Finite Group Databasebeta

← #11803371

Subgroups — #11803371

Order 1152.

1359 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C2×#63969C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#10592644C211yesmaximal, characteristic, complemented
5C3×#4945C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic
7#10591718C211yesmaximal, characteristic, complemented
8#10591693C211yesmaximal, characteristic, complemented
9#10591373C211yesmaximal, characteristic, complemented
10#10591362C211yesmaximal, characteristic, complemented
11#10591337C211yesmaximal, characteristic, complemented
12#10591333C211yesmaximal, characteristic, complemented
13#10591331C211yesmaximal, characteristic, complemented
14#10591330C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#82326—31nomaximal
17#75828—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#67⋊C4—24no—
36#63969C418yescomplemented
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45D3×Dic3⋊C4—24no—
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×C4×D4—31no—
57C2×#935—31no—
58C22×Dic3⋊C4—31no—
59C2×D3×C4⋊C4—31no—
60C2×#883—31no—
61C2×#67⋊C4D311yescharacteristic
62C3×#388—31no—
63#5220—31no—
64#5210—31no—
65#5210—31no—
66C4×#217—31no—
67#4976—31no—
68#4976—31no—
69#4976—31no—
70#4956—31no—
71#4950—31no—
72#4946—31no—
73#4946—31no—
74#4945—31no—
75#4945—31no—
76#4945—61no—
77#4945D311yescharacteristic, complemented
78#4943—31no—
79C4×(C2×D3)⋊C4—31no—
80#4933—31no—
81#4933—31no—
82#4928—31no—
83#4668—31no—
84#4664—31no—
85#4655—31no—
86#4654—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C3×#67—22no—
96C2×C3×#67—22no—
97C2×C3×#67C2×C414yes—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3—41no—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×C4×D3—41no—
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3D414yes—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—41no—
115C2×D3×Dic3—41no—
116C2×D3×Dic3C2×C414yescomplemented
117C32×C22⋊C4—22no—
118#3757—41no—
119#3757C2×C414yescomplemented
120#3750—22no—
121C4×C3⋊Dic3—41no—
122C3×#217—41no—
123C3×#217C2×C414yescomplemented
124C3×(C2×D3)⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—41no—
129#3724—22no—
130#3724—41no—
131#3724C2×C414yescomplemented
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—41no—
134Dic3⋊Dic3C2×C414yescomplemented
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3C2×C414yescomplemented
137#2322—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—31no—
140C23×C3×C4—31no—
141C22×#67C2×D311yescharacteristic
142C23×Dic3—31no—
143C23×Dic3—31no—
144C23×Dic3C2×D311yescharacteristic
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3C2×D311yescharacteristic
148C3×C4×D4—64no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4C2×D311yescharacteristic
156C2×C3×C22⋊C4C2×D311yescharacteristic
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—61no—
166C2×#217—61no—
167C2×#217C2×D311yescharacteristic
168C2×#217C2×D311yescharacteristic
169#935—38no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—61no—
188C2×Dic3⋊C4—64no—
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—61no—
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196D3×C4⋊C4—64no—
197#883—38no—
198#67⋊C4—24no—
199C3×#95—31no—
200C3×#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—61no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32C22×C412yes—
228C23×C32C2411yescharacteristic
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3C22×C412yes—
234C22×C3×D3C2×D412yes—
235C22×C3×D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D412yes—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C22×C412yes—
253C2×C3⋊Dic3C22×C412yes—
254C3×#67—28no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—44no—
273C2×C3×Dic3C22×C412yes—
274C2×C3×Dic3C22×C412yes—
275C2×C3×Dic3C22×C412yes—
276C2×C3×Dic3C2×D412yes—
277C3×C4×D3—44no—
278D3×Dic3—28no—
279D3×Dic3—44no—
280C2×#123—91no—
281C2×C4×D4—31no—
282C22×C4⋊C4—91no—
283#389—91no—
284#389—91no—
285#388—31no—
286#388—91no—
287#387—91no—
288#387—91no—
289#386—91no—
290#385—91no—
291#385—91no—
292#385—91no—
293#381—91no—
294C4×C22⋊C4—91no—
295C24×C3—21no—
296C24×C3—31no—
297C24×C3C22×D311yescharacteristic
298C24×C3C22×D311yescharacteristic
