Finite Group Databasebeta

← C3×#80500 #11884518

Subgroups — C3×#80500 #11884518

Order 1152.

1010 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2C2×C3×#918C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C32×#462C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8C3×#5086C211yesmaximal, characteristic, complemented
9C3×#5026C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×#4812C211yesmaximal, characteristic, complemented
14C3×#4810C211yesmaximal, characteristic, complemented
15C3×#4808C211yesmaximal, characteristic, complemented
16C3×#3269—31nomaximal
17#80500C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic
23C2×C32×Q16C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C3×#919—24no—
34C3×#918—24no—
35C2×C3×D24C2211yescharacteristic
36C2×C3×#204C2211yescharacteristic
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C2×C3×D3×C8C2211yescharacteristic
39C3×#897—21no—
40C3×#897C2211yescharacteristic
41C3×#895—21no—
42C3×#895—21no—
43C3×#895C2211yescharacteristic
44C3×#894—21no—
45C3×#894—21no—
46C3×D3×C4⋊C4—21no—
47C3×#875—21no—
48C3×#875C2211yescharacteristic
49C3×C4×D12—21no—
50C3×C4×D12C2211yescharacteristic
51C3×C4×D12C2211yescharacteristic
52C32×C4⋊C8C2211yescharacteristic
53C32×#103C2211yescharacteristic
54C32×#103C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#816C2211yescharacteristic
60C3×#809C2211yescharacteristic
61C3×#807C2211yescharacteristic
62C3×#803C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#548—31no—
66C3×#547—31no—
67C2×#919C2×C311yescharacteristic, complemented
68C2×#918C2×C311yescharacteristic, complemented
69#5726C2×C311yescharacteristic, complemented
70#5576C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#463—31no—
75C3×#462—21no—
76C3×#462D311yescharacteristic, complemented
77C3×#462C2×C311yescharacteristic, complemented
78C3×#452—31no—
79C3×#452—31no—
80C3×#451—31no—
81C3×#449—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5187C2×C311yescharacteristic, complemented
85#5186C2×C311yescharacteristic, complemented
86#5086C2×C311yescharacteristic, complemented
87#5026C2×C311yescharacteristic, complemented
88#4844C2×C311yescharacteristic, complemented
89#4836C2×C311yescharacteristic, complemented
90#4813C2×C311yescharacteristic, complemented
91#4812C2×C311yescharacteristic, complemented
92#4810C2×C311yescharacteristic, complemented
93#4808C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C3×#239—22no—
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—41no—
101C3×#239—41no—
102C3×#239—41no—
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12D411yescharacteristic
110C2×C3×D12C2311yescharacteristic
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×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C32×Q16—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4—21no—
128C32×C4⋊C4C2311yescharacteristic
129C32×C42—21no—
130C32×C42C2311yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×#215—22no—
134C3×#215—41no—
135C3×#215D414yescomplemented
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#3269—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×Q8—31no—
161C2×#239C22×C311yescharacteristic
162C2×#239C22×C311yescharacteristic
163C2×#239C22×C311yescharacteristic
164C2×D3×Q8C22×C311yescharacteristic
165C3×#137—64no—
166C3×#135—64no—
167C2×C3×Q16—21no—
168C2×C3×Q16—21no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×Q16C2×D311yescharacteristic
172C2×C3×Q16C2×D311yescharacteristic
173C2×C3×Q16C22×C311yescharacteristic
174C2×C3×Q16C22×C311yescharacteristic
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—31no—
178C2×C3×SD16—31no—
179C2×C3×D8—31no—
180C2×C3×M16—31no—
181C22×C3×C8—31no—
182C3×C4⋊Q8—21no—
183C3×C4⋊Q8C2×D311yescharacteristic
184C3×C4⋊Q8C22×C311yescharacteristic
185C3×#124—31no—
186C3×#124—61no—
187C3×#123—61no—
