Finite Group Databasebeta

← C3×#81652 #11887196

Subgroups — C3×#81652 #11887196

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic, complemented
2C3×#5676C211yesmaximal, characteristic
3C32×#488C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5054C211yesmaximal, characteristic, complemented
6C3×#4813C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8C3×#4805C211yesmaximal, characteristic, complemented
9C3×#4804C211yesmaximal, characteristic, complemented
10C3×#4779C211yesmaximal, characteristic, complemented
11C3×#4778C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C8×D12C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#81652C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#125C2211yescharacteristic, complemented
21C32×#124C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#898—21no—
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic, complemented
32C3×#894—21no—
33C3×#892—21no—
34C3×#892C2211yescharacteristic, complemented
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#890—21no—
37C3×#884—21no—
38C3×#883—21no—
39C3×#882—21no—
40C3×D3×C22⋊C4—21no—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5694C2×C311yescharacteristic, complemented
64#5676C2×C311yescharacteristic
65C3×#488—21no—
66C3×#488D311yescharacteristic, complemented
67C3×#488C2×C311yescharacteristic, complemented
68C3×#483—31no—
69C3×#482—31no—
70C3×#478—31no—
71C3×#467—31no—
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#450—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5066C2×C311yescharacteristic, complemented
81#5054C2×C311yescharacteristic, complemented
82#4813C2×C311yescharacteristic, complemented
83#4808C2×C311yescharacteristic, complemented
84#4805C2×C311yescharacteristic, complemented
85#4804C2×C311yescharacteristic, complemented
86#4779C2×C311yescharacteristic, complemented
87#4778C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic, complemented
89D3×#102C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91C8×D12C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×#239—22no—
98C3×#239—41no—
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C2×C3×D12—21no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#216—41no—
121C3×#214—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×D3×C8—41no—
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C22×C311yescharacteristic
148C2×D3×D4C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—21no—
156C3×#125—61no—
157C3×#125C2×D311yescharacteristic, complemented
158C3×#125C22×C311yescharacteristic, complemented
159C3×#124—21no—
160C3×#124C2×D311yescharacteristic
161C3×#124C22×C311yescharacteristic
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#120—61no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×#117—31no—
174C3×#117—61no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—61no—
177#946C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic, complemented
179#938C22×C311yescharacteristic
180C2×#214C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182C2×D3×C8C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic, complemented
184#898—21no—
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic, complemented
187#894—21no—
188#892—21no—
189#892C22×C311yescharacteristic, complemented
190D3×C4⋊C4C22×C311yescharacteristic
191#890—21no—
192#884—21no—
193#883—21no—
194#882—21no—
195D3×C22⋊C4—21no—
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic, complemented
199C3×#107—31no—
200C3×#106—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103C2×D311yescharacteristic, complemented
208C3×#103C2×D311yescharacteristic, complemented
209C3×#103C22×C311yescharacteristic, complemented
210C3×#103C22×C311yescharacteristic, complemented
211C3×#102—21no—
212C3×#102—21no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C2×D311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—21no—
224C3×C4×C8C2×D311yescharacteristic, complemented
225C3×C4×C8C22×C311yescharacteristic, complemented
226#835C22×C311yescharacteristic, complemented
