Finite Group Databasebeta

← C3×#73779 #11808890

Subgroups — C3×#73779 #11808890

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
2C3×#4994C211yesmaximal, characteristic
3C3×#4992C211yesmaximal, characteristic
4C3×#4986C211yesmaximal, characteristic, complemented
5C3×#4985C211yesmaximal, characteristic, complemented
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
7C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
8C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
9C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C3×#4932C211yesmaximal, characteristic, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#4675C211yesmaximal, characteristic
13C3×#4674C211yesmaximal, characteristic
14C3×C3⋊#401C211yesmaximal, characteristic, complemented
15C3×#4660C211yesmaximal, characteristic, complemented
16C3×#2401—31nomaximal
17#73779C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
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—21no—
62C3×C4×C4⋊C4—31no—
63C3×C4×C4⋊C4—31no—
64C3×C4×C4⋊C4D311yescharacteristic, complemented
65C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
66C3×C4×C22⋊C4—31no—
67C3×C4×C22⋊C4—31no—
68C3×C4×C22⋊C4—31no—
69C3×#376—31no—
70#4994C2×C311yescharacteristic
71#4992C2×C311yescharacteristic
72#4986C2×C311yescharacteristic, complemented
73#4985C2×C311yescharacteristic, complemented
74C4×(C2×D3)⋊C4C2×C311yescharacteristic
75C4×(C2×D3)⋊C4C2×C311yescharacteristic
76C4×(C2×D3)⋊C4C2×C311yescharacteristic
77C4×C4⋊Dic3C2×C311yescharacteristic, complemented
78#4932C2×C311yescharacteristic, complemented
79C4×Dic3⋊C4C2×C311yescharacteristic, complemented
80#4675C2×C311yescharacteristic
81#4674C2×C311yescharacteristic
82C3⋊#401C2×C311yescharacteristic, complemented
83#4660C2×C311yescharacteristic, complemented
84C23×C3×D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C32×C4⋊C4—22no—
103C32×C4⋊C4—22no—
104C32×C42—22no—
105C32×C42—22no—
106C32×C42—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×(C2×D3)⋊C4—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×(C2×D3)⋊C4—22no—
113C3×C4⋊Dic3—22no—
114C3×C4⋊Dic3—22no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120#2401—31noSylow
121C23×C3×C4—31no—
122C22×C4×D3C22×C311yescharacteristic
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C22×C311yescharacteristic
132C2×C3×C4⋊C4C22×C311yescharacteristic
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C42—21no—
140C2×C3×C42—21no—
141C2×C3×C42—21no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42C2×D311yescharacteristic
146C2×C3×C42C2×D311yescharacteristic
147C2×C3×C42C2×D311yescharacteristic
148C2×C3×C42C22×C311yescharacteristic
149C2×C3×C42C22×C311yescharacteristic
150C2×C3×C42C22×C311yescharacteristic
151C2×(C2×D3)⋊C4C22×C311yescharacteristic
152C2×(C2×D3)⋊C4C22×C311yescharacteristic
153C2×(C2×D3)⋊C4C22×C311yescharacteristic
154C2×(C2×D3)⋊C4C22×C311yescharacteristic
155C2×(C2×D3)⋊C4C22×C311yescharacteristic
156C2×(C2×D3)⋊C4C22×C311yescharacteristic
157C2×C4⋊Dic3C22×C311yescharacteristic
158C2×C4⋊Dic3C22×C311yescharacteristic
159C2×Dic3⋊C4C22×C311yescharacteristic
160C2×Dic3⋊C4C22×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×C32C2411yescharacteristic
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3#4112yes—
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—21no—
221C2×C32×C4—21no—
222C2×C32×C4#4112yes—
223C2×C32×C4#4112yes—
224C2×C32×C4#4112yes—
225C2×C32×C4#4112yes—
226C2×C32×C4#4112yes—
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—
248C3×C4×D3—44no—
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⋊C4C3×D311yescharacteristic, complemented
260C4×C22⋊C4—31no—
261C4×C22⋊C4—31no—
262C4×C22⋊C4—31no—
263#376—31no—
264C24×C3—31no—
265C23×D3C23×C311yescharacteristic
