Finite Group Databasebeta

← #13170765

Subgroups — #13170765

Order 1728.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89022C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723688C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723498C211yesmaximal, characteristic, complemented
6C3×#63904C211yesmaximal, characteristic, complemented
7C3×#63896C211yesmaximal, characteristic, complemented
8C3×#63879C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722966C211yesmaximal, characteristic, complemented
11#11722958C211yesmaximal, characteristic, complemented
12#11722949C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic, complemented
14#11722932C211yesmaximal, characteristic, complemented
15#11722918C211yesmaximal, characteristic, complemented
16#10595076—31nomaximal
17#10594623—31nomaximal
18#10594066—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic, complemented
22C2×C32×C4×D3C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic, complemented
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic, complemented
31#89022—24no—
32C2×C3×#626C2211yescharacteristic
33C2×C3×#625C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37D3×#624—24no—
38C3×#3752C2211yescharacteristic
39C3×#3750C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×Dic32C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3828—31no—
57C22×#624—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3799—31no—
62C2×#3799—61no—
63#64103—31no—
64#64091—31no—
65C3×C4×#67—31no—
66C3×C4×#67—31no—
67C3×#896—31no—
68C3×#893—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63983—31no—
72#63981—31no—
73#63978—31no—
74#63975—31no—
75#63971—31no—
76#63971—31no—
77#63952—31no—
78#63923—31no—
79#63923—31no—
80#63923—61no—
81#63922—31no—
82#63910—31no—
83#63906—31no—
84#63904—31no—
85#63904D311yescharacteristic, complemented
86C4×#626—31no—
87C4×#626—31no—
88#63897—31no—
89#63897—31no—
90#63897—61no—
91#63896—31no—
92#63896D311yescharacteristic, complemented
93#63894—31no—
94#63888—31no—
95#63887—31no—
96#63886—31no—
97#63880—31no—
98#63879D311yescharacteristic, complemented
99#63874—31no—
100#63854—31no—
101#63853—31no—
102#63836—31no—
103#63836—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×D3×C3⋊D3—22no—
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×C33×C4C2311yescharacteristic
113C4⋊(C3⋊(C3⋊D3))—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C3×#634—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×C4×D3—22no—
125#6294—22no—
126#6292—22no—
127#6291—22no—
128#6291—22no—
129#6291—22no—
130#6289—22no—
131#6289—22no—
132#6289D414yescomplemented
133C3×#626—22no—
134C3×#625—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5547—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C22×C32×C4—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149#3828—64no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—31no—
