Finite Group Databasebeta

← Dic3×#889 #11802484

Subgroups — Dic3×#889 #11802484

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#889C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic
4#10591269C211yesmaximal, characteristic
5#10591268C211yesmaximal, characteristic
6Dic3×C4⋊Dic3C211yesmaximal, characteristic
7#10591265C211yesmaximal, characteristic
8#10591262C211yesmaximal, characteristic
9Dic3×Dic3⋊C4C211yesmaximal, characteristic
10Dic3×Dic3⋊C4C211yesmaximal, characteristic
11Dic3×Dic3⋊C4C211yesmaximal, characteristic
12Dic3×Dic3⋊C4C211yesmaximal, characteristic
13C4×Dic32C211yesmaximal, characteristic
14#10591206C211yesmaximal, characteristic
15#10591192C211yesmaximal, characteristic
16Dic3×#125—31nomaximal
17C4×#889—31nomaximal
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#889C418yescomplemented
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#125—31no—
55C2×#889D311yescharacteristic
56C3×C4×C4⋊C4—31no—
57#4984—31no—
58#4984—31no—
59#4980—31no—
60#4980—31no—
61#4980—31no—
62#4980—31no—
63#4980—31no—
64#4980—61no—
65#4978—31no—
66#4976—31no—
67Dic3×C4⋊C4—31no—
68Dic3×C4⋊C4—31no—
69Dic3×C4⋊C4—31no—
70Dic3×C4⋊C4—31no—
71Dic3×C4⋊C4—31no—
72Dic3×C4⋊C4D311yescharacteristic
73#4936—31no—
74C4×C4⋊Dic3—31no—
75C4×Dic3⋊C4—31no—
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4—31no—
78C4×Dic3⋊C4—31no—
79C42×Dic3—31no—
80C42×Dic3—31no—
81#4653—31no—
82#4652—31no—
83#4650—31no—
84#4647—31no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C32×C4⋊C4C2×C414yes—
101C4⋊(C3⋊Dic3)—22no—
102C4×C3⋊Dic3—22no—
103C3×C4⋊Dic3—22no—
104C3×C4⋊Dic3C2×C414yes—
105C3×Dic3⋊C4C2×C414yes—
106C3×Dic3⋊C4C2×C414yes—
107C3×Dic3⋊C4C2×C414yes—
108C3×Dic3⋊C4C2×C414yes—
109C3×C4×Dic3—22no—
110C3×C4×Dic3—22no—
111C3×C4×Dic3—22no—
112C3×C4×Dic3C2×C414yes—
113Dic3⋊Dic3—22no—
114Dic3⋊Dic3—22no—
115Dic3⋊Dic3—22no—
116Dic3⋊Dic3—22no—
117Dic32—22no—
118Dic32—22no—
119Dic32—22no—
120Dic32—22no—
121Dic32—22no—
122Dic32Q814yes—
123C4×#125—91noSylow
124C3×#125—38no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—61no—
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4C2×D311yescharacteristic
152C2×Dic3⋊C4C2×D311yescharacteristic
153C2×Dic3⋊C4C2×D311yescharacteristic
154C2×Dic3⋊C4C2×D311yescharacteristic
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—61no—
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D311yescharacteristic
174#889Dic318yesdirect product factor
175C3×#95—31no—
176C3×#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—61no—
198C3⋊#95—61no—
199C3⋊#95—61no—
200C3⋊#95—61no—
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C23×C32C2411yescharacteristic
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4C22×C412yes—
211C2×C32×C4C22×C412yes—
212C2×C32×C4C22×C412yes—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3C2×Q812yes—
224C2×C3⋊Dic3#4112yes—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3C22×C412yes—
240C2×C3×Dic3C22×C412yes—
241C2×C3×Dic3C22×C412yes—
242C2×C3×Dic3C22×C412yes—
243C2×C3×Dic3C2×Q812yes—
244C2×C3×Dic3C2×Q812yes—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248C2×C3×Dic3#4112yes—
249C2×#125—31no—
250#389—91no—
251#389—91no—
252#387—91no—
253#387—91no—
254#387—91no—
255#387—91no—
