Finite Group Databasebeta

← C3×#80600 #11866315

Subgroups — C3×#80600 #11866315

Order 1152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3C3×#5674C211yesmaximal, characteristic
4C3×#5572C211yesmaximal, characteristic, complemented
5C32×#464C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7C3×#5163C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5027C211yesmaximal, characteristic, complemented
10C3×#4848C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4798C211yesmaximal, characteristic, complemented
14C3×#4770C211yesmaximal, characteristic, complemented
15C3×#4762C211yesmaximal, characteristic, complemented
16C3×#3043—31nomaximal
17#80600C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic
23C32×#124C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#918—24no—
33C3×D3×SD16—24no—
34C2×C3×#204C2211yescharacteristic
35C2×C3×#204C2211yescharacteristic, complemented
36C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#892—21no—
39C3×#892C2211yescharacteristic
40C3×#887—21no—
41C3×#887C2211yescharacteristic, complemented
42C3×#884—21no—
43C3×#884—21no—
44C3×#882—21no—
45C3×#882—21no—
46C3×#874C2211yescharacteristic
47C3×#872—21no—
48C3×#872C2211yescharacteristic
49C3×C4×Dic6—21no—
50C3×C4×Dic6C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic
61C3×#809C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×#535—31no—
66C3×#519—31no—
67C2×#918C2×C311yescharacteristic, complemented
68C2×D3×SD16C2×C311yescharacteristic, complemented
69#5674C2×C311yescharacteristic
70#5572C2×C311yescharacteristic, complemented
71C3×#464—21no—
72C3×#464—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#464D311yescharacteristic, complemented
76C3×#464C2×C311yescharacteristic, complemented
77C3×#460—31no—
78C3×#460—31no—
79C3×#460—31no—
80C3×#460—31no—
81C3×#424—31no—
82C3×#418—31no—
83C3×#416—31no—
84#5185C2×C311yescharacteristic, complemented
85#5163C2×C311yescharacteristic, complemented
86#5054C2×C311yescharacteristic, complemented
87#5027C2×C311yescharacteristic, complemented
88#4848C2×C311yescharacteristic, complemented
89#4839C2×C311yescharacteristic, complemented
90#4804C2×C311yescharacteristic, complemented
91#4798C2×C311yescharacteristic, complemented
92#4770C2×C311yescharacteristic, complemented
93#4762C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×D3×Q8—22no—
104C3×D3×Q8D414yescomplemented
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C32×Q16—22no—
118C32×SD16—22no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124C32×C22⋊C4—21no—
125C32×C42—21no—
126C32×C42C2311yescharacteristic
127C3×#216—22no—
128C3×#215—22no—
129C3×#215—22no—
130C3×#214—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3—21no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—21no—
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×#204—22no—
150C3×#204—22no—
151C3×ΓL(1,𝔽25)—22no—
152C3×D3×C8—22no—
153#3043—31noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C22×C3×D4—31no—
157C2×#239C22×C311yescharacteristic
158C2×D3×Q8C22×C311yescharacteristic
159C2×D3×D4C22×C311yescharacteristic
160C3×#137—64no—
161C2×C3×Q16—21no—
162C2×C3×Q16—31no—
163C2×C3×Q16C2×D311yescharacteristic, complemented
164C2×C3×Q16C22×C311yescharacteristic, complemented
165C2×C3×SD16—21no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—64no—
172C2×C3×SD16C2×D311yescharacteristic
173C2×C3×SD16C22×C311yescharacteristic
174C2×C3×M16—31no—
175C22×C3×C8—31no—
176C3×#127—31no—
177C3×#127—31no—
178C3×#124—21no—
179C3×#124—31no—
180C3×#124C2×D311yescharacteristic
181C3×#124C22×C311yescharacteristic
182C3×#121—61no—
183C3×#121—61no—
184C3×#120—61no—
185C3×#120—61no—
186C3×C4×Q8—21no—
187C3×C4×Q8—31no—
188C3×C4×Q8—31no—
189C3×C4×Q8—31no—
190C3×C4×Q8—61no—
191C3×C4×Q8—61no—
192C3×C4×Q8C2×D311yescharacteristic, complemented
193C3×C4×Q8C22×C311yescharacteristic, complemented
194C3×#117—31no—
195C3×#117—31no—
196C3×#117—61no—
197C3×#117—61no—
198#947C22×C311yescharacteristic
199Q8×Dic3C22×C311yescharacteristic, complemented
200C2×#216C22×C311yescharacteristic, complemented
201C2×#215C22×C311yescharacteristic
202C2×#215C22×C311yescharacteristic, complemented