153C2×C4⋊(C3⋊D3)—31no—
154C2×C4⋊(C3⋊D3)—61no—
155C2×C4⋊(C3⋊D3)—61no—
156C2×C4⋊(C3⋊D3)—61no—
157C2×C4⋊(C3⋊D3)—121no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—31no—
160C2×C4×C3⋊D3—31no—
161C2×#634C2×D311yescharacteristic, complemented
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C2×C3×D12—31no—
168C2×C3×C4×D3—21no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3C2×D311yescharacteristic, complemented
174C2×C3×C4×D3C2×D311yescharacteristic, complemented
175C2×C3×Dic6—31no—
176C2×C3×Dic6—31no—
177C2×C3×Dic6—61no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—61no—
187C2×#626—61no—
188C2×#626—61no—
189C2×#626—61no—
190C2×#626C2×D311yescharacteristic
191C2×#625C2×D311yescharacteristic
192C2×#624—31no—
193C2×#624—31no—
194C2×#624—31no—
195C2×#624—31no—
196C2×#624—31no—
197C2×#624—31no—
198C2×#624—31no—
199C2×#624—64no—
200C2×#624—61no—
201C2×#624—61no—
202C2×#624—61no—
203C2×#624C2×D311yescharacteristic
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3C2×D311yescharacteristic
207C2×D3×Dic3C2×D311yescharacteristic
208C4×D32—64no—
209C4×D32—64no—
210#3799—64no—
211#3799—64no—
212#3799—68no—
213C32×C4⋊C4—31no—
214C32×C22⋊C4—31no—
215#3752—31no—
216#3752—31no—
217#3752—31no—
218#3752—31no—
219#3752C2×D311yescharacteristic
220#3750C2×D311yescharacteristic, complemented
221C3×#217—31no—
222C3×#217—31no—
223C3×#217—31no—
224C3×(C2×D3)⋊C4—21no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—61no—
231C3×(C2×D3)⋊C4C2×D311yescharacteristic
232C3×(C2×D3)⋊C4C2×D311yescharacteristic
233C3×C4⋊Dic3—31no—
234C3×Dic3⋊C4—21no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—61no—
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4C2×D311yescharacteristic, complemented
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247#3724—31no—
248#3724—31no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—61no—
265#3722—61no—
266#3722—61no—
267#3722—61no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273Dic32C2×D311yescharacteristic, complemented
274Dic32C2×D311yescharacteristic, complemented
275C22×C33C2411yescharacteristic
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)—21no—
278C2×C3⋊(C3⋊D3)—21no—
279C2×C3⋊(C3⋊D3)—21no—
280C2×C3⋊(C3⋊D3)—21no—
281C2×C3⋊(C3⋊D3)C2×D412yes—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3#4112yescomplemented
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3#4112yescomplemented
291D3×C3⋊D3—28no—
292C33×C4—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C3×C3⋊Dic3C2×D412yes—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3C2×D412yes—
302C2×#239—91no—
303C2×#235—91no—
304C2×#235—91no—
305C2×#235—181no—
306C22×C4×D3—91no—
307C22×C4×D3—91no—
308C22×C4×D3—91no—
309C3×C22⋊Q8—91no—
310C3×C4×D4—91no—
311C3×C4×D4—91no—
312#946—91no—
313#939—91no—
314#939—91no—
315#937—91no—
316#937—91no—
317#930—91no—
318C4×#67—31no—
319C4×#67—31no—
