Finite Group Databasebeta

← C3×#79795 #11884074

Subgroups — C3×#79795 #11884074

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 870 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×Q8×D12C211yesmaximal, characteristic, complemented
4C3×#5554C211yesmaximal, characteristic
5C32×#440C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7C3×#5019C211yesmaximal, characteristic, complemented
8C3×#4887C211yesmaximal, characteristic, complemented
9C3×#4886C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×#4806C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4776C211yesmaximal, characteristic, complemented
14C3×#4715C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#79795C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#930—21no—
30C2×C3×(C2×D3)⋊C4—21no—
31C3×#915—24no—
32C3×D3×SD16—24no—
33C2×C3×Dic12C2211yescharacteristic, complemented
34C2×C3×Dic12C2211yescharacteristic, complemented
35C2×C3×#204C2211yescharacteristic
36C2×C3×#204C2211yescharacteristic
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39C3×#897—21no—
40C3×#897—21no—
41C3×#897C2211yescharacteristic
42C3×#897C2211yescharacteristic
43C3×#897C2211yescharacteristic, complemented
44C3×#895C2211yescharacteristic
45C3×#886—21no—
46C3×#882—21no—
47C3×#875C2211yescharacteristic
48C3×C4×D12—21no—
49C3×C4×D12C2211yescharacteristic
50C3×#869—21no—
51C3×#869C2211yescharacteristic, complemented
52C32×#107C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic
55C32×#97C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67C2×#915C2×C311yescharacteristic, complemented
68C2×D3×SD16C2×C311yescharacteristic, complemented
69Q8×D12C2×C311yescharacteristic, complemented
70#5554C2×C311yescharacteristic
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—21no—
81C3×#440D311yescharacteristic, complemented
82C3×#440C2×C311yescharacteristic, complemented
83C3×#435—31no—
84#5028C2×C311yescharacteristic, complemented
85#5019C2×C311yescharacteristic, complemented
86#4887C2×C311yescharacteristic, complemented
87#4886C2×C311yescharacteristic, complemented
88#4809C2×C311yescharacteristic, complemented
89#4806C2×C311yescharacteristic, complemented
90#4783C2×C311yescharacteristic, complemented
91#4776C2×C311yescharacteristic, complemented
92#4715C2×C311yescharacteristic, complemented
93#4706C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×Q8—22no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×D3×Q8—41no—
105C3×#237—22no—
106C3×#237—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×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×SD16D414yescomplemented
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4—21no—
125C32×C4⋊C4C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C42—21no—
129C32×C42C2311yescharacteristic
130C3×#216—22no—
131C3×#215—22no—
132C3×#214—22no—
133C3×#214—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—21no—
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3—21no—
147C3×C4⋊Dic3D411yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C3×Dic12—22no—
151C3×Dic12—41no—
152C3×#204—22no—
153C3×#204—41no—
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×D3×Q8C22×C311yescharacteristic
162C2×D3×Q8C22×C311yescharacteristic, complemented
163C2×#237C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C3×#137—64no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
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×SD16C2×D311yescharacteristic
177C2×C3×SD16C22×C311yescharacteristic
178C2×C3×M16—31no—
179C22×C3×C8—31no—
180C3×C4⋊Q8—31no—
181C3×C4⋊Q8—61no—
182C3×#124—31no—
183C3×#123—61no—
184C3×C22⋊Q8—31no—
185C3×C22⋊Q8—31no—
186C3×C22⋊Q8—31no—
187C3×C22⋊Q8—61no—
188C3×C22⋊Q8—61no—
189C3×#121—31no—
190C3×#121—61no—
191C3×#120—61no—
192C3×C4×Q8—21no—
193C3×C4×Q8C2×D311yescharacteristic, complemented
194C3×C4×Q8C22×C311yescharacteristic, complemented
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—
201C2×#216C22×C311yescharacteristic, complemented
202C2×#215C22×C311yescharacteristic
203C2×#214C22×C311yescharacteristic
204C2×#214C22×C311yescharacteristic
205#930—21no—
206C2×(C2×D3)⋊C4—21no—
207#915—24no—
208D3×SD16—24no—