256#382—91no—
257C4×C4⋊C4—31no—
258C4×C4⋊C4—91no—
259C4×C4⋊C4—91no—
260C4×C4⋊C4—91no—
261C4×C4⋊C4—91no—
262C4×C4⋊C4—91no—
263C43—91no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C3×C4⋊C4—24no—
302C3×C4⋊C4—34no—
303C3×C4⋊C4—34no—
304C3×C4⋊C4—34no—
305C3×C4⋊C4—34no—
306C3×C4⋊C4—34no—
307C3×C4⋊C4—62no—
308C3×C4⋊C4C4×D314yes—
309C3×C4⋊C4C2×Dic314yes—
310C3×C42—34no—
311C3×C42—62no—
312C3×C42—62no—
313C3×C42—62no—
314C4⋊Dic3—22no—
315C4⋊Dic3—62no—
316C4⋊Dic3—62no—
317C4⋊Dic3—62no—
318C4⋊Dic3—62no—
319C4⋊Dic3—62no—
320C4⋊Dic3—62no—
321C4⋊Dic3—122no—
322C4⋊Dic3C2×Dic314yes—
323Dic3⋊C4—62no—
324Dic3⋊C4—62no—
325Dic3⋊C4—62no—
326Dic3⋊C4—62no—
327Dic3⋊C4C2×Dic314yes—
328Dic3⋊C4C2×Dic314yes—
329Dic3⋊C4C2×Dic314yes—
330Dic3⋊C4C2×Dic314yes—
331C4×Dic3—22no—
332C4×Dic3—22no—
333C4×Dic3—22no—
334C4×Dic3—34no—
335C4×Dic3—34no—
336C4×Dic3—62no—
337C4×Dic3—62no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—62no—
344C4×Dic3—62no—
345C4×Dic3—62no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C4×Dic3—122no—
349C4×Dic3C2×Dic314yes—
350C22×C32C23×C411yescharacteristic
351C22×C32C22×Q811yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C32×C4—22no—
358C32×C4—22no—
359C32×C4—22no—
360C3⋊Dic3—22no—
361C3⋊Dic3—22no—
362C3⋊Dic3—41no—
363C3⋊Dic3—41no—
364C3×Dic3—22no—
365C3×Dic3—22no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—41no—
369C3×Dic3—41no—
370C3×Dic3C4×Q814yes—
371C3×Dic3#12514yescomplemented
372#125—38no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4D3211yescharacteristic
385C2×C42—31no—
386C2×C42—31no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—91no—
390C2×C42—91no—
391C2×C42—91no—
392C2×C42—91no—
393C2×C42—91no—
394C2×C42—91no—
395C2×C42—91no—
396#95—31no—
397#95—31no—
398#95—91no—
399#95—91no—
400#95—91no—
401#95—91no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408C23×C3—21no—
409C23×C3C23×D311yescharacteristic
410C23×C3C23×D311yescharacteristic
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4C2×C4×D312yes—
457C2×C3×C4C2×C4×D312yes—
458C2×C3×C4C2×C4×D312yes—
459C2×C3×C4C22×Dic312yes—
460C2×C3×C4C22×Dic312yes—
461C2×C3×C4C22×Dic312yes—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—32no—
477C2×Dic3—32no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—62no—
481C2×Dic3—62no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3—121no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3#23512yes—
513C2×Dic3#23512yes—
514C2×Dic3#23712yes—
515C2×Dic3D3×Q812yes—
516C2×Dic3D3×Q812yes—
517C2×Dic3#23912yes—
518C2×Dic3C22×Dic312yes—
519C2×Dic3C22×Dic312yes—
520C2×Dic3C22×Dic312yes—
521C2×Dic3C22×Dic312yes—
522C2×C32C2×C4×Q811yescharacteristic
523C2×C32C4×#4111yescharacteristic
524C2×C32C4×#4111yescharacteristic
525C2×C32C2×#12511yescharacteristic
526C2×C32#52911yescharacteristic
527C2×C32#52911yescharacteristic
528C2×C32#53311yescharacteristic
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4C2×D3211yescharacteristic
542C22×C4C2×D3211yescharacteristic
543C22×C4C2×D3211yescharacteristic
544C4⋊C4—34no—
545C4⋊C4—34no—
546C4⋊C4—34no—
547C4⋊C4—34no—
548C4⋊C4—34no—
549C4⋊C4—62no—
550C4⋊C4—182no—
551C4⋊C4—182no—
552C4⋊C4—182no—
553C4⋊C4—182no—
554C4⋊C4—182no—
555C4⋊C4D3×Dic314yes—
556C42—34no—
