Finite Group Databasebeta

← C3×#79775 #11860474

Subgroups — C3×#79775 #11860474

Order 1152.

1072 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic
2C3×#5574C211yesmaximal, characteristic, complemented
3C3×#5545C211yesmaximal, characteristic, complemented
4C32×#440C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×C4×#215C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4881C211yesmaximal, characteristic, complemented
9C3×#4872C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4804C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×#4711C211yesmaximal, characteristic, complemented
15C3×#4708C211yesmaximal, characteristic, complemented
16C3×#2946—31nomaximal
17#79775C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×#914C418yescomplemented
30C2×C3×D24C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C3×#893—21no—
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic, complemented
36C3×#892C2211yescharacteristic
37C3×D3×C4⋊C4—21no—
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#67⋊C4—21no—
40C3×D3×C22⋊C4—21no—
41C3×C4×D12—21no—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic, complemented
44C3×#872—21no—
45C3×#872C2211yescharacteristic
46C32×#107C2211yescharacteristic, complemented
47C32×#103C2211yescharacteristic, complemented
48C32×#102C2211yescharacteristic
49C32×#97C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×C4×C3⋊C8C2211yescharacteristic, complemented
62C2×C3×AGL(1,ℤ/8)—31no—
63C3×#520—31no—
64C3×#518—31no—
65C2×#914C2×C311yescharacteristic
66#5574C2×C311yescharacteristic, complemented
67#5545C2×C311yescharacteristic, complemented
68C3×#442—31no—
69C3×#442—31no—
70C3×#440—21no—
71C3×#440—31no—
72C3×#440D311yescharacteristic, complemented
73C3×#440C2×C311yescharacteristic, complemented
74C3×C4×SD16—31no—
75C3×C4×SD16—31no—
76C3×C4×D8—31no—
77C3×C4×D8—31no—
78C3×#428—31no—
79C3×#416—31no—
80C2×C3×#102—31no—
81C3×#405—31no—
82Dic3×SD16C2×C311yescharacteristic, complemented
83C4×#215C2×C311yescharacteristic, complemented
84C4×#213C2×C311yescharacteristic, complemented
85#4881C2×C311yescharacteristic, complemented
86#4872C2×C311yescharacteristic, complemented
87#4817C2×C311yescharacteristic, complemented
88#4804C2×C311yescharacteristic, complemented
89#4785C2×C311yescharacteristic, complemented
90D3×#102C2×C311yescharacteristic, complemented
91#4711C2×C311yescharacteristic, complemented
92#4708C2×C311yescharacteristic, complemented
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#239—22no—
100C3×#239C2×C414yescomplemented
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yescomplemented
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C32×SD16C2×C414yescomplemented
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C42—21no—
121C32×C42C2311yescharacteristic
122C3×#217—21no—
123C3×#215C2×C414yescomplemented
124C3×#213C2×C414yescomplemented
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24C2×C414yescomplemented
144C3×ΓL(1,𝔽25)C2×C414yescomplemented
145C3×D3×C8—22no—
146#2946—31noSylow
147C2×C3×#41—31no—
148C22×C3×D4—31no—
149C2×#239C22×C311yescharacteristic
150C2×D3×D4C22×C311yescharacteristic
151C3×AGL(1,ℤ/8)—38no—
152C2×C3×SD16—21no—
153C2×C3×SD16—31no—
154C2×C3×SD16C2×D311yescharacteristic
155C2×C3×SD16C22×C311yescharacteristic
156C2×C3×D8—31no—
157C2×C3×D8—31no—
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8C2×D311yescharacteristic, complemented
163C3×C4×Q8C22×C311yescharacteristic, complemented
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—61no—
171C3×C4×D4—61no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C3×#117—31no—
178C3×#117—61no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—61no—
181C2×C3×C22⋊C4—61no—
182C2×C3×C22⋊C4—61no—
183Q8×Dic3C22×C311yescharacteristic, complemented
184C2×#215C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#213C22×C311yescharacteristic
187C4×#67—21no—
188C2×(C2×D3)⋊C4—21no—
189#914C3×C418yescomplemented
190C2×D24C22×C311yescharacteristic
191C2×ΓL(1,𝔽25)C22×C311yescharacteristic
192C2×D3×C8C22×C311yescharacteristic
193#893—21no—
194#893C22×C311yescharacteristic
195#893C22×C311yescharacteristic, complemented
196#892C22×C311yescharacteristic
197D3×C4⋊C4—21no—
198D3×C4⋊C4C22×C311yescharacteristic
199#67⋊C4—21no—
