Finite Group Databasebeta

← C3×#10594518 #13173933

Subgroups — C3×#10594518 #13173933

Order 1728.

1522 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3799C212yesmaximal, complemented
2C3×#64104C211yesmaximal, characteristic, complemented
3C32×#893C211yesmaximal, characteristic, complemented
4C32×#888C211yesmaximal, characteristic, complemented
5C3×#63916C211yesmaximal, characteristic, complemented
6C3×#63911C211yesmaximal, characteristic, complemented
7C3×#63910C212yesmaximal, complemented
8C3×#63907C212yesmaximal, complemented
9C3×#63904C212yesmaximal, complemented
10C3×#63894C211yesmaximal, characteristic, complemented
11C3×C4×#624C211yesmaximal, characteristic, complemented
12C3×#5725—31nomaximal
13C3×#5548—31nomaximal
14#10594518C311yesmaximal, characteristic, direct product factor
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic
19C2×C32×C4×D3C2212yes—
20C2×C32×Dic6C2212yes—
21C2×C3×#626C2212yes—
22C2×C3×#626C2212yes—
23C2×C3×#626C2212yes—
24C2×C3×#624C2211yescharacteristic
25C2×C3×#624C2212yes—
26C2×C3×#624C2211yescharacteristic
27C3×#3799—28no—
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2212yes—
30C32×(C2×D3)⋊C4C2212yes—
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2212yes—
33C32×C4×Dic3C2211yescharacteristic
34C32×C4×Dic3C2211yescharacteristic
35C3×#3722C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2211yescharacteristic
38C3×Dic32C2211yescharacteristic
39C2×C3×#239—32no—
40C2×C3×#235—32no—
41C2×#3799C2×C312yescomplemented
42C32×C4⋊Q8—31no—
43C32×C4×D4—31no—
44#64104C2×C311yescharacteristic, complemented
45C3×#947—32no—
46C3×#940—31no—
47C3×#938—31no—
48C3×C4×#67—32no—
49C3×#895—31no—
50C3×#895—31no—
51C3×#895—31no—
52C3×#895—32no—
53C3×#895—61no—
54C3×#893—21no—
55C3×#893—32no—
56C3×#893—31no—
57C3×#893D311yescharacteristic, complemented
58C3×#893C2×C311yescharacteristic, complemented
59C3×#888—21no—
60C3×#888D311yescharacteristic, complemented
61C3×#888C2×C311yescharacteristic, complemented
62C3×#885—32no—
63C3×#884—32no—
64C3×#874—31no—
65C3×C4×D12—31no—
66C3×C42×D3—31no—
67C3×C42×D3—31no—
68#63916C2×C311yescharacteristic, complemented
69#63911C2×C311yescharacteristic, complemented
70#63910C2×C312yescomplemented
71#63907C2×C312yescomplemented
72#63904C2×C312yescomplemented
73#63894C2×C311yescharacteristic, complemented
74C4×#624C2×C311yescharacteristic, complemented
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2312yes—
78C2×C33×C4C2312yes—
79C2×C33×C4C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)—24no—
82C3×C4⋊(C3⋊D3)—22no—
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C32×D12—22no—
90C32×C4×D3—24no—
91C32×Dic6—24no—
92C3×#626—24no—
93C3×#626—24no—
94C3×#626—24no—
95C3×#624—24no—
96C3×#624—22no—
97C3×#624D414yescomplemented
98C3×#532—91no—
99#5725—31no—
100#5548—31no—
101C2×C32×Q8—32no—
102C2×C32×D4—31no—
103C22×C32×C4—32no—
104C2×C4⋊(C3⋊D3)C22×C312yes—
105C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
106C2×C4×C3⋊D3C22×C311yescharacteristic
