Finite Group Databasebeta

← C3×#81881 #11884065

Subgroups — C3×#81881 #11884065

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 876 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×#5727C211yesmaximal, characteristic, complemented
4C3×#5676C211yesmaximal, characteristic
5C32×#497C211yesmaximal, characteristic, complemented
6C3×#5188C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5186C211yesmaximal, characteristic, complemented
9C3×#5174C211yesmaximal, characteristic, complemented
10C3×#5170C211yesmaximal, characteristic, complemented
11C3×#5169C211yesmaximal, characteristic, complemented
12C3×#5083C211yesmaximal, characteristic, complemented
13C3×#5054C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#81881C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×C32×Q16C2211yescharacteristic, complemented
24C2×C32×SD16C2211yescharacteristic
25C2×C32×SD16C2211yescharacteristic
26C32×C4⋊Q8C2211yescharacteristic, complemented
27C32×#124C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C3×#946C2211yescharacteristic, complemented
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C3×#938C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C3×#918—24no—
37C3×D3×SD16—24no—
38C2×C3×#204C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
40C2×C3×D3×C8C2211yescharacteristic
41C3×#896—21no—
42C3×#896—21no—
43C3×#893—21no—
44C3×#888—21no—
45C3×#884—21no—
46C3×#883—21no—
47C3×#882—21no—
48C3×D3×C22⋊C4—21no—
49C3×C4×D12C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic, complemented
52C32×#97C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×#818C2211yescharacteristic, complemented
61C3×#816C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67C2×#918C2×C311yescharacteristic, complemented
68C2×D3×SD16C2×C311yescharacteristic, complemented
69#5727C2×C311yescharacteristic, complemented
70#5676C2×C311yescharacteristic
71C3×#497—21no—
72C3×#497D311yescharacteristic, complemented
73C3×#497C2×C311yescharacteristic, complemented
74C3×#468—31no—
75C3×#467—31no—
76C3×#464—31no—
77C3×#461—31no—
78C3×#452—31no—
79C3×#451—31no—
80C3×#450—31no—
81C3×#448—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5188C2×C311yescharacteristic, complemented
85#5187C2×C311yescharacteristic, complemented
86#5186C2×C311yescharacteristic, complemented
87#5174C2×C311yescharacteristic, complemented
88#5170C2×C311yescharacteristic, complemented
89#5169C2×C311yescharacteristic, complemented
90#5083C2×C311yescharacteristic, complemented
91#5054C2×C311yescharacteristic, complemented
92#4710C2×C311yescharacteristic, complemented
93#4706C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#239—22no—
102C3×#239—41no—
103C3×D3×Q8—22no—
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C3×D3×Q8—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12—21no—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C32×Q16—41no—
123C32×SD16—22no—
124C32×SD16—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4—21no—
128C32×C4⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#216—22no—
134C3×#215—22no—
135C3×#215—22no—
136C3×#214—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3D411yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×C4⋊Dic3C2311yescharacteristic
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×Dic3⋊C4—21no—
150C3×C4×Dic3—21no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×#204D414yescomplemented
154C3×ΓL(1,𝔽25)—22no—
155C3×D3×C8—22no—
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C2×#239C22×C311yescharacteristic
162C2×D3×Q8C22×C311yescharacteristic
163C2×D3×Q8C22×C311yescharacteristic, complemented
164C2×D3×D4C22×C311yescharacteristic
165C3×#137—64no—
166C2×C3×Q16—21no—
167C2×C3×Q16—21no—
168C2×C3×Q16—31no—
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×Q16C22×C311yescharacteristic, complemented
172C2×C3×Q16C22×C311yescharacteristic, complemented
173C2×C3×SD16—21no—
174C2×C3×SD16—21no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—31no—
178C2×C3×SD16—31no—
179C2×C3×SD16—64no—
180C2×C3×SD16C2×D311yescharacteristic
181C2×C3×SD16C2×D311yescharacteristic
182C2×C3×SD16C22×C311yescharacteristic
183C2×C3×SD16C22×C311yescharacteristic
184C2×C3×M16—31no—
185C22×C3×C8—31no—
186C3×C4⋊Q8—21no—
187C3×C4⋊Q8—61no—
188C3×C4⋊Q8C2×D311yescharacteristic, complemented
189C3×C4⋊Q8C22×C311yescharacteristic, complemented
190C3×#124—21no—
191C3×#124C2×D311yescharacteristic
192C3×#124C22×C311yescharacteristic
193C3×#123—61no—
194C3×C22⋊Q8—31no—
195C3×C22⋊Q8—31no—
196C3×C22⋊Q8—31no—
197C3×C22⋊Q8—61no—
198C3×C22⋊Q8—61no—
199C3×#121—31no—
200C3×#121—61no—
201C3×#120—61no—
202C3×C4×Q8—31no—
203C3×C4×D4—31no—
204C3×C4×D4—31no—
205C3×C4×D4—61no—
206C2×C3×C22⋊C4—61no—
207#946C22×C311yescharacteristic
208#946C22×C311yescharacteristic
209#946C22×C311yescharacteristic, complemented
210C2×#216C22×C311yescharacteristic, complemented
211C2×#215C22×C311yescharacteristic