209C2×Dic12C22×C311yescharacteristic, complemented
210C2×Dic12C22×C311yescharacteristic, complemented
211C2×#204C22×C311yescharacteristic
212C2×#204C22×C311yescharacteristic
213C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
214C2×D3×C8C22×C311yescharacteristic
215#897—21no—
216#897—21no—
217#897C22×C311yescharacteristic
218#897C22×C311yescharacteristic
219#897C22×C311yescharacteristic, complemented
220#895C22×C311yescharacteristic
221#886—21no—
222#882—21no—
223#875C22×C311yescharacteristic
224C4×D12—21no—
225C4×D12C22×C311yescharacteristic
226#869—21no—
227#869C22×C311yescharacteristic, complemented
228C3×#107—21no—
229C3×#107C2×D311yescharacteristic, complemented
230C3×#107C22×C311yescharacteristic, complemented
231C3×C4⋊C8—31no—
232C3×#103—21no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic, complemented
237C3×#103C22×C311yescharacteristic, complemented
238C3×#102—21no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic
241C3×#102C22×C311yescharacteristic
242C3×C22⋊C8—31no—
243C3×C22⋊C8—31no—
244C3×#97—21no—
245C3×#97C2×D311yescharacteristic, complemented
246C3×#97C22×C311yescharacteristic, complemented
247(C2×D3)⋊C8C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic, complemented
249#810C22×C311yescharacteristic, complemented
250#810C22×C311yescharacteristic, complemented
251#810C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic
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×Q8C2×D412yes—
263C32×D4—21no—
264C32×D4C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—81no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—22no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—81no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6—42no—
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#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#440C3×D311yescharacteristic, complemented
316#435—31no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
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×Q8C23×C311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C23×C311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—41no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C2×#67—21no—
352C2×#67—21no—
353C22×Dic3—21no—
354D3×Q8—22no—
355D3×Q8—22no—
356D3×Q8—41no—
357D3×Q8—41no—
358#237—22no—
359#237—41no—
360D3×D4—22no—
361D3×D4—41no—
362C2×D12—21no—
363C2×D12C3×D411yescharacteristic
364C2×D12C23×C311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3C23×C311yescharacteristic
368C2×C4×D3C23×C311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6C23×C311yescharacteristic
372C2×Dic6C23×C311yescharacteristic
373C2×Dic6C23×C311yescharacteristic
374C3×Q16—62no—
375C3×Q16—62no—
376C3×Q16—121no—
377C3×SD16—24no—
378C3×SD16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×SD16—62no—
382C3×SD16—121no—
383C3×SD16D1214yescomplemented
384C3×SD16C3×D414yescomplemented
385C3×M16—62no—
386C2×C3×C8—21no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—62no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C23×C311yescharacteristic
394C2×C3×C8C23×C311yescharacteristic
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—41no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C4⋊C4C22×D311yescharacteristic
408C3×C4⋊C4C23×C311yescharacteristic
409C3×C4⋊C4C23×C311yescharacteristic
410C3×C22⋊C4—21no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—41no—
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×C42—21no—
422C3×C42—21no—
423C3×C42—21no—
424C3×C42—41no—
425C3×C42C22×D311yescharacteristic
426C3×C42C23×C311yescharacteristic
427#216—22no—
428#215—22no—
429#214—22no—
430#214—22no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4C3×D411yescharacteristic
438(C2×D3)⋊C4C3×D411yescharacteristic
439C4⋊Dic3—21no—
440C4⋊Dic3—21no—
441C4⋊Dic3—21no—
442C4⋊Dic3—21no—
443C4⋊Dic3—21no—
444C4⋊Dic3C3×D411yescharacteristic
445C2×C3⋊C8C23×C311yescharacteristic
446C2×C3⋊C8C23×C311yescharacteristic
447Dic12—22no—
448Dic12—41no—
449#204—22no—
450#204—41no—
451ΓL(1,𝔽25)—22no—
452D3×C8—22no—
453C22×C32—22no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—84no—
466C2×C3×D3#13712yescomplemented
467C32×C4—22no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C22×Q8—31no—
