Finite Group Databasebeta

← #11805164

Subgroups — #11805164

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63883C211yesmaximal, characteristic
2C2×#63874C211yesmaximal, characteristic
3C2×#63836C211yesmaximal, characteristic
4#10592363C211yesmaximal, characteristic
5C3×#4652C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591371C211yesmaximal, characteristic
8#10591367C211yesmaximal, characteristic
9#10591331C211yesmaximal, characteristic, complemented
10#10591327C211yesmaximal, characteristic, complemented
11#10591250C211yesmaximal, characteristic, complemented
12#10591246C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic
15#10591201C211yesmaximal, characteristic, complemented
16#74961—31nomaximal
17#73767—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
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
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63883C418yescomplemented
42#63874—24no—
43#63836—24no—
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#892—31no—
57C2×D3×C4⋊C4—31no—
58C2×D3×C4⋊C4—31no—
59C2×#872—31no—
60C2×#872—31no—
61C2×#872—31no—
62C3×#387—31no—
63C3×C4×C4⋊C4—31no—
64#4987—31no—
65#4980—31no—
66#4976—31no—
67Dic3×C4⋊C4—31no—
68#4972—31no—
69C4×(C2×D3)⋊C4—31no—
70#4933—31no—
71#4933—31no—
72C4×Dic3⋊C4—31no—
73#4928—31no—
74#4667—31no—
75#4666—31no—
76#4664—31no—
77#4664—31no—
78#4664—31no—
79#4664—31no—
80#4664—61no—
81#4654—31no—
82#4653—31no—
83#4652—31no—
84#4652D311yescharacteristic, complemented
85#4649D311yescharacteristic, complemented
86#4647—31no—
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3C2×C414yes—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C2×#624—22no—
106C2×#624—22no—
107C2×#624—22no—
108C2×#624—22no—
109C2×#624C2×C414yes—
110C2×#624C2×C414yes—
111#3752—22no—
112#3752—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4C2×C414yes—
116C3×Dic3⋊C4C2×C414yes—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3—22no—
121#3724—22no—
122#3724—22no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3C2×C414yes—
126Dic3⋊Dic3C2×C414yes—
127#3722—22no—
128#3722D414yes—
129Dic32—22no—
130Dic32—22no—
131#2344—91noSylow
132C22×C4×D3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—61no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42—31no—
146C2×C3×C42—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—61no—
156C2×(C2×D3)⋊C4—61no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×Dic3⋊C4C2×D311yescharacteristic
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179C2×C4×Dic3C2×D311yescharacteristic
180C2×C4×Dic3C2×D311yescharacteristic
181#892—64no—
182D3×C4⋊C4—38no—
183D3×C4⋊C4—38no—
184#872—64no—
185#872—64no—
186#872—64no—
187C3×#95—21no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95C2×D311yescharacteristic
193C3×#95C2×D311yescharacteristic
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
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—61no—
209C3⋊#95—61no—
210C3⋊#95—61no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C23×C32C2411yescharacteristic
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3C22×C412yes—
221C22×C3⋊D3C2×D412yes—
222C22×C3⋊D3#4112yes—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4C22×C412yes—
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⋊Dic3—21no—
240C2×C3⋊Dic3C22×C412yes—
241C4×C3⋊D3—28no—
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×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C22×C412yes—
259C2×C3×Dic3C22×C412yes—
260C2×C3×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C2×D412yes—
263C2×C3×Dic3C2×D412yes—
264C2×C3×Dic3#4112yes—
265C2×C3×Dic3#4112yes—
266#624—28no—
267#624—28no—
