Finite Group Databasebeta

← C3×#80264 #11884235

Subgroups — C3×#80264 #11884235

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×C3×#914C211yesmaximal, characteristic, complemented
4C3×#5631C211yesmaximal, characteristic, complemented
5C32×#452C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5162C211yesmaximal, characteristic, complemented
9C3×#5048C211yesmaximal, characteristic, complemented
10C3×#4819C211yesmaximal, characteristic, complemented
11C3×#4816C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4776C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3267—31nomaximal
17#80264C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic, complemented
25C3×#950—24no—
26C3×#947C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C3×#944C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#939—21no—
33C3×#937—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#930C2211yescharacteristic
38C3×#929—21no—
39C3×C4×#67C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4—21no—
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42C3×#914—24no—
43C2×C3×D24C2211yescharacteristic
44C2×C3×#204C2211yescharacteristic
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
46C3×#897C2211yescharacteristic
47C3×#894—21no—
48C3×#893C2211yescharacteristic, complemented
49C3×D3×C4⋊C4—21no—
50C3×#884—21no—
51C3×#883—21no—
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×#816C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic
62C3×#808C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#547—31no—
66C3×#546—31no—
67#5829C2×C311yescharacteristic, complemented
68C2×#950C2×C311yescharacteristic, complemented
69C2×#914C2×C311yescharacteristic, complemented
70#5631C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#470—31no—
73C3×#465—31no—
74C3×#463—31no—
75C3×#461—31no—
76C3×#452—21no—
77C3×#452—31no—
78C3×#452D311yescharacteristic, complemented
79C3×#452C2×C311yescharacteristic, complemented
80C3×#450—31no—
81C3×#449—31no—
82C3×#442—31no—
83C3×#435—31no—
84#5190C2×C311yescharacteristic, complemented
85#5187C2×C311yescharacteristic, complemented
86#5162C2×C311yescharacteristic, complemented
87#5048C2×C311yescharacteristic, complemented
88#4819C2×C311yescharacteristic, complemented
89#4816C2×C311yescharacteristic, complemented
90#4785C2×C311yescharacteristic, complemented
91#4776C2×C311yescharacteristic, complemented
92#4734C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C22×C3×Dic3—21no—
108C3×#239—22no—
109C3×#239—41no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C32×Q16—41no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#215—22no—
133C3×#215—22no—
134C3×#214—22no—
135C3×#213D414yescomplemented
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3C2311yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4D411yescharacteristic
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—22no—
154C3×#204—41no—
155C3×ΓL(1,𝔽25)—22no—
156#3267—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C22×C311yescharacteristic
162C22×C3×D4—31no—
163C2×#239C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C2×#235C22×C311yescharacteristic, complemented
166C3×AGL(1,ℤ/8)—64no—
167C3×#135—64no—
168C2×C3×Q16—21no—
169C2×C3×Q16—31no—
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×Q16C22×C311yescharacteristic, complemented
172C2×C3×SD16—21no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16C2×D311yescharacteristic
178C2×C3×SD16C22×C311yescharacteristic
179C2×C3×D8—31no—
180C2×C3×D8—31no—
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×C4⋊Q8—31no—
184C3×#124—31no—
185C3×#123—61no—
186C3×#123—61no—
187C3×#123—61no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—31no—
191C3×C22⋊Q8C2×D311yescharacteristic, complemented
192C3×C22⋊Q8C22×C311yescharacteristic, complemented
193C3×#121—31no—
194C3×#121—61no—
195C3×#121—61no—
196C3×#120—61no—
197C3×C4×D4—31no—
198C3×C4×D4—31no—
199C3×C4×D4—31no—
200C2×C3×C4⋊C4—61no—
201C2×C3×C22⋊C4—61no—
202#950—24no—
203#947C22×C311yescharacteristic
204#946C22×C311yescharacteristic
205#944C22×C311yescharacteristic, complemented
206C2×#216C22×C311yescharacteristic, complemented
207C2×#215C22×C311yescharacteristic
208C2×#215C22×C311yescharacteristic, complemented
209#939—21no—
