Finite Group Databasebeta

← C3×#80385 #11866306

Subgroups — C3×#80385 #11866306

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3C3×#5715C211yesmaximal, characteristic
4C3×#5572C211yesmaximal, characteristic, complemented
5C32×#460C211yesmaximal, characteristic, complemented
6C3×#5166C211yesmaximal, characteristic, complemented
7C3×#5163C211yesmaximal, characteristic, complemented
8C3×#5075C211yesmaximal, characteristic, complemented
9C3×#5028C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic, complemented
12C3×#4772C211yesmaximal, characteristic, complemented
13C3×#4770C211yesmaximal, characteristic, complemented
14C3×#4767C211yesmaximal, characteristic, complemented
15C3×#4762C211yesmaximal, characteristic, complemented
16C3×#3043—31nomaximal
17#80385C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C32×#127C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#940C2211yescharacteristic
29C3×#939—21no—
30C3×#939—21no—
31C3×#937—21no—
32C3×#937—21no—
33C3×#936C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic, complemented
36C3×#915—24no—
37C3×D3×SD16—24no—
38C2×C3×Dic12C2211yescharacteristic, complemented
39C2×C3×#204C2211yescharacteristic
40C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
41C2×C3×D3×C8C2211yescharacteristic
42C3×#892—21no—
43C3×#892C2211yescharacteristic
44C3×#887—21no—
45C3×#887C2211yescharacteristic, complemented
46C3×#875C2211yescharacteristic
47C3×#872—21no—
48C3×#872C2211yescharacteristic
49C3×C4×Dic6—21no—
50C3×C4×Dic6C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic
53C32×#102C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×#535—31no—
66C3×#519—31no—
67C2×#915C2×C311yescharacteristic, complemented
68C2×D3×SD16C2×C311yescharacteristic, complemented
69#5715C2×C311yescharacteristic
70#5572C2×C311yescharacteristic, complemented
71C3×#464—31no—
72C3×#464—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#460—21no—
76C3×#460—31no—
77C3×#460—31no—
78C3×#460—31no—
79C3×#460D311yescharacteristic, complemented
80C3×#460C2×C311yescharacteristic, complemented
81C3×#424—31no—
82C3×#418—31no—
83C3×#416—31no—
84#5166C2×C311yescharacteristic, complemented
85#5163C2×C311yescharacteristic, complemented
86#5075C2×C311yescharacteristic, complemented
87#5028C2×C311yescharacteristic, complemented
88#4845C2×C311yescharacteristic, complemented
89#4839C2×C311yescharacteristic, complemented
90#4772C2×C311yescharacteristic, complemented
91#4770C2×C311yescharacteristic, complemented
92#4767C2×C311yescharacteristic, complemented
93#4762C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×Q8—22no—
106C3×D3×Q8D414yescomplemented
107C3×#237—22no—
108C3×#237—22no—
109C3×D3×D4—22no—
110C3×D3×D4—22no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C32×SD16—22no—
118C32×SD16—22no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C42—21no—
124C32×C42C2311yescharacteristic
125C3×#217—21no—
126C3×#217—21no—
127C3×#216—22no—
128C3×#215—22no—
129C3×#214—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×Dic12—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×D3×Q8C22×C311yescharacteristic
158C2×#237C22×C311yescharacteristic
159C2×D3×D4C22×C311yescharacteristic
160C3×#137—64no—
161C2×C3×Q16—31no—
162C2×C3×Q16—31no—
163C2×C3×SD16—21no—
164C2×C3×SD16—21no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—64no—
170C2×C3×SD16C2×D311yescharacteristic
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×SD16C22×C311yescharacteristic
173C2×C3×SD16C22×C311yescharacteristic, complemented
174C2×C3×M16—31no—
175C22×C3×C8—31no—
176C3×#127—21no—
177C3×#127—31no—
178C3×#127C2×D311yescharacteristic
179C3×#127C22×C311yescharacteristic
180C3×#124—31no—
181C3×#124—31no—
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—
198Q8×Dic3C22×C311yescharacteristic, complemented
199C2×#216C22×C311yescharacteristic, complemented
200C2×#215C22×C311yescharacteristic
201#940C22×C311yescharacteristic
202#939—21no—
203#939—21no—
