Finite Group Databasebeta

← C3×#80452 #11888597

Subgroups — C3×#80452 #11888597

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic, complemented
2C3×#5558C211yesmaximal, characteristic, complemented
3C32×#461C211yesmaximal, characteristic, complemented
4C3×#5174C211yesmaximal, characteristic, complemented
5C3×#5172C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7C3×#5171C211yesmaximal, characteristic, complemented
8C3×#5082C211yesmaximal, characteristic, complemented
9C3×#5014C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4814C211yesmaximal, characteristic, complemented
13C3×#4805C211yesmaximal, characteristic, complemented
14C3×#4804C211yesmaximal, characteristic, complemented
15C3×#4803C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#80452C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#929—21no—
30C3×C4×#67—21no—
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C3×#895—21no—
34C3×#894—21no—
35C3×#894—21no—
36C3×#892C2211yescharacteristic
37C3×D3×C4⋊C4—21no—
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#884—21no—
40C3×#879—21no—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×#870C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×#818C2211yescharacteristic
57C3×#817C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5726C2×C311yescharacteristic, complemented
64#5558C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#478—31no—
69C3×#468—31no—
70C3×#465—31no—
71C3×#461—21no—
72C3×#461D311yescharacteristic, complemented
73C3×#461C2×C311yescharacteristic, complemented
74C3×#449—31no—
75C3×#449—31no—
76C3×#442—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5174C2×C311yescharacteristic, complemented
81#5172C2×C311yescharacteristic, complemented
82#5172C2×C311yescharacteristic, complemented
83#5171C2×C311yescharacteristic, complemented
84#5082C2×C311yescharacteristic, complemented
85#5014C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4836C2×C311yescharacteristic, complemented
88#4814C2×C311yescharacteristic, complemented
89#4805C2×C311yescharacteristic, complemented
90#4804C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—41no—
101C3×#239—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
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×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C32×SD16—41no—
113C32×SD16—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4—21no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#239C22×C311yescharacteristic
149C2×C3×SD16—21no—
150C2×C3×SD16—21no—
151C2×C3×SD16C2×D311yescharacteristic
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C22×C311yescharacteristic
154C2×C3×SD16C22×C311yescharacteristic
155C2×C3×D8—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C4⋊Q8—21no—
159C3×C4⋊Q8C2×D311yescharacteristic
160C3×C4⋊Q8C22×C311yescharacteristic
161C3×#126—61no—
162C3×#125—31no—
163C3×#123—61no—
164C3×#123—61no—
165C3×#123—61no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—61no—
172C3×C4×D4—21no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4—61no—
176C3×C4×D4C2×D311yescharacteristic
177C3×C4×D4C22×C311yescharacteristic
178C3×#117—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—61no—
181#946C22×C311yescharacteristic
182#946C22×C311yescharacteristic
183#938C22×C311yescharacteristic
184#938C22×C311yescharacteristic
185C2×#213C22×C311yescharacteristic
186#929—21no—
187C4×#67—21no—
188C2×ΓL(1,𝔽25)C22×C311yescharacteristic
189C2×D3×C8C22×C311yescharacteristic
190#895—21no—
191#894—21no—
192#894—21no—
193#892C22×C311yescharacteristic
194D3×C4⋊C4—21no—
195D3×C4⋊C4C22×C311yescharacteristic
196#884—21no—
197#879—21no—
198C4×D12C22×C311yescharacteristic
199C4×D12C22×C311yescharacteristic
200#870C22×C311yescharacteristic
201C3×#107—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—21no—
205C3×C4⋊C8C2×D311yescharacteristic
206C3×C4⋊C8C22×C311yescharacteristic
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103C2×D311yescharacteristic
214C3×#103C2×D311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×#97—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#832C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic
232(C2×D3)⋊C8C22×C311yescharacteristic
233#818C22×C311yescharacteristic
234#817C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—21no—
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—81no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—41no—
264C3×D12—42no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—31no—
281#491—31no—
282#485—31no—
283#483—31no—
284#478—31no—
285#468—31no—
286#465—31no—
287#461C3×D311yescharacteristic, complemented
288#449—31no—
289#449—31no—
290#442—31no—
291#435—31no—
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C23×C311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C2×#67—21no—
323C2×#67—21no—
324#239—22no—
325#239—22no—
326#239—41no—
327#239—41no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12C3×D411yescharacteristic
331C2×D12C23×C311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3C23×C311yescharacteristic
337C2×C4×D3C23×C311yescharacteristic
338C3×SD16—41no—
339C3×SD16—41no—
340C3×SD16—41no—
341C3×SD16—41no—
342C3×SD16—42no—
343C3×SD16—42no—
344C3×D8—62no—
345C3×M16—121no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C23×C311yescharacteristic
354C2×C3×C8C23×C311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—41no—
365C3×C4⋊C4—41no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
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—61no—
386C3×C42C22×D311yescharacteristic
387C3×C42C23×C311yescharacteristic
388#217—21no—