188C3×#123—61no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—31no—
191C3×C22⋊Q8—31no—
192C3×C22⋊Q8—61no—
193C3×#121—31no—
194C3×#121—61no—
195C3×#121—61no—
196C3×C4×Q8—21no—
197C3×C4×Q8C2×D311yescharacteristic
198C3×C4×Q8C22×C311yescharacteristic
199C3×C4×D4—31no—
200C3×C4×D4—31no—
201C3×C4×D4—61no—
202C2×C3×C4⋊C4—61no—
203#946C22×C311yescharacteristic
204#946C22×C311yescharacteristic
205C2×#216C22×C311yescharacteristic
206C2×#216C22×C311yescharacteristic
207C2×#215C22×C311yescharacteristic
208C2×#215C22×C311yescharacteristic
209C2×#215C22×C311yescharacteristic
210#919—24no—
211#918—24no—
212C2×D24C22×C311yescharacteristic
213C2×#204C22×C311yescharacteristic
214C2×ΓL(1,𝔽25)C22×C311yescharacteristic
215C2×D3×C8C22×C311yescharacteristic
216#897—21no—
217#897C22×C311yescharacteristic
218#895—21no—
219#895—21no—
220#895C22×C311yescharacteristic
221#894—21no—
222#894—21no—
223D3×C4⋊C4—21no—
224#875—21no—
225#875C22×C311yescharacteristic
226C4×D12—21no—
227C4×D12C22×C311yescharacteristic
228C4×D12C22×C311yescharacteristic
229C3×#107—31no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic
232C3×C4⋊C8C22×C311yescharacteristic
233C3×#103—21no—
234C3×#103—21no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#103C2×D311yescharacteristic
238C3×#103C2×D311yescharacteristic
239C3×#103C22×C311yescharacteristic
240C3×#103C22×C311yescharacteristic
241C3×#102—31no—
242C3×#102—31no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#835C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic
250#816C22×C311yescharacteristic
251#809C22×C311yescharacteristic
252#807C22×C311yescharacteristic
253#803C22×C311yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—41no—
279C3×D12—42no—
280C3×D12—42no—
281C3×D12—42no—
282C3×D12—42no—
283C3×D12C2×D412yes—
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×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C32×C8—21no—
297C32×C8—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8C2×D412yes—
300C2×#137—31no—
301C2×#135—31no—
302#548—31no—
303#547—31no—
304#497—31no—
305#468—31no—
306#467—31no—
307#463—31no—
308#462C3×D311yescharacteristic, complemented
309#452—31no—
310#452—31no—
311#451—31no—
312#449—31no—
313#440—31no—
314#435—31no—
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—62no—
318C3×#41—121no—
319C3×#41—121no—
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—62no—
327C2×C3×Q8—121no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×Q8C23×C311yescharacteristic
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—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348#239—22no—
349#239—22no—
350#239—22no—
351#239—41no—
352#239—41no—
353#239—41no—
354D3×Q8—22no—
355D3×Q8—41no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12C3×D411yescharacteristic
361C2×D12C23×C311yescharacteristic
362C2×D12C23×C311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3C23×C311yescharacteristic
369C2×C4×D3C23×C311yescharacteristic
370C2×Dic6—21no—
371C2×Dic6C23×C311yescharacteristic
372C3×Q16—22no—
373C3×Q16—22no—
374C3×Q16—22no—
375C3×Q16—22no—
376C3×Q16—42no—
377C3×Q16—42no—
378C3×Q16—62no—
379C3×Q16—121no—
380C3×SD16—34no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—121no—
384C3×D8—62no—
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—21no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—41no—
405C3×C4⋊C4—41no—
406C3×C4⋊C4—41no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4C22×D311yescharacteristic
411C3×C4⋊C4C23×C311yescharacteristic
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
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×C42—21no—
422C3×C42—21no—
423C3×C42—21no—
424C3×C42—41no—
425C3×C42C22×D311yescharacteristic
426C3×C42C23×C311yescharacteristic
427#216—22no—
428#216—41no—
429#215—22no—
430#215—41no—
431#215C3×D414yescomplemented
