Finite Group Databasebeta

← C3×#80581 #11895607

Subgroups — C3×#80581 #11895607

Order 1152.

752 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5681C211yesmaximal, characteristic
2C3×#5569C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic, complemented
4C3×#5185C211yesmaximal, characteristic, complemented
5C3×Dic3×Q16C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic
7C3×Dic3×SD16C211yesmaximal, characteristic, complemented
8C3×#5056C211yesmaximal, characteristic, complemented
9C3×C4×#215C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4830C211yesmaximal, characteristic, complemented
12C3×#4800C211yesmaximal, characteristic, complemented
13C3×#4791C211yesmaximal, characteristic, complemented
14C3×#4766C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic
16C3×#3365—31nomaximal
17#80581C311yesmaximal, characteristic, direct product factor
18C2×C32×Q16C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×#890—21no—
30C3×#890C2211yescharacteristic
31C3×#888—21no—
32C3×#888C2211yescharacteristic
33C3×#886—21no—
34C3×#885—21no—
35C3×#883—21no—
36C3×#67⋊C4—21no—
37C3×C4×D12C2211yescharacteristic
38C3×#870—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6—21no—
41C3×C4×Dic6C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62C3×#557—31no—
63#5681C2×C311yescharacteristic
64#5569C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#488—31no—
67C3×#486—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#475—31no—
71C3×#464—21no—
72C3×#464—31no—
73C3×#464D311yescharacteristic, complemented
74C3×#464C2×C311yescharacteristic, complemented
75C3×#460—31no—
76C3×C8×Q8—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×C4×SD16—31no—
80#5185C2×C311yescharacteristic, complemented
81Dic3×Q16C2×C311yescharacteristic, complemented
82#5163C2×C311yescharacteristic
83Dic3×SD16C2×C311yescharacteristic, complemented
84#5056C2×C311yescharacteristic, complemented
85C4×#215C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4830C2×C311yescharacteristic, complemented
88#4800C2×C311yescharacteristic, complemented
89#4791C2×C311yescharacteristic, complemented
90#4766C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6D411yescharacteristic
102C32×Q16—22no—
103C32×SD16—22no—
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C22⋊C4—21no—
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112C3×#217—21no—
113C3×#215—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3365—31noSylow
139C2×C3×Q16—21no—
140C2×C3×Q16C2×D311yescharacteristic
141C2×C3×Q16C22×C311yescharacteristic
142C2×C3×SD16—21no—
143C2×C3×SD16—31no—
144C2×C3×SD16C2×D311yescharacteristic
145C2×C3×SD16C22×C311yescharacteristic
146C3×C4⋊Q8—31no—
147C3×C4⋊Q8—61no—
148C3×#127—31no—
149C3×#125—31no—
150C3×#125—31no—
151C3×#125—61no—
152C3×#125—61no—
153C3×#124—21no—
154C3×#124—31no—
155C3×#124—61no—
156C3×#124C2×D311yescharacteristic
157C3×#124C22×C311yescharacteristic
158C3×#123—61no—
159C3×#123—61no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—61no—
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×Q8C22×C311yescharacteristic
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—61no—
171#947C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173Q8×Dic3C22×C311yescharacteristic
174Q8×Dic3C22×C311yescharacteristic
175C2×#215C22×C311yescharacteristic
176#940C22×C311yescharacteristic
177D4×Dic3C22×C311yescharacteristic
178#890—21no—
179#890C22×C311yescharacteristic
180#888—21no—
181#888C22×C311yescharacteristic
182#886—21no—
183#885—21no—
184#883—21no—
185#67⋊C4—21no—
186C4×D12C22×C311yescharacteristic
187#870—21no—
188#870C22×C311yescharacteristic
189C4×Dic6—21no—
190C4×Dic6C22×C311yescharacteristic
191C3×#107—31no—
192C3×#106—31no—
193C3×#106—31no—
194C3×C4⋊C8—21no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8C2×D311yescharacteristic
198C3×C4⋊C8C22×C311yescharacteristic
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic
204C3×#103C22×C311yescharacteristic
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215C3×C4×C8—31no—
216#835C22×C311yescharacteristic
217#835C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#818C22×C311yescharacteristic
224#817C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231C4×C3⋊C8C22×C311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×Q8#4112yes—
238C32×D4—21no—
239C32×D4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C3×#67—42no—
247C3×#67—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—81no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×C4×D3—81no—
259C3×Dic6—22no—
260C3×Dic6—42no—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
266#557—31no—
267#488—31no—
268#488—31no—
269#486—31no—
270#478—31no—
271#478—31no—
272#475—31no—
273#464—31no—
274#464C3×D311yescharacteristic, complemented
275#460—31no—
276C8×Q8—31no—
277C4×Q16—31no—
278C4×SD16—31no—
279C4×SD16—31no—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C23×C311yescharacteristic
287C2×C3×Q8C23×C311yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—31no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C23×C311yescharacteristic
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C2×#67—21no—
297C2×#67—21no—
298C22×Dic3—21no—
299C2×D12C23×C311yescharacteristic
300C2×C4×D3—21no—
301C2×Dic6—21no—
302C2×Dic6C3×D411yescharacteristic
303C3×Q16—22no—
304C3×Q16—22no—
305C3×Q16—42no—
306C3×SD16—22no—
307C3×SD16—22no—
308C3×SD16—42no—
309C3×SD16—62no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C23×C311yescharacteristic
317C2×C3×C8C23×C311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—41no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—41no—