299C23×D3C22×D311yescharacteristic
300C2×C3×D4—34no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—34no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—62no—
314C22×C3×C4—121no—
315C22×C3×C4—121no—
316C22×C3×C4—121no—
317C22×C3×C4—121no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—22no—
323C2×#67—22no—
324C2×#67C4×D314yes—
325C22×Dic3—22no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—34no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—41no—
336C22×Dic3—41no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—62no—
344C22×Dic3—121no—
345C22×Dic3—121no—
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C2×C4×D3—34no—
354C2×C4×D3—41no—
355C2×C4×D3—41no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—121no—
360C2×C4×D3—121no—
361C2×C4×D3#6714yes—
362C3×C4⋊C4—62no—
363C3×C4⋊C4—62no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—22no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—42no—
368C3×C22⋊C4—62no—
369C3×C22⋊C4—121no—
370C3×C42—62no—
371C3×C42—121no—
372#217—34no—
373#217—34no—
374#217—34no—
375#217—41no—
376#217—64no—
377#217—62no—
378#217—121no—
379#217—121no—
380#217—122no—
381#217C4×D314yescomplemented
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—62no—
385C4⋊Dic3—34no—
386C4⋊Dic3—62no—
387C4⋊Dic3—121no—
388Dic3⋊C4—22no—
389Dic3⋊C4—22no—
390Dic3⋊C4—34no—
391Dic3⋊C4—34no—
392Dic3⋊C4—34no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—122no—
399Dic3⋊C4—121no—
400Dic3⋊C4—121no—
401Dic3⋊C4—121no—
402C4×Dic3—22no—
403C4×Dic3—41no—
404C4×Dic3—121no—
405C4×Dic3—121no—
406C4×Dic3—122no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C23×C411yescharacteristic
415C22×C32C22×D411yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32H(5,𝔽2)11yescharacteristic
418C22×C32H(5,𝔽2)11yescharacteristic
419C22×C322−1+411yescharacteristic
420C22×C322−1+411yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3C4×D414yes—
428C32×C4—22no—
429C32×C4—41no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C22×D4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—91no—
445C23×C4—91no—
446#123—98no—
447C4×D4—64no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—184no—
458C2×C22⋊C4—31no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4D3211yescharacteristic
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—91no—
469#95—31no—
470#95—31no—
471#95—91no—
472#95—91no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—22no—
493C23×C3—32no—
494C23×C3—32no—
495C23×C3—32no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3C2×C4×D312yes—
507C23×C3C2×C4×D312yes—
508C23×C3C23×D311yescharacteristic
509C23×C3C23×D311yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3C2×C4×D312yes—
515C22×D3#23512yes—
516C22×D3C2×#6712yes—
517C3×D4—68no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—32no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—124no—
556C2×C3×C4—124no—
557C2×C3×C4D3×D412yes—
558C2×C3×C4C2×#6712yes—
559#67—28no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—44no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—68no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—62no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—124no—
616C2×Dic3C2×C4×D312yes—
617C2×Dic3C2×C4×D312yes—
618C2×Dic3C2×C4×D312yes—
619C2×Dic3C2×#6712yes—
620C4×D3—44no—
621C4×D3—68no—
622C4×D3—124no—
623C2×C32—42no—
624C2×C32C2×C4×D411yescharacteristic
625C2×C32#52011yescharacteristic
626C2×C32#52011yescharacteristic
627C2×C32#53411yescharacteristic
628C2×C32#53611yescharacteristic
629C2×C32#53911yescharacteristic
630C2×C32#53911yescharacteristic
631C3×D3—24no—
632C24—31no—
633C24C2×D3211yescharacteristic
634C2×D4—34no—
635C2×D4—62no—
636C2×D4—62no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—34no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—62no—
646C22×C4—94no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—121no—
652C22×C4—121no—
653C22×C4—121no—
654C22×C4—121no—
655C22×C4—182no—
656C22×C4—182no—
657C22×C4—182no—
658C22×C4—361no—
659C22×C4—361no—
660C22×C4C2×D3211yescharacteristic
661C22×C4C2×D3211yescharacteristic
662C4⋊C4—62no—
663C4⋊C4—62no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—182no—
667C4⋊C4—182no—