210#937—21no—
211D4×Dic3C22×C311yescharacteristic
212C2×#214C22×C311yescharacteristic
213C2×#213C22×C311yescharacteristic
214#930C22×C311yescharacteristic
215#929—21no—
216C4×#67C22×C311yescharacteristic
217C2×(C2×D3)⋊C4—21no—
218C22×C3⋊C8C22×C311yescharacteristic, complemented
219#914—24no—
220C2×D24C22×C311yescharacteristic
221C2×#204C22×C311yescharacteristic
222C2×ΓL(1,𝔽25)C22×C311yescharacteristic
223#897C22×C311yescharacteristic
224#894—21no—
225#893C22×C311yescharacteristic, complemented
226D3×C4⋊C4—21no—
227#884—21no—
228#883—21no—
229C3×#106—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103C2×D311yescharacteristic, complemented
235C3×#103C22×C311yescharacteristic, complemented
236C3×#102—21no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic
240C3×#102C22×C311yescharacteristic
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic, complemented
244C3×C22⋊C8C22×C311yescharacteristic, complemented
245C3×#97—31no—
246#835C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic, complemented
248(C2×D3)⋊C8C22×C311yescharacteristic
249#816C22×C311yescharacteristic, complemented
250#815C22×C311yescharacteristic, complemented
251Dic3⋊C8C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic
253#808C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×D4—21no—
267C32×D4—42no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277C3×#67—41no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—81no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C32×C8—21no—
300C32×C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—31no—
304C2×#135—31no—
305#547—31no—
306#546—31no—
307#497—31no—
308#470—31no—
309#465—31no—
310#463—31no—
311#461—31no—
312#452—31no—
313#452C3×D311yescharacteristic, complemented
314#450—31no—
315#449—31no—
316#442—31no—
317#435—31no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—22no—
321C3×#41—22no—
322C3×#41—42no—
323C3×#41—41no—
324C3×#41—41no—
325C3×#41—42no—
326C3×#41—62no—
327C3×#41—62no—
328C3×#41—121no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—21no—
332C2×C3×Q8—31no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C23×C311yescharacteristic
336C2×C3×Q8C23×C311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—41no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—62no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—121no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C23×C311yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—41no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4—61no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C2×#67C3×D411yescharacteristic
367C22×Dic3—21no—
368#239—22no—
369#239—41no—
370D3×D4—22no—
371D3×D4—41no—
372#235—22no—
373#235—41no—
374C2×D12—21no—
375C2×D12C23×C311yescharacteristic
376C2×D12C23×C311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×C4×D3C23×C311yescharacteristic
381C2×Dic6C23×C311yescharacteristic
382C3×Q16—41no—
383C3×Q16—41no—
384C3×Q16—42no—
385C3×Q16—62no—
386C3×SD16—22no—
387C3×SD16—22no—
388C3×SD16—42no—
389C3×SD16—62no—
390C3×SD16—62no—
391C3×SD16—62no—
392C3×SD16—121no—
393C3×D8—34no—
394C3×D8—62no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—62no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C23×C311yescharacteristic
404C2×C3×C8C23×C311yescharacteristic
405C3×C4⋊C4—21no—
406C3×C4⋊C4—21no—
407C3×C4⋊C4—21no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—41no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—61no—
414C3×C4⋊C4—61no—
415C3×C4⋊C4C22×D311yescharacteristic
416C3×C4⋊C4C23×C311yescharacteristic
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—41no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C42—31no—
430#217—21no—
431#217C3×D411yescharacteristic
432#216—22no—
433#215—22no—
434#215—22no—
435#214—22no—
436#213C3×D414yescomplemented
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4C3×D411yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3C23×C311yescharacteristic
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4C3×D411yescharacteristic
450C4×Dic3C23×C311yescharacteristic
451C2×C3⋊C8—22no—
452C2×C3⋊C8C23×C311yescharacteristic
453C2×C3⋊C8C23×C311yescharacteristic
454D24—22no—
455#204—41no—
