Finite Group Databasebeta

← C3×#81814 #11898409

Subgroups — C3×#81814 #11898409

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5681C211yesmaximal, characteristic, complemented
2C3×#5671C211yesmaximal, characteristic, complemented
3C32×#495C211yesmaximal, characteristic, complemented
4C3×#5185C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6C3×#5175C211yesmaximal, characteristic, complemented
7C3×#5168C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×Dic3×SD16C211yesmaximal, characteristic, complemented
10C3×#5153C211yesmaximal, characteristic, complemented
11C3×#5150C211yesmaximal, characteristic
12C3×#5057C211yesmaximal, characteristic, complemented
13C3×#5054C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C8×Dic6C211yesmaximal, characteristic, complemented
16C3×#3394—31nomaximal
17#81814C311yesmaximal, characteristic, direct product factor
18C2×C32×Q16C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22C32×#124C2211yescharacteristic
23C32×#124C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×#944C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#940C2211yescharacteristic
31C3×#936C2211yescharacteristic
32C3×D4×Dic3C2211yescharacteristic
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic
36C2×C3×#204C2211yescharacteristic
37C3×#886—21no—
38C3×#885—21no—
39C3×#883—21no—
40C3×#67⋊C4—21no—
41C3×#879—21no—
42C3×#879—21no—
43C3×#878—21no—
44C3×#877—21no—
45C3×C4×D12C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×C8×Dic3C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#556—31no—
63#5681C2×C311yescharacteristic, complemented
64#5671C2×C311yescharacteristic, complemented
65C3×#495—21no—
66C3×#495—31no—
67C3×#495D311yescharacteristic, complemented
68C3×#495C2×C311yescharacteristic, complemented
69C3×#492—31no—
70C3×#464—31no—
71C3×#464—31no—
72C3×#463—31no—
73C3×#463—31no—
74C3×#462—31no—
75C3×#459—31no—
76C3×C8×Q8—31no—
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×C4×SD16—31no—
80#5185C2×C311yescharacteristic, complemented
81#5182C2×C311yescharacteristic, complemented
82#5175C2×C311yescharacteristic, complemented
83#5168C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85Dic3×SD16C2×C311yescharacteristic, complemented
86#5153C2×C311yescharacteristic, complemented
87#5150C2×C311yescharacteristic
88#5057C2×C311yescharacteristic, complemented
89#5054C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91C8×Dic6C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6D411yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C32×Q16—41no—
105C32×SD16—22no—
106C32×SD16—22no—
107C32×D8—41no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#216—41no—
120C3×#215—41no—
121C3×#214—41no—
122C3×#213—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144#3394—31noSylow
145C2×C3×Q16—21no—
146C2×C3×Q16—31no—
147C2×C3×Q16C2×D311yescharacteristic
148C2×C3×Q16C22×C311yescharacteristic
149C2×C3×SD16—21no—
150C2×C3×SD16—21no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16C2×D311yescharacteristic
155C2×C3×SD16C2×D311yescharacteristic
156C2×C3×SD16C22×C311yescharacteristic
157C2×C3×SD16C22×C311yescharacteristic
158C2×C3×D8—21no—
159C2×C3×D8—31no—
160C2×C3×D8C2×D311yescharacteristic
161C2×C3×D8C22×C311yescharacteristic
162C3×C4⋊Q8—31no—
163C3×#127—31no—
164C3×#126—61no—
165C3×#126—61no—
166C3×#124—21no—
167C3×#124—21no—
168C3×#124—31no—
169C3×#124—31no—
170C3×#124—61no—
171C3×#124C2×D311yescharacteristic
172C3×#124C2×D311yescharacteristic
173C3×#124C22×C311yescharacteristic
174C3×#124C22×C311yescharacteristic
175C3×#123—61no—
176C3×#123—61no—
177C3×C22⋊Q8—61no—
178C3×C4×Q8—31no—
179C3×C4×Q8—31no—
180C3×C4×Q8—31no—
181C3×C4×Q8—31no—
182C3×C4×D4—31no—
183C3×C4×D4—31no—
184C3×C4×D4—31no—
185C3×C4×D4—61no—
186C3×#117—61no—
187#947C22×C311yescharacteristic
188Q8×Dic3C22×C311yescharacteristic
189Q8×Dic3C22×C311yescharacteristic
190#944C22×C311yescharacteristic
191C2×#216C22×C311yescharacteristic
192C2×#215C22×C311yescharacteristic
193#940C22×C311yescharacteristic
194#936C22×C311yescharacteristic
195D4×Dic3C22×C311yescharacteristic
196D4×Dic3C22×C311yescharacteristic
197C2×#214C22×C311yescharacteristic
198C2×#213C22×C311yescharacteristic
199C2×#204C22×C311yescharacteristic
200#886—21no—
201#885—21no—
202#883—21no—
203#67⋊C4—21no—
204#879—21no—
205#879—21no—
206#878—21no—
207#877—21no—
208C4×D12C22×C311yescharacteristic
209C4×Dic6C22×C311yescharacteristic
210C4×Dic6C22×C311yescharacteristic
211C3×#106—31no—
212C3×C4⋊C8—31no—
213C3×C4⋊C8—31no—
214C3×C4⋊C8—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C4×C8—21no—
222C3×C4×C8—31no—
223C3×C4×C8—31no—
224C3×C4×C8C2×D311yescharacteristic
225C3×C4×C8C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#832C22×C311yescharacteristic
229#832C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231#817C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233Dic3⋊C8C22×C311yescharacteristic
234Dic3⋊C8C22×C311yescharacteristic
235C8×Dic3C22×C311yescharacteristic
236C8×Dic3C22×C311yescharacteristic
237C4⋊(C3⋊C8)C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32—21no—
240C22×C3×D3—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—42no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—81no—
268C3×Dic6—22no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C32×C8—21no—
272C32×C8#4112yes—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#559—31no—
276#556—31no—
277#495—31no—
278#495C3×D311yescharacteristic, complemented
279#492—31no—
280#464—31no—
281#464—31no—
282#463—31no—
283#463—31no—
284#462—31no—
285#459—31no—
286C8×Q8—31no—
287C4×SD16—31no—
288C4×SD16—31no—