320C4×#67—91no—
321C4×#67—91no—
322#896—31no—
323#896—91no—
324#895—91no—
325#894—91no—
326#894—91no—
327#894—91no—
328#894—91no—
329#894—181no—
330#893—31no—
331#893—91no—
332#892—91no—
333#884—91no—
334#884—91no—
335#883—91no—
336#883—91no—
337#882—91no—
338#882—91no—
339#882—91no—
340#882—91no—
341#882—181no—
342#67⋊C4—31no—
343#67⋊C4—91no—
344#878—31no—
345#878—91no—
346C4×D12—91no—
347C4×D12—91no—
348#872—91no—
349#872—91no—
350C23×C32—31no—
351C23×C32—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—31no—
356C22×C3⋊D3—31no—
357C22×C3⋊D3—31no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—61no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—61no—
363C22×C3⋊D3—61no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—62no—
366C22×C3⋊D3—62no—
367C22×C3⋊D3—121no—
368C22×C3⋊D3—121no—
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—21no—
371C22×C3×D3—21no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—61no—
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C22×C3×D3C22×D311yescharacteristic
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—62no—
382C2×D32—62no—
383C2×D32—62no—
384C2×D32—62no—
385C2×D32—122no—
386C2×D32—122no—
387C2×D32—122no—
388C2×C32×C4—21no—
389C2×C32×C4—21no—
390C2×C32×C4—21no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—31no—
395C2×C32×C4—41no—
396C2×C32×C4—62no—
397C2×C32×C4C22×D311yescharacteristic
398C2×C32×C4C22×D311yescharacteristic
399C2×C32×C4C22×D311yescharacteristic
400#638—62no—
401#638—62no—
402#638—62no—
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—62no—
410C4⋊(C3⋊D3)—62no—
411C4⋊(C3⋊D3)—64no—
412C4⋊(C3⋊D3)—62no—
413C4⋊(C3⋊D3)—122no—
414C4⋊(C3⋊D3)—122no—
415C4⋊(C3⋊D3)—124no—
416C4×C3⋊D3—34no—
417C4×C3⋊D3—62no—
418C4×C3⋊D3—62no—
419#634—22no—
420C3×#67—62no—
421C3×#67—62no—
422C3×#67—62no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C3×D12—62no—
453C3×C4×D3—24no—
454C3×C4×D3—22no—
455C3×C4×D3—22no—
456C3×C4×D3—62no—
457C3×C4×D3—62no—
458C3×C4×D3—62no—
459C3×C4×D3—62no—
460C3×Dic6—62no—
461C3×Dic6—62no—
462C3×Dic6—64no—
463#626—22no—
464#626—62no—
465#626—62no—
466#626—62no—
467#626—62no—
468#626—62no—
469#626—62no—
470#626—64no—
471#626—64no—
472#626—62no—
473#626—62no—
474#626—122no—
475#626—122no—
476#625—22no—
477#624—22no—
478#624—34no—
479#624—34no—
480#624—64no—
481#624—62no—
482#624—62no—
483#624—64no—
484#624—62no—
485#624—62no—
486#624—62no—
487#624—122no—
488D3×Dic3—22no—
489D3×Dic3—22no—
490D3×Dic3—62no—
491D3×Dic3—62no—
492#525—271noSylow
493C2×C33C22×D411yescharacteristic
494C2×C33C2×#4111yescharacteristic
495C2×C33C2×#4111yescharacteristic
496C3⋊(C3⋊D3)—22no—
497C3⋊(C3⋊D3)—41no—
498C3×C3⋊D3—22no—
499C32×D3—22no—
500C32×D3—41no—
501C23×D3—91no—
502C23×D3—91no—
503C23×D3—91no—
504C23×D3—181no—
505C2×C3×Q8—91no—
506C2×C3×D4—91no—
507C2×C3×D4—91no—
508C22×C3×C4—31no—
509C22×C3×C4—31no—
510C22×C3×C4—61no—