204#937—21no—
205#937—21no—
206#936C22×C311yescharacteristic
207C2×#214C22×C311yescharacteristic
208C2×#214C22×C311yescharacteristic, complemented
209#915—24no—
210D3×SD16—24no—
211C2×Dic12C22×C311yescharacteristic, complemented
212C2×#204C22×C311yescharacteristic
213C2×ΓL(1,𝔽25)C22×C311yescharacteristic
214C2×D3×C8C22×C311yescharacteristic
215#892—21no—
216#892C22×C311yescharacteristic
217#887—21no—
218#887C22×C311yescharacteristic, complemented
219#875C22×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—31no—
231C3×#103—31no—
232C3×#102—21no—
233C3×#102—21no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102C2×D311yescharacteristic
239C3×#102C2×D311yescharacteristic, complemented
240C3×#102C22×C311yescharacteristic
241C3×#102C22×C311yescharacteristic, complemented
242#832C22×C311yescharacteristic
243#832C22×C311yescharacteristic, complemented
244#821C22×C311yescharacteristic
245#816C22×C311yescharacteristic, complemented
246Dic3⋊C8C22×C311yescharacteristic, complemented
247Dic3⋊C8C22×C311yescharacteristic, complemented
248#810C22×C311yescharacteristic, complemented
249#809C22×C311yescharacteristic
250C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
251C23×C32—21no—
252C23×C32—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×Q8C2×D412yes—
260C32×D4—21no—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—81no—
265C32×D4—81no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C3×#67—42no—
272C3×#67—42no—
273C3×#67—81no—
274C3×#67—81no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×C4×D3—24no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287C3×Dic6—21no—
288C3×Dic6—24no—
289C3×Dic6—21no—
290C3×Dic6—21no—
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#464—31no—
304#460—31no—
305#460—31no—
306#460—31no—
307#460C3×D311yescharacteristic, complemented
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—34no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C23×C311yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—41no—
331C2×C3×D4—41no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C23×C311yescharacteristic
341C2×C3×D4C23×C311yescharacteristic
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—21no—
349C22×Dic3—21no—
350D3×Q8—22no—
351D3×Q8C3×D414yescomplemented
352#237—22no—
353#237—22no—
354D3×D4—22no—
355D3×D4—22no—
356C2×D12C23×C311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3C23×C311yescharacteristic
359C2×Dic6—21no—
360C2×Dic6C23×C311yescharacteristic
361C2×Dic6C23×C311yescharacteristic
362C3×Q16—62no—
363C3×Q16—62no—
364C3×SD16—22no—
365C3×SD16—22no—
366C3×SD16—22no—
367C3×SD16—22no—
368C3×SD16—42no—
369C3×SD16—42no—
370C3×SD16—62no—
371C3×SD16—62no—
372C3×SD16—62no—
373C3×SD16—62no—
374C3×M16—62no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8—62no—
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C23×C311yescharacteristic
383C2×C3×C8C23×C311yescharacteristic
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—41no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C23×C311yescharacteristic
396C3×C22⋊C4—31no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—21no—
406C3×C42—31no—
407C3×C42—41no—
408C3×C42—61no—
409C3×C42—61no—
410C3×C42—61no—
411C3×C42—61no—
412C3×C42C22×D311yescharacteristic
413C3×C42C23×C311yescharacteristic
414#217—21no—
415#217—21no—
416#216—22no—
417#215—22no—
418#214—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
438Dic12—22no—
439#204—22no—
440ΓL(1,𝔽25)—22no—
441D3×C8—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32C22×D411yescharacteristic
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3#12112yes—
456C32×C4—21no—
457C32×C4—22no—
458C32×C4—21no—
459C32×C4—41no—
460C32×C4C22×D411yescharacteristic
461C32×C4C2×#4111yescharacteristic
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—31no—
470C22×D4—31no—
471#137—64no—
472C2×Q16—31no—
473C2×Q16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—31no—
478C2×SD16—64no—
