Finite Group Databasebeta

← C3×#80445 #11884241

Subgroups — C3×#80445 #11884241

Order 1152.

1060 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4C3×#5554C211yesmaximal, characteristic, complemented
5C32×#461C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7C3×#5169C211yesmaximal, characteristic, complemented
8C3×#5086C211yesmaximal, characteristic, complemented
9C3×#5014C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4816C211yesmaximal, characteristic, complemented
13C3×#4810C211yesmaximal, characteristic, complemented
14C3×#4808C211yesmaximal, characteristic, complemented
15C3×#4807C211yesmaximal, characteristic, complemented
16C3×#3267—31nomaximal
17#80445C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic, complemented
25C32×C4×D4C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930—21no—
34C2×C3×(C2×D3)⋊C4—21no—
35C3×#916—24no—
36C3×#914—24no—
37C2×C3×D24C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic, complemented
41C3×#897C2211yescharacteristic
42C3×#895—21no—
43C3×#895C2211yescharacteristic
44C3×#894—21no—
45C3×#894—21no—
46C3×D3×C4⋊C4—21no—
47C3×#886—21no—
48C3×#882—21no—
49C3×#875C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic
51C3×C4×D12C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#103C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61C3×#808C2211yescharacteristic, complemented
62C3×#803C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#547—31no—
66C3×#546—31no—
67C2×#916C2×C311yescharacteristic, complemented
68C2×#914C2×C311yescharacteristic, complemented
69#5726C2×C311yescharacteristic, complemented
70#5554C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#470—31no—
73C3×#465—31no—
74C3×#463—31no—
75C3×#461—21no—
76C3×#461D311yescharacteristic, complemented
77C3×#461C2×C311yescharacteristic, complemented
78C3×#452—31no—
79C3×#452—31no—
80C3×#450—31no—
81C3×#449—31no—
82C3×#442—31no—
83C3×#435—31no—
84#5173C2×C311yescharacteristic, complemented
85#5169C2×C311yescharacteristic, complemented
86#5086C2×C311yescharacteristic, complemented
87#5014C2×C311yescharacteristic, complemented
88#4844C2×C311yescharacteristic, complemented
89#4836C2×C311yescharacteristic, complemented
90#4816C2×C311yescharacteristic, complemented
91#4810C2×C311yescharacteristic, complemented
92#4808C2×C311yescharacteristic, complemented
93#4807C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#239—22no—
103C3×#239—22no—
104C3×#239—41no—
105C3×#239—41no—
106C3×#237—22no—
107C3×#237—41no—
108C3×D3×D4—22no—
109C3×D3×D4—41no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12D411yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C32×SD16—22no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4—21no—
127C32×C4⋊C4—21no—
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C32×C42C2311yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×#215—22no—
134C3×#215—41no—
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)⋊C4—21no—
143C3×(C2×D3)⋊C4D411yescharacteristic
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3D411yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×Dic3⋊C4—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×D24—22no—
153C3×#204—22no—
154C3×ΓL(1,𝔽25)—22no—
155C3×D3×C8—22no—
156#3267—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#239C22×C311yescharacteristic
162C2×#239C22×C311yescharacteristic, complemented
163C2×#237C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C2×D311yescharacteristic
176C2×C3×SD16C22×C311yescharacteristic
177C2×C3×SD16C22×C311yescharacteristic
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×M16—31no—
181C22×C3×C8—31no—
182C3×C4⋊Q8—21no—
183C3×C4⋊Q8C2×D311yescharacteristic, complemented
184C3×C4⋊Q8C22×C311yescharacteristic, complemented
185C3×#124—31no—
186C3×#123—61no—
187C3×#123—61no—
188C3×#123—61no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—31no—
191C3×C22⋊Q8—31no—
