Finite Group Databasebeta

← C3×#79495 #11884083

Subgroups — C3×#79495 #11884083

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×#909C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C3×#5550C211yesmaximal, characteristic
4C3×D4×Dic6C211yesmaximal, characteristic, complemented
5C32×#435C211yesmaximal, characteristic, complemented
6C3×#5134C211yesmaximal, characteristic, complemented
7C3×#5116C211yesmaximal, characteristic, complemented
8C3×#4845C211yesmaximal, characteristic, complemented
9C3×#4841C211yesmaximal, characteristic, complemented
10C3×#4739C211yesmaximal, characteristic, complemented
11C3×#4738C211yesmaximal, characteristic, complemented
12C3×#4733C211yesmaximal, characteristic, complemented
13C3×#4731C211yesmaximal, characteristic, complemented
14C3×#4715C211yesmaximal, characteristic, complemented
15C3×#4710C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#79495C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C2×C32×M16C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25C3×#937—21no—
26C3×D4×Dic3—21no—
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C3×#909—24no—
32C2×C3×Dic12C2211yescharacteristic, complemented
33C2×C3×Dic12C2211yescharacteristic, complemented
34C2×C3×Dic12C2211yescharacteristic, complemented
35C2×C3×#204—24no—
36C2×C3×#204C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic
41C2×C3×#204C2211yescharacteristic
42C3×#894—21no—
43C3×#888—21no—
44C3×#884—21no—
45C3×D3×C22⋊C4—21no—
46C3×#878—21no—
47C3×#878—21no—
48C3×#875C2211yescharacteristic
49C3×C4×D12C2211yescharacteristic
50C3×#869C2211yescharacteristic, complemented
51C3×C4×Dic6C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×C22⋊C8C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic, complemented
55C32×#97C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×#818C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#816C2211yescharacteristic, complemented
62C3×#816C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67C2×#909C2×C311yescharacteristic, complemented
68C22×#204C2×C311yescharacteristic, complemented
69#5550C2×C311yescharacteristic
70D4×Dic6C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#464—31no—
75C3×#461—31no—
76C3×#452—31no—
77C3×#451—31no—
78C3×#450—31no—
79C3×#448—31no—
80C3×#440—31no—
81C3×#435—21no—
82C3×#435D311yescharacteristic, complemented
83C3×#435C2×C311yescharacteristic, complemented
84#5134C2×C311yescharacteristic, complemented
85#5116C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4841C2×C311yescharacteristic, complemented
88#4739C2×C311yescharacteristic, complemented
89#4738C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#4731C2×C311yescharacteristic, complemented
92#4715C2×C311yescharacteristic, complemented
93#4710C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×Dic6—22no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—21no—
114C2×C3×Dic6—21no—
115C2×C3×Dic6—41no—
116C2×C3×Dic6—41no—
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×M16—22no—
122C2×C32×C8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4D411yescharacteristic
128C32×C22⋊C4D411yescharacteristic
129C32×C22⋊C4D411yescharacteristic
130C32×C42C2311yescharacteristic
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×C4×Dic3—21no—
147C3×Dic12—22no—
148C3×Dic12—22no—
149C3×Dic12—41no—
150C3×#204—22no—
151C3×#204—22no—
152C3×#204—22no—
153C3×#204—22no—
154C3×#204—41no—
155C3×#204D414yescomplemented
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C2×#235C22×C311yescharacteristic
162C22×D12C22×C311yescharacteristic
163C22×Dic6C22×C311yescharacteristic
164C22×Dic6C22×C311yescharacteristic, complemented
165C3×#137—64no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—64no—
176C2×C3×M16—21no—
177C2×C3×M16C2×D311yescharacteristic, complemented
178C2×C3×M16C22×C311yescharacteristic, complemented
179C22×C3×C8—21no—
180C22×C3×C8C2×D311yescharacteristic
181C22×C3×C8C22×C311yescharacteristic
182C3×C4⋊Q8—31no—
183C3×C4⋊Q8—61no—
184C3×#124—31no—
185C3×#123—61no—
186C3×C22⋊Q8—31no—
187C3×C22⋊Q8—31no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—61no—
190C3×C22⋊Q8—61no—
191C3×#121—31no—
192C3×#121—61no—
193C3×#120—61no—
194C3×C4×Q8—31no—
195C3×C4×D4—21no—
196C3×C4×D4—31no—
197C3×C4×D4—61no—
198C3×C4×D4C2×D311yescharacteristic