511C22×C3×C4—91no—
512C22×C3×C4—91no—
513C22×C3×C4—91no—
514C2×#67—31no—
515C2×#67—31no—
516C2×#67—31no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—91no—
522C2×#67—91no—
523C2×#67—91no—
524C2×#67—181no—
525C2×#67—181no—
526C2×#67—181no—
527C22×Dic3—31no—
528C22×Dic3—31no—
529C22×Dic3—91no—
530#239—184no—
531#235—184no—
532#235—184no—
533#235—188no—
534C2×D12—31no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—91no—
538C2×D12—91no—
539C2×D12—91no—
540C2×D12—91no—
541C2×D12—91no—
542C2×D12—91no—
543C2×D12—181no—
544C2×D12—181no—
545C2×D12—181no—
546C2×D12—181no—
547C2×D12—361no—
548C2×C4×D3—31no—
549C2×C4×D3—31no—
550C2×C4×D3—31no—
551C2×C4×D3—31no—
552C2×C4×D3—91no—
553C2×C4×D3—91no—
554C2×C4×D3—91no—
555C2×C4×D3—91no—
556C2×C4×D3—91no—
557C2×C4×D3—91no—
558C2×C4×D3—91no—
559C2×C4×D3—91no—
560C2×C4×D3—91no—
561C2×C4×D3—91no—
562C2×C4×D3—91no—
563C2×C4×D3—181no—
564C2×C4×D3—181no—
565C2×C4×D3—181no—
566C2×C4×D3—184no—
567C2×C4×D3—184no—
568C2×C4×D3—184no—
569C2×C4×D3D3211yescharacteristic, complemented
570C2×Dic6—31no—
571C2×Dic6—31no—
572C2×Dic6—61no—
573C3×C4⋊C4—31no—
574C3×C4⋊C4—31no—
575C3×C4⋊C4—61no—
576C3×C4⋊C4—91no—
577C3×C4⋊C4—91no—
578C3×C4⋊C4—91no—
579C3×C22⋊C4—31no—
580C3×C22⋊C4—31no—
581C3×C22⋊C4—61no—
582C3×C22⋊C4—91no—
583C3×C22⋊C4—91no—
584C3×C22⋊C4—91no—
585C3×C22⋊C4—91no—
586C3×C42—91no—
587C3×C42—91no—
588#217—31no—
589#217—31no—
590#217—31no—
591#217—91no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—31no—
596(C2×D3)⋊C4—31no—
597(C2×D3)⋊C4—61no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—91no—
607(C2×D3)⋊C4—91no—
608(C2×D3)⋊C4—91no—
609(C2×D3)⋊C4—91no—
610(C2×D3)⋊C4—91no—
611(C2×D3)⋊C4—91no—
612(C2×D3)⋊C4—181no—
613(C2×D3)⋊C4—181no—
614(C2×D3)⋊C4—181no—
615(C2×D3)⋊C4—181no—
616(C2×D3)⋊C4D3211yescharacteristic
617C4⋊Dic3—31no—
618C4⋊Dic3—91no—
619C4⋊Dic3—91no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—31no—
624Dic3⋊C4—31no—
625Dic3⋊C4—61no—
626Dic3⋊C4—91no—
627Dic3⋊C4—91no—
628Dic3⋊C4—91no—
629Dic3⋊C4—91no—
630Dic3⋊C4D3211yescharacteristic, complemented
631C4×Dic3—31no—
632C4×Dic3—31no—
633C4×Dic3—31no—
634C4×Dic3—31no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—32no—
639C22×C32—41no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—61no—
645C22×C32C23×D311yescharacteristic
646C22×C32C23×D311yescharacteristic
647C22×C32C23×D311yescharacteristic
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—32no—
651C2×C3⋊D3—32no—
652C2×C3⋊D3—32no—
653C2×C3⋊D3—62no—
654C2×C3⋊D3—62no—
655C2×C3⋊D3—62no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—68no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—61no—
661C2×C3⋊D3—61no—
662C2×C3⋊D3—61no—
663C2×C3⋊D3—61no—
664C2×C3⋊D3—62no—
665C2×C3⋊D3—61no—
666C2×C3⋊D3—61no—
667C2×C3⋊D3—61no—
668C2×C3⋊D3—61no—
669C2×C3⋊D3—61no—
670C2×C3⋊D3—61no—
671C2×C3⋊D3—61no—
672C2×C3⋊D3—61no—
673C2×C3⋊D3—122no—
674C2×C3⋊D3—121no—