192C3×#121—31no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#120—61no—
196C3×C4×D4—21no—
197C3×C4×D4—31no—
198C3×C4×D4—31no—
199C3×C4×D4C2×D311yescharacteristic
200C3×C4×D4C22×C311yescharacteristic
201C2×C3×C4⋊C4—61no—
202C2×C3×C22⋊C4—61no—
203#946C22×C311yescharacteristic
204#946C22×C311yescharacteristic, complemented
205C2×#216C22×C311yescharacteristic, complemented
206C2×#216C22×C311yescharacteristic, complemented
207C2×#215C22×C311yescharacteristic
208C2×#215C22×C311yescharacteristic
209C2×#213C22×C311yescharacteristic
210#930—21no—
211C2×(C2×D3)⋊C4—21no—
212#916—24no—
213#914—24no—
214C2×D24C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic, complemented
216C2×ΓL(1,𝔽25)C22×C311yescharacteristic
217C2×D3×C8C22×C311yescharacteristic, complemented
218#897C22×C311yescharacteristic
219#895—21no—
220#895C22×C311yescharacteristic
221#894—21no—
222#894—21no—
223D3×C4⋊C4—21no—
224#886—21no—
225#882—21no—
226#875C22×C311yescharacteristic
227C4×D12C22×C311yescharacteristic
228C4×D12C22×C311yescharacteristic, complemented
229C3×#106—31no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×C4⋊C8C22×C311yescharacteristic, complemented
233C3×#103—21no—
234C3×#103—21no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic, complemented
237C3×#103C2×D311yescharacteristic, complemented
238C3×#103C22×C311yescharacteristic, complemented
239C3×#103C22×C311yescharacteristic, complemented
240C3×#102—31no—
241C3×#102—31no—
242C3×#102—31no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#832C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#816C22×C311yescharacteristic, complemented
251#809C22×C311yescharacteristic, complemented
252#808C22×C311yescharacteristic, complemented
253#803C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—81no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—41no—
286C3×D12—42no—
287C3×D12—42no—
288C3×D12—81no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
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#461C3×D311yescharacteristic, complemented
312#452—31no—
313#452—31no—
314#450—31no—
315#449—31no—
316#442—31no—
317#435—31no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—121no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C23×C311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—41no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C2×#67—21no—
356C2×#67—21no—
357C22×Dic3—21no—
358#239—22no—
359#239—22no—
360#239—41no—
361#239—41no—
362#237—22no—
363#237—41no—
364D3×D4—22no—
365D3×D4—41no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—21no—
369C2×D12C3×D411yescharacteristic
370C2×D12C23×C311yescharacteristic
371C2×D12C23×C311yescharacteristic
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—21no—
375C2×C4×D3C23×C311yescharacteristic
376C2×C4×D3C23×C311yescharacteristic
377C2×Dic6C23×C311yescharacteristic
378C3×Q16—62no—
379C3×Q16—121no—
380C3×SD16—22no—
381C3×SD16—22no—
382C3×SD16—22no—
383C3×SD16—22no—
384C3×SD16—42no—
385C3×SD16—42no—
386C3×SD16—62no—
387C3×SD16—62no—
388C3×SD16—121no—
389C3×D8—34no—
390C3×D8—62no—
391C3×M16—62no—
392C2×C3×C8—21no—
393C2×C3×C8—21no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—62no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C23×C311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C3×C4⋊C4—21no—
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—41no—
409C3×C4⋊C4—41no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C23×C311yescharacteristic
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C42—21no—
428C3×C42C22×D311yescharacteristic
429C3×C42C23×C311yescharacteristic
430#216—22no—
431#216—41no—
432#215—22no—
433#215—41no—
434#213C3×D414yescomplemented
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
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)⋊C4C3×D411yescharacteristic
443(C2×D3)⋊C4C3×D411yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3C3×D411yescharacteristic