200D3×C22⋊C4—21no—
201C4×D12—21no—
202C4×D12C22×C311yescharacteristic
203C4×D12C22×C311yescharacteristic, complemented
204#872—21no—
205#872C22×C311yescharacteristic
206C3×#107—21no—
207C3×#107—31no—
208C3×#107C2×D311yescharacteristic, complemented
209C3×#107C22×C311yescharacteristic, complemented
210C3×#106—31no—
211C3×#106—31no—
212C3×#103—21no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic, complemented
215C3×#103C22×C311yescharacteristic, complemented
216C3×#102—21no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×#97—21no—
225C3×#97—31no—
226C3×#97C2×D311yescharacteristic, complemented
227C3×#97C22×C311yescharacteristic, complemented
228C3×C4×C8—31no—
229C3×C4×C8—31no—
230#835C22×C311yescharacteristic, complemented
231#832C22×C311yescharacteristic
232#821C22×C311yescharacteristic
233#821C22×C311yescharacteristic, complemented
234#817C22×C311yescharacteristic, complemented
235#815C22×C311yescharacteristic, complemented
236C8×Dic3C22×C311yescharacteristic, complemented
237#809C22×C311yescharacteristic
238#809C22×C311yescharacteristic, complemented
239#808C22×C311yescharacteristic, complemented
240#807C22×C311yescharacteristic, complemented
241C4×C3⋊C8C22×C311yescharacteristic, complemented
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—81no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C32×Q8—21no—
250C32×Q8C22×C412yes—
251C32×D4—21no—
252C32×D4C22×C412yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—81no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—24no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12C22×C412yes—
271C3×D12C22×C412yes—
272C3×C4×D3—24no—
273C3×C4×D3—81no—
274C3×C4×D3—81no—
275C3×C4×D3—81no—
276C3×C4×D3—81no—
277C3×C4×D3—81no—
278C3×C4×D3C22×C412yes—
279C3×C4×D3#4112yes—
280C32×C8—21no—
281C32×C8C22×C412yes—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C2×AGL(1,ℤ/8)—31no—
285#520—31no—
286#518—31no—
287#442—31no—
288#442—31no—
289#440—31no—
290#440C3×D311yescharacteristic, complemented
291C4×SD16—31no—
292C4×SD16—31no—
293C4×D8—31no—
294C4×D8—31no—
295#428—31no—
296#416—31no—
297C2×#102—31no—
298#405—31no—
299C24×C3—61no—
300C23×D3—21no—
301C3×#41—34no—
302C3×#41—62no—
303C2×C3×Q8—21no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—34no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C2×C3×D4—62no—
312C2×C3×D4—61no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C23×C311yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—41no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C2×#67—21no—
327C22×Dic3—21no—
328#239—22no—
329#239C2×C3×C414yescomplemented
330D3×D4—22no—
331D3×D4C2×C3×C414yescomplemented
332C2×D12—21no—
333C2×D12C23×C311yescharacteristic
334C2×D12C23×C311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3C23×C311yescharacteristic
342C3×SD16—24no—
343C3×SD16—34no—
344C3×SD16C4×D314yescomplemented
345C3×SD16C2×C3×C414yescomplemented
346C3×D8—34no—
347C3×D8—34no—
348C3×M16—34no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—62no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C23×C311yescharacteristic
357C2×C3×C8C23×C311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—41no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—21no—
385C3×C42—21no—
386C3×C42—21no—
387C3×C42—31no—
388C3×C42—41no—
389C3×C42—61no—
390C3×C42—61no—
391C3×C42C22×D311yescharacteristic
392C3×C42C23×C311yescharacteristic
393#217—21no—
394#215C2×C3×C414yescomplemented
395#213C2×C3×C414yescomplemented
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4C3×D411yescharacteristic
402(C2×D3)⋊C4C3×D411yescharacteristic
403C4⋊Dic3—21no—
404C4⋊Dic3C23×C311yescharacteristic
405C4⋊Dic3C23×C311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4C3×D411yescharacteristic
408Dic3⋊C4C3×D411yescharacteristic
409C4×Dic3—21no—
410C4×Dic3—21no—
411C4×Dic3C23×C311yescharacteristic
412C2×C3⋊C8C23×C311yescharacteristic
413C2×C3⋊C8C23×C311yescharacteristic
414D24C2×C3×C414yescomplemented
415ΓL(1,𝔽25)C2×C3×C414yescomplemented
416D3×C8—22no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3C4×D412yes—
431C32×C4—22no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—41no—
435C32×C4—41no—
436C32×C4C23×C411yescharacteristic
437C32×C4C2×#4111yescharacteristic
