Finite Group Databasebeta

← C3×#80461 #11873275

Subgroups — C3×#80461 #11873275

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 701 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5731C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic
3C32×#462C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic
5C3×#5186C211yesmaximal, characteristic
6C3×#5184C211yesmaximal, characteristic, complemented
7C3×Dic3×Q16C211yesmaximal, characteristic, complemented
8C3×#5090C211yesmaximal, characteristic, complemented
9C3×#5022C211yesmaximal, characteristic, complemented
10C3×#4840C211yesmaximal, characteristic
11C3×#4829C211yesmaximal, characteristic, complemented
12C3×#4815C211yesmaximal, characteristic
13C3×#4814C211yesmaximal, characteristic
14C3×#4790C211yesmaximal, characteristic, complemented
15C3×#4789C211yesmaximal, characteristic, complemented
16C3×#3127—31nomaximal
17#80461C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C3×#898—21no—
31C3×#898—21no—
32C3×#892—21no—
33C3×#892C2211yescharacteristic
34C3×#889—21no—
35C3×#889—21no—
36C3×#887—21no—
37C3×#887C2211yescharacteristic
38C3×#872—21no—
39C3×#872C2211yescharacteristic
40C3×#870C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#815C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#541—31no—
62C3×#519—31no—
63#5731C2×C311yescharacteristic
64#5572C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#479—31no—
68C3×#479—31no—
69C3×#462—21no—
70C3×#462—31no—
71C3×#462D311yescharacteristic, complemented
72C3×#462C2×C311yescharacteristic, complemented
73C3×#451—31no—
74C3×#451—31no—
75C3×#441—31no—
76C3×#441—31no—
77C3×C4×Q16—31no—
78C3×C4×Q16—31no—
79C3×#433—31no—
80#5186C2×C311yescharacteristic
81#5186C2×C311yescharacteristic
82#5184C2×C311yescharacteristic, complemented
83Dic3×Q16C2×C311yescharacteristic, complemented
84#5090C2×C311yescharacteristic, complemented
85#5022C2×C311yescharacteristic, complemented
86#4840C2×C311yescharacteristic
87#4829C2×C311yescharacteristic, complemented
88#4815C2×C311yescharacteristic
89#4814C2×C311yescharacteristic
90#4790C2×C311yescharacteristic, complemented
91#4789C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C32×Q16—22no—
103C2×C32×C8C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111C3×#216—22no—
112C3×#216—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4D411yescharacteristic
117C3×(C2×D3)⋊C4D411yescharacteristic
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3127—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16—21no—
146C2×C3×Q16—31no—
147C2×C3×Q16—31no—
148C2×C3×Q16C2×D311yescharacteristic
149C2×C3×Q16C2×D311yescharacteristic
150C2×C3×Q16C22×C311yescharacteristic
151C2×C3×Q16C22×C311yescharacteristic
152C3×C4⋊Q8—21no—
153C3×C4⋊Q8C2×D311yescharacteristic
154C3×C4⋊Q8C22×C311yescharacteristic
155C3×#126—61no—
156C3×#126—61no—
157C3×#125—31no—
158C3×#125—61no—
159C3×#125—61no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C4×Q8—21no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—31no—
168C3×C4×Q8—61no—
169C3×C4×Q8—61no—
170C3×C4×Q8C2×D311yescharacteristic
171C3×C4×Q8C22×C311yescharacteristic
172C3×#117—31no—
173C3×#117—31no—
174C3×#117—61no—
175C3×#117—61no—
176#946C22×C311yescharacteristic
177#946C22×C311yescharacteristic
178Q8×Dic3C22×C311yescharacteristic
179Q8×Dic3C22×C311yescharacteristic
180Q8×Dic3C22×C311yescharacteristic
181C2×#216C22×C311yescharacteristic
182C2×#216C22×C311yescharacteristic
183#898—21no—
184#898—21no—
185#892—21no—
186#892C22×C311yescharacteristic
187#889—21no—
188#889—21no—
189#887—21no—
190#887C22×C311yescharacteristic
191#872—21no—
192#872C22×C311yescharacteristic
193#870C22×C311yescharacteristic
194C4×Dic6—21no—
195C4×Dic6C22×C311yescharacteristic