203#940C22×C311yescharacteristic
204C2×#214C22×C311yescharacteristic
205#918—24no—
206D3×SD16—24no—
207C2×#204C22×C311yescharacteristic
208C2×#204C22×C311yescharacteristic, complemented
209C2×ΓL(1,𝔽25)C22×C311yescharacteristic
210C2×D3×C8C22×C311yescharacteristic
211#892—21no—
212#892C22×C311yescharacteristic
213#887—21no—
214#887C22×C311yescharacteristic, complemented
215#884—21no—
216#884—21no—
217#882—21no—
218#882—21no—
219#874C22×C311yescharacteristic
220#872—21no—
221#872C22×C311yescharacteristic
222C4×Dic6—21no—
223C4×Dic6C22×C311yescharacteristic, complemented
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C22×C311yescharacteristic, complemented
230C3×#103—21no—
231C3×#103—31no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C22×C311yescharacteristic, complemented
234C3×#102—21no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic
241C3×#102C22×C311yescharacteristic
242#835C22×C311yescharacteristic, complemented
243#832C22×C311yescharacteristic
244#821C22×C311yescharacteristic
245#821C22×C311yescharacteristic, complemented
246Dic3⋊C8C22×C311yescharacteristic, complemented
247Dic3⋊C8C22×C311yescharacteristic, complemented
248#809C22×C311yescharacteristic
249#809C22×C311yescharacteristic, complemented
250C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—42no—
255C22×C3×D3—81no—
256C22×C3×D3—81no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8C2×D412yes—
262C32×D4—21no—
263C32×D4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C3×#67—42no—
271C3×#67—81no—
272C3×#67—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12—81no—
284C3×D12—81no—
285C3×C4×D3—24no—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—24no—
291C3×Dic6C2×D412yes—
292C32×C8—21no—
293C32×C8—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—31no—
297C22×SD16—31no—
298#535—31no—
299#519—31no—
300#464—31no—
301#464—31no—
302#464—31no—
303#464C3×D311yescharacteristic, complemented
304#460—31no—
305#460—31no—
306#460—31no—
307#460—31no—
308#424—31no—
309#418—31no—
310#416—31no—
311C24×C3—61no—
312C23×D3—21no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—21no—
317C2×C3×Q8—34no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C23×C311yescharacteristic
324C2×C3×Q8C23×C311yescharacteristic
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C23×C311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344#239—22no—
345#239—22no—
346D3×Q8—22no—
347D3×Q8C3×D414yescomplemented
348D3×D4—22no—
349D3×D4—22no—
350C2×D12—21no—
351C2×D12—21no—
352C2×D12—21no—
353C2×D12C23×C311yescharacteristic
354C2×D12C23×C311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×C4×D3C23×C311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6C23×C311yescharacteristic
360C3×Q16—22no—
361C3×Q16—22no—
362C3×Q16—42no—
363C3×Q16—62no—
364C3×SD16—22no—
365C3×SD16—22no—
366C3×SD16—42no—
367C3×SD16—62no—
368C3×SD16—62no—
369C3×SD16—62no—
370C3×SD16—62no—
371C3×SD16—62no—
372C3×M16—62no—
373C2×C3×C8—21no—
374C2×C3×C8—21no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C2×C3×C8—62no—
378C2×C3×C8C22×D311yescharacteristic
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C23×C311yescharacteristic
381C2×C3×C8C23×C311yescharacteristic
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—41no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C23×C311yescharacteristic
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—41no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—21no—
406C3×C42—21no—
407C3×C42—21no—
408C3×C42—31no—
409C3×C42—41no—
410C3×C42—61no—
411C3×C42—61no—
412C3×C42—61no—
413C3×C42—61no—
414C3×C42C22×D311yescharacteristic
415C3×C42C23×C311yescharacteristic
416#216—22no—
417#215—22no—
418#215—22no—
419#214—22no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4C3×D411yescharacteristic
424(C2×D3)⋊C4C3×D411yescharacteristic
425C4⋊Dic3—21no—
426C4⋊Dic3C23×C311yescharacteristic
427Dic3⋊C4—21no—
428Dic3⋊C4—21no—
429Dic3⋊C4C3×D411yescharacteristic
430Dic3⋊C4C3×D411yescharacteristic
431C4×Dic3—21no—
432C4×Dic3—21no—
433C4×Dic3—21no—
434C4×Dic3—21no—
435C4×Dic3C23×C311yescharacteristic
436C2×C3⋊C8C23×C311yescharacteristic