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D412yes—
443C2×#41—31no—
444C22×D4—31no—
445AGL(1,ℤ/8)—38no—
446C2×SD16—31no—
447C2×SD16C2×C3×D311yescharacteristic
448C2×D8—31no—
449C2×D8—31no—
450C2×M16—31no—
451C22×C8—31no—
452C4×Q8—31no—
453C4×Q8C2×C3×D311yescharacteristic, complemented
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—61no—
460C4×D4—61no—
461C4×D4—61no—
462C4×D4—61no—
463C4×D4C2×C3×D311yescharacteristic
464#117—31no—
465#117—31no—
466#117—61no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—61no—
469C2×C22⋊C4—61no—
470C2×C22⋊C4—61no—
471#107—31no—
472#107C2×C3×D311yescharacteristic, complemented
473#106—31no—
474#106—31no—
475#103—31no—
476#103C2×C3×D311yescharacteristic, complemented
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102C2×C3×D311yescharacteristic
483#97—31no—
484#97C2×C3×D311yescharacteristic, complemented
485C4×C8—31no—
486C4×C8—31no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—64no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—241no—
495C23×C3—241no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—24no—
499C22×D3—81no—
500C22×D3—81no—
501C22×D3C2×C3×D411yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—22no—
505C3×Q8—41no—
506C3×Q8C2×C4×D312yes—
507C3×Q8C22×C3×C412yes—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—32no—
513C3×D4—41no—
514C3×D4—64no—
515C3×D4—64no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4C2×C4×D312yes—
519C3×D4C22×C3×C412yes—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—64no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—81no—
541C2×C3×C4—81no—
542C2×C3×C4—82no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4—241no—
546C2×C3×C4—241no—
547C2×C3×C4—241no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C2×C3×D411yescharacteristic
552C2×C3×C4C2×C3×D411yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C24×C311yescharacteristic
555#67—24no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—81no—
559C2×Dic3C2×C3×D411yescharacteristic
560C2×Dic3C2×C3×D411yescharacteristic
561C2×Dic3C2×C3×D411yescharacteristic
562D12—24no—
563D12—21no—
564D12—21no—
565D12C22×C3×C412yes—
566D12C22×C3×C412yes—
567C4×D3—24no—
568C4×D3—81no—
569C4×D3—81no—
570C4×D3—81no—
571C4×D3—81no—
572C4×D3—81no—
573C4×D3C22×C3×C412yes—
574C4×D3C3×#4112yes—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—22no—
578C3×C8—32no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8C2×C4×D312yes—
582C3×C8C22×C3×C412yes—
583C3⋊C8—21no—
584C3⋊C8C22×C3×C412yes—
585C2×C32—42no—
586C2×C32C2×C4×D411yescharacteristic
587C2×C32#57611yescharacteristic
588C2×C32#57711yescharacteristic
589C3×D3—22no—
590C3×D3—42no—
591C3×D3—42no—
592C24—61no—
593#41—34no—
594#41—62no—
595C2×Q8C22×C3×D311yescharacteristic
596C2×D4—34no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—62no—
601C2×D4—61no—
602C2×D4C22×C3×D311yescharacteristic
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612SD16—34no—
613SD16C3×C4×D314yescomplemented
614D8—34no—
615D8—34no—
616M16—34no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—62no—
620C2×C8C22×C3×D311yescharacteristic
621C2×C8C22×C3×D311yescharacteristic
622C4⋊C4—21no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4C22×C3×D311yescharacteristic
630C4⋊C4C22×C3×D311yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C42—21no—
641C42—31no—
642C42—61no—
643C42—61no—
644C42C22×C3×D311yescharacteristic
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—244no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C22×C3×D411yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—84no—
676C2×D3C3×C4×D412yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—32no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4C22×C4×D311yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4C23×C3×C411yescharacteristic
702C3×C4C2×C3×#4111yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—41no—
706Dic3—41no—
707Dic3C3×C4×D412yes—
708C32#294611yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—64no—
712C23—61no—
713C23—61no—
714C23—241no—
715C23—241no—
716Q8—21no—
717Q8C2×C3×C4×D312yes—
718D4—21no—
719D4—32no—
720D4—32no—
721D4—64no—
722D4—64no—
723D4—61no—
724D4—61no—