675C2×C3⋊D3—121no—
676C2×C3⋊D3—122no—
677C2×C3⋊D3—121no—
678C2×C3⋊D3—121no—
679C2×C3⋊D3—121no—
680C2×C3⋊D3—121no—
681C2×C3⋊D3—121no—
682C2×C3⋊D3—121no—
683C2×C3⋊D3—121no—
684C2×C3⋊D3—121no—
685C2×C3⋊D3—121no—
686C2×C3⋊D3—121no—
687C2×C3⋊D3—121no—
688C2×C3⋊D3—121no—
689C2×C3⋊D3—241no—
690C2×C3⋊D3—241no—
691C2×C3⋊D3—241no—
692C2×C3⋊D3—241no—
693C2×C3⋊D3#23512yescomplemented
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—22no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—21no—
702C2×C3×D3—21no—
703C2×C3×D3—21no—
704C2×C3×D3—21no—
705C2×C3×D3—22no—
706C2×C3×D3—32no—
707C2×C3×D3—32no—
708C2×C3×D3—41no—
709C2×C3×D3—41no—
710C2×C3×D3—41no—
711C2×C3×D3—41no—
712C2×C3×D3—62no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—121no—
718C2×C3×D3—121no—
719C2×C3×D3#23512yescomplemented
720C2×C3×D3#23912yescomplemented
721D32—68no—
722D32—68no—
723D32—128no—
724C32×C4—21no—
725C32×C4—22no—
726C32×C4—21no—
727C32×C4—21no—
728C32×C4—32no—
729C32×C4—41no—
730C32×C4—41no—
731C32×C4—42no—
732C32×C4—61no—
733C32×C4—61no—
734C32×C4—61no—
735C3⋊Dic3—21no—
736C3⋊Dic3—21no—
737C3⋊Dic3—21no—
738C3⋊Dic3—21no—
739C3⋊Dic3D3×D412yes—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—22no—
747C3×Dic3—32no—
748C3×Dic3—32no—
749C3×Dic3—41no—
750C3×Dic3—41no—
751C3×Dic3—41no—
752C3×Dic3—62no—
753C3×Dic3—62no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—61no—
758C3×Dic3—61no—
759C3×Dic3—61no—
760C3×Dic3—61no—
761C3×Dic3—61no—
762C3×Dic3—121no—
763C3×Dic3—121no—
764C3×Dic3—121no—
765C3×Dic3D3×D412yes—
766C3×Dic3D3×D412yes—
767C2×#41—271no—
768C23×C4—271no—
769#123—271no—
770#123—271no—
771C22⋊Q8—91no—
772C22⋊Q8—271no—
773#121—271no—
774#121—271no—
775#120—271no—
776#120—271no—
777C4×D4—91no—
778C4×D4—91no—
779C4×D4—271no—
780C4×D4—271no—
781#117—271no—
782C33#52511yescharacteristic, complemented, Sylow
783C23×C3—31no—
784C23×C3—31no—
785C23×C3—31no—
786C23×C3—31no—
787C23×C3—61no—
788C23×C3—61no—
789C23×C3—91no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—61no—
793C22×D3—91no—
794C22×D3—91no—
795C22×D3—91no—
796C22×D3—91no—
797C22×D3—91no—
798C22×D3—91no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—181no—
802C22×D3—181no—
803C22×D3—181no—
804C22×D3—181no—
805C22×D3—182no—
806C22×D3—182no—
807C22×D3—182no—
808C22×D3—182no—
809C22×D3—182no—
810C22×D3—182no—
811C22×D3—182no—
812C22×D3—182no—
813C22×D3—182no—
814C22×D3—361no—
815C22×D3—361no—
816C22×D3—362no—
817C22×D3—362no—
818C22×D3—362no—
819C22×D3C2×D3211yescharacteristic
820C22×D3C2×D3211yescharacteristic
821C3×Q8—182no—
822C3×D4—182no—
823C3×D4—182no—
824C2×C3×C4—21no—
825C2×C3×C4—21no—
826C2×C3×C4—21no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—31no—
835C2×C3×C4—41no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—61no—
839C2×C3×C4—61no—
840C2×C3×C4—62no—
841C2×C3×C4—62no—
842C2×C3×C4—64no—
843C2×C3×C4—91no—
844C2×C3×C4—91no—