289C4×SD16—31no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C23×C311yescharacteristic
297C2×C3×Q8C23×C311yescharacteristic
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C2×D12C23×C311yescharacteristic
315C2×C4×D3—21no—
316C2×Dic6C3×D411yescharacteristic
317C2×Dic6C23×C311yescharacteristic
318C3×Q16—41no—
319C3×Q16—41no—
320C3×Q16—42no—
321C3×Q16—121no—
322C3×SD16—22no—
323C3×SD16—22no—
324C3×SD16—22no—
325C3×SD16—22no—
326C3×SD16—42no—
327C3×SD16—42no—
328C3×SD16—62no—
329C3×SD16—121no—
330C3×SD16—121no—
331C3×D8—41no—
332C3×D8—41no—
333C3×D8—42no—
334C3×D8—121no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—21no—
373C3×C42—31no—
374C3×C42—31no—
375C3×C42—61no—
376C3×C42—61no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C23×C311yescharacteristic
380#217—21no—
381#217—21no—
382#217—21no—
383#217—21no—
384#216—41no—
385#215—41no—
386#214—41no—
387#213—41no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3C3×D411yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4C3×D411yescharacteristic
400Dic3⋊C4C3×D411yescharacteristic
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3C23×C311yescharacteristic
405C4×Dic3C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408#204—22no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3#13512yes—
432C2×Q16—31no—
433C2×Q16C2×C3×D311yescharacteristic
434C2×SD16—31no—
435C2×SD16—31no—
436C2×SD16—31no—
437C2×SD16C2×C3×D311yescharacteristic
438C2×SD16C2×C3×D311yescharacteristic
439C2×D8—31no—
440C2×D8C2×C3×D311yescharacteristic
441C4⋊Q8—31no—
442#127—31no—
443#126—61no—
444#126—61no—
445#124—31no—
446#124—31no—
447#124—61no—
448#124C2×C3×D311yescharacteristic
449#124C2×C3×D311yescharacteristic
450#123—61no—
451#123—61no—
452C22⋊Q8—61no—
453C4×Q8—31no—
454C4×Q8—31no—
455C4×Q8—31no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—61no—
461#117—61no—
462#106—31no—
463C4⋊C8—31no—
464C4⋊C8—31no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#102—31no—
470#102—31no—
471#102—31no—
472C4×C8—31no—
473C4×C8—31no—
474C4×C8C2×C3×D311yescharacteristic
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—61no—
482C22×D3—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—62no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4—241no—
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—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C24×C311yescharacteristic
539#67—42no—
540#67—81no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—42no—
545C2×Dic3—81no—
546C2×Dic3C2×C3×D411yescharacteristic
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550D12—21no—
551D12—21no—
552C4×D3—81no—
553Dic6—22no—
554Dic6—21no—
555Dic6—21no—
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—22no—
560C3×C8—61no—
561C3×C8—61no—
562C3×C8#23712yes—
563C3×C8C3×#4112yes—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32—81no—
567C2×C32—81no—
568C2×C32#55011yescharacteristic
569C2×C32C2×#13511yescharacteristic
570C2×C32#57711yescharacteristic
571C3×D3—81no—
572C2×Q8—31no—
573C2×Q8—31no—
574C2×Q8C22×C3×D311yescharacteristic
575C2×Q8C22×C3×D311yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C22×C3×D311yescharacteristic
580C2×D4C22×C3×D311yescharacteristic
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584Q16—41no—
585Q16—121no—
586SD16—22no—
587SD16—22no—
588SD16—62no—
589SD16—121no—
590SD16—121no—
591D8—41no—
592D8—121no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8C22×C3×D311yescharacteristic
596C2×C8C22×C3×D311yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C42—31no—
619C42—31no—
620C42—61no—
621C42—61no—
622C42—61no—
623C42C22×C3×D311yescharacteristic
624C22×C3—21no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C22×C3×D411yescharacteristic
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—32no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23711yescharacteristic
673C3×C4#100411yescharacteristic
674C3×C4C2×C3×#4111yescharacteristic
675C3×C4C3×H(5,𝔽2)11yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3C3×#13512yes—
683C32#339411yescharacteristic, complemented, Sylow
684C23—21no—
685C23—21no—
686C23—61no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—62no—
692Q8—61no—
693Q8—61no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—61no—
699D4—61no—
700D4—122no—
701D4—241no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—122no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4C3×D3×D411yescharacteristic
715C2×C4C3×D3×D411yescharacteristic
716C2×C4C23×C3×D311yescharacteristic
717C8—21no—
718C8—61no—
719C8—61no—
720C8C3×#23712yes—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—81no—
725C2×C3—81no—
726C2×C3—81no—
727C2×C3—81no—
728C2×C3—161no—
729C2×C3—161no—
730C2×C3—241no—
731C2×C3#571811yescharacteristic
732C2×C3D3×#13511yescharacteristic
733C2×C3#577011yescharacteristic
734C2×C3C3×#55011yescharacteristic
735C2×C3C2×C3×#13511yescharacteristic
736C2×C3C3×#57711yescharacteristic
737D3—81no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22C2×C3×D3×D411yescharacteristic
748C4—21no—
749C4—21no—
750C4—32no—
751C4—41no—
752C4—41no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4C2×C3×#23711yescharacteristic
760C4C3×#100411yescharacteristic
761C3—21no—
762C3#8181411yescharacteristic, direct product factor
763C3C3×#339411yescharacteristic, complemented
764C2—81no—
765C2—81no—
766C2—241no—
767C2C3×#571811yescharacteristic
768C2C3×D3×#13511yescharacteristic
769C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#495C2
socleC22×C32C22×D4
prime radicalC3×#5150C2
hypercenterC3×#495D3
hypocenterC3C3×#3394
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#495