107C2×C3×#67—32no—
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C3×#239—68no—
111C3×#235—68no—
112C2×C3×D12—21no—
113C2×C3×D12—32no—
114C2×C3×D12—32no—
115C2×C3×D12—32no—
116C2×C3×D12—32no—
117C2×C3×D12—31no—
118C2×C3×D12—32no—
119C2×C3×D12—31no—
120C2×C3×D12—61no—
121C2×C3×D12—62no—
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×D12C22×C311yescharacteristic
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—32no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—32no—
133C2×C3×C4×D3—61no—
134C2×C3×C4×D3C2×D312yes—
135C2×C3×C4×D3C22×C312yes—
136C2×C3×Dic6—22no—
137C2×C3×Dic6C2×D312yes—
138C2×C3×Dic6C22×C312yes—
139C2×#626C22×C312yes—
140C2×#626C22×C312yes—
141C2×#626C22×C312yes—
142C2×#624C22×C312yes—
143C2×#624C22×C311yescharacteristic
144C2×#624C22×C311yescharacteristic
145#3799—28no—
146C32×C4⋊C4—21no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—21no—
149C32×C4⋊C4—32no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—41no—
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C2×D311yescharacteristic
154C32×C4⋊C4C22×C311yescharacteristic
155C32×C22⋊C4—32no—
156C32×C42—31no—
157C32×C42—31no—
158#3752C22×C312yes—
159C3×#217—32no—
160C3×(C2×D3)⋊C4—22no—
161C3×(C2×D3)⋊C4—32no—
162C3×(C2×D3)⋊C4—32no—
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—62no—
167C3×(C2×D3)⋊C4C2×D312yes—
168C3×(C2×D3)⋊C4C22×C312yes—
169C3×C4⋊Dic3—21no—
170C3×C4⋊Dic3C2×D311yescharacteristic
171C3×C4⋊Dic3C22×C311yescharacteristic
172C3×Dic3⋊C4—22no—
173C3×Dic3⋊C4C2×D312yes—
174C3×Dic3⋊C4C22×C312yes—
175C3×C4×Dic3—21no—
176C3×C4×Dic3—21no—
177C3×C4×Dic3—31no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—31no—
181C3×C4×Dic3C2×D311yescharacteristic
182C3×C4×Dic3C2×D311yescharacteristic
183C3×C4×Dic3C22×C311yescharacteristic
184C3×C4×Dic3C22×C311yescharacteristic
185#3722C22×C312yes—
186(C2×D3)⋊Dic3C22×C312yes—
187Dic32C22×C311yescharacteristic
188Dic32C22×C311yescharacteristic
189C22×C33C2411yescharacteristic
190C2×C3×C3⋊D3—21no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—22no—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3C2×D412yes—
196C2×C32×D3—22no—
197C2×C32×D3—22no—
198C2×C32×D3—22no—
199C33×C4—22no—
200C33×C4#4112yescomplemented
201C3×C3⋊Dic3—21no—
202C32×Dic3—22no—
203C32×Dic3—21no—
204C32×Dic3C2×D412yes—
205C32×Dic3C2×D412yes—
206C32×Dic3#4112yescomplemented
207C2×C3×#41—92no—
208C2×#239—32no—
209C2×#235—32no—
210C3×C4⋊Q8—31no—
211C3×C4⋊Q8—31no—
212C3×C4⋊Q8—61no—
213C3×#127—91no—
214C3×#124—92no—
215C3×#121—92no—
216C3×#121—91no—
217C3×#121—91no—
218C3×C4×D4—31no—
219C3×C4×D4—31no—
220C3×C4×D4—61no—
221C3×C4×D4—91no—
222C3×C4×D4—92no—
223C2×C3×C42—91no—
224#947—32no—
225#940—31no—
226#938—31no—
227C4×#67—32no—
228#895—31no—
229#895—31no—
230#895—31no—
231#895—32no—
232#895—61no—
233#893—32no—
234#893—31no—
235#893C3×D311yescharacteristic, complemented
236#888C3×D311yescharacteristic, complemented
237#885—32no—
238#884—32no—
239#874—31no—
240C4×D12—31no—
241C42×D3—31no—
