×Dic3—22no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32C2×#4111yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32C2×#4111yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C22×C32C2×#4111yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C32×C4—22no—
365C32×C4—41no—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4—41no—
369C32×C4#12614yes—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C23×C4C2×C3×D311yescharacteristic
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4C2×C3×D311yescharacteristic
390C2×C22⋊C4C2×C3×D311yescharacteristic
391C2×C42—31no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42C2×C3×D311yescharacteristic
396C2×C42C2×C3×D311yescharacteristic
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—31no—
402#95—31no—
403#95—31no—
404#95—31no—
405#95—31no—
406#95—31no—
407#95—31no—
408#95—31no—
409#95—31no—
410#95—31no—
411#95C2×C3×D311yescharacteristic
412#95C2×C3×D311yescharacteristic
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3#23512yes—
434C23×C3C3×#4112yes—
435C23×C3C23×D311yescharacteristic
436C23×C3C24×C311yescharacteristic
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
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—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—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—48no—
486C2×C3×C4—44no—
487C2×C3×C4—44no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
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#23512yes—
511C2×C3×C4#23512yes—
512C2×C3×C4#23712yes—
513C2×C3×C4#23712yes—
514C2×C3×C4C3×#4112yes—
515C2×C3×C4C3×#4112yes—
516C2×C3×C4C3×#4112yes—
517C2×C3×C4C3×#4112yes—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
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×Dic3C3×#4112yes—
541C2×Dic3C3×#4112yes—
542C2×C32—42no—
543C2×C32C2×#12611yescharacteristic
544C2×C32#52911yescharacteristic
545C2×C32#52911yescharacteristic
546C2×C32#52911yescharacteristic
547C2×C32#52911yescharacteristic
548C2×C32#52911yescharacteristic
549C2×C32#52911yescharacteristic
550C24C22×C3×D311yescharacteristic
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4C22×C3×D311yescharacteristic
563C22×C4C22×C3×D311yescharacteristic
564C22×C4C22×C3×D311yescharacteristic
565C22×C4C22×C3×D311yescharacteristic
566C22×C4C22×C3×D311yescharacteristic
567C22×C4C22×C3×D311yescharacteristic
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—62no—
573C4⋊C4—62no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C42—22no—
581C42—22no—
582C42—62no—
583C42—62no—
584C42—62no—
585C42—62no—
586C22×C3—24no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3C2×#23511yescharacteristic
615C22×C3C2×#23511yescharacteristic
616C22×C3C2×#23511yescharacteristic
617C22×C3C2×#23711yescharacteristic
618C22×C3C2×#23711yescharacteristic
619C22×C3D3×#4111yescharacteristic
620C22×C3D3×#4111yescharacteristic
621C22×C3C2×C3×#4111yescharacteristic
622C22×C3C2×C3×#4111yescharacteristic
623C22×C3C2×C3×#4111yescharacteristic
624C22×C3C2×C3×#4111yescharacteristic
625C22×C3C2×C3×#4111yescharacteristic
626C22×C3C2×C3×#4111yescharacteristic
627C22×C3C2×C3×#4111yescharacteristic
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—24no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—62no—
645C3×C4—62no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4#87914yes—
653C3×C4C3×#12614yes—
654Dic3—22no—
655Dic3—22no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662C32#240111yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23C3×#23512yes—
670C23C23×C3×D311yescharacteristic
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
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—32no—
686C2×C4—32no—
687C2×C4—44no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
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×C4C3×#23512yes—
711C2×C4C3×#23512yes—
712C2×C4C3×#23712yes—
713C2×C4C3×#23712yes—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—44no—
722C2×C3—42no—
723C2×C3—42no—
724C2×C3#547911yescharacteristic
725C2×C3C2×#87911yescharacteristic
726C2×C3#552811yescharacteristic
727C2×C3#553811yescharacteristic
728C2×C3#553811yescharacteristic
729C2×C3#553811yescharacteristic
730C2×C3#555711yescharacteristic
731C2×C3C2×C3×#12611yescharacteristic
732C2×C3C3×#52911yescharacteristic
733C2×C3C3×#52911yescharacteristic
734C2×C3C3×#52911yescharacteristic
735C2×C3C3×#52911yescharacteristic
736C2×C3C3×#52911yescharacteristic
737C2×C3C3×#52911yescharacteristic
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22C2×C3×#23511yescharacteristic
746C22C2×C3×#23511yescharacteristic
747C22C2×C3×#23511yescharacteristic
748C22C2×C3×#23711yescharacteristic
749C22C2×C3×#23711yescharacteristic
750C22C3×D3×#4111yescharacteristic
751C22C3×D3×#4111yescharacteristic
752C4—22no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—62no—
758C4—62no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4C3×#87914yes—
766C3—21no—
767C3#7348211yescharacteristic, direct product factor
768C3C3×#240111yescharacteristic, complemented
769C2—42no—
770C2C3×#547911yescharacteristic
771C2C2×C3×#87911yescharacteristic
772C2C3×#552811yescharacteristic
773C2C3×#553811yescharacteristic
774C2C3×#553811yescharacteristic
775C2C3×#553811yescharacteristic
776C2C3×#555711yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2401
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C3×C4×C4⋊Dic3C2semidirect
9. C3×#4932C2semidirect
10. C3×C4×Dic3⋊C4C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
12. C3×C3⋊#401C2semidirect
13. C3×#4660C2semidirect
14. C3×#4659C2semidirect
15. C3×#4658C2semidirect
17. #73482C3direct (N × H)
76. C4×C4⋊Dic3C2×C3semidirect
77. #4932C2×C3semidirect
78. C4×Dic3⋊C4C2×C3semidirect
79. C4×Dic3⋊C4C2×C3semidirect
80. C3⋊#401C2×C3semidirect
81. #4660C2×C3semidirect
82. #4659C2×C3semidirect
83. #4658C2×C3semidirect
662. C32#2401semidirect
767. C3#73482direct (N × H)
768. C3C3×#2401semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C22⋊C42
C3×C4×#2172
C3×#49532
C3×#49522
C3×#49482
C3×C4×C4⋊Dic32
C3×#49322
C3×C4×Dic3⋊C42
C3×C3⋊#4012
C3×#46602
C3×#46592
C3×#46582
C3×#24013
#734823