725D4C2×C3×C4×D312yes—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—31no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—64no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—81no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—241no—
743C2×C4—241no—
744C2×C4C3×D3×D411yescharacteristic
745C2×C4C3×D3×D411yescharacteristic
746C2×C4C23×C3×D311yescharacteristic
747C8—21no—
748C8—32no—
749C8—61no—
750C8C2×C3×C4×D312yes—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—42no—
756C2×C3—62no—
757C2×C3—82no—
758C2×C3—122no—
759C2×C3—122no—
760C2×C3C4×D3×D411yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3#577811yescharacteristic
763C2×C3C2×C3×C4×D411yescharacteristic
764C2×C3C3×#57611yescharacteristic
765C2×C3C3×#57711yescharacteristic
766D3—22no—
767D3—42no—
768D3—42no—
769C22—22no—
770C22—32no—
771C22—41no—
772C22—41no—
773C22—61no—
774C22—61no—
775C22—62no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—244no—
782C22C2×C3×D3×D411yescharacteristic
783C4—21no—
784C4—21no—
785C4—22no—
786C4—32no—
787C4—41no—
788C4—41no—
789C4—61no—
790C4—61no—
791C4—121no—
792C4—121no—
793C4C22×C3×C4×D311yescharacteristic
794C4C3×D3×#4111yescharacteristic
795C3—21no—
796C3#7977511yescharacteristic, direct product factor
797C3C3×#294611yescharacteristic, complemented
798C2—42no—
799C2—62no—
800C2—122no—
801C2—122no—
802C2C3×C4×D3×D411yescharacteristic
803C2C3×#577411yescharacteristic
804C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C3×#914C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#440D3
hypocenterC3C3×#2946
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
2. C3×#5574C2semidirect
3. C3×#5545C2semidirect
4. C32×#440C2semidirect
5. C3×Dic3×SD16C2semidirect
6. C3×C4×#215C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4881C2semidirect
9. C3×#4872C2semidirect
10. C3×#4817C2semidirect
11. C3×#4804C2semidirect
12. C3×#4785C2semidirect
13. C3×D3×#102C2semidirect
14. C3×#4711C2semidirect
15. C3×#4708C2semidirect
17. #79775C3direct (N × H)
21. C32×C4×Q8C22semidirect
23. C3×Q8×Dic3C22semidirect
29. C3×#914C4semidirect
35. C3×#893C22semidirect
43. C3×C4×D12C22semidirect
46. C32×#107C22semidirect
47. C32×#103C22semidirect
49. C32×#97C22semidirect
50. C3×#835C22semidirect
53. C3×#821C22semidirect
54. C3×#817C22semidirect
55. C3×#815C22semidirect
56. C3×C8×Dic3C22semidirect
58. C3×#809C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
61. C3×C4×C3⋊C8C22semidirect
66. #5574C2×C3semidirect
67. #5545C2×C3semidirect
72. C3×#440D3semidirect
73. C3×#440C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. C4×#215C2×C3semidirect
84. C4×#213C2×C3semidirect
85. #4881C2×C3semidirect
86. #4872C2×C3semidirect
87. #4817C2×C3semidirect
88. #4804C2×C3semidirect
89. #4785C2×C3semidirect
90. D3×#102C2×C3semidirect
91. #4711C2×C3semidirect
92. #4708C2×C3semidirect
100. C3×#239C2×C4semidirect
102. C3×D3×D4C2×C4semidirect
113. C32×SD16C2×C4semidirect
123. C3×#215C2×C4semidirect
124. C3×#213C2×C4semidirect
143. C3×D24C2×C4semidirect
144. C3×ΓL(1,𝔽25)C2×C4semidirect
162. C3×C4×Q8C2×D3semidirect
163. C3×C4×Q8C22×C3semidirect
183. Q8×Dic3C22×C3semidirect
189. #914C3×C4semidirect
195. #893C22×C3semidirect
203. C4×D12C22×C3semidirect
208. C3×#107C2×D3semidirect
209. C3×#107C22×C3semidirect
214. C3×#103C2×D3semidirect
215. C3×#103C22×C3semidirect
226. C3×#97C2×D3semidirect
227. C3×#97C22×C3semidirect
230. #835C22×C3semidirect
233. #821C22×C3semidirect
234. #817C22×C3semidirect
235. #815C22×C3semidirect
236. C8×Dic3C22×C3semidirect
238. #809C22×C3semidirect
239. #808C22×C3semidirect
240. #807C22×C3semidirect
241. C4×C3⋊C8C22×C3semidirect
290. #440C3×D3semidirect
329. #239C2×C3×C4semidirect
331. D3×D4C2×C3×C4semidirect
344. C3×SD16C4×D3semidirect
345. C3×SD16C2×C3×C4semidirect
394. #215C2×C3×C4semidirect
395. #213C2×C3×C4semidirect
414. D24C2×C3×C4semidirect
415. ΓL(1,𝔽25)C2×C3×C4semidirect
453. C4×Q8C2×C3×D3semidirect
472. #107C2×C3×D3semidirect
476. #103C2×C3×D3semidirect
484. #97C2×C3×D3semidirect
613. SD16C3×C4×D3semidirect
708. C32#2946semidirect
796. C3#79775direct (N × H)
797. C3C3×#2946semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
C3×#55742
C3×#55452
C32×#4402
C3×Dic3×SD162
C3×C4×#2152
C3×C4×#2132
C3×#48812
C3×#48722
C3×#48172
C3×#48042
C3×#47852
C3×D3×#1022
C3×#47112
C3×#47082
C3×#29463
#797753