212C2×#215C22×C311yescharacteristic
213#938C22×C311yescharacteristic
214C2×#214C22×C311yescharacteristic
215#918—24no—
216D3×SD16—24no—
217C2×#204C22×C311yescharacteristic
218C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
219C2×D3×C8C22×C311yescharacteristic
220#896—21no—
221#896—21no—
222#893—21no—
223#888—21no—
224#884—21no—
225#883—21no—
226#882—21no—
227D3×C22⋊C4—21no—
228C4×D12C22×C311yescharacteristic
229C4×D12C22×C311yescharacteristic
230C4×Dic6C22×C311yescharacteristic, complemented
231C3×#107—31no—
232C3×C4⋊C8—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×C22⋊C8—31no—
240C3×C22⋊C8—31no—
241C3×#97—21no—
242C3×#97C2×D311yescharacteristic, complemented
243C3×#97C22×C311yescharacteristic, complemented
244#835C22×C311yescharacteristic, complemented
245#835C22×C311yescharacteristic, complemented
246#835C22×C311yescharacteristic, complemented
247#832C22×C311yescharacteristic
248#821C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic
250(C2×D3)⋊C8C22×C311yescharacteristic, complemented
251#818C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×Q8—21no—
267C32×D4—21no—
268C32×D4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C3×#67—42no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—22no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×C4×D3—81no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C32×C8—21no—
299C32×C8C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—31no—
303C22×SD16—31no—
304D4×Q8—31no—
305#546—31no—
306#497C3×D311yescharacteristic, complemented
307#468—31no—
308#467—31no—
309#464—31no—
310#461—31no—
311#452—31no—
312#451—31no—
313#450—31no—
314#448—31no—
315#440—31no—
316#435—31no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8—62no—
329C2×C3×Q8—121no—
330C2×C3×Q8—121no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C23×C311yescharacteristic
335C2×C3×Q8C23×C311yescharacteristic
336C2×C3×Q8C23×C311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—121no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C23×C311yescharacteristic
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C2×#67—21no—
354C2×#67—21no—
355#239—22no—
356#239—41no—
357D3×Q8—22no—
358D3×Q8—22no—
359D3×Q8—41no—
360D3×Q8—41no—
361D3×D4—22no—
362D3×D4—41no—
363C2×D12—21no—
364C2×D12C3×D411yescharacteristic
365C2×D12C23×C311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3C23×C311yescharacteristic
371C2×C4×D3C23×C311yescharacteristic
372C2×Dic6—21no—
373C2×Dic6—21no—
374C2×Dic6C23×C311yescharacteristic
375C3×Q16—22no—
376C3×Q16—22no—
377C3×Q16—42no—
378C3×Q16—41no—
379C3×Q16—41no—
380C3×Q16—42no—
381C3×Q16—62no—
382C3×SD16—22no—
383C3×SD16—22no—
384C3×SD16—34no—
385C3×SD16—42no—
386C3×SD16—41no—
387C3×SD16—41no—
388C3×SD16—42no—
389C3×SD16—62no—
390C3×SD16—62no—
391C3×SD16—62no—
392C3×M16—62no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C2×C3×C8C23×C311yescharacteristic
402C3×C4⋊C4—21no—
403C3×C4⋊C4—21no—
404C3×C4⋊C4—21no—
405C3×C4⋊C4—21no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—41no—
410C3×C4⋊C4—41no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—61no—
414C3×C4⋊C4—61no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—41no—
422C3×C22⋊C4—41no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C42—21no—
429C3×C42—61no—
430C3×C42C22×D311yescharacteristic
431C3×C42C23×C311yescharacteristic
432#217—21no—
433#216—22no—
434#215—22no—
435#215—22no—
436#214—22no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4C3×D411yescharacteristic
442(C2×D3)⋊C4C3×D411yescharacteristic
443C4⋊Dic3C3×D411yescharacteristic
444C4⋊Dic3C23×C311yescharacteristic
445C4⋊Dic3C23×C311yescharacteristic
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4—21no—
450C4×Dic3—21no—
451C2×C3⋊C8C23×C311yescharacteristic
452C2×C3⋊C8C23×C311yescharacteristic
453#204C3×D414yescomplemented
454ΓL(1,𝔽25)—22no—
455D3×C8—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32C22×D411yescharacteristic
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—22no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—84no—
469C2×C3×D3#13712yescomplemented
470C32×C4—21no—
471C32×C4—21no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—31no—
484C22×Q8—31no—
485C22×D4—31no—
486#137—64no—
487C2×Q16—31no—
488C2×Q16C2×C3×D311yescharacteristic, complemented
489C2×Q16C2×C3×D311yescharacteristic, complemented
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—64no—
495C2×SD16C2×C3×D311yescharacteristic
496C2×SD16C2×C3×D311yescharacteristic
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—61no—
500C4⋊Q8C2×C3×D311yescharacteristic, complemented
501#124C2×C3×D311yescharacteristic
502#123—61no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—31no—
506C22⋊Q8—61no—
507C22⋊Q8—61no—
508#121—31no—
509#121—61no—
510#120—61no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—61no—
515C2×C22⋊C4—61no—
516#107—31no—
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103—31no—