Complements

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

NH ≅ G/Ntype
1. C3×#5681C2semidirect
2. C3×#5671C2semidirect
3. C32×#495C2semidirect
4. C3×#5185C2semidirect
5. C3×#5182C2semidirect
6. C3×#5175C2semidirect
7. C3×#5168C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×Dic3×SD16C2semidirect
10. C3×#5153C2semidirect
12. C3×#5057C2semidirect
13. C3×#5054C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C8×Dic6C2semidirect
17. #81814C3direct (N × H)
63. #5681C2×C3semidirect
64. #5671C2×C3semidirect
67. C3×#495D3semidirect
68. C3×#495C2×C3semidirect
80. #5185C2×C3semidirect
81. #5182C2×C3semidirect
82. #5175C2×C3semidirect
83. #5168C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. Dic3×SD16C2×C3semidirect
86. #5153C2×C3semidirect
88. #5057C2×C3semidirect
89. #5054C2×C3semidirect
90. C4×#204C2×C3semidirect
91. C8×Dic6C2×C3semidirect
278. #495C3×D3semidirect
683. C32#3394semidirect
762. C3#81814direct (N × H)
763. C3C3×#3394semidirect

Maximal subgroups

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

subgroupindex
C3×#56812
C3×#56712
C32×#4952
C3×#51852
C3×#51822
C3×#51752
C3×#51682
C3×Dic3×SD162
C3×#51532
C3×#51502
C3×#50572
C3×#50542
C3×C4×#2042
C3×C8×Dic62
C3×#33943
#818143