456ΓL(1,𝔽25)—22no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3×D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—84no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4—41no—
477C32×C4—41no—
478C32×C4C22×D411yescharacteristic
479C32×C4H(5,𝔽2)11yescharacteristic
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
487C2×#41C2×C3×D311yescharacteristic
488C22×D4—31no—
489AGL(1,ℤ/8)—64no—
490#135—64no—
491C2×Q16—31no—
492C2×Q16C2×C3×D311yescharacteristic, complemented
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16C2×C3×D311yescharacteristic
498C2×D8—31no—
499C2×D8—31no—
500C2×M16—31no—
501C22×C8—31no—
502C4⋊Q8—31no—
503#124—31no—
504#123—61no—
505#123—61no—
506#123—61no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8C2×C3×D311yescharacteristic, complemented
510#121—31no—
511#121—61no—
512#121—61no—
513#120—61no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—31no—
517C2×C4⋊C4—61no—
518C2×C22⋊C4—61no—
519#106—31no—
520C4⋊C8—31no—
521#103—31no—
522#103—31no—
523#103C2×C3×D311yescharacteristic, complemented
524#102—31no—
525#102—31no—
526#102C2×C3×D311yescharacteristic
527C22⋊C8—31no—
528C22⋊C8C2×C3×D311yescharacteristic, complemented
529#97—31no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—122no—
539C23×C3—241no—
540C23×C3D3×D411yescharacteristic
541C23×C3C2×C3×D411yescharacteristic
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—81no—
547C22×D3C2×C3×D411yescharacteristic
548C3×Q8—22no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—41no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—22no—
565C3×D4—32no—
566C3×D4—41no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—121no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—241no—
578C3×D4D3×D412yes—
579C3×D4C2×C3×D412yes—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—42no—
601C2×C3×C4—42no—
602C2×C3×C4—44no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—122no—
608C2×C3×C4—122no—
609C2×C3×C4—122no—
610C2×C3×C4—241no—
611C2×C3×C4D3×D411yescharacteristic
612C2×C3×C4C2×C3×D411yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C24×C311yescharacteristic
615#67—41no—
616#67—42no—
617#67—42no—
618#67—81no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—81no—
622C2×Dic3C2×C3×D411yescharacteristic
623C2×Dic3C2×C3×D411yescharacteristic
624C2×Dic3C2×C3×D411yescharacteristic
625D12—21no—
626D12—21no—
627D12—21no—
628D12—42no—
629D12C2×C3×D412yes—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—42no—
634C4×D3—42no—
635Dic6—21no—
636Dic6—21no—
637C3×C8—21no—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—41no—
644C3×C8—61no—
645C3⋊C8—21no—
646C3⋊C8C2×C3×D412yes—
647C2×C32—42no—
648C2×C32—41no—
649C2×C32D4211yescharacteristic
650C2×C32#57511yescharacteristic
651C2×C32#57711yescharacteristic
652C3×D3—41no—
653C3×D3—42no—
654C3×D3—81no—
655C24—61no—
656#41—22no—
657#41—41no—
658#41—62no—
659#41—62no—
660#41—121no—
661#41—121no—
662C2×Q8—31no—
663C2×Q8C22×C3×D311yescharacteristic
664C2×Q8C22×C3×D311yescharacteristic
665C2×D4—21no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—62no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—121no—
675C2×D4C22×C3×D311yescharacteristic
676C22×C4—21no—
677C22×C4—31no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4C22×C3×D311yescharacteristic
683Q16—41no—
684Q16—62no—
685SD16—22no—
686SD16—62no—
687SD16—62no—
688SD16—62no—
689SD16—121no—
690D8—34no—
691D8—62no—
692M16—62no—
693C2×C8—31no—
694C2×C8—31no—
695C2×C8—62no—
696C2×C8C22×C3×D311yescharacteristic
697C2×C8C22×C3×D311yescharacteristic
698C4⋊C4—21no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4C22×C3×D311yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—31no—
708C22⋊C4—31no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C42—31no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—62no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—244no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C22×C3×D411yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—22no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—84no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—41no—
763C3×C4—42no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—61no—
773C3×C4—81no—
774C3×C4—81no—
775C3×C4—121no—
776C3×C4—121no—