521#103—31no—
522#102—31no—
523#102—31no—
524C22⋊C8—31no—
525C22⋊C8—31no—
526#97C2×C3×D311yescharacteristic, complemented
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C22×D3—21no—
537C22×D3—42no—
538C22×D3—42no—
539C22×D3—81no—
540C22×D3C2×C3×D411yescharacteristic
541C22×D3C2×C3×D411yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—32no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8—41no—
561C3×Q8—61no—
562C3×Q8—122no—
563C3×Q8—122no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—32no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—62no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—241no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—122no—
598C2×C3×C4—122no—
599C2×C3×C4—122no—
600C2×C3×C4—241no—
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4D3×D411yescharacteristic
603C2×C3×C4C2×C3×D411yescharacteristic
604C2×C3×C4C2×C3×D411yescharacteristic
605C2×C3×C4C23×D311yescharacteristic
606C2×C3×C4C24×C311yescharacteristic
607#67—42no—
608#67—81no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3C2×C3×D411yescharacteristic
613C2×Dic3C2×C3×D411yescharacteristic
614D12—22no—
615D12—21no—
616D12—42no—
617D12C2×C3×D412yes—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—42no—
623C4×D3—42no—
624C4×D3—42no—
625C4×D3—81no—
626Dic6—21no—
627Dic6—42no—
628Dic6—42no—
629Dic6C2×C3×D412yes—
630C3×C8—22no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—22no—
634C3×C8—61no—
635C3×C8—61no—
636C3×C8D3×D412yes—
637C3×C8C2×C3×D412yes—
638C3⋊C8—21no—
639C3⋊C8—21no—
640C2×C32—81no—
641C2×C32D4211yescharacteristic
642C2×C32C2×#13711yescharacteristic
643C2×C32#57711yescharacteristic
644C3×D3—22no—
645C3×D3—41no—
646C3×D3—42no—
647C24—61no—
648#41—62no—
649#41—121no—
650C2×Q8—31no—
651C2×Q8—61no—
652C2×Q8—61no—
653C2×Q8—62no—
654C2×Q8—62no—
655C2×Q8—121no—
656C2×Q8—121no—
657C2×Q8C22×C3×D311yescharacteristic
658C2×Q8C22×C3×D311yescharacteristic
659C2×Q8C22×C3×D311yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—62no—
665C2×D4—61no—
666C2×D4—121no—
667C2×D4C22×C3×D311yescharacteristic
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674Q16—22no—
675Q16—41no—
676Q16—62no—
677SD16—22no—
678SD16—34no—
679SD16—41no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683M16—62no—
684C2×C8—31no—
685C2×C8—31no—
686C2×C8—62no—
687C2×C8C22×C3×D311yescharacteristic
688C2×C8C22×C3×D311yescharacteristic
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C42—61no—
708C42C22×C3×D311yescharacteristic
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—62no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—244no—
729C22×C3C2×D3×D411yescharacteristic
730C22×C3C22×C3×D411yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—84no—
740C2×D3C3×#13712yescomplemented
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—62no—
758C3×C4—81no—
759C3×C4—81no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4C2×D3×D411yescharacteristic
764C3×C4#100411yescharacteristic
765C3×C4C22×C3×D411yescharacteristic
766C3×C4C3×H(5,𝔽2)11yescharacteristic
767Dic3—22no—
768Dic3—21no—
769Dic3—21no—
770Dic3—41no—
771Dic3—41no—
772C32#326611yescharacteristic, complemented, Sylow
773C23—21no—
774C23—31no—
775C23—31no—
776C23—61no—
777C23—122no—
778C23—122no—
779C23—241no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—21no—
786Q8—32no—
787Q8—61no—
788Q8—122no—
789Q8—122no—
790D4—21no—
791D4—21no—
792D4—32no—
793D4—62no—
794D4—61no—
795D4—122no—
796D4—122no—
797D4—241no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—122no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—241no—
814C2×C4C3×D3×D411yescharacteristic
815C2×C4C3×D3×D411yescharacteristic
816C2×C4C23×C3×D311yescharacteristic
817C8—21no—
818C8—61no—
819C8—61no—
820C8C3×D3×D412yes—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—62no—
825C2×C3—81no—
826C2×C3—81no—
827C2×C3—121no—
828C2×C3—122no—
829C2×C3—161no—
830C2×C3#571711yescharacteristic
831C2×C3D3×#13711yescharacteristic
832C2×C3#577811yescharacteristic
833C2×C3C3×D4211yescharacteristic
834C2×C3C2×C3×#13711yescharacteristic
835C2×C3C3×#57711yescharacteristic
836D3—22no—
837D3—41no—
838D3—42no—
839C22—32no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—61no—
847C22—61no—
848C22—62no—
849C22—121no—
850C22—121no—
851C22—244no—
852C22C2×C3×D3×D411yescharacteristic
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—61no—
859C4—61no—
860C4—62no—
861C4—121no—
862C4—121no—
863C4C2×C3×D3×D411yescharacteristic
864C4C3×#100411yescharacteristic
865C3—21no—
866C3#8188111yescharacteristic, direct product factor
867C3C3×#326611yescharacteristic, complemented
868C2—62no—
869C2—81no—
870C2—121no—
871C2—122no—
872C2C3×#571711yescharacteristic
873C2C3×D3×#13711yescharacteristic
874C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#497C2
socleC22×C32C22×D4
prime radicalC3×#5676C2
hypercenterC3×#497D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#497