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)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4C3×D411yescharacteristic
440(C2×D3)⋊C4C3×D411yescharacteristic
441C4⋊Dic3—21no—
442C4⋊Dic3C3×D411yescharacteristic
443C4⋊Dic3C23×C311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—21no—
446C2×C3⋊C8C23×C311yescharacteristic
447C2×C3⋊C8C23×C311yescharacteristic
448D24—22no—
449#204—22no—
450ΓL(1,𝔽25)—22no—
451D3×C8—22no—
452C22×C32C22×D411yescharacteristic
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—22no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C32×C4—21no—
466C32×C4—22no—
467C32×C4—21no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—31no—
478C2×#41—31no—
479C2×#41—31no—
480C22×Q8—31no—
481#137—64no—
482#135—64no—
483C2×Q16—31no—
484C2×Q16—31no—
485C2×Q16C2×C3×D311yescharacteristic
486C2×Q16C2×C3×D311yescharacteristic
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×D8—31no—
492C2×M16—31no—
493C22×C8—31no—
494C4⋊Q8C2×C3×D311yescharacteristic
495#124—31no—
496#124—61no—
497#123—61no—
498#123—61no—
499C22⋊Q8—31no—
500C22⋊Q8—31no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503#121—31no—
504#121—61no—
505#121—61no—
506C4×Q8C2×C3×D311yescharacteristic
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—61no—
510C2×C4⋊C4—61no—
511#107—31no—
512C4⋊C8C2×C3×D311yescharacteristic
513#103—31no—
514#103—31no—
515#103C2×C3×D311yescharacteristic
516#103C2×C3×D311yescharacteristic
517#102—31no—
518#102—31no—
519C22⋊C8—31no—
520C22⋊C8—31no—
521#97—31no—
522C23×C3—31no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3—61no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3C2×C3×D411yescharacteristic
529C22×D3C2×C3×D411yescharacteristic
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—21no—
540C3×Q8—22no—
541C3×Q8—41no—
542C3×Q8—41no—
543C3×Q8—41no—
544C3×Q8—41no—
545C3×Q8—41no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—122no—
549C3×Q8D3×D412yes—
550C3×Q8C2×C3×D412yes—
551C3×D4—32no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—121no—
556C3×D4—122no—
557C3×D4—122no—
558C3×D4—122no—
559C3×D4—122no—
560C2×C3×C4—21no—
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—31no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—122no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4—122no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4C2×C3×D411yescharacteristic
591C2×C3×C4C2×C3×D411yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C24×C311yescharacteristic
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3C2×C3×D411yescharacteristic
597C2×Dic3C2×C3×D411yescharacteristic
598D12—21no—
599D12—21no—
600D12—21no—
601D12—41no—
602D12—42no—
603D12—42no—
604D12—42no—
605D12—42no—
606D12C2×C3×D412yes—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—42no—
612C4×D3—42no—
613C4×D3—42no—
614C4×D3—42no—
615C4×D3—42no—
616Dic6—21no—
617Dic6—21no—
618Dic6—42no—
619C3×C8—21no—
620C3×C8—21no—
621C3×C8—21no—
622C3×C8—21no—
623C3×C8—32no—
624C3×C8—41no—
625C3×C8—41no—
626C3×C8—61no—
627C3⋊C8—21no—
628C3⋊C8C2×C3×D412yes—
629C2×C32D4211yescharacteristic
630C2×C32#57511yescharacteristic
631C2×C32#57811yescharacteristic
632C3×D3—41no—
633C3×D3—41no—
634C3×D3—42no—
635C3×D3—81no—
636#41—62no—
637#41—62no—
638#41—62no—
639#41—121no—
640#41—121no—
641#41—121no—
642C2×Q8—31no—
643C2×Q8—61no—
644C2×Q8—62no—
645C2×Q8—121no—
646C2×Q8C22×C3×D311yescharacteristic
647C2×Q8C22×C3×D311yescharacteristic
648C2×Q8C22×C3×D311yescharacteristic
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—61no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663Q16—22no—
664Q16—22no—
665Q16—62no—
666Q16—121no—
667SD16—34no—
668SD16—62no—
669SD16—62no—
670SD16—121no—
671D8—62no—
672M16—62no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—62no—
676C2×C8C22×C3×D311yescharacteristic
677C2×C8C22×C3×D311yescharacteristic
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—31no—