268C2×#117—91no—
269C2×#117—91no—
270C22×C4⋊C4—91no—
271#389—91no—
272#389—91no—
273#387—31no—
274#387—91no—
275#387—91no—
276#387—91no—
277#381—91no—
278#381—91no—
279#380—91no—
280C4×C4⋊C4—31no—
281C4×C4⋊C4—91no—
282C4×C22⋊C4—91no—
283C23×D3—31no—
284C23×D3—31no—
285C23×D3—61no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C2×C4×D3—34no—
321C2×C4×D3—34no—
322C2×C4×D3—34no—
323C2×C4×D3—34no—
324C2×C4×D3—34no—
325C2×C4×D3—34no—
326C2×C4×D3—64no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C2×C4×D3—62no—
339C2×C4×D3—122no—
340C2×C4×D3—122no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C42—62no—
346C3×C42—62no—
347C3×C42—62no—
348C3×C42—62no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—122no—
358(C2×D3)⋊C4—122no—
359C4⋊Dic3—34no—
360C4⋊Dic3—34no—
361C4⋊Dic3—62no—
362C4⋊Dic3—62no—
363Dic3⋊C4—22no—
364Dic3⋊C4—22no—
365Dic3⋊C4—34no—
366Dic3⋊C4—34no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4C4×D314yes—
374Dic3⋊C4C4×D314yes—
375C4×Dic3—22no—
376C4×Dic3—22no—
377C4×Dic3—22no—
378C4×Dic3—22no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C22×C32C23×C411yescharacteristic
384C22×C32C22×D411yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C22×C32C2×#4111yescharacteristic
388C22×C322−1+411yescharacteristic
389C22×C322−1+411yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—22no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3C4×D414yes—
397C32×C4—22no—
398C32×C4—41no—
399C32×C4—41no—
400C3⋊Dic3—22no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3#11714yescomplemented
411C23×C4—91no—
412C23×C4—91no—
413C23×C4—91no—
414#117—184no—
415#117—184no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—98no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C4⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C22⋊C4—91no—
429C2×C22⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C42—31no—
432C2×C42—31no—
433C2×C42—31no—
434C2×C42—31no—
435C2×C42—91no—
436C2×C42—91no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95—31no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95—91no—
446#95—91no—
447#95—91no—
448#95D3211yescharacteristic
449C23×C3—21no—
450C23×C3C23×D311yescharacteristic
451C23×C3C23×D311yescharacteristic
452C22×D3—32no—
453C22×D3—32no—
454C22×D3—32no—
455C22×D3—32no—
456C22×D3—32no—
457C22×D3—32no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—121no—
470C22×D3—121no—
471C22×D3—121no—
472C22×D3—121no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4C2×C4×D312yes—
523C2×C3×C4C2×C4×D312yes—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3C2×C4×D312yes—
568C2×Dic3C2×C4×D312yes—
569C2×Dic3C2×C4×D312yes—
570C2×Dic3C2×C4×D312yes—
571C2×Dic3#23512yes—
572C2×Dic3#23512yes—
573C2×Dic3D3×D412yes—
574C2×Dic3D3×D412yes—
575C4×D3—68no—
576C4×D3—68no—
577C4×D3—68no—
578C4×D3—68no—
579C4×D3—68no—
580C4×D3—68no—
581C4×D3—128no—
582C2×C32C2×#11711yescharacteristic
583C2×C32C2×C4×D411yescharacteristic
584C2×C32#51911yescharacteristic
585C2×C32#54711yescharacteristic
586C2×C32#54711yescharacteristic
587C2×C32#55211yescharacteristic
588C2×C32#55211yescharacteristic
589C3⋊D3—24no—
590C24—91no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—94no—
600C22×C4—94no—
601C22×C4—91no—
602C22×C4—94no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—182no—
606C22×C4—182no—
607C22×C4—182no—
608C22×C4—182no—
609C22×C4—182no—
610C22×C4—182no—
611C22×C4C2×D3211yescharacteristic
612C22×C4C2×D3211yescharacteristic
613C22×C4C2×D3211yescharacteristic
614C4⋊C4—34no—
615C4⋊C4—34no—
616C4⋊C4—62no—
617C4⋊C4—62no—
618C4⋊C4—94no—
619C4⋊C4—94no—
620C4⋊C4—182no—
621C4⋊C4—182no—
622C4⋊C4—182no—
623C4⋊C4—182no—
624C22⋊C4—94no—