227#832C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230(C2×D3)⋊C8C22×C311yescharacteristic, complemented
231#817C22×C311yescharacteristic, complemented
232#816C22×C311yescharacteristic, complemented
233#809C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#808C22×C311yescharacteristic, complemented
236#807C22×C311yescharacteristic, complemented
237C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
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—22no—
263C3×D12—21no—
264C3×D12—42no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488C3×D311yescharacteristic, complemented
282#483—31no—
283#482—31no—
284#478—31no—
285#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C23×C311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C2×#67—21no—
318C2×#67—21no—
319#239—22no—
320#239—41no—
321D3×D4—22no—
322D3×D4—41no—
323C2×D12—21no—
324C2×D12C3×D411yescharacteristic
325C2×D12C23×C311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3C23×C311yescharacteristic
330C2×C4×D3C23×C311yescharacteristic
331C2×Dic6C23×C311yescharacteristic
332C3×Q16—121no—
333C3×SD16—62no—
334C3×SD16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—41no—
372C3×C22⋊C4—41no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C42—21no—
380C3×C42—61no—
381C3×C42—61no—
382C3×C42C22×D311yescharacteristic
383C3×C42C23×C311yescharacteristic
384#217—21no—
385#216—41no—
386#214—41no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4C3×D411yescharacteristic
393(C2×D3)⋊C4C3×D411yescharacteristic
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3C3×D411yescharacteristic
397C4⋊Dic3C23×C311yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406#204—22no—
407D3×C8—41no—
408D3×C8—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—84no—
422C2×C3×D3#13512yes—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—31no—
440C22×C8—31no—
441C22×C8—31no—
442#126—61no—
443#125—61no—
444#125C2×C3×D311yescharacteristic, complemented
445#124C2×C3×D311yescharacteristic
446#123—61no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451#121—31no—
452#121—61no—
453#120—61no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4—31no—
457#117—31no—
458#117—61no—
459C2×C4⋊C4—31no—
460C2×C22⋊C4—61no—
461#107—31no—
462#106—31no—
463#106—31no—
464C4⋊C8—31no—
465#103—31no—
466#103—31no—
467#103C2×C3×D311yescharacteristic, complemented
468#103C2×C3×D311yescharacteristic, complemented
469#102—31no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102C2×C3×D311yescharacteristic
474#102C2×C3×D311yescharacteristic
475C22⋊C8—31no—
476C22⋊C8—31no—
477C4×C8C2×C3×D311yescharacteristic, complemented
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3C2×C3×D411yescharacteristic
492C22×D3C2×C3×D411yescharacteristic
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—62no—
509C3×D4—61no—
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—122no—
535C2×C3×C4—122no—
536C2×C3×C4—241no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C24×C311yescharacteristic
543#67—42no—
544#67—81no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550D12—22no—
551D12—21no—
552D12—42no—
553D12C3×#4112yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—42no—
559C4×D3—42no—
560C4×D3—81no—
561Dic6—21no—
562Dic6—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—81no—
574C2×C32#54611yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—22no—
578C3×D3—41no—
579C3×D3—42no—
580C24—61no—
581#41—62no—
582#41—121no—
583C2×Q8—31no—
584C2×Q8C22×C3×D311yescharacteristic
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—121no—
592C2×D4C22×C3×D311yescharacteristic
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598Q16—121no—
599SD16—62no—
600SD16—121no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—121no—
604C2×C8—121no—
605C2×C8C22×C3×D311yescharacteristic
606C2×C8C22×C3×D311yescharacteristic
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4C22×C3×D311yescharacteristic
618C4⋊C4C22×C3×D311yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C42—61no—
630C42—61no—
631C42C22×C3×D311yescharacteristic