199C3×C4×D4C22×C311yescharacteristic
200C2×C3×C22⋊C4—61no—
201#937—21no—
202D4×Dic3—21no—
203#930C22×C311yescharacteristic
204#924C22×C311yescharacteristic
205#924C22×C311yescharacteristic
206#924C22×C311yescharacteristic, complemented
207#909—24no—
208C2×Dic12C22×C311yescharacteristic, complemented
209C2×Dic12C22×C311yescharacteristic, complemented
210C2×Dic12C22×C311yescharacteristic, complemented
211C2×#204—24no—
212C2×#204C22×C311yescharacteristic
213C2×#204C22×C311yescharacteristic
214C2×#204C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic
216C2×#204C22×C311yescharacteristic
217C2×#204C22×C311yescharacteristic
218#894—21no—
219#888—21no—
220#884—21no—
221D3×C22⋊C4—21no—
222#878—21no—
223#878—21no—
224#875C22×C311yescharacteristic
225C4×D12C22×C311yescharacteristic
226#869C22×C311yescharacteristic, complemented
227C4×Dic6C22×C311yescharacteristic, complemented
228C3×#107—31no—
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C22×C311yescharacteristic, complemented
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×C22⋊C8—21no—
239C3×C22⋊C8—21no—
240C3×C22⋊C8C2×D311yescharacteristic
241C3×C22⋊C8C2×D311yescharacteristic, complemented
242C3×C22⋊C8C22×C311yescharacteristic
243C3×C22⋊C8C22×C311yescharacteristic, complemented
244C3×#97—21no—
245C3×#97C2×D311yescharacteristic, complemented
246C3×#97C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic
248#821C22×C311yescharacteristic
249#818C22×C311yescharacteristic, complemented
250#816C22×C311yescharacteristic, complemented
251#816C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253#816C22×C311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C32×D4—22no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C3×#67—42no—
272C3×#67—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—42no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—42no—
287C3×C4×D3—81no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C32×C8—21no—
299C32×C8—21no—
300C32×C8—21no—
301C32×C8C2×D412yes—
302C2×#137—31no—
303C22×SD16—31no—
304D4×Q8—31no—
305#546—31no—
306#497—31no—
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#435C3×D311yescharacteristic, complemented
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8—61no—
328C2×C3×Q8—61no—
329C2×C3×Q8—121no—
330C2×C3×Q8—121no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—121no—
339C2×C3×D4D1211yescharacteristic
340C2×C3×D4C3×D411yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C23×C311yescharacteristic
350C22×C3×C4C23×C311yescharacteristic
351C2×#67—21no—
352C2×#67—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355#235—22no—
356#235—41no—
357C2×D12—22no—
358C2×D12—21no—
359C2×D12—41no—
360C2×D12C23×C311yescharacteristic
361C2×D12C23×C311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×Dic6—22no—
365C2×Dic6—22no—
366C2×Dic6—21no—
367C2×Dic6—21no—
368C2×Dic6—41no—
369C2×Dic6—41no—
370C2×Dic6C23×C311yescharacteristic
371C2×Dic6C23×C311yescharacteristic
372C2×Dic6C23×C311yescharacteristic
373C2×Dic6C23×C311yescharacteristic
374C3×Q16—62no—
375C3×Q16—62no—
376C3×Q16—121no—
377C3×SD16—34no—
378C3×SD16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×SD16—62no—
382C3×SD16—121no—
383C3×M16—22no—
384C3×M16—22no—
385C3×M16—42no—
386C2×C3×C8—22no—
387C2×C3×C8—22no—
388C2×C3×C8—21no—
389C2×C3×C8—21no—
390C2×C3×C8—21no—
391C2×C3×C8—21no—
392C2×C3×C8—42no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C23×C311yescharacteristic
398C2×C3×C8C23×C311yescharacteristic
399C2×C3×C8C23×C311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4D1211yescharacteristic
411C3×C4⋊C4C3×D411yescharacteristic
412C3×C22⋊C4—21no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4D1211yescharacteristic
422C3×C22⋊C4D1211yescharacteristic
423C3×C22⋊C4C3×D411yescharacteristic
424C3×C22⋊C4C3×D411yescharacteristic
425C3×C42—21no—
426C3×C42—61no—
427C3×C42C22×D311yescharacteristic
428C3×C42C23×C311yescharacteristic
429#217—21no—
430#217—21no—
431#217—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436C4⋊Dic3—21no—
437C4⋊Dic3—21no—
438C4⋊Dic3C23×C311yescharacteristic
439C4⋊Dic3C23×C311yescharacteristic
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444C4×Dic3—21no—
445Dic12—22no—
446Dic12—22no—
447Dic12—41no—
448#204—22no—
449#204—22no—
450#204—22no—