625C22⋊C4—182no—
626C22⋊C4—182no—
627C22⋊C4—182no—
628C42—62no—
629C42—62no—
630C42—62no—
631C42—62no—
632C42—182no—
633C42—182no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3C22×C4×D311yescharacteristic
642C22×C3C22×C4×D311yescharacteristic
643C22×C3C2×#23511yescharacteristic
644C22×C3C2×#23511yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C22×C3#100711yescharacteristic
648C22×C3#100711yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C22×C3D3×#4111yescharacteristic
651C22×C3D3×#4111yescharacteristic
652C22×C3D3×#4111yescharacteristic
653C22×C3#101011yescharacteristic
654C22×C3#101011yescharacteristic
655C2×D3—34no—
656C2×D3—34no—
657C2×D3—64no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—122no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—34no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—62no—
689C3×C4—81no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693Dic3—22no—
694Dic3—22no—
695Dic3—22no—
696Dic3—22no—
697Dic3—22no—
698Dic3—41no—
699Dic3—41no—
700Dic3—62no—
701Dic3—62no—
702Dic3—122no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—241no—
708Dic3—241no—
709Dic3#87214yescomplemented
710C32#234411yescharacteristic, complemented, Sylow
711C23—92no—
712C23—92no—
713C23—92no—
714C23—181no—
715C23—181no—
716C23—181no—
717C23—181no—
718C23C22×D3211yescharacteristic
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—92no—
752C2×C4—188no—
753C2×C4—188no—
754C2×C4—188no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4C4×D3212yes—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3C2×#87211yescharacteristic
772C2×C3#550711yescharacteristic
773C2×C3D3×#11711yescharacteristic
774C2×C3#552911yescharacteristic
775C2×C3C4×D3×D411yescharacteristic
776C2×C3C4×D3×D411yescharacteristic
777C2×C3#555111yescharacteristic
778C2×C3#557211yescharacteristic
779C2×C3#557211yescharacteristic
780C2×C3#558111yescharacteristic
781C2×C3#563111yescharacteristic
782C2×C3#565511yescharacteristic
783C2×C3#569311yescharacteristic
784C2×C3#570811yescharacteristic
785D3—64no—
786D3—64no—
787D3—124no—
788C22—94no—
789C22—182no—
790C22—182no—
791C22—182no—
792C22—182no—
793C22—182no—
794C22—182no—
795C22C2×C4×D3211yescharacteristic
796C22D3×#23511yescharacteristic
797C22D3×#23511yescharacteristic
798C22#6430911yescharacteristic
799C22D32×D411yescharacteristic
800C22#6431211yescharacteristic
801C22#6431611yescharacteristic
802C4—22no—
803C4—34no—
804C4—41no—
805C4—41no—
806C4—62no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—62no—
811C4—121no—
812C4—121no—
813C4—182no—
814C4—361no—
815C4—361no—
816C3—21no—
817C3#7376711yescharacteristic, complemented
818C3#7496111yescharacteristic, complemented
819C2—184no—
820C2D3×#87211yescharacteristic
821C2#1059402411yescharacteristic
822C2#1059418811yescharacteristic
823C2#1059425511yescharacteristic
824C2#1059434711yescharacteristic
825C2#1059434911yescharacteristic
826C2#1059451611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C3×#4652C2semidirect
6. C3×#4649C2semidirect
9. #10591331C2semidirect
10. #10591327C2semidirect
11. #10591250C2semidirect
12. #10591246C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
15. #10591201C2semidirect
41. #63883C4semidirect
84. #4652D3semidirect
85. #4649D3semidirect
410. C3×Dic3#117semidirect
709. Dic3#872semidirect
710. C32#2344semidirect
817. C3#73767semidirect
818. C3#74961semidirect

Maximal subgroups

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

subgroupindex
C2×#638832
C2×#638742
C2×#638362
#105923632
C3×#46522
C3×#46492
#105913712
#105913672
#105913312
#105913272
#105912502
#105912462
Dic3×Dic3⋊C42
#105912332
#105912012
#749613
#737673