389#217—21no—
390#213—22no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4C3×D411yescharacteristic
396(C2×D3)⋊C4C3×D411yescharacteristic
397C4⋊Dic3C3×D411yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399C4⋊Dic3C23×C311yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406C4×Dic3—21no—
407C2×C3⋊C8C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409ΓL(1,𝔽25)—41no—
410D3×C8—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—31no—
438C2×SD16C2×C3×D311yescharacteristic
439C2×SD16C2×C3×D311yescharacteristic
440C2×D8—31no—
441C2×M16—31no—
442C22×C8—31no—
443C4⋊Q8C2×C3×D311yescharacteristic
444#126—61no—
445#125—31no—
446#123—61no—
447#123—61no—
448#123—61no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451#121—31no—
452#121—31no—
453#121—61no—
454#121—61no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—61no—
458C4×D4C2×C3×D311yescharacteristic
459#117—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—61no—
462#107—31no—
463#106—31no—
464#106—31no—
465C4⋊C8C2×C3×D311yescharacteristic
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103C2×C3×D311yescharacteristic
471#103C2×C3×D311yescharacteristic
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478#97—31no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3C2×C3×D411yescharacteristic
487C22×D3C2×C3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×D4—22no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—61no—
508C3×D4—121no—
509C3×D4—122no—
510C3×D4—122no—
511C3×D4—122no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—81no—
535C2×C3×C4—81no—
536C2×C3×C4—82no—
537C2×C3×C4—122no—
538C2×C3×C4—122no—
539C2×C3×C4—122no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×C3×D411yescharacteristic
544C2×C3×C4C2×C3×D411yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C24×C311yescharacteristic
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554D12—21no—
555D12—41no—
556D12—42no—
557D12—42no—
558D12C3×#4112yes—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—81no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—81no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—62no—
586#41—121no—
587#41—121no—
588C2×Q8C22×C3×D311yescharacteristic
589C2×Q8C22×C3×D311yescharacteristic
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4C22×C3×D311yescharacteristic
597C22×C4—21no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604SD16—41no—
605SD16—41no—
606D8—62no—
607M16—121no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—121no—
611C2×C8C22×C3×D311yescharacteristic
612C2×C8C22×C3×D311yescharacteristic
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4C22×C3×D311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—31no—
627C22⋊C4—31no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C42—61no—
635C42C22×C3×D311yescharacteristic
636C22×C3—21no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C22×C3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—22no—
664C2×D3—41no—
665C2×D3—41no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4C2×C3×#4111yescharacteristic
691C3×C4C3×H(5,𝔽2)11yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—21no—
699C23—31no—
700C23—31no—
701C23—61no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706D4—21no—
707D4—21no—
708D4—32no—
709D4—61no—
710D4—121no—
711D4—122no—
712D4—122no—
713D4—122no—
714D4—241no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—81no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—241no—
732C2×C4C3×D3×D411yescharacteristic
733C2×C4C3×D3×D411yescharacteristic
734C2×C4C23×C3×D311yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—82no—
743C2×C3—81no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—121no—
747C2×C3—122no—
748C2×C3#561211yescharacteristic
749C2×C3#576211yescharacteristic
750C2×C3#577711yescharacteristic
751C2×C3C3×#54611yescharacteristic
752C2×C3C3×#57511yescharacteristic
753C2×C3C3×#57711yescharacteristic
754D3—41no—
755D3—41no—
756D3—42no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—62no—
767C22—121no—
768C22—121no—
769C22C2×C3×D3×D411yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4C3×#100411yescharacteristic
781C4C3×D3×#4111yescharacteristic
782C3—21no—
783C3#8045211yescharacteristic, direct product factor
784C3C3×#330711yescharacteristic, complemented
785C2—81no—
786C2—121no—
787C2—121no—
788C2—122no—
789C2C3×#561211yescharacteristic
790C2C3×#576211yescharacteristic
791C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
hypercenterC3×#461D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C3×#5726C2semidirect
2. C3×#5558C2semidirect
3. C32×#461C2semidirect
4. C3×#5174C2semidirect
5. C3×#5172C2semidirect
6. C3×#5172C2semidirect
7. C3×#5171C2semidirect
8. C3×#5082C2semidirect
9. C3×#5014C2semidirect
10. C3×#4847C2semidirect
11. C3×#4836C2semidirect
12. C3×#4814C2semidirect
13. C3×#4805C2semidirect
14. C3×#4804C2semidirect
15. C3×#4803C2semidirect
17. #80452C3direct (N × H)
63. #5726C2×C3semidirect
64. #5558C2×C3semidirect
72. C3×#461D3semidirect
73. C3×#461C2×C3semidirect
80. #5174C2×C3semidirect
81. #5172C2×C3semidirect
82. #5172C2×C3semidirect
83. #5171C2×C3semidirect
84. #5082C2×C3semidirect
85. #5014C2×C3semidirect
86. #4847C2×C3semidirect
87. #4836C2×C3semidirect
88. #4814C2×C3semidirect
89. #4805C2×C3semidirect
90. #4804C2×C3semidirect
91. #4803C2×C3semidirect
287. #461C3×D3semidirect
697. C32#3307semidirect
783. C3#80452direct (N × H)
784. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C3×#55582
C32×#4612
C3×#51742
C3×#51722
C3×#51712
C3×#50822
C3×#50142
C3×#48472
C3×#48362
C3×#48142
C3×#48052
C3×#48042
C3×#48032
C3×#33073
#804523