451#204—22no—
452#204—41no—
453#204C3×D414yescomplemented
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32#13712yescomplemented
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—22no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4—21no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—31no—
484#137—64no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16—31no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—64no—
495C2×M16C2×C3×D311yescharacteristic, complemented
496C22×C8C2×C3×D311yescharacteristic
497C4⋊Q8—31no—
498C4⋊Q8—61no—
499#124—31no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—31no—
504C22⋊Q8—61no—
505C22⋊Q8—61no—
506#121—31no—
507#121—61no—
508#120—61no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—61no—
512C4×D4C2×C3×D311yescharacteristic
513C2×C22⋊C4—61no—
514#107—31no—
515C4⋊C8C2×C3×D311yescharacteristic, complemented
516#103—31no—
517#103—31no—
518#103—31no—
519#103—31no—
520#102—31no—
521#102—31no—
522C22⋊C8C2×C3×D311yescharacteristic
523C22⋊C8C2×C3×D311yescharacteristic, complemented
524#97C2×C3×D311yescharacteristic, complemented
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—241no—
532C23×C3C2×D1211yescharacteristic
533C23×C3C2×D1211yescharacteristic
534C23×C3C2×C3×D411yescharacteristic
535C23×C3C2×C3×D411yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—81no—
541C3×Q8—32no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×Q8—122no—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—32no—
554C3×D4—42no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—122no—
559C3×D4—122no—
560C3×D4—241no—
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—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4—241no—
588C2×C3×C4C2×D1211yescharacteristic
589C2×C3×C4C2×D1211yescharacteristic
590C2×C3×C4C2×D1211yescharacteristic
591C2×C3×C4C2×D1211yescharacteristic
592C2×C3×C4C2×C3×D411yescharacteristic
593C2×C3×C4C2×C3×D411yescharacteristic
594C2×C3×C4C2×C3×D411yescharacteristic
595C2×C3×C4C2×C3×D411yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C24×C311yescharacteristic
598#67—42no—
599#67—81no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—42no—
607C2×Dic3—42no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—42no—
612D12C2×C3×D412yes—
613C4×D3—42no—
614C4×D3—81no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—42no—
624Dic6C2×C3×D412yes—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—22no—
632C3×C8—41no—
633C3×C8—41no—
634C3×C8—41no—
635C3×C8D3×D412yes—
636C3×C8C2×C3×D412yes—
637C2×C32—22no—
638C2×C32—41no—
639C2×C32D4211yescharacteristic
640C2×C32C2×#13711yescharacteristic
641C2×C32#57711yescharacteristic
642C3×D3—42no—
643C3×D3—81no—
644C24—61no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—31no—
651C2×Q8—62no—
652C2×Q8—62no—
653C2×Q8—61no—
654C2×Q8—61no—
655C2×Q8—121no—
656C2×Q8—121no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—121no—
664C2×D4C3×D1211yescharacteristic
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4C22×C3×D311yescharacteristic
670C22×C4C22×C3×D311yescharacteristic
671Q16—62no—
672Q16—62no—
673Q16—121no—
674SD16—34no—
675SD16—62no—
676SD16—62no—
677SD16—62no—
678SD16—62no—
679SD16—121no—
680M16—22no—
681C2×C8—22no—
682C2×C8C22×C3×D311yescharacteristic
683C2×C8C22×C3×D311yescharacteristic
684C2×C8C22×C3×D311yescharacteristic
685C2×C8C22×C3×D311yescharacteristic
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C3×D1211yescharacteristic
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4C3×D1211yescharacteristic
703C22⋊C4C3×D1211yescharacteristic
704C42—61no—
705C42C22×C3×D311yescharacteristic
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—62no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—244no—
730C22×C3#90912yescomplemented
731C22×C3C3×#13712yescomplemented
732C22×C3C22×D1211yescharacteristic
733C22×C3C22×C3×D411yescharacteristic
734C2×D3—22no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—84no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—62no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4#100911yescharacteristic
763C3×C4C22×C3×D411yescharacteristic
764C3×C4C3×H(5,𝔽2)11yescharacteristic
765Dic3—22no—
766Dic3—41no—
767Dic3—41no—
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771C32#326611yescharacteristic, complemented, Sylow