845C2×C3×C4—91no—
846C2×C3×C4—91no—
847C2×C3×C4—91no—
848C2×C3×C4—182no—
849C2×C3×C4—182no—
850C2×C3×C4—182no—
851C2×C3×C4C2×D3211yescharacteristic
852C2×C3×C4C2×D3211yescharacteristic
853C2×C3×C4C2×D3211yescharacteristic
854#67—62no—
855#67—62no—
856#67—62no—
857#67—182no—
858#67—182no—
859#67—182no—
860#67—182no—
861#67—182no—
862#67—182no—
863#67—182no—
864#67—184no—
865#67—184no—
866#67—362no—
867C2×Dic3—31no—
868C2×Dic3—31no—
869C2×Dic3—31no—
870C2×Dic3—31no—
871C2×Dic3—31no—
872C2×Dic3—31no—
873C2×Dic3—31no—
874C2×Dic3—31no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—61no—
878C2×Dic3—61no—
879C2×Dic3—61no—
880C2×Dic3—61no—
881C2×Dic3—61no—
882C2×Dic3—62no—
883C2×Dic3—62no—
884C2×Dic3—182no—
885C2×Dic3C2×D3211yescharacteristic
886C2×Dic3C2×D3211yescharacteristic
887C2×Dic3C2×D3211yescharacteristic
888C2×Dic3C2×D3211yescharacteristic
889D12—62no—
890D12—182no—
891D12—182no—
892D12—182no—
893D12—184no—
894D12—182no—
895D12—182no—
896D12—182no—
897D12—182no—
898D12—182no—
899D12—362no—
900D12—362no—
901D12—364no—
902D12—362no—
903C4×D3—22no—
904C4×D3—62no—
905C4×D3—62no—
906C4×D3—62no—
907C4×D3—62no—
908C4×D3—94no—
909C4×D3—94no—
910C4×D3—94no—
911C4×D3—184no—
912C4×D3—182no—
913C4×D3—182no—
914C4×D3—182no—
915C4×D3—182no—
916C4×D3—182no—
917C4×D3—182no—
918C4×D3—184no—
919C4×D3—182no—
920C4×D3—182no—
921C4×D3—362no—
922Dic6—62no—
923Dic6—62no—
924Dic6—64no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—21no—
929C2×C32—21no—
930C2×C32—21no—
931C2×C32—21no—
932C2×C32—21no—
933C2×C32—21no—
934C2×C32—41no—
935C2×C32—41no—
936C2×C32—41no—
937C2×C32—62no—
938C2×C32—121no—
939C2×C32C2×#23511yescharacteristic
940C2×C32C2×#23511yescharacteristic
941C2×C32C2×D3×D411yescharacteristic
942C2×C32C2×D3×D411yescharacteristic
943C2×C32C2×D3×D411yescharacteristic
944C2×C32C2×#23911yescharacteristic
945C2×C32D3×#4111yescharacteristic
946C2×C32D3×#4111yescharacteristic
947C2×C32D3×#4111yescharacteristic
948C3⋊D3—22no—
949C3⋊D3—62no—
950C3⋊D3—62no—
951C3⋊D3—62no—
952C3⋊D3—122no—
953C3⋊D3—122no—
954C3⋊D3—122no—
955C3⋊D3—121no—
956C3⋊D3—122no—
957C3⋊D3—121no—
958C3⋊D3—121no—
959C3⋊D3—242no—
960C3⋊D3—241no—
961C3⋊D3—241no—
962C3⋊D3—242no—
963C3×D3—22no—
964C3×D3—22no—
965C3×D3—42no—
966C3×D3—42no—
967C3×D3—41no—
968C3×D3—41no—
969C3×D3—62no—
970C3×D3—62no—
971C3×D3—122no—
972C24—271no—
973#41—544no—
974C2×Q8—91no—
975C2×D4—91no—
976C2×D4—91no—
977C2×D4—271no—
978C2×D4—271no—
979C2×D4—271no—
980C2×D4—271no—
981C2×D4—271no—
982C22×C4—31no—
983C22×C4—91no—
984C22×C4—91no—
985C22×C4—91no—
986C22×C4—271no—
987C22×C4—271no—
988C22×C4—271no—
989C22×C4—271no—
990C22×C4—544no—
991C4⋊C4—31no—
992C4⋊C4—91no—
993C4⋊C4—91no—
994C4⋊C4—91no—
995C4⋊C4—271no—
996C4⋊C4—271no—
997C22⋊C4—31no—
998C22⋊C4—91no—
999C22⋊C4—91no—
1000C22⋊C4—91no—
1001C22⋊C4—91no—
1002C22⋊C4—271no—
1003C22⋊C4—271no—
1004C22⋊C4—271no—
1005C22⋊C4—271no—
1006C22⋊C4—271no—