481C22×Q8—31no—
482C22×D4—31no—
483#137—64no—
484C2×Q16—31no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—64no—
493C2×SD16C2×C3×D311yescharacteristic
494C2×M16—31no—
495C22×C8—31no—
496C4⋊Q8—31no—
497C4⋊Q8—61no—
498#124—31no—
499#123—61no—
500C22⋊Q8—31no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—61no—
504C22⋊Q8—61no—
505#121—31no—
506#121—61no—
507#120—61no—
508C4×Q8C2×C3×D311yescharacteristic, complemented
509C4×D4—31no—
510C4×D4—61no—
511C4×D4C2×C3×D311yescharacteristic
512C2×C22⋊C4—61no—
513#107C2×C3×D311yescharacteristic, complemented
514C4⋊C8—31no—
515#103—31no—
516#103—31no—
517#103—31no—
518#103C2×C3×D311yescharacteristic, complemented
519#102—31no—
520#102C2×C3×D311yescharacteristic
521C22⋊C8—31no—
522C22⋊C8—31no—
523#97C2×C3×D311yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—61no—
530C23×C3—122no—
531C23×C3—122no—
532C23×C3—241no—
533C22×D3—21no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3—81no—
537C22×D3C2×C3×D411yescharacteristic
538C22×D3C2×C3×D411yescharacteristic
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—22no—
542C3×Q8—41no—
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×Q8C2×D1212yes—
552C3×Q8C2×C3×D412yes—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—22no—
556C3×D4—41no—
557C3×D4—62no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—122no—
561C3×D4—122no—
562C3×D4—241no—
563C3×D4C2×D1212yes—
564C3×D4C2×C3×D412yes—
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—31no—
575C2×C3×C4—31no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—81no—
587C2×C3×C4—81no—
588C2×C3×C4—82no—
589C2×C3×C4—122no—
590C2×C3×C4—122no—
591C2×C3×C4—122no—
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4D3×D411yescharacteristic
594C2×C3×C4C2×C3×D411yescharacteristic
595C2×C3×C4C2×C3×D411yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C24×C311yescharacteristic
598#67—42no—
599#67—42no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—42no—
604C2×Dic3C2×C3×D411yescharacteristic
605C2×Dic3C2×C3×D411yescharacteristic
606D12—22no—
607D12—21no—
608D12—21no—
609D12—81no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—42no—
615C4×D3—42no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—42no—
624C3×C8—21no—
625C3×C8—21no—
626C3×C8—22no—
627C3×C8—41no—
628C3×C8—61no—
629C3×C8—61no—
630C3×C8C2×D1212yes—
631C3×C8C2×C3×D412yes—
632C3⋊C8—21no—
633C3⋊C8—21no—
634C2×C32—42no—
635C2×C32D4211yescharacteristic
636C2×C32C2×#13711yescharacteristic
637C2×C32#57711yescharacteristic
638C3×D3—22no—
639C3×D3—41no—
640C3×D3—81no—
641C24—61no—
642#41—62no—
643#41—121no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—31no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—62no—
650C2×Q8—62no—
651C2×Q8—121no—
652C2×Q8—121no—
653C2×Q8C22×C3×D311yescharacteristic
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—121no—
661C2×D4C22×C3×D311yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668Q16—62no—
669Q16—62no—
670Q16—121no—
671SD16—62no—
672SD16—62no—
673SD16—62no—
674SD16—62no—
675SD16—121no—
676SD16C3×D1214yescomplemented
677M16—62no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—62no—
681C2×C8C22×C3×D311yescharacteristic
682C2×C8C22×C3×D311yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—31no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4C22×C3×D311yescharacteristic
691C4⋊C4C22×C3×D311yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—31no—
694C22⋊C4—31no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C42—21no—
702C42C22×C3×D311yescharacteristic
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—42no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C22×C3×D411yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—84no—
734C2×D3C3×#13712yescomplemented
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—22no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—42no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—81no—
753C3×C4—81no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C22×D1211yescharacteristic
758C3×C4#100911yescharacteristic
759C3×C4C22×C3×D411yescharacteristic
760C3×C4C3×H(5,𝔽2)11yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—41no—