668C4⋊C4—182no—
669C4⋊C4—361no—
670C4⋊C4—361no—
671C22⋊C4—22no—
672C22⋊C4—34no—
673C22⋊C4—62no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4—121no—
677C22⋊C4—182no—
678C22⋊C4—361no—
679C42—62no—
680C42—121no—
681C42—361no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—34no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3C22×C4×D311yescharacteristic
718C22×C3C22×C4×D311yescharacteristic
719C22×C3C2×#23511yescharacteristic
720C22×C3C2×D3×D411yescharacteristic
721C22×C3#100411yescharacteristic
722C22×C3#100411yescharacteristic
723C22×C3#100411yescharacteristic
724C22×C3D3×#4111yescharacteristic
725C22×C3#100911yescharacteristic
726C22×C3#101011yescharacteristic
727C22×C3#101011yescharacteristic
728C22×C3#101011yescharacteristic
729C22×C3#101011yescharacteristic
730C22×C3C22×#6711yescharacteristic
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3C4×#6714yes—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—42no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—62no—
744C3×C4—62no—
745C3×C4—62no—
746C3×C4—62no—
747C3×C4—81no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4—121no—
751Dic3—22no—
752Dic3—22no—
753Dic3—22no—
754Dic3—22no—
755Dic3—41no—
756Dic3—41no—
757Dic3—41no—
758Dic3—62no—
759Dic3—62no—
760Dic3—62no—
761Dic3—62no—
762Dic3—122no—
763Dic3—122no—
764Dic3—122no—
765Dic3—121no—
766Dic3—121no—
767Dic3—121no—
768Dic3—121no—
769Dic3—241no—
770C32#232211yescharacteristic, complemented, Sylow
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—32no—
778C23—32no—
779C23—32no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23C4×D3212yes—
785C23C22×D3211yescharacteristic
786D4—68no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—92no—
814C2×C4—92no—
815C2×C4—124no—
816C2×C4—124no—
817C2×C4—188no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—364no—
829C2×C4D3×#6712yes—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3—64no—
840C2×C3—82no—
841C2×C3#552311yescharacteristic
842C2×C3C4×D3×D411yescharacteristic
843C2×C3#554611yescharacteristic
844C2×C3#554611yescharacteristic
845C2×C3#554611yescharacteristic
846C2×C3#556411yescharacteristic
847C2×C3#556411yescharacteristic
848C2×C3#560511yescharacteristic
849C2×C3#566011yescharacteristic
850C2×C3#567511yescharacteristic
851C2×C3#570711yescharacteristic
852C2×C3C2×C4×#6711yescharacteristic
853C2×C3#580411yescharacteristic
854C2×C3#582511yescharacteristic
855D3—24no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—34no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22—62no—
869C22—62no—
870C22C2×C4×D3211yescharacteristic
871C22D3×#23511yescharacteristic
872C22#6430911yescharacteristic
873C22#6430911yescharacteristic
874C22#6431311yescharacteristic
875C22#6431411yescharacteristic
876C22C2×D3×#6711yescharacteristic
877C4—22no—
878C4—41no—
879C4—62no—
880C4—62no—
881C4—62no—
882C4—62no—
883C4—121no—
884C4—121no—
885C4—121no—
886C4—182no—
887C4—182no—
888C4—361no—
889C4—361no—
890C3—21no—
891C3#7582811yescharacteristic, complemented
892C3#8232611yescharacteristic, complemented
893C2—42no—
894C2—64no—
895C2#1059404911yescharacteristic
896C2#1059405111yescharacteristic
897C2#1059409011yescharacteristic
898C2#1059409111yescharacteristic
899C2C4×D3×#6711yescharacteristic
900C2#1059514711yescharacteristic
901C2#1059530211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×D3×Dic3⋊C4C2semidirect
4. #10592644C2semidirect
5. C3×#4945C2semidirect
7. #10591718C2semidirect
8. #10591693C2semidirect
9. #10591373C2semidirect
10. #10591362C2semidirect
11. #10591337C2semidirect
12. #10591333C2semidirect
13. #10591331C2semidirect
14. #10591330C2semidirect
15. C4×(C2×D3)⋊Dic3C2semidirect
36. #63969C4semidirect
77. #4945D3semidirect
116. C2×D3×Dic3C2×C4semidirect
119. #3757C2×C4semidirect
123. C3×#217C2×C4semidirect
131. #3724C2×C4semidirect
134. Dic3⋊Dic3C2×C4semidirect
136. (C2×D3)⋊Dic3C2×C4semidirect
381. #217C4×D3semidirect
770. C32#2322semidirect
891. C3#75828semidirect
892. C3#82326semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639692
C2×D3×Dic3⋊C42
#105926442
C3×#49452
#105917212
#105917182
#105916932
#105913732
#105913622
#105913372
#105913332
#105913312
#105913302
C4×(C2×D3)⋊Dic32
#823263
#758283