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—21no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8C2×D311yescharacteristic
203C3×C4⋊C8C22×C311yescharacteristic
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#835C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#818C22×C311yescharacteristic
227#817C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#815C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×C4×D3—24no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×Dic6—24no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262C32×C8—21no—
263C32×C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—31no—
268#485—31no—
269#485—31no—
270#479—31no—
271#479—31no—
272#462—31no—
273#462C3×D311yescharacteristic, complemented
274#451—31no—
275#451—31no—
276#441—31no—
277#441—31no—
278C4×Q16—31no—
279C4×Q16—31no—
280#433—31no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8—62no—
287C2×C3×Q8—62no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C23×C311yescharacteristic
292C2×C3×Q8C23×C311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296D3×Q8—22no—
297D3×Q8—22no—
298C2×C4×D3—21no—
299C2×C4×D3C23×C311yescharacteristic
300C2×Dic6—21no—
301C2×Dic6C23×C311yescharacteristic
302C3×Q16—22no—
303C3×Q16—22no—
304C3×Q16—22no—
305C3×Q16—22no—
306C3×Q16—42no—
307C3×Q16—42no—
308C3×Q16—62no—
309C3×Q16—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—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—41no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4—41no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—31no—
353C3×C42—41no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42C22×D311yescharacteristic
361C3×C42C23×C311yescharacteristic
362#216—22no—
363#216—22no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4C3×D411yescharacteristic
368(C2×D3)⋊C4C3×D411yescharacteristic
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3C23×C311yescharacteristic
373C4⋊Dic3C23×C311yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4C3×D411yescharacteristic
382Dic3⋊C4C3×D411yescharacteristic
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C32×C4—21no—
397C32×C4—22no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3×Dic3—21no—
405C3×Dic3—22no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C22×Q8—31no—
412C2×Q16—31no—
413C2×Q16—31no—
414C2×Q16C2×C3×D311yescharacteristic
415C2×Q16C2×C3×D311yescharacteristic
416C4⋊Q8C2×C3×D311yescharacteristic
417#126—61no—
418#126—61no—
419#125—31no—
420#125—61no—
421#125—61no—
422C22⋊Q8—31no—
423C22⋊Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—61no—
430C4×Q8—61no—
431C4×Q8C2×C3×D311yescharacteristic
432#117—31no—
433#117—31no—
434#117—61no—
435#117—61no—
436#107—31no—
437#107—31no—
438#106—31no—
439#106—31no—
440C4⋊C8—31no—
441C4⋊C8C2×C3×D311yescharacteristic
442#103—31no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103C2×C3×D311yescharacteristic
449#103C2×C3×D311yescharacteristic
450C22⋊C8—31no—
451C22⋊C8—31no—
452#97—31no—
453C4×C8—31no—
454C23×C3—31no—
455C22×D3C2×C3×D411yescharacteristic
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—22no—
467C3×Q8—32no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—64no—
474C3×Q8—61no—
475C3×Q8#23712yes—
476C3×Q8C3×#4112yes—
477C2×C3×C4—21no—
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—21no—
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—41no—
495C2×C3×C4—64no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C2×C3×D411yescharacteristic
505C2×C3×C4C2×C3×D411yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C24×C311yescharacteristic
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3C2×C3×D411yescharacteristic
513C2×Dic3C2×C3×D411yescharacteristic
514C2×Dic3C2×C3×D411yescharacteristic
515C4×D3—24no—
516C4×D3—21no—