764Dic3—41no—
765Dic3—41no—
766C32#326611yescharacteristic, complemented, Sylow
767C23—21no—
768C23—31no—
769C23—31no—
770C23—61no—
771C23—122no—
772C23—122no—
773C23—241no—
774Q8—21no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—122no—
782Q8—122no—
783Q8C2×C3×D1212yes—
784D4—21no—
785D4—62no—
786D4—61no—
787D4—61no—
788D4—122no—
789D4—122no—
790D4—241no—
791D4C2×C3×D1212yes—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—31no—
796C2×C4—31no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—81no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4C3×D3×D411yescharacteristic
809C2×C4C3×D3×D411yescharacteristic
810C2×C4C23×C3×D311yescharacteristic
811C8—21no—
812C8—61no—
813C8—61no—
814C8C2×C3×D1212yes—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—42no—
819C2×C3—42no—
820C2×C3—62no—
821C2×C3—82no—
822C2×C3—121no—
823C2×C3—241no—
824C2×C3D4×D1211yescharacteristic
825C2×C3#577511yescharacteristic
826C2×C3D3×#13711yescharacteristic
827C2×C3C3×D4211yescharacteristic
828C2×C3C2×C3×#13711yescharacteristic
829C2×C3C3×#57711yescharacteristic
830D3—22no—
831D3—41no—
832D3—81no—
833C22—22no—
834C22—32no—
835C22—41no—
836C22—41no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—244no—
846C22C2×C3×D3×D411yescharacteristic
847C4—21no—
848C4—21no—
849C4—22no—
850C4—41no—
851C4—41no—
852C4—61no—
853C4—61no—
854C4—121no—
855C4—121no—
856C4—121no—
857C4C22×C3×D1211yescharacteristic
858C4C3×#100911yescharacteristic
859C3—21no—
860C3#7979511yescharacteristic, direct product factor
861C3C3×#326611yescharacteristic, complemented
862C2—42no—
863C2—62no—
864C2—121no—
865C2—241no—
866C2C3×D4×D1211yescharacteristic
867C2C3×#577511yescharacteristic
868C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC3×#440D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. C3×Q8×D12C2semidirect
5. C32×#440C2semidirect
6. C3×#5028C2semidirect
7. C3×#5019C2semidirect
8. C3×#4887C2semidirect
9. C3×#4886C2semidirect
10. C3×#4809C2semidirect
11. C3×#4806C2semidirect
12. C3×#4783C2semidirect
13. C3×#4776C2semidirect
14. C3×#4715C2semidirect
15. C3×#4706C2semidirect
17. #79795C3direct (N × H)
19. C2×C3×D3×Q8C22semidirect
23. C32×C4×Q8C22semidirect
25. C2×C3×#216C22semidirect
33. C2×C3×Dic12C22semidirect
34. C2×C3×Dic12C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
43. C3×#897C22semidirect
51. C3×#869C22semidirect
52. C32×#107C22semidirect
53. C32×#103C22semidirect
55. C32×#97C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#810C22semidirect
59. C3×#810C22semidirect
60. C3×#810C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#915C2×C3semidirect
68. C2×D3×SD16C2×C3semidirect
69. Q8×D12C2×C3semidirect
81. C3×#440D3semidirect
82. C3×#440C2×C3semidirect
84. #5028C2×C3semidirect
85. #5019C2×C3semidirect
86. #4887C2×C3semidirect
87. #4886C2×C3semidirect
88. #4809C2×C3semidirect
89. #4806C2×C3semidirect
90. #4783C2×C3semidirect
91. #4776C2×C3semidirect
92. #4715C2×C3semidirect
93. #4706C2×C3semidirect
121. C32×SD16D4semidirect
162. C2×D3×Q8C22×C3semidirect
193. C3×C4×Q8C2×D3semidirect
194. C3×C4×Q8C22×C3semidirect
201. C2×#216C22×C3semidirect
209. C2×Dic12C22×C3semidirect
210. C2×Dic12C22×C3semidirect
213. C2×ΓL(1,𝔽25)C22×C3semidirect
219. #897C22×C3semidirect
227. #869C22×C3semidirect
229. C3×#107C2×D3semidirect
230. C3×#107C22×C3semidirect
236. C3×#103C2×D3semidirect
237. C3×#103C22×C3semidirect
245. C3×#97C2×D3semidirect
246. C3×#97C22×C3semidirect
248. (C2×D3)⋊C8C22×C3semidirect
249. #810C22×C3semidirect
250. #810C22×C3semidirect
251. #810C22×C3semidirect
253. C4⋊(C3⋊C8)C22×C3semidirect
315. #440C3×D3semidirect
383. C3×SD16D12semidirect
384. C3×SD16C3×D4semidirect
466. C2×C3×D3#137semidirect
508. C4×Q8C2×C3×D3semidirect
513. #107C2×C3×D3semidirect
518. #103C2×C3×D3semidirect
523. #97C2×C3×D3semidirect
676. SD16C3×D12semidirect
734. C2×D3C3×#137semidirect
766. C32#3266semidirect
860. C3#79795direct (N × H)
861. C3C3×#3266semidirect

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×Q8×D122
C3×#55542
C32×#4402
C3×#50282
C3×#50192
C3×#48872
C3×#48862
C3×#48092
C3×#48062
C3×#47832
C3×#47762
C3×#47152
C3×#47062
C3×#32663
#797953