479C2×SD16C2×C3×D311yescharacteristic
480C2×SD16C2×C3×D311yescharacteristic, complemented
481C2×M16—31no—
482C22×C8—31no—
483#127—31no—
484#127C2×C3×D311yescharacteristic
485#124—31no—
486#124—31no—
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#103—31no—
507#102—31no—
508#102—31no—
509#102—31no—
510#102—31no—
511#102C2×C3×D311yescharacteristic
512#102C2×C3×D311yescharacteristic, complemented
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—31no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—61no—
521C23×C3—122no—
522C23×C3—241no—
523C23×C3—241no—
524C22×D3—21no—
525C22×D3—42no—
526C22×D3—81no—
527C22×D3—81no—
528C22×D3C2×C3×D411yescharacteristic
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—22no—
532C3×Q8—32no—
533C3×Q8—41no—
534C3×Q8—64no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8D3×D412yes—
539C3×Q8C2×C3×D412yes—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—41no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—41no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—81no—
555C3×D4—81no—
556C3×D4—81no—
557C3×D4—81no—
558C3×D4—82no—
559C3×D4—82no—
560C3×D4—122no—
561C3×D4—122no—
562C3×D4—241no—
563C3×D4—241no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—64no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—122no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4C2×C3×D411yescharacteristic
586C2×C3×C4C2×C3×D411yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C24×C311yescharacteristic
589#67—42no—
590#67—42no—
591#67—81no—
592#67—81no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—42no—
597C2×Dic3C2×C3×D411yescharacteristic
598C2×Dic3C2×C3×D411yescharacteristic
599C2×Dic3C2×C3×D411yescharacteristic
600D12—21no—
601D12—21no—
602C4×D3—24no—
603C4×D3C2×C3×D412yes—
604C4×D3C3×#4112yes—
605Dic6—21no—
606Dic6—24no—
607Dic6—21no—
608Dic6—21no—
609Dic6C2×C3×D412yes—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—21no—
614C3×C8—41no—
615C3×C8—41no—
616C3×C8—61no—
617C3×C8—61no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C2×C32—81no—
621C2×C32—81no—
622C2×C32C2×#12111yescharacteristic
623C2×C32#57711yescharacteristic
624C2×C32#57711yescharacteristic
625C3×D3—22no—
626C3×D3—81no—
627C24—61no—
628#41—62no—
629#41—62no—
630C2×Q8—34no—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×Q8—61no—
634C2×Q8—62no—
635C2×Q8C22×C3×D311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—31no—
639C2×D4—62no—
640C2×D4—62no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4—61no—
645C2×D4C22×C3×D311yescharacteristic
646C2×D4C22×C3×D311yescharacteristic
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—61no—
650Q16—62no—
651Q16—62no—
652SD16—22no—
653SD16—22no—
654SD16—62no—
655SD16—62no—
656SD16—62no—
657SD16—62no—
658M16—62no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—62no—
662C2×C8C22×C3×D311yescharacteristic
663C2×C8C22×C3×D311yescharacteristic
664C4⋊C4—21no—
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4C22×C3×D311yescharacteristic
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C42—21no—
680C42—31no—
681C42—61no—
682C42—61no—
683C42—61no—
684C42—61no—
685C42C22×C3×D311yescharacteristic
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3—244no—
712C22×C3C2×D3×D411yescharacteristic
713C22×C3C22×C3×D411yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—84no—
720C2×D3C3×#12112yes—
721C3×C4—22no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—32no—
731C3×C4—41no—
732C3×C4—42no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—62no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4C2×D3×D411yescharacteristic
742C3×C4D3×#4111yescharacteristic
743C3×C4C22×C3×D411yescharacteristic
744C3×C4C2×C3×#4111yescharacteristic
745Dic3—21no—
746Dic3—21no—
747Dic3—22no—
748Dic3—41no—
749Dic3—41no—
750Dic3C3×#12112yes—
751C32#304311yescharacteristic, complemented, Sylow
752C23—21no—
753C23—21no—
754C23—31no—
755C23—61no—
756C23—122no—
757C23—241no—
758C23—241no—