446C4⋊Dic3C23×C311yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449C2×C3⋊C8C23×C311yescharacteristic
450C2×C3⋊C8C23×C311yescharacteristic
451D24—22no—
452#204—22no—
453ΓL(1,𝔽25)—22no—
454D3×C8—22no—
455C22×C32—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4—41no—
476C32×C4—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—31no—
486C22×D4—31no—
487AGL(1,ℤ/8)—64no—
488#135—64no—
489C2×Q16—31no—
490C2×Q16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16C2×C3×D311yescharacteristic
495C2×SD16C2×C3×D311yescharacteristic
496C2×D8—31no—
497C2×D8—31no—
498C2×M16—31no—
499C22×C8—31no—
500C4⋊Q8C2×C3×D311yescharacteristic, complemented
501#124—31no—
502#123—61no—
503#123—61no—
504#123—61no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—31no—
508#121—31no—
509#121—61no—
510#121—61no—
511#120—61no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4C2×C3×D311yescharacteristic
515C2×C4⋊C4—61no—
516C2×C22⋊C4—61no—
517#106—31no—
518C4⋊C8C2×C3×D311yescharacteristic, complemented
519#103—31no—
520#103C2×C3×D311yescharacteristic, complemented
521#103C2×C3×D311yescharacteristic, complemented
522#102—31no—
523#102—31no—
524#102—31no—
525C22⋊C8—31no—
526C22⋊C8—31no—
527#97—31no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—241no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—81no—
543C22×D3C2×C3×D411yescharacteristic
544C22×D3C2×C3×D411yescharacteristic
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—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—22no—
562C3×D4—32no—
563C3×D4—41no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—121no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—241no—
573C3×D4D3×D412yes—
574C3×D4C2×C3×D412yes—
575C2×C3×C4—21no—
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—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—81no—
596C2×C3×C4—81no—
597C2×C3×C4—82no—
598C2×C3×C4—122no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4—122no—
602C2×C3×C4D3×D411yescharacteristic
603C2×C3×C4D3×D411yescharacteristic
604C2×C3×C4C2×C3×D411yescharacteristic
605C2×C3×C4C2×C3×D411yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C24×C311yescharacteristic
608#67—42no—
609#67—42no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—42no—
613C2×Dic3C2×C3×D411yescharacteristic
614C2×Dic3C2×C3×D411yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—41no—
619D12—42no—
620D12—42no—
621D12—81no—
622D12C2×C3×D412yes—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—42no—
628C4×D3—42no—
629C4×D3—42no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8C2×C3×D412yes—
642C2×C32—42no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—81no—
650C24—61no—
651#41—62no—
652#41—62no—
653#41—62no—
654#41—121no—
655#41—121no—
656#41—121no—
657C2×Q8—31no—
658C2×Q8C22×C3×D311yescharacteristic
659C2×Q8C22×C3×D311yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4—121no—
670C2×D4C22×C3×D311yescharacteristic
671C22×C4—21no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678Q16—62no—
679Q16—121no—
680SD16—22no—
681SD16—22no—
682SD16—62no—
683SD16—62no—
684SD16—121no—
685D8—34no—
686D8—62no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8C22×C3×D311yescharacteristic
692C2×C8C22×C3×D311yescharacteristic
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4C22×C3×D311yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C42C22×C3×D311yescharacteristic
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—62no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—244no—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C22×C3×D411yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—22no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—84no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—81no—
767C3×C4—81no—
768C3×C4—81no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4C2×D3×D411yescharacteristic
772C3×C4#100911yescharacteristic
773C3×C4C22×C3×D411yescharacteristic