242C42×D3—31no—
243C23×C32—32no—
244C22×C3⋊D3C23×C312yes—
245C22×C3⋊D3C23×C311yescharacteristic
246C22×C3×D3—22no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—32no—
250C22×C3×D3—32no—
251C22×C3×D3—61no—
252C22×C3×D3—62no—
253C22×C3×D3C22×D312yes—
254C22×C3×D3C23×C312yes—
255C32×Q8—64no—
256C32×D4—62no—
257C2×C32×C4—21no—
258C2×C32×C4—22no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—22no—
262C2×C32×C4—22no—
263C2×C32×C4—31no—
264C2×C32×C4—31no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—32no—
268C2×C32×C4—41no—
269C2×C32×C4—42no—
270C2×C32×C4—64no—
271C2×C32×C4C22×D312yes—
272C2×C32×C4C22×D312yes—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C23×C312yes—
276C2×C32×C4C23×C311yescharacteristic
277C2×C3⋊Dic3C23×C311yescharacteristic
278C4⋊(C3⋊D3)—24no—
279C4⋊(C3⋊D3)—22no—
280C4×C3⋊D3—22no—
281C3×#67—64no—
282C3×#67—64no—
283C3×#67—64no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C23×C311yescharacteristic
298C2×C3×Dic3C23×C312yes—
299C2×C3×Dic3C23×C311yescharacteristic
300C2×C3×Dic3C23×C311yescharacteristic
301C2×C3×Dic3C23×C311yescharacteristic
302C3×D12—24no—
303C3×D12—22no—
304C3×D12—22no—
305C3×D12—64no—
306C3×D12—64no—
307C3×D12—64no—
308C3×D12—64no—
309C3×D12—64no—
310C3×D12—62no—
311C3×D12—62no—
312C3×D12—122no—
313C3×D12—124no—
314C3×C4×D3—24no—
315C3×C4×D3—24no—
316C3×C4×D3—34no—
317C3×C4×D3—34no—
318C3×C4×D3—44no—
319C3×C4×D3—62no—
320C3×C4×D3—64no—
321C3×C4×D3—62no—
322C3×C4×D3—62no—
323C3×C4×D3—64no—
324C3×C4×D3—62no—
325C3×C4×D3—122no—
326C3×Dic6—24no—
327C3×Dic6—24no—
328C3×Dic6—44no—
329#626—24no—
330#626—24no—
331#626—24no—
332#624—24no—
333#624—22no—
334#624C3×D414yescomplemented
335#532—91noSylow
336C2×C33C22×D411yescharacteristic
337C2×C33C2×#4111yescharacteristic
338C2×C33C2×#4111yescharacteristic
339C3×C3⋊D3—22no—
340C3×C3⋊D3—42no—
341C32×D3—42no—
342C3×#41—188no—
343C2×C3×Q8—32no—
344C2×C3×Q8—32no—
345C2×C3×Q8—62no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—61no—
349C2×C3×D4—92no—
350C2×C3×D4—92no—
351C2×C3×D4—92no—
352C2×C3×D4—91no—
353C2×C3×D4—92no—
354C22×C3×C4—32no—
355C22×C3×C4—32no—
356C22×C3×C4—62no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C22×C3×C4—92no—
360C22×C3×C4—91no—
361C2×#67—32no—
362C2×#67—32no—
363C2×#67—32no—
364#239—68no—
365#235—68no—
366C2×D12—32no—
367C2×D12—32no—
368C2×D12—32no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—32no—
372C2×D12—32no—
373C2×D12—61no—
374C2×D12—62no—
375C2×D12C2×C3×D311yescharacteristic
376C2×C4×D3—31no—
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—32no—
383C2×C4×D3—32no—
384C2×C4×D3—61no—
385C2×C4×D3C2×C3×D312yes—
386C2×Dic6C2×C3×D312yes—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—32no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—32no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—41no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4D3211yescharacteristic
398C3×C4⋊C4C2×C3×D311yescharacteristic
399C3×C4⋊C4C2×C3×D311yescharacteristic