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C22×C3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—84no—
663C2×D3C3×#13512yes—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4D3×#4111yescharacteristic
687C3×C4#100911yescharacteristic
688C3×C4C2×C3×#4111yescharacteristic
689C3×C4C3×H(5,𝔽2)11yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695C32#329611yescharacteristic, complemented, Sylow
696C23—21no—
697C23—31no—
698C23—31no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—241no—
703Q8—21no—
704Q8—21no—
705Q8—61no—
706Q8—61no—
707D4—21no—
708D4—21no—
709D4—32no—
710D4—62no—
711D4—61no—
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—122no—
728C2×C4—122no—
729C2×C4—241no—
730C2×C4C3×D3×D411yescharacteristic
731C2×C4C3×D3×D411yescharacteristic
732C2×C4C23×C3×D311yescharacteristic
733C8—21no—
734C8—21no—
735C8—61no—
736C8—61no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—62no—
741C2×C3—81no—
742C2×C3—81no—
743C2×C3—121no—
744C2×C3—122no—
745C2×C3—161no—
746C2×C3#567611yescharacteristic
747C2×C3D3×#13511yescharacteristic
748C2×C3#577011yescharacteristic
749C2×C3C3×#54611yescharacteristic
750C2×C3C2×C3×#13511yescharacteristic
751C2×C3C3×#57711yescharacteristic
752D3—22no—
753D3—41no—
754D3—42no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—62no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22C2×C3×D3×D411yescharacteristic
769C4—21no—
770C4—21no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4C3×D3×#4111yescharacteristic
780C4C3×#100911yescharacteristic
781C3—21no—
782C3#8165211yescharacteristic, direct product factor
783C3C3×#329611yescharacteristic, complemented
784C2—62no—
785C2—81no—
786C2—121no—
787C2—122no—
788C2C3×#567611yescharacteristic
789C2C3×D3×#13511yescharacteristic
790C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
prime radicalC3×#5676C2
hypercenterC3×#488D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×#5694C2semidirect
3. C32×#488C2semidirect
4. C3×#5066C2semidirect
5. C3×#5054C2semidirect
6. C3×#4813C2semidirect
7. C3×#4808C2semidirect
8. C3×#4805C2semidirect
9. C3×#4804C2semidirect
10. C3×#4779C2semidirect
11. C3×#4778C2semidirect
12. C3×#4776C2semidirect
13. C3×D3×#102C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C8×D12C2semidirect
17. #81652C3direct (N × H)
20. C32×#125C22semidirect
23. C2×C3×#216C22semidirect
28. C2×C3×D3×C8C22semidirect
31. C3×#897C22semidirect
34. C3×#892C22semidirect
43. C3×C4×Dic6C22semidirect
44. C32×#103C22semidirect
45. C32×#103C22semidirect
48. C32×C4×C8C22semidirect
49. C3×#835C22semidirect
53. C3×(C2×D3)⋊C8C22semidirect
54. C3×#817C22semidirect
55. C3×#816C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5694C2×C3semidirect
66. C3×#488D3semidirect
67. C3×#488C2×C3semidirect
80. #5066C2×C3semidirect
81. #5054C2×C3semidirect
82. #4813C2×C3semidirect
83. #4808C2×C3semidirect
84. #4805C2×C3semidirect
85. #4804C2×C3semidirect
86. #4779C2×C3semidirect
87. #4778C2×C3semidirect
88. #4776C2×C3semidirect
89. D3×#102C2×C3semidirect
90. C4×#204C2×C3semidirect
91. C8×D12C2×C3semidirect
157. C3×#125C2×D3semidirect
158. C3×#125C22×C3semidirect
178. C2×#216C22×C3semidirect
183. C2×D3×C8C22×C3semidirect
186. #897C22×C3semidirect
189. #892C22×C3semidirect
198. C4×Dic6C22×C3semidirect
207. C3×#103C2×D3semidirect
208. C3×#103C2×D3semidirect
209. C3×#103C22×C3semidirect
210. C3×#103C22×C3semidirect
224. C3×C4×C8C2×D3semidirect
225. C3×C4×C8C22×C3semidirect
226. #835C22×C3semidirect
230. (C2×D3)⋊C8C22×C3semidirect
231. #817C22×C3semidirect
232. #816C22×C3semidirect
235. #808C22×C3semidirect
236. #807C22×C3semidirect
237. C4⋊(C3⋊C8)C22×C3semidirect
281. #488C3×D3semidirect
444. #125C2×C3×D3semidirect
467. #103C2×C3×D3semidirect
468. #103C2×C3×D3semidirect
477. C4×C8C2×C3×D3semidirect
695. C32#3296semidirect
782. C3#81652direct (N × H)
783. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
C3×#56762
C32×#4882
C3×#50662
C3×#50542
C3×#48132
C3×#48082
C3×#48052
C3×#48042
C3×#47792
C3×#47782
C3×#47762
C3×D3×#1022
C3×C4×#2042
C3×C8×D122
C3×#32963
#816523