517C4×D3—21no—
518Dic6—24no—
519Dic6—21no—
520Dic6C3×#4112yes—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—21no—
525C3×C8—41no—
526C3×C8—41no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C2×C32#52511yescharacteristic
532C2×C32#57811yescharacteristic
533C2×C32#57811yescharacteristic
534C3×D3—41no—
535C2×Q8—31no—
536C2×Q8—61no—
537C2×Q8—62no—
538C2×Q8—62no—
539C2×Q8C22×C3×D311yescharacteristic
540C2×Q8C22×C3×D311yescharacteristic
541C2×Q8C22×C3×D311yescharacteristic
542C22×C4—31no—
543C22×C4—61no—
544Q16—22no—
545Q16—22no—
546Q16—62no—
547Q16—62no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8C22×C3×D311yescharacteristic
551C2×C8C22×C3×D311yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4C22×C3×D311yescharacteristic
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—61no—
573C22⋊C4—61no—
574C22⋊C4—61no—
575C42—21no—
576C42—31no—
577C42—61no—
578C42—61no—
579C42—61no—
580C42—61no—
581C42—61no—
582C42—61no—
583C42C22×C3×D311yescharacteristic
584C22×C3—21no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C22×C3×D411yescharacteristic
590C2×D3—21no—
591C2×D3—21no—
592C2×D3—21no—
593C3×C4—22no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—41no—
603C3×C4—42no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—62no—
614C3×C4—81no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4C2×#23711yescharacteristic
621C3×C4D3×#4111yescharacteristic
622C3×C4C2×C3×#4111yescharacteristic
623C3×C4C2×C3×#4111yescharacteristic
624Dic3—21no—
625Dic3—21no—
626Dic3—21no—
627Dic3—22no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631C32#312711yescharacteristic, complemented, Sylow
632C23—31no—
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—21no—
637Q8—21no—
638Q8—32no—
639Q8—64no—
640Q8—61no—
641Q8C3×#23712yes—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—64no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4C3×D3×D411yescharacteristic
657C2×C4C3×D3×D411yescharacteristic
658C2×C4C23×C3×D311yescharacteristic
659C8—21no—
660C8—21no—
661C8—61no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—121no—
667C2×C3#560611yescharacteristic
668C2×C3#576611yescharacteristic
669C2×C3#577911yescharacteristic
670C2×C3C3×#52511yescharacteristic
671C2×C3C3×#57811yescharacteristic
672C2×C3C3×#57811yescharacteristic
673D3—41no—
674C22—61no—
675C22—61no—
676C22—61no—
677C22C2×C3×D3×D411yescharacteristic
678C4—21no—
679C4—21no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—61no—
685C4—61no—
686C4—61no—
687C4—62no—
688C4—121no—
689C4—121no—
690C4—121no—
691C4C2×C3×#23711yescharacteristic
692C4C3×D3×#4111yescharacteristic
693C3—21no—
694C3#8046111yescharacteristic, direct product factor
695C3C3×#312711yescharacteristic, complemented
696C2—121no—
697C2C3×#560611yescharacteristic
698C2C3×#576611yescharacteristic
699C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#462D3
hypocenterC3C3×#3127
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
3. C32×#462C2semidirect
6. C3×#5184C2semidirect
7. C3×Dic3×Q16C2semidirect
8. C3×#5090C2semidirect
9. C3×#5022C2semidirect
11. C3×#4829C2semidirect
14. C3×#4790C2semidirect
15. C3×#4789C2semidirect
17. #80461C3direct (N × H)
71. C3×#462D3semidirect
72. C3×#462C2×C3semidirect
82. #5184C2×C3semidirect
83. Dic3×Q16C2×C3semidirect
84. #5090C2×C3semidirect
85. #5022C2×C3semidirect
87. #4829C2×C3semidirect
90. #4790C2×C3semidirect
91. #4789C2×C3semidirect
273. #462C3×D3semidirect
631. C32#3127semidirect
694. C3#80461direct (N × H)
695. C3C3×#3127semidirect

Maximal subgroups

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

subgroupindex
C3×#57312
C3×#55722
C32×#4622
C3×#51862
C3×#51842
C3×Dic3×Q162
C3×#50902
C3×#50222
C3×#48402
C3×#48292
C3×#48152
C3×#48142
C3×#47902
C3×#47892
C3×#31273
#804613