400C3×C22⋊C4—32no—
401C3×C22⋊C4—32no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—92no—
404C3×C22⋊C4—92no—
405C3×C22⋊C4—92no—
406C3×C42—31no—
407C3×C42—31no—
408C3×C42—31no—
409C3×C42—31no—
410C3×C42—61no—
411C3×C42—61no—
412C3×C42—91no—
413C3×C42—91no—
414#217—32no—
415(C2×D3)⋊C4—32no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—32no—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—32no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4C2×C3×D312yes—
422C4⋊Dic3C2×C3×D311yescharacteristic
423Dic3⋊C4C2×C3×D312yes—
424C4×Dic3—31no—
425C4×Dic3—31no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3C2×C3×D311yescharacteristic
429C4×Dic3C2×C3×D311yescharacteristic
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—41no—
434C22×C32—62no—
435C22×C32—62no—
436C22×C32—62no—
437C22×C32C23×D311yescharacteristic
438C22×C32C23×D311yescharacteristic
439C22×C32C24×C311yescharacteristic
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3C2×C3×D412yes—
446C2×C3×D3—24no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—32no—
454C2×C3×D3—32no—
455C2×C3×D3—42no—
456C2×C3×D3—42no—
457C2×C3×D3—62no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—62no—
465C2×C3×D3—62no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—121no—
469C2×C3×D3—121no—
470C2×C3×D3—122no—
471C2×C3×D3—122no—
472C2×C3×D3—122no—
473C32×C4—22no—
474C32×C4—22no—
475C32×C4—22no—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—32no—
480C32×C4—32no—
481C32×C4—32no—
482C32×C4—42no—
483C32×C4—42no—
484C32×C4—42no—
485C32×C4—42no—
486C32×C4—62no—
487C32×C4—61no—
488C32×C4—82no—
489C32×C4#23512yescomplemented
490C32×C4#23912yescomplemented
491C32×C4C3×#4112yescomplemented
492C3⋊Dic3—21no—
493C3×Dic3—22no—
494C3×Dic3—21no—
495C3×Dic3—22no—
496C3×Dic3—21no—
497C3×Dic3—22no—
498C3×Dic3—22no—
499C3×Dic3—22no—
500C3×Dic3—42no—
501C3×Dic3—41no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—121no—
505C3×Dic3D3×D412yes—
506C3×Dic3D3×D412yes—
507C3×Dic3#23912yescomplemented
508C3×Dic3C2×C3×D412yes—
509C3×Dic3C2×C3×D412yes—
510C3×Dic3C3×#4112yescomplemented
511C2×#41—92no—
512C4⋊Q8—31no—
513#127—91no—
514#124—92no—
515#121—92no—
516#121—91no—
517#121—91no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—92no—
521C2×C42—91no—
522C33#53211yescharacteristic, complemented, Sylow
523C23×C3—32no—
524C23×C3—32no—
525C23×C3—62no—
526C23×C3—91no—
527C23×C3—92no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—32no—
531C22×D3—32no—
532C22×D3—61no—
533C22×D3—62no—
534C22×D3C22×C3×D312yes—
535C3×Q8—64no—
536C3×Q8—64no—
537C3×Q8—124no—
538C3×D4—64no—
539C3×D4—62no—
540C3×D4—62no—
541C3×D4—184no—
542C3×D4—184no—
543C3×D4—184no—
544C3×D4—184no—
545C3×D4—182no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—41no—
563C2×C3×C4—42no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—62no—
569C2×C3×C4—64no—
570C2×C3×C4—64no—
571C2×C3×C4—94no—
572C2×C3×C4—91no—
573C2×C3×C4—124no—
574C2×C3×C4—182no—
575C2×C3×C4—184no—
576C2×C3×C4—182no—