343C3×C22⋊C4—41no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—31no—
353C3×C42—41no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42C22×D311yescharacteristic
358C3×C42C23×C311yescharacteristic
359#217—21no—
360#215—22no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364C4⋊Dic3—21no—
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—21no—
368C4⋊Dic3C3×D411yescharacteristic
369C4⋊Dic3C23×C311yescharacteristic
370C4⋊Dic3C23×C311yescharacteristic
371C4⋊Dic3C23×C311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4C3×D411yescharacteristic
377Dic3⋊C4C3×D411yescharacteristic
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3C23×C311yescharacteristic
382C4×Dic3C23×C311yescharacteristic
383C2×C3⋊C8C23×C311yescharacteristic
384C2×C3⋊C8C23×C311yescharacteristic
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—22no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3#13512yes—
406C2×Q16C2×C3×D311yescharacteristic
407C2×SD16—31no—
408C2×SD16C2×C3×D311yescharacteristic
409C4⋊Q8—31no—
410C4⋊Q8—61no—
411#127—31no—
412#125—31no—
413#125—31no—
414#125—61no—
415#125—61no—
416#124—31no—
417#124—61no—
418#124C2×C3×D311yescharacteristic
419#123—61no—
420#123—61no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—61no—
426C4×Q8C2×C3×D311yescharacteristic
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—61no—
430#107—31no—
431#106—31no—
432#106—31no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8C2×C3×D311yescharacteristic
436#103—31no—
437#103—31no—
438#103—31no—
439#103C2×C3×D311yescharacteristic
440#102—31no—
441#102—31no—
442#102—31no—
443#102—31no—
444#102—31no—
445#102C2×C3×D311yescharacteristic
446C4×C8—31no—
447C4×C8—31no—
448C4×C8—31no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—41no—
452C23×C3—61no—
453C22×D3—21no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—22no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8—62no—
465C3×Q8—122no—
466C3×Q8#23712yes—
467C3×Q8C3×#4112yes—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—122no—
477C3×D4—241no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—241no—
498C2×C3×C4—241no—
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4C2×C3×D411yescharacteristic
502C2×C3×C4C2×C3×D411yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C24×C311yescharacteristic
505#67—42no—
506#67—81no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—81no—
511C2×Dic3C2×C3×D411yescharacteristic
512C2×Dic3C2×C3×D411yescharacteristic
513C2×Dic3C2×C3×D411yescharacteristic
514C2×Dic3C2×C3×D411yescharacteristic
515D12—21no—
516D12—21no—
517C4×D3—81no—
518Dic6—22no—
519Dic6—42no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—41no—
525C3×C8—41no—
526C3×C8—61no—
527C3×C8—61no—
528C3⋊C8—21no—
529C3⋊C8—21no—
530C2×C32—81no—
531C2×C32#54811yescharacteristic
532C2×C32C2×#13511yescharacteristic
533C2×C32#57711yescharacteristic
534C3×D3—81no—
535C2×Q8—31no—
536C2×Q8—61no—
537C2×Q8C22×C3×D311yescharacteristic
538C2×Q8C22×C3×D311yescharacteristic
539C2×D4—31no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4C22×C3×D311yescharacteristic
543C22×C4—61no—
544C22×C4—61no—
545Q16—22no—
546SD16—22no—
547SD16—62no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8C22×C3×D311yescharacteristic
551C2×C8C22×C3×D311yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4C22×C3×D311yescharacteristic
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—61no—
574C42—21no—
575C42—31no—
576C42—31no—
577C42—61no—
578C42—61no—
579C42—61no—
580C42C22×C3×D311yescharacteristic
581C22×C3—21no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—81no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3C2×D3×D411yescharacteristic
595C22×C3C22×C3×D411yescharacteristic
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—32no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—42no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—81no—
619C3×C4—81no—
620C3×C4—121no—
621C3×C4—121no—
622C3×C4—121no—
623C3×C4C2×#23711yescharacteristic
624C3×C4#101011yescharacteristic
625C3×C4C2×C3×#4111yescharacteristic
626C3×C4C3×2−1+411yescharacteristic
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—41no—
631Dic3—41no—
632Dic3—41no—
633Dic3C3×#13512yes—
634C32#336511yescharacteristic, complemented, Sylow
635C23—21no—
636C23—61no—
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—62no—
641Q8—122no—
642Q8C3×#23712yes—
643D4—21no—
644D4—21no—
645D4—61no—
646D4—61no—
647D4—122no—
648D4—241no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—241no—
660C2×C4—241no—
661C2×C4C3×D3×D411yescharacteristic
662C2×C4C3×D3×D411yescharacteristic
663C2×C4C23×C3×D311yescharacteristic
664C8—21no—
665C8—21no—
666C8—61no—
667C8—61no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—81no—
672C2×C3—81no—
673C2×C3—161no—
674C2×C3—241no—
675C2×C3#559811yescharacteristic
676C2×C3D3×#13511yescharacteristic
677C2×C3#577811yescharacteristic
678C2×C3C3×#54811yescharacteristic
679C2×C3C2×C3×#13511yescharacteristic
680C2×C3C3×#57711yescharacteristic
681D3—81no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22C2×C3×D3×D411yescharacteristic
689C4—21no—
690C4—21no—
691C4—22no—
692C4—32no—
693C4—41no—
694C4—41no—
695C4—61no—
696C4—61no—
697C4—61no—
698C4—121no—
699C4—121no—
700C4—121no—
701C4C2×C3×#23711yescharacteristic
702C4C3×#101011yescharacteristic
703C3—21no—
704C3#8058111yescharacteristic, direct product factor
705C3C3×#336511yescharacteristic, complemented
706C2—81no—
707C2—241no—
708C2C3×#559811yescharacteristic
709C2C3×D3×#13511yescharacteristic
710C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC3×#464D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#464