Complements

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

NH ≅ G/Ntype
1. C2×C3×#918C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. C3×#5727C2semidirect
5. C32×#497C2semidirect
6. C3×#5188C2semidirect
7. C3×#5187C2semidirect
8. C3×#5186C2semidirect
9. C3×#5174C2semidirect
10. C3×#5170C2semidirect
11. C3×#5169C2semidirect
12. C3×#5083C2semidirect
13. C3×#5054C2semidirect
14. C3×#4710C2semidirect
15. C3×#4706C2semidirect
17. #81881C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
22. C2×C32×Q16C22semidirect
23. C2×C32×Q16C22semidirect
26. C32×C4⋊Q8C22semidirect
30. C3×#946C22semidirect
31. C2×C3×#216C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
51. C3×C4×Dic6C22semidirect
52. C32×#97C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
55. C3×#835C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×#818C22semidirect
61. C3×#816C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#918C2×C3semidirect
68. C2×D3×SD16C2×C3semidirect
69. #5727C2×C3semidirect
72. C3×#497D3semidirect
73. C3×#497C2×C3semidirect
84. #5188C2×C3semidirect
85. #5187C2×C3semidirect
86. #5186C2×C3semidirect
87. #5174C2×C3semidirect
88. #5170C2×C3semidirect
89. #5169C2×C3semidirect
90. #5083C2×C3semidirect
91. #5054C2×C3semidirect
92. #4710C2×C3semidirect
93. #4706C2×C3semidirect
153. C3×#204D4semidirect
163. C2×D3×Q8C22×C3semidirect
169. C2×C3×Q16C2×D3semidirect
170. C2×C3×Q16C2×D3semidirect
171. C2×C3×Q16C22×C3semidirect
172. C2×C3×Q16C22×C3semidirect
188. C3×C4⋊Q8C2×D3semidirect
189. C3×C4⋊Q8C22×C3semidirect
209. #946C22×C3semidirect
210. C2×#216C22×C3semidirect
218. C2×ΓL(1,𝔽25)C22×C3semidirect
230. C4×Dic6C22×C3semidirect
242. C3×#97C2×D3semidirect
243. C3×#97C22×C3semidirect
244. #835C22×C3semidirect
245. #835C22×C3semidirect
246. #835C22×C3semidirect
250. (C2×D3)⋊C8C22×C3semidirect
251. #818C22×C3semidirect
252. #816C22×C3semidirect
253. C4⋊(C3⋊C8)C22×C3semidirect
306. #497C3×D3semidirect
453. #204C3×D4semidirect
469. C2×C3×D3#137semidirect
488. C2×Q16C2×C3×D3semidirect
489. C2×Q16C2×C3×D3semidirect
500. C4⋊Q8C2×C3×D3semidirect
526. #97C2×C3×D3semidirect
740. C2×D3C3×#137semidirect
772. C32#3266semidirect
866. C3#81881direct (N × H)
867. C3C3×#3266semidirect

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×#57272
C3×#56762
C32×#4972
C3×#51882
C3×#51872
C3×#51862
C3×#51742
C3×#51702
C3×#51692
C3×#50832
C3×#50542
C3×#47102
C3×#47062
C3×#32663
#818813