577C2×C3×C4C2×D3212yes—
578C2×C3×C4C2×D3211yescharacteristic
579C2×C3×C4C22×C3×D312yes—
580C2×C3×C4C22×C3×D312yes—
581C2×C3×C4C22×C3×D311yescharacteristic
582C2×C3×C4C22×C3×D311yescharacteristic
583#67—64no—
584#67—64no—
585#67—64no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—61no—
589C2×Dic3C22×C3×D311yescharacteristic
590C2×Dic3C22×C3×D312yes—
591C2×Dic3C22×C3×D311yescharacteristic
592C2×Dic3C22×C3×D311yescharacteristic
593C2×Dic3C22×C3×D311yescharacteristic
594D12—22no—
595D12—64no—
596D12—64no—
597D12—64no—
598D12—64no—
599D12—64no—
600D12—62no—
601D12—62no—
602D12—122no—
603D12—124no—
604C4×D3—24no—
605C4×D3—34no—
606C4×D3—34no—
607C4×D3—62no—
608C4×D3—64no—
609C4×D3—62no—
610C4×D3—62no—
611C4×D3—64no—
612C4×D3—62no—
613C4×D3—122no—
614Dic6—24no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—41no—
625C2×C32—41no—
626C2×C32—41no—
627C2×C32—122no—
628C2×C32C2×#23511yescharacteristic
629C2×C32C2×D3×D411yescharacteristic
630C2×C32C2×D3×D411yescharacteristic
631C2×C32C2×#23911yescharacteristic
632C2×C32C2×#23911yescharacteristic
633C2×C32D3×#4111yescharacteristic
634C2×C32C22×C3×D411yescharacteristic
635C2×C32C2×C3×#4111yescharacteristic
636C2×C32C2×C3×#4111yescharacteristic
637C3⋊D3—22no—
638C3⋊D3—42no—
639C3×D3—44no—
640C3×D3—42no—
641C3×D3—42no—
642C3×D3—62no—
643C3×D3—62no—
644C3×D3—122no—
645C3×D3—122no—
646C3×D3—122no—
647C3×D3—242no—
648#41—188no—
649C2×Q8—32no—
650C2×D4—31no—
651C2×D4—92no—
652C2×D4—92no—
653C2×D4—92no—
654C2×D4—91no—
655C2×D4—92no—
656C22×C4—32no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—92no—
660C22×C4—91no—
661C4⋊C4—32no—
662C4⋊C4—31no—
663C4⋊C4C3×D3211yescharacteristic
664C22⋊C4—32no—
665C22⋊C4—92no—
666C22⋊C4—92no—
667C22⋊C4—92no—
668C42—31no—
669C42—31no—
670C42—91no—
671C42—91no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—41no—
676C22×C3—64no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—62no—
683C22×C3—92no—
684C22×C3—122no—
685C22×C3—122no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—182no—
689C22×C3—182no—
690C22×C3—182no—
691C22×C3C22×D3211yescharacteristic
692C22×C3C23×C3×D311yescharacteristic
693C22×C3C23×C3×D311yescharacteristic
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—32no—
698C2×D3—32no—
699C2×D3—62no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—122no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—32no—
724C3×C4—32no—
725C3×C4—32no—
726C3×C4—32no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—61no—
736C3×C4—62no—
737C3×C4—61no—
738C3×C4—82no—
739C3×C4—122no—
740C3×C4—121no—
741C3×C4—181no—
742C3×C4#379912yescomplemented
743C3×C4C3×#23512yescomplemented
744C3×C4C3×#23912yescomplemented
745Dic3—22no—
746Dic3—21no—
747Dic3—61no—
748Dic3—61no—
749Dic3—121no—
750Dic3C3×D3×D412yes—
751Dic3C3×D3×D412yes—
752Dic3C3×#23912yescomplemented
753C32—21no—
754C32—21no—
755C32—21no—
756C32—41no—
757C32#554811yescharacteristic, complemented
758C32#572511yescharacteristic, complemented
759C32C3×#53211yescharacteristic, complemented