437C2×C3⋊C8C23×C311yescharacteristic
438#204—22no—
439#204—22no—
440ΓL(1,𝔽25)—22no—
441D3×C8—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3#12112yes—
456C32×C4—22no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—41no—
460C32×C4—41no—
461C32×C4C22×D411yescharacteristic
462C32×C4C2×#4111yescharacteristic
463C3×Dic3—22no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—31no—
470C22×D4—31no—
471#137—64no—
472C2×Q16—31no—
473C2×Q16C2×C3×D311yescharacteristic, complemented
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—31no—
478C2×SD16—31no—
479C2×SD16—64no—
480C2×SD16C2×C3×D311yescharacteristic
481C2×M16—31no—
482C22×C8—31no—
483#127—31no—
484#127—31no—
485#124—31no—
486#124C2×C3×D311yescharacteristic
487#121—61no—
488#121—61no—
489#120—61no—
490#120—61no—
491C4×Q8—31no—
492C4×Q8—31no—
493C4×Q8—31no—
494C4×Q8—61no—
495C4×Q8—61no—
496C4×Q8C2×C3×D311yescharacteristic, complemented
497#117—31no—
498#117—31no—
499#117—61no—
500#117—61no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8C2×C3×D311yescharacteristic, complemented
505#103—31no—
506#103C2×C3×D311yescharacteristic, complemented
507#102—31no—
508#102—31no—
509#102—31no—
510#102—31no—
511#102—31no—
512#102C2×C3×D311yescharacteristic
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—122no—
520C23×C3—241no—
521C23×C3—241no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—42no—
525C22×D3—81no—
526C22×D3—81no—
527C22×D3C2×C3×D411yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—22no—
535C3×Q8—32no—
536C3×Q8—41no—
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—64no—
540C3×Q8—61no—
541C3×Q8D3×D412yes—
542C3×Q8C2×C3×D412yes—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—122no—
554C3×D4—122no—
555C3×D4—241no—
556C3×D4—241no—
557C3×D4—241no—
558C3×D4—241no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—64no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4D3×D411yescharacteristic
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4C2×C3×D411yescharacteristic
583C2×C3×C4C2×C3×D411yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C24×C311yescharacteristic
586#67—42no—
587#67—81no—
588#67—81no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3C2×C3×D411yescharacteristic
592C2×Dic3C2×C3×D411yescharacteristic
593C2×Dic3C2×C3×D411yescharacteristic
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—42no—
599D12—81no—
600D12—81no—
601C4×D3—24no—
602C4×D3—42no—
603C4×D3C2×C3×D412yes—
604C4×D3C3×#4112yes—
605Dic6—21no—
606Dic6—24no—
607Dic6C2×C3×D412yes—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C2×C32—81no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3×D3—22no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626#41—62no—
627#41—62no—
628C2×Q8—34no—
629C2×Q8—31no—
630C2×Q8—61no—
631C2×Q8—62no—
632C2×Q8C22×C3×D311yescharacteristic
633C2×Q8C22×C3×D311yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—62no—
638C2×D4—62no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4C22×C3×D311yescharacteristic
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—61no—
648Q16—22no—
649Q16—62no—
650SD16—22no—
651SD16—62no—
652SD16—62no—
653SD16—62no—
654SD16—62no—
655SD16—62no—
656M16—62no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—62no—
660C2×C8C22×C3×D311yescharacteristic
661C2×C8C22×C3×D311yescharacteristic
662C4⋊C4—21no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4C22×C3×D311yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C42—21no—
678C42—31no—
679C42—61no—
680C42—61no—
681C42—61no—
682C42—61no—
683C42C22×C3×D311yescharacteristic
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—244no—
704C22×C3C2×D3×D411yescharacteristic
705C22×C3C22×C3×D411yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—84no—
715C2×D3C3×#12112yes—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—42no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—62no—
735C3×C4—81no—
736C3×C4—81no—
737C3×C4—121no—
738C3×C4C2×D3×D411yescharacteristic
739C3×C4D3×#4111yescharacteristic
740C3×C4C22×C3×D411yescharacteristic
741C3×C4C2×C3×#4111yescharacteristic
742Dic3—21no—
743Dic3—21no—
744Dic3—22no—