774C3×C4C3×H(5,𝔽2)11yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—21no—
781C23—31no—
782C23—31no—
783C23—61no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—241no—
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—61no—
793Q8—61no—
794D4—21no—
795D4—32no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—121no—
800D4—122no—
801D4—122no—
802D4—122no—
803D4—122no—
804D4—241no—
805D4C3×D3×D412yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—81no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4C3×D3×D411yescharacteristic
823C2×C4C3×D3×D411yescharacteristic
824C2×C4C23×C3×D311yescharacteristic
825C8—21no—
826C8—21no—
827C8—32no—
828C8—61no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—82no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3—122no—
838C2×C3—241no—
839C2×C3#560911yescharacteristic
840C2×C3#576211yescharacteristic
841C2×C3#577711yescharacteristic
842C2×C3C3×D4211yescharacteristic
843C2×C3C3×#57511yescharacteristic
844C2×C3C3×#57711yescharacteristic
845D3—41no—
846D3—41no—
847D3—42no—
848D3—81no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—244no—
865C22C2×C3×D3×D411yescharacteristic
866C4—21no—
867C4—21no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4C2×C3×D3×D411yescharacteristic
876C4C3×#100911yescharacteristic
877C3—21no—
878C3#8044511yescharacteristic, direct product factor
879C3C3×#326711yescharacteristic, complemented
880C2—42no—
881C2—121no—
882C2—121no—
883C2—122no—
884C2—241no—
885C2C3×#560911yescharacteristic
886C2C3×#576211yescharacteristic
887C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
hypercenterC3×#461D3
hypocenterC3C3×#3267
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C2×C3×#914C2semidirect
3. C3×#5726C2semidirect
4. C3×#5554C2semidirect
5. C32×#461C2semidirect
6. C3×#5173C2semidirect
7. C3×#5169C2semidirect
8. C3×#5086C2semidirect
9. C3×#5014C2semidirect
10. C3×#4844C2semidirect
11. C3×#4836C2semidirect
12. C3×#4816C2semidirect
13. C3×#4810C2semidirect
14. C3×#4808C2semidirect
15. C3×#4807C2semidirect
17. #80445C3direct (N × H)
19. C2×C3×#239C22semidirect
24. C32×C4⋊Q8C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
38. C2×C3×#204C22semidirect
40. C2×C3×D3×C8C22semidirect
51. C3×C4×D12C22semidirect
52. C32×C4⋊C8C22semidirect
53. C32×#103C22semidirect
54. C32×#103C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#816C22semidirect
60. C3×#809C22semidirect
61. C3×#808C22semidirect
62. C3×#803C22semidirect
67. C2×#916C2×C3semidirect
68. C2×#914C2×C3semidirect
69. #5726C2×C3semidirect
70. #5554C2×C3semidirect
76. C3×#461D3semidirect
77. C3×#461C2×C3semidirect
84. #5173C2×C3semidirect
85. #5169C2×C3semidirect
86. #5086C2×C3semidirect
87. #5014C2×C3semidirect
88. #4844C2×C3semidirect
89. #4836C2×C3semidirect
90. #4816C2×C3semidirect
91. #4810C2×C3semidirect
92. #4808C2×C3semidirect
93. #4807C2×C3semidirect
135. C3×#213D4semidirect
162. C2×#239C22×C3semidirect
183. C3×C4⋊Q8C2×D3semidirect
184. C3×C4⋊Q8C22×C3semidirect
204. #946C22×C3semidirect
205. C2×#216C22×C3semidirect
206. C2×#216C22×C3semidirect
215. C2×#204C22×C3semidirect
217. C2×D3×C8C22×C3semidirect
228. C4×D12C22×C3semidirect
231. C3×C4⋊C8C2×D3semidirect
232. C3×C4⋊C8C22×C3semidirect
236. C3×#103C2×D3semidirect
237. C3×#103C2×D3semidirect
238. C3×#103C22×C3semidirect
239. C3×#103C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #816C22×C3semidirect
251. #809C22×C3semidirect
252. #808C22×C3semidirect
253. #803C22×C3semidirect
311. #461C3×D3semidirect
434. #213C3×D4semidirect
500. C4⋊Q8C2×C3×D3semidirect
518. C4⋊C8C2×C3×D3semidirect
520. #103C2×C3×D3semidirect
521. #103C2×C3×D3semidirect
779. C32#3267semidirect
878. C3#80445direct (N × H)
879. C3C3×#3267semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C2×C3×#9142
C3×#57262
C3×#55542
C32×#4612
C3×#51732
C3×#51692
C3×#50862
C3×#50142
C3×#48442
C3×#48362
C3×#48162
C3×#48102
C3×#48082
C3×#48072
C3×#32673
#804453