759Q8—21no—
760Q8—32no—
761Q8—64no—
762Q8—61no—
763Q8—61no—
764Q8—61no—
765Q8C3×D3×D412yes—
766D4—21no—
767D4—21no—
768D4—21no—
769D4—21no—
770D4—61no—
771D4—61no—
772D4—81no—
773D4—81no—
774D4—122no—
775D4—122no—
776D4—241no—
777D4—241no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—31no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—64no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—122no—
790C2×C4C3×D3×D411yescharacteristic
791C2×C4C3×D3×D411yescharacteristic
792C2×C4C23×C3×D311yescharacteristic
793C8—21no—
794C8—21no—
795C8—61no—
796C8—61no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—62no—
801C2×C3—81no—
802C2×C3—81no—
803C2×C3—81no—
804C2×C3—81no—
805C2×C3—161no—
806C2×C3—161no—
807C2×C3—241no—
808C2×C3D3×#12111yescharacteristic
809C2×C3#576211yescharacteristic
810C2×C3#577511yescharacteristic
811C2×C3C2×C3×#12111yescharacteristic
812C2×C3C3×#57711yescharacteristic
813C2×C3C3×#57711yescharacteristic
814D3—22no—
815D3—81no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—61no—
824C22—61no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—244no—
829C22C2×C3×D3×D411yescharacteristic
830C4—21no—
831C4—21no—
832C4—22no—
833C4—32no—
834C4—41no—
835C4—61no—
836C4—61no—
837C4—62no—
838C4—121no—
839C4—121no—
840C4C2×C3×D3×D411yescharacteristic
841C4C3×D3×#4111yescharacteristic
842C3—21no—
843C3#8038511yescharacteristic, direct product factor
844C3C3×#304311yescharacteristic, complemented
845C2—62no—
846C2—81no—
847C2—81no—
848C2—241no—
849C2C3×D3×#12111yescharacteristic
850C2C3×#576211yescharacteristic
851C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radicalC3×#5715C2
hypercenterC3×#460D3
hypocenterC3C3×#3043
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. C2×C3×D3×SD16C2semidirect
4. C3×#5572C2semidirect
5. C32×#460C2semidirect
6. C3×#5166C2semidirect
7. C3×#5163C2semidirect
8. C3×#5075C2semidirect
9. C3×#5028C2semidirect
10. C3×#4845C2semidirect
11. C3×#4839C2semidirect
12. C3×#4772C2semidirect
13. C3×#4770C2semidirect
14. C3×#4767C2semidirect
15. C3×#4762C2semidirect
17. #80385C3direct (N × H)
22. C2×C32×SD16C22semidirect
24. C32×C4×Q8C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
35. C2×C3×#214C22semidirect
38. C2×C3×Dic12C22semidirect
45. C3×#887C22semidirect
50. C3×C4×Dic6C22semidirect
51. C32×C4⋊C8C22semidirect
53. C32×#102C22semidirect
55. C3×#832C22semidirect
57. C3×#816C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. C3×#810C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#915C2×C3semidirect
68. C2×D3×SD16C2×C3semidirect
70. #5572C2×C3semidirect
79. C3×#460D3semidirect
80. C3×#460C2×C3semidirect
84. #5166C2×C3semidirect
85. #5163C2×C3semidirect
86. #5075C2×C3semidirect
87. #5028C2×C3semidirect
88. #4845C2×C3semidirect
89. #4839C2×C3semidirect
90. #4772C2×C3semidirect
91. #4770C2×C3semidirect
92. #4767C2×C3semidirect
93. #4762C2×C3semidirect
106. C3×D3×Q8D4semidirect
171. C2×C3×SD16C2×D3semidirect
173. C2×C3×SD16C22×C3semidirect
192. C3×C4×Q8C2×D3semidirect
193. C3×C4×Q8C22×C3semidirect
198. Q8×Dic3C22×C3semidirect
199. C2×#216C22×C3semidirect
208. C2×#214C22×C3semidirect
211. C2×Dic12C22×C3semidirect
218. #887C22×C3semidirect
223. C4×Dic6C22×C3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C22×C3semidirect
239. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
243. #832C22×C3semidirect
245. #816C22×C3semidirect
246. Dic3⋊C8C22×C3semidirect
247. Dic3⋊C8C22×C3semidirect
248. #810C22×C3semidirect
250. C4⋊(C3⋊C8)C22×C3semidirect
307. #460C3×D3semidirect
351. D3×Q8C3×D4semidirect
480. C2×SD16C2×C3×D3semidirect
496. C4×Q8C2×C3×D3semidirect
504. C4⋊C8C2×C3×D3semidirect
512. #102C2×C3×D3semidirect
751. C32#3043semidirect
843. C3#80385direct (N × H)
844. C3C3×#3043semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
C2×C3×D3×SD162
C3×#57152
C3×#55722
C32×#4602
C3×#51662
C3×#51632
C3×#50752
C3×#50282
C3×#48452
C3×#48392
C3×#47722
C3×#47702
C3×#47672
C3×#47622
C3×#30433
#803853