760C23—32no—
761C23—91no—
762C23—92no—
763Q8—64no—
764D4—62no—
765D4—184no—
766D4—184no—
767D4—184no—
768D4—184no—
769D4—182no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—32no—
775C2×C4—64no—
776C2×C4—94no—
777C2×C4—91no—
778C2×C4—184no—
779C2×C4—182no—
780C2×C4—182no—
781C2×C4C2×C3×D3212yes—
782C2×C4C2×C3×D3211yescharacteristic
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—124no—
796C2×C3—122no—
797C2×C3—122no—
798C2×C3—182no—
799C2×C3—362no—
800C2×C3C2×#379911yescharacteristic
801C2×C3D32×D411yescharacteristic
802C2×C3D3×#23911yescharacteristic
803C2×C3C2×C3×#23511yescharacteristic
804C2×C3C2×C3×D3×D411yescharacteristic
805C2×C3C2×C3×D3×D411yescharacteristic
806C2×C3C2×C3×#23911yescharacteristic
807C2×C3C2×C3×#23911yescharacteristic
808C2×C3C3×D3×#4111yescharacteristic
809D3—42no—
810D3—62no—
811D3—62no—
812D3—122no—
813D3—122no—
814D3—122no—
815D3—242no—
816C22—62no—
817C22—62no—
818C22—62no—
819C22—92no—
820C22—181no—
821C22—181no—
822C22—182no—
823C22—182no—
824C22—182no—
825C22C22×C3×D3211yescharacteristic
826C4—22no—
827C4—32no—
828C4—32no—
829C4—32no—
830C4—61no—
831C4—62no—
832C4—181no—
833C4C3×#379912yescomplemented
834C3—21no—
835C3—21no—
836C3—21no—
837C3—41no—
838C3#1059451811yescharacteristic, direct product factor
839C3C3×#554811yescharacteristic, complemented
840C3C3×#572511yescharacteristic, complemented
841C2—122no—
842C2—182no—
843C2—362no—
844C2C2×C3×#379911yescharacteristic
845C2C3×D32×D411yescharacteristic
846C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3799C2semidirect
2. C3×#64104C2semidirect
3. C32×#893C2semidirect
4. C32×#888C2semidirect
5. C3×#63916C2semidirect
6. C3×#63911C2semidirect
7. C3×#63910C2semidirect
8. C3×#63907C2semidirect
9. C3×#63904C2semidirect
10. C3×#63894C2semidirect
11. C3×C4×#624C2semidirect
14. #10594518C3direct (N × H)
41. C2×#3799C2×C3semidirect
44. #64104C2×C3semidirect
57. C3×#893D3semidirect
58. C3×#893C2×C3semidirect
60. C3×#888D3semidirect
61. C3×#888C2×C3semidirect
68. #63916C2×C3semidirect
69. #63911C2×C3semidirect
70. #63910C2×C3semidirect
71. #63907C2×C3semidirect
72. #63904C2×C3semidirect
73. #63894C2×C3semidirect
74. C4×#624C2×C3semidirect
97. C3×#624D4semidirect
200. C33×C4#41semidirect
206. C32×Dic3#41semidirect
235. #893C3×D3semidirect
236. #888C3×D3semidirect
334. #624C3×D4semidirect
489. C32×C4#235semidirect
490. C32×C4#239semidirect
491. C32×C4C3×#41semidirect
507. C3×Dic3#239semidirect
510. C3×Dic3C3×#41semidirect
522. C33#532semidirect
742. C3×C4#3799semidirect
743. C3×C4C3×#235semidirect
744. C3×C4C3×#239semidirect
752. Dic3C3×#239semidirect
757. C32#5548semidirect
758. C32#5725semidirect
759. C32C3×#532semidirect
833. C4C3×#3799semidirect
838. C3#10594518direct (N × H)
839. C3C3×#5548semidirect
840. C3C3×#5725semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37992
C3×#641042
C32×#8932
C32×#8882
C3×#639162
C3×#639112
C3×#639102
C3×#639072
C3×#639042
C3×#638942
C3×C4×#6242
C3×#57253
C3×#55483
#105945183