745Dic3—41no—
746Dic3C3×#12112yes—
747C32#304311yescharacteristic, complemented, Sylow
748C23—21no—
749C23—31no—
750C23—61no—
751C23—61no—
752C23—122no—
753C23—241no—
754C23—241no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758Q8—32no—
759Q8—64no—
760Q8—61no—
761Q8C3×D3×D412yes—
762D4—21no—
763D4—21no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—122no—
769D4—122no—
770D4—241no—
771D4—241no—
772D4—241no—
773D4—241no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—31no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—64no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—122no—
786C2×C4C3×D3×D411yescharacteristic
787C2×C4C3×D3×D411yescharacteristic
788C2×C4C23×C3×D311yescharacteristic
789C8—21no—
790C8—21no—
791C8—61no—
792C8—61no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—81no—
798C2×C3—81no—
799C2×C3—161no—
800C2×C3—241no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3#577011yescharacteristic
804C2×C3#577811yescharacteristic
805C2×C3C2×C3×#12111yescharacteristic
806C2×C3C3×#57711yescharacteristic
807C2×C3C3×#57711yescharacteristic
808D3—22no—
809D3—81no—
810D3—81no—
811C22—32no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—61no—
816C22—61no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—244no—
824C22C2×C3×D3×D411yescharacteristic
825C4—21no—
826C4—21no—
827C4—22no—
828C4—32no—
829C4—41no—
830C4—41no—
831C4—61no—
832C4—61no—
833C4—62no—
834C4—121no—
835C4C2×C3×D3×D411yescharacteristic
836C4C3×D3×#4111yescharacteristic
837C3—21no—
838C3#8060011yescharacteristic, direct product factor
839C3C3×#304311yescharacteristic, complemented
840C2—62no—
841C2—81no—
842C2—241no—
843C2—241no—
844C2C3×D3×#12111yescharacteristic
845C2C3×#577011yescharacteristic
846C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC3×#5674C2
hypercenterC3×#464D3
hypocenterC3C3×#3043
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
1. C2×C3×#918C2semidirect
2. C2×C3×D3×SD16C2semidirect
4. C3×#5572C2semidirect
5. C32×#464C2semidirect
6. C3×#5185C2semidirect
7. C3×#5163C2semidirect
8. C3×#5054C2semidirect
9. C3×#5027C2semidirect
10. C3×#4848C2semidirect
11. C3×#4839C2semidirect
12. C3×#4804C2semidirect
13. C3×#4798C2semidirect
14. C3×#4770C2semidirect
15. C3×#4762C2semidirect
17. #80600C3direct (N × H)
21. C2×C32×Q16C22semidirect
24. C32×C4×Q8C22semidirect
26. C3×Q8×Dic3C22semidirect
27. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
35. C2×C3×#204C22semidirect
41. C3×#887C22semidirect
50. C3×C4×Dic6C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#103C22semidirect
54. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
61. C3×#809C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#918C2×C3semidirect
68. C2×D3×SD16C2×C3semidirect
70. #5572C2×C3semidirect
75. C3×#464D3semidirect
76. C3×#464C2×C3semidirect
84. #5185C2×C3semidirect
85. #5163C2×C3semidirect
86. #5054C2×C3semidirect
87. #5027C2×C3semidirect
88. #4848C2×C3semidirect
89. #4839C2×C3semidirect
90. #4804C2×C3semidirect
91. #4798C2×C3semidirect
92. #4770C2×C3semidirect
93. #4762C2×C3semidirect
104. C3×D3×Q8D4semidirect
163. C2×C3×Q16C2×D3semidirect
164. C2×C3×Q16C22×C3semidirect
192. C3×C4×Q8C2×D3semidirect
193. C3×C4×Q8C22×C3semidirect
199. Q8×Dic3C22×C3semidirect
200. C2×#216C22×C3semidirect
202. C2×#215C22×C3semidirect
208. C2×#204C22×C3semidirect
214. #887C22×C3semidirect
223. C4×Dic6C22×C3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C22×C3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C22×C3semidirect
242. #835C22×C3semidirect
245. #821C22×C3semidirect
246. Dic3⋊C8C22×C3semidirect
247. Dic3⋊C8C22×C3semidirect
249. #809C22×C3semidirect
250. C4⋊(C3⋊C8)C22×C3semidirect
303. #464C3×D3semidirect
347. D3×Q8C3×D4semidirect
473. C2×Q16C2×C3×D3semidirect
496. C4×Q8C2×C3×D3semidirect
504. C4⋊C8C2×C3×D3semidirect
506. #103C2×C3×D3semidirect
747. C32#3043semidirect
838. C3#80600direct (N × H)
839. C3C3×#3043semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
C2×C3×D3×SD162
C3×#56742
C3×#55722
C32×#4642
C3×#51852
C3×#51632
C3×#50542
C3×#50272
C3×#48482
C3×#48392
C3×#48042
C3×#47982
C3×#47702
C3×#47622
C3×#30433
#806003