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—62no—
281C22×C3×C4—62no—
282C22×C3×C4—62no—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C23×C311yescharacteristic
291C22×C3×C4C23×C311yescharacteristic
292C22×C3×C4C23×C311yescharacteristic
293C22×C3×C4C23×C311yescharacteristic
294C22×C3×C4C23×C311yescharacteristic
295C22×C3×C4C23×C311yescharacteristic
296C22×C3×C4C23×C311yescharacteristic
297C22×Dic3C23×C311yescharacteristic
298C22×Dic3C23×C311yescharacteristic
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C311yescharacteristic
301C22×Dic3C23×C311yescharacteristic
302C22×Dic3C23×C311yescharacteristic
303C22×Dic3C23×C311yescharacteristic
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—22no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4—62no—
315C3×C4⋊C4—62no—
316C3×C4⋊C4—62no—
317C3×C22⋊C4—62no—
318C3×C22⋊C4—62no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—62no—
322C3×C22⋊C4—62no—
323C3×C42—24no—
324C3×C42—22no—
325C3×C42—22no—
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—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—22no—
337(C2×D3)⋊C4—22no—
338(C2×D3)⋊C4—22no—
339(C2×D3)⋊C4—22no—
340(C2×D3)⋊C4—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—22no—
343Dic3⋊C4—22no—
344Dic3⋊C4—22no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C4×Dic3—22no—
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C2×C3×D3—22no—
356C2×C3×D3—22no—
357C2×C3×D3—22no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C2×C3×D3—41no—
361C2×C3×D3—41no—
362C32×C4—22no—
363C32×C4—22no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4#12614yes—
369C3×Dic3—22no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C23×C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4C2×C3×D311yescharacteristic
382C2×C4⋊C4C2×C3×D311yescharacteristic
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—31no—
392C2×C42C2×C3×D311yescharacteristic
393C2×C42C2×C3×D311yescharacteristic
394C2×C42C2×C3×D311yescharacteristic
395#95—31no—
396#95—31no—
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#95C2×C3×D311yescharacteristic
410#95C2×C3×D311yescharacteristic
411C23×C3—21no—
412C23×C3—32no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3—61no—
419C23×C3C23×D311yescharacteristic
420C23×C3C24×C311yescharacteristic
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3C3×#4112yes—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
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—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—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—32no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
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—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
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—124no—
503C2×C3×C4#23512yes—
504C2×C3×C4#23512yes—
505C2×C3×C4#23512yes—
506C2×C3×C4#23712yes—
507C2×C3×C4#23912yes—
508C2×C3×C4C3×#4112yes—
509C2×C3×C4C3×#4112yes—
510C2×C3×C4C3×#4112yes—
511C2×C3×C4C3×#4112yes—
512C2×C3×C4C3×#4112yes—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
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×Dic3C3×#4112yes—
534C4×D3—44no—
535C2×C32C2×#12611yescharacteristic
536C2×C32#52911yescharacteristic
537C2×C32#52911yescharacteristic
538C2×C32#52911yescharacteristic
539C2×C32#52911yescharacteristic
540C2×C32#52911yescharacteristic
541C2×C32#52911yescharacteristic
542C3×D3—42no—
543C24—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4C22×C3×D311yescharacteristic
555C22×C4C22×C3×D311yescharacteristic
556C22×C4C22×C3×D311yescharacteristic
557C22×C4C22×C3×D311yescharacteristic
558C22×C4C22×C3×D311yescharacteristic
559C22×C4C22×C3×D311yescharacteristic
560C22×C4C22×C3×D311yescharacteristic
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C22⋊C4—62no—