557C42—62no—
558C42—62no—
559C42—62no—
560C42—94no—
561C42—182no—
562C42—182no—
563C42—182no—
564C42—182no—
565C42—182no—
566C42—182no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3C22×C4×D311yescharacteristic
575C22×C3C2×#23511yescharacteristic
576C22×C3C2×#23511yescharacteristic
577C22×C3C2×#23711yescharacteristic
578C22×C3C2×D3×Q811yescharacteristic
579C22×C3C2×D3×Q811yescharacteristic
580C22×C3C2×#23911yescharacteristic
581C22×C3D3×#4111yescharacteristic
582C22×C3D3×#4111yescharacteristic
583C22×C3D3×#4111yescharacteristic
584C22×C3D3×#4111yescharacteristic
585C22×C3D3×#4111yescharacteristic
586C22×C3D3×#4111yescharacteristic
587C22×C3C23×Dic311yescharacteristic
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—22no—
594C3×C4—34no—
595C3×C4—34no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—42no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—121no—
604C3×C4—121no—
605Dic3—22no—
606Dic3—22no—
607Dic3—22no—
608Dic3—22no—
609Dic3—41no—
610Dic3—41no—
611Dic3—62no—
612Dic3—62no—
613Dic3—62no—
614Dic3—62no—
615Dic3—122no—
616Dic3—122no—
617Dic3—121no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—241no—
622Dic3—241no—
623Dic3#88914yesdirect product factor
624Dic3Q8×Dic314yes—
625C32C4×#12511yescharacteristic, complemented, Sylow
626C23C22×D3211yescharacteristic
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—92no—
658C2×C4—92no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4C2×D3×Dic312yes—
670C2×C4C2×D3×Dic312yes—
671C2×C4C2×D3×Dic312yes—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3C4×#23511yescharacteristic
680C2×C3C2×#88911yescharacteristic
681C2×C3#552811yescharacteristic
682C2×C3C4×#23711yescharacteristic
683C2×C3#553811yescharacteristic
684C2×C3C4×D3×Q811yescharacteristic
685C2×C3#557811yescharacteristic
686C2×C3D3×#12511yescharacteristic
687C2×C3#568811yescharacteristic
688C2×C3#569111yescharacteristic
689C2×C3#569111yescharacteristic
690C2×C3C2×Q8×Dic311yescharacteristic
691C2×C3Dic3×#4111yescharacteristic
692C2×C3Dic3×#4111yescharacteristic
693C22D3×#23511yescharacteristic
694C22D3×#23511yescharacteristic
695C22D3×#23711yescharacteristic
696C22#6431211yescharacteristic
697C22D32×Q811yescharacteristic
698C22D3×#23911yescharacteristic
699C22C22×D3×Dic311yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—34no—
704C4—34no—
705C4—62no—
706C4—62no—
707C4—62no—
708C4—62no—
709C4—121no—
710C4—121no—
711C4—182no—
712C4—182no—
713C4—361no—
714C4—361no—
715C3—21no—
716C3C4×#88911yescharacteristic, complemented
717C3Dic3×#12511yescharacteristic, complemented
718C2D3×#88911yescharacteristic
719C2#1059439811yescharacteristic
720C2#1059440311yescharacteristic
721C2#1059442211yescharacteristic
722C2Dic3×#23511yescharacteristic
723C2Dic3×#23711yescharacteristic
724C2D3×Q8×Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. C3×#889C4semidirect
174. #889Dic3direct (N × H)
371. C3×Dic3#125semidirect
623. Dic3#889direct (N × H)
625. C32C4×#125semidirect
716. C3C4×#889semidirect
717. C3Dic3×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8892
#105926792
C3×Dic3×C4⋊C42
#105912692
#105912682
Dic3×C4⋊Dic32
#105912652
#105912622
Dic3×Dic3⋊C42
C4×Dic322
#105912062
#105911922
Dic3×#1253
C4×#8893