682C4⋊C4—31no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C4⋊C4—61no—
686C4⋊C4C22×C3×D311yescharacteristic
687C22⋊C4—31no—
688C22⋊C4—31no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—61no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C42—21no—
697C42C22×C3×D311yescharacteristic
698C22×C3—21no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—62no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3C2×D3×D411yescharacteristic
712C22×C3C22×C3×D411yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—22no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C3×C4—22no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—41no—
735C3×C4—42no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—81no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4—121no—
748C3×C4—121no—
749C3×C4C2×D3×D411yescharacteristic
750C3×C4#100911yescharacteristic
751C3×C4C22×C3×D411yescharacteristic
752C3×C4C3×H(5,𝔽2)11yescharacteristic
753Dic3—21no—
754Dic3—21no—
755Dic3—41no—
756Dic3—41no—
757C32#326911yescharacteristic, complemented, Sylow
758C23—31no—
759C23—31no—
760C23—61no—
761C23—61no—
762Q8—21no—
763Q8—21no—
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—61no—
768Q8—61no—
769Q8—122no—
770Q8C3×D3×D412yes—
771D4—32no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—121no—
776D4—122no—
777D4—122no—
778D4—122no—
779D4—122no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—122no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4C3×D3×D411yescharacteristic
798C2×C4C3×D3×D411yescharacteristic
799C2×C4C23×C3×D311yescharacteristic
800C8—21no—
801C8—21no—
802C8—32no—
803C8—61no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—121no—
808C2×C3—121no—
809C2×C3—122no—
810C2×C3—241no—
811C2×C3#560911yescharacteristic
812C2×C3#576611yescharacteristic
813C2×C3#577711yescharacteristic
814C2×C3C3×D4211yescharacteristic
815C2×C3C3×#57511yescharacteristic
816C2×C3C3×#57811yescharacteristic
817D3—41no—
818D3—41no—
819D3—42no—
820D3—81no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—62no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22C2×C3×D3×D411yescharacteristic
834C4—21no—
835C4—21no—
836C4—22no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—61no—
841C4—61no—
842C4—121no—
843C4—121no—
844C4C2×C3×D3×D411yescharacteristic
845C4C3×#100911yescharacteristic
846C3—21no—
847C3#8050011yescharacteristic, direct product factor
848C3C3×#326911yescharacteristic, complemented
849C2—121no—
850C2—121no—
851C2—122no—
852C2—241no—
853C2C3×#560911yescharacteristic
854C2C3×#576611yescharacteristic
855C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
hypercenterC3×#462D3
hypocenterC3C3×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. C2×C3×#918C2semidirect
3. C3×#5726C2semidirect
4. C3×#5576C2semidirect
5. C32×#462C2semidirect
6. C3×#5187C2semidirect
7. C3×#5186C2semidirect
8. C3×#5086C2semidirect
9. C3×#5026C2semidirect
10. C3×#4844C2semidirect
11. C3×#4836C2semidirect
12. C3×#4813C2semidirect
13. C3×#4812C2semidirect
14. C3×#4810C2semidirect
15. C3×#4808C2semidirect
17. #80500C3direct (N × H)
67. C2×#919C2×C3semidirect
68. C2×#918C2×C3semidirect
69. #5726C2×C3semidirect
70. #5576C2×C3semidirect
76. C3×#462D3semidirect
77. C3×#462C2×C3semidirect
84. #5187C2×C3semidirect
85. #5186C2×C3semidirect
86. #5086C2×C3semidirect
87. #5026C2×C3semidirect
88. #4844C2×C3semidirect
89. #4836C2×C3semidirect
90. #4813C2×C3semidirect
91. #4812C2×C3semidirect
92. #4810C2×C3semidirect
93. #4808C2×C3semidirect
135. C3×#215D4semidirect
308. #462C3×D3semidirect
431. #215C3×D4semidirect
757. C32#3269semidirect
847. C3#80500direct (N × H)
848. C3C3×#3269semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C2×C3×#9182
C3×#57262
C3×#55762
C32×#4622
C3×#51872
C3×#51862
C3×#50862
C3×#50262
C3×#48442
C3×#48362
C3×#48132
C3×#48122
C3×#48102
C3×#48082
C3×#32693
#805003