777C3×C4C2×D3×D411yescharacteristic
778C3×C4#100411yescharacteristic
779C3×C4C22×C3×D411yescharacteristic
780C3×C4C3×H(5,𝔽2)11yescharacteristic
781Dic3—21no—
782Dic3—21no—
783Dic3—21no—
784Dic3—41no—
785Dic3—41no—
786C32#326711yescharacteristic, complemented, Sylow
787C23—21no—
788C23—31no—
789C23—61no—
790C23—61no—
791C23—122no—
792C23—122no—
793C23—241no—
794C23C3×D3×D411yescharacteristic
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—21no—
799Q8—61no—
800Q8—61no—
801D4—21no—
802D4—32no—
803D4—42no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—122no—
808D4—121no—
809D4—122no—
810D4—122no—
811D4—241no—
812D4C3×D3×D412yes—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—42no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—241no—
830C2×C4C3×D3×D411yescharacteristic
831C2×C4C23×C3×D311yescharacteristic
832C8—21no—
833C8—21no—
834C8—32no—
835C8—61no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—41no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—41no—
843C2×C3—81no—
844C2×C3—82no—
845C2×C3—121no—
846C2×C3—122no—
847C2×C3—241no—
848C2×C3#559011yescharacteristic
849C2×C3#576811yescharacteristic
850C2×C3#577811yescharacteristic
851C2×C3C3×D4211yescharacteristic
852C2×C3C3×#57511yescharacteristic
853C2×C3C3×#57711yescharacteristic
854D3—41no—
855D3—42no—
856D3—81no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—244no—
873C22C2×C3×D3×D411yescharacteristic
874C4—21no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—61no—
879C4—61no—
880C4—61no—
881C4—121no—
882C4—121no—
883C4C2×C3×D3×D411yescharacteristic
884C4C3×#100411yescharacteristic
885C3—21no—
886C3#8026411yescharacteristic, direct product factor
887C3C3×#326711yescharacteristic, complemented
888C2—41no—
889C2—42no—
890C2—121no—
891C2—122no—
892C2—241no—
893C2C3×#559011yescharacteristic
894C2C3×#576811yescharacteristic
895C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
hypercenterC3×#452D3
hypocenterC3C3×#3267
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C3×#5829C2semidirect
2. C2×C3×#950C2semidirect
3. C2×C3×#914C2semidirect
4. C3×#5631C2semidirect
5. C32×#452C2semidirect
6. C3×#5190C2semidirect
7. C3×#5187C2semidirect
8. C3×#5162C2semidirect
9. C3×#5048C2semidirect
10. C3×#4819C2semidirect
11. C3×#4816C2semidirect
12. C3×#4785C2semidirect
13. C3×#4776C2semidirect
14. C3×#4734C2semidirect
15. C3×#4730C2semidirect
17. #80264C3direct (N × H)
21. C2×C3×#235C22semidirect
22. C2×C32×Q16C22semidirect
24. C32×C22⋊Q8C22semidirect
28. C3×#944C22semidirect
29. C2×C3×#216C22semidirect
31. C2×C3×#215C22semidirect
41. C22×C3×C3⋊C8C22semidirect
48. C3×#893C22semidirect
52. C32×#103C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
58. C3×#816C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
62. C3×#808C22semidirect
67. #5829C2×C3semidirect
68. C2×#950C2×C3semidirect
69. C2×#914C2×C3semidirect
70. #5631C2×C3semidirect
78. C3×#452D3semidirect
79. C3×#452C2×C3semidirect
84. #5190C2×C3semidirect
85. #5187C2×C3semidirect
86. #5162C2×C3semidirect
87. #5048C2×C3semidirect
88. #4819C2×C3semidirect
89. #4816C2×C3semidirect
90. #4785C2×C3semidirect
91. #4776C2×C3semidirect
92. #4734C2×C3semidirect
93. #4730C2×C3semidirect
135. C3×#213D4semidirect
165. C2×#235C22×C3semidirect
170. C2×C3×Q16C2×D3semidirect
171. C2×C3×Q16C22×C3semidirect
191. C3×C22⋊Q8C2×D3semidirect
192. C3×C22⋊Q8C22×C3semidirect
205. #944C22×C3semidirect
206. C2×#216C22×C3semidirect
208. C2×#215C22×C3semidirect
218. C22×C3⋊C8C22×C3semidirect
225. #893C22×C3semidirect
234. C3×#103C2×D3semidirect
235. C3×#103C22×C3semidirect
243. C3×C22⋊C8C2×D3semidirect
244. C3×C22⋊C8C22×C3semidirect
246. #835C22×C3semidirect
247. #821C22×C3semidirect
249. #816C22×C3semidirect
250. #815C22×C3semidirect
251. Dic3⋊C8C22×C3semidirect
253. #808C22×C3semidirect
313. #452C3×D3semidirect
436. #213C3×D4semidirect
492. C2×Q16C2×C3×D3semidirect
509. C22⋊Q8C2×C3×D3semidirect
523. #103C2×C3×D3semidirect
528. C22⋊C8C2×C3×D3semidirect
786. C32#3267semidirect
886. C3#80264direct (N × H)
887. C3C3×#3267semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C2×C3×#9502
C2×C3×#9142
C3×#56312
C32×#4522
C3×#51902
C3×#51872
C3×#51622
C3×#50482
C3×#48192
C3×#48162
C3×#47852
C3×#47762
C3×#47342
C3×#47302
C3×#32673
#802643