568C22⋊C4—62no—
569C22⋊C4—62no—
570C22⋊C4—62no—
571C22⋊C4—62no—
572C22⋊C4—62no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—62no—
577C42—62no—
578C42—62no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3C2×#23511yescharacteristic
594C22×C3C2×#23511yescharacteristic
595C22×C3C2×#23511yescharacteristic
596C22×C3C2×#23711yescharacteristic
597C22×C3C2×#23911yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3D3×#4111yescharacteristic
600C22×C3C2×C3×#4111yescharacteristic
601C22×C3C2×C3×#4111yescharacteristic
602C22×C3C2×C3×#4111yescharacteristic
603C22×C3C2×C3×#4111yescharacteristic
604C22×C3C2×C3×#4111yescharacteristic
605C22×C3C2×C3×#4111yescharacteristic
606C22×C3C2×C3×#4111yescharacteristic
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C3×C4—24no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—24no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—62no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4#89814yes—
641C3×C4C3×#12614yes—
642Dic3—22no—
643Dic3—41no—
644Dic3—41no—
645Dic3—41no—
646Dic3—41no—
647Dic3—41no—
648Dic3—41no—
649C32#240111yescharacteristic, complemented, Sylow
650C23—32no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23C23×C3×D311yescharacteristic
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—32no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—124no—
696C2×C4C3×#23512yes—
697C2×C4C3×#23512yes—
698C2×C4C3×#23512yes—
699C2×C4C3×#23712yes—
700C2×C4C3×#23912yes—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—122no—
709C2×C3#547911yescharacteristic
710C2×C3C2×#89811yescharacteristic
711C2×C3#552811yescharacteristic
712C2×C3#553811yescharacteristic
713C2×C3#555711yescharacteristic
714C2×C3#558011yescharacteristic
715C2×C3#558011yescharacteristic
716C2×C3C2×C3×#12611yescharacteristic
717C2×C3C3×#52911yescharacteristic
718C2×C3C3×#52911yescharacteristic
719C2×C3C3×#52911yescharacteristic
720C2×C3C3×#52911yescharacteristic
721C2×C3C3×#52911yescharacteristic
722C2×C3C3×#52911yescharacteristic
723D3—42no—
724C22—62no—
725C22—62no—
726C22—62no—
727C22—121no—
728C22—121no—
729C22—121no—
730C22—121no—
731C22C2×C3×#23511yescharacteristic
732C22C2×C3×#23511yescharacteristic
733C22C2×C3×#23511yescharacteristic
734C22C2×C3×#23711yescharacteristic
735C22C2×C3×#23911yescharacteristic
736C22C3×D3×#4111yescharacteristic
737C22C3×D3×#4111yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—62no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4C3×#89814yes—
752C3—21no—
753C3#7377911yescharacteristic, direct product factor
754C3C3×#240111yescharacteristic, complemented
755C2—122no—
756C2C3×#547911yescharacteristic
757C2C2×C3×#89811yescharacteristic
758C2C3×#552811yescharacteristic
759C2C3×#553811yescharacteristic
760C2C3×#555711yescharacteristic
761C2C3×#558011yescharacteristic
762C2C3×#558011yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2401
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C32×C4×C4⋊C4C2semidirect
4. C3×#4986C2semidirect
5. C3×#4985C2semidirect
9. C3×C4×C4⋊Dic3C2semidirect
10. C3×#4932C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
14. C3×C3⋊#401C2semidirect
15. C3×#4660C2semidirect
17. #73779C3direct (N × H)
64. C3×C4×C4⋊C4D3semidirect
65. C3×C4×C4⋊C4C2×C3semidirect
72. #4986C2×C3semidirect
73. #4985C2×C3semidirect
77. C4×C4⋊Dic3C2×C3semidirect
78. #4932C2×C3semidirect
79. C4×Dic3⋊C4C2×C3semidirect
82. C3⋊#401C2×C3semidirect
83. #4660C2×C3semidirect
259. C4×C4⋊C4C3×D3semidirect
649. C32#2401semidirect
753. C3#73779direct (N × H)
754. C3C3×#2401semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C4⋊C42
C3×#49942
C3×#49922
C3×#49862
C3×#49852
C3×C4×(C2×D3)⋊C42
C3×C4×C4⋊Dic32
C3×#49322
C3×C4×Dic3⋊C42
C3×#46752
C3×#46742
C3×C3⋊#4012
C3×#46602
C3×#24013
#737793