Complements

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

NH ≅ G/Ntype
2. C3×#5569C2semidirect
3. C32×#464C2semidirect
4. C3×#5185C2semidirect
5. C3×Dic3×Q16C2semidirect
7. C3×Dic3×SD16C2semidirect
8. C3×#5056C2semidirect
9. C3×C4×#215C2semidirect
10. C3×#4847C2semidirect
11. C3×#4830C2semidirect
12. C3×#4800C2semidirect
13. C3×#4791C2semidirect
14. C3×#4766C2semidirect
17. #80581C3direct (N × H)
64. #5569C2×C3semidirect
73. C3×#464D3semidirect
74. C3×#464C2×C3semidirect
80. #5185C2×C3semidirect
81. Dic3×Q16C2×C3semidirect
83. Dic3×SD16C2×C3semidirect
84. #5056C2×C3semidirect
85. C4×#215C2×C3semidirect
86. #4847C2×C3semidirect
87. #4830C2×C3semidirect
88. #4800C2×C3semidirect
89. #4791C2×C3semidirect
90. #4766C2×C3semidirect
274. #464C3×D3semidirect
634. C32#3365semidirect
704. C3#80581direct (N × H)
705. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C3×#56812
C3×#55692
C32×#4642
C3×#51852
C3×Dic3×Q162
C3×#51632
C3×Dic3×SD162
C3×#50562
C3×C4×#2152
C3×#48472
C3×#48302
C3×#48002
C3×#47912
C3×#47662
C3×#47602
C3×#33653
#805813