772C23—61no—
773C23—61no—
774C23—122no—
775C23—122no—
776C23—241no—
777C23C2×C3×D1211yescharacteristic
778C23C2×C3×D1211yescharacteristic
779Q8—32no—
780Q8—61no—
781Q8—61no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—61no—
787Q8—122no—
788Q8—122no—
789D4—22no—
790D4—32no—
791D4—61no—
792D4—61no—
793D4—61no—
794D4—122no—
795D4—122no—
796D4—241no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—122no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—241no—
811C2×C4C2×C3×D1211yescharacteristic
812C2×C4C2×C3×D1211yescharacteristic
813C2×C4C2×C3×D1211yescharacteristic
814C2×C4C2×C3×D1211yescharacteristic
815C2×C4C23×C3×D311yescharacteristic
816C8—21no—
817C8—21no—
818C8—21no—
819C8C3×D3×D412yes—
820C2×C3—22no—
821C2×C3—22no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—42no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—81no—
829C2×C3—122no—
830C2×C3—241no—
831C2×C3D4×D1211yescharacteristic
832C2×C3C2×#90911yescharacteristic
833C2×C3#575111yescharacteristic
834C2×C3C3×D4211yescharacteristic
835C2×C3C2×C3×#13711yescharacteristic
836C2×C3C3×#57711yescharacteristic
837D3—42no—
838D3—81no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—62no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—244no—
851C22C3×#90912yescomplemented
852C22C22×C3×D1211yescharacteristic
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—62no—
858C4—121no—
859C4—121no—
860C4—121no—
861C4—121no—
862C4—121no—
863C4C2×C3×D3×D411yescharacteristic
864C4C3×#100911yescharacteristic
865C3—21no—
866C3#7949511yescharacteristic, direct product factor
867C3C3×#326611yescharacteristic, complemented
868C2—22no—
869C2—41no—
870C2—122no—
871C2—241no—
872C2C3×D4×D1211yescharacteristic
873C2C2×C3×#90911yescharacteristic
874C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#435C2
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC3×#435D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#909C2semidirect
2. C22×C3×#204C2semidirect
4. C3×D4×Dic6C2semidirect
5. C32×#435C2semidirect
6. C3×#5134C2semidirect
7. C3×#5116C2semidirect
8. C3×#4845C2semidirect
9. C3×#4841C2semidirect
10. C3×#4739C2semidirect
11. C3×#4738C2semidirect
12. C3×#4733C2semidirect
13. C3×#4731C2semidirect
14. C3×#4715C2semidirect
15. C3×#4710C2semidirect
17. #79495C3direct (N × H)
21. C22×C3×Dic6C22semidirect
22. C2×C32×M16C22semidirect
30. C3×#924C22semidirect
32. C2×C3×Dic12C22semidirect
33. C2×C3×Dic12C22semidirect
34. C2×C3×Dic12C22semidirect
50. C3×#869C22semidirect
51. C3×C4×Dic6C22semidirect
52. C32×C4⋊C8C22semidirect
54. C32×C22⋊C8C22semidirect
55. C32×#97C22semidirect
58. C3×#818C22semidirect
59. C3×#816C22semidirect
60. C3×#816C22semidirect
61. C3×#816C22semidirect
62. C3×#816C22semidirect
67. C2×#909C2×C3semidirect
68. C22×#204C2×C3semidirect
70. D4×Dic6C2×C3semidirect
82. C3×#435D3semidirect
83. C3×#435C2×C3semidirect
84. #5134C2×C3semidirect
85. #5116C2×C3semidirect
86. #4845C2×C3semidirect
87. #4841C2×C3semidirect
88. #4739C2×C3semidirect
89. #4738C2×C3semidirect
90. #4733C2×C3semidirect
91. #4731C2×C3semidirect
92. #4715C2×C3semidirect
93. #4710C2×C3semidirect
155. C3×#204D4semidirect
164. C22×Dic6C22×C3semidirect
177. C2×C3×M16C2×D3semidirect
178. C2×C3×M16C22×C3semidirect
206. #924C22×C3semidirect
208. C2×Dic12C22×C3semidirect
209. C2×Dic12C22×C3semidirect
210. C2×Dic12C22×C3semidirect
226. #869C22×C3semidirect
227. C4×Dic6C22×C3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C22×C3semidirect
241. C3×C22⋊C8C2×D3semidirect
243. C3×C22⋊C8C22×C3semidirect
245. C3×#97C2×D3semidirect
246. C3×#97C22×C3semidirect
249. #818C22×C3semidirect
250. #816C22×C3semidirect
251. #816C22×C3semidirect
252. #816C22×C3semidirect
253. #816C22×C3semidirect
316. #435C3×D3semidirect
453. #204C3×D4semidirect
459. C22×C32#137semidirect
495. C2×M16C2×C3×D3semidirect
515. C4⋊C8C2×C3×D3semidirect
523. C22⋊C8C2×C3×D3semidirect
524. #97C2×C3×D3semidirect
730. C22×C3#909semidirect
731. C22×C3C3×#137semidirect
771. C32#3266semidirect
851. C22C3×#909semidirect
866. C3#79495direct (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×#9092
C22×C3×#2042
C3×#55502
C3×D4×Dic62
C32×#4352
C3×#51342
C3×#51162
C3×#48452
C3×#48412
C3×#47392
C3×#47382
C3×#47332
C3×#47312
C3×#47152
C3×#47102
C3×#32663
#794953