1007C42—91no—
1008C42—91no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—32no—
1013C22×C3—32no—
1014C22×C3—41no—
1015C22×C3—62no—
1016C22×C3—62no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—61no—
1021C22×C3—61no—
1022C22×C3—61no—
1023C22×C3—61no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—92no—
1028C22×C3—121no—
1029C22×C3—121no—
1030C22×C3—121no—
1031C22×C3—121no—
1032C22×C3—181no—
1033C22×C3—181no—
1034C22×C3C22×D3211yescharacteristic
1035C22×C3C22×D3211yescharacteristic
1036C22×C3C22×D3211yescharacteristic
1037C2×D3—21no—
1038C2×D3—21no—
1039C2×D3—21no—
1040C2×D3—21no—
1041C2×D3—21no—
1042C2×D3—32no—
1043C2×D3—32no—
1044C2×D3—62no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—92no—
1050C2×D3—92no—
1051C2×D3—92no—
1052C2×D3—121no—
1053C2×D3—121no—
1054C2×D3—182no—
1055C2×D3—182no—
1056C2×D3—182no—
1057C2×D3—188no—
1058C2×D3—188no—
1059C2×D3—188no—
1060C2×D3—181no—
1061C2×D3—181no—
1062C2×D3—181no—
1063C2×D3—181no—
1064C2×D3—181no—
1065C2×D3—181no—
1066C2×D3—182no—
1067C2×D3—181no—
1068C2×D3—181no—
1069C2×D3—181no—
1070C2×D3—181no—
1071C2×D3—181no—
1072C2×D3—181no—
1073C2×D3—181no—
1074C2×D3—181no—
1075C2×D3—181no—
1076C2×D3—362no—
1077C2×D3—368no—
1078C2×D3—361no—
1079C2×D3—361no—
1080C2×D3—361no—
1081C2×D3—361no—
1082C2×D3—361no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—361no—
1087C2×D3—361no—
1088C2×D3—361no—
1089C2×D3—361no—
1090C2×D3—361no—
1091C2×D3—361no—
1092C2×D3—362no—
1093C2×D3—721no—
1094C2×D3—721no—
1095C2×D3—721no—
1096C2×D3—721no—
1097C2×D3#379912yescomplemented
1098C3×C4—22no—
1099C3×C4—21no—
1100C3×C4—21no—
1101C3×C4—21no—
1102C3×C4—32no—
1103C3×C4—32no—
1104C3×C4—41no—
1105C3×C4—41no—
1106C3×C4—42no—
1107C3×C4—62no—
1108C3×C4—61no—
1109C3×C4—61no—
1110C3×C4—61no—
1111C3×C4—61no—
1112C3×C4—61no—
1113C3×C4—61no—
1114C3×C4—92no—
1115C3×C4—121no—
1116C3×C4—121no—
1117C3×C4—121no—
1118C3×C4—181no—
1119C3×C4—181no—
1120C3×C4—181no—
1121C3×C4—181no—
1122Dic3—21no—
1123Dic3—21no—
1124Dic3—21no—
1125Dic3—32no—
1126Dic3—32no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—61no—
1130Dic3—61no—
1131Dic3—61no—
1132Dic3—61no—
1133Dic3—61no—
1134Dic3—61no—
1135Dic3—61no—
1136Dic3—61no—
1137Dic3—121no—
1138Dic3—121no—
1139Dic3—121no—
1140Dic3#381112yes—
1141C32—21no—
1142C32—21no—
1143C32—21no—
1144C32—41no—
1145C32#554711yescharacteristic, complemented
1146C32#554711yescharacteristic, complemented
1147C32#562711yescharacteristic, complemented
1148C23—31no—
1149C23—31no—
1150C23—91no—
1151C23—271no—
1152C23—271no—
1153C23—542no—
1154C23—542no—
1155C23—542no—
1156Q8—182no—
1157D4—182no—
1158D4—182no—
1159D4—542no—
1160D4—542no—
1161D4—542no—
1162D4—542no—
1163D4—542no—
1164C2×C4—31no—
1165C2×C4—31no—
1166C2×C4—31no—
1167C2×C4—31no—
1168C2×C4—62no—
1169C2×C4—91no—
1170C2×C4—91no—
1171C2×C4—91no—
1172C2×C4—91no—
1173C2×C4—91no—
1174C2×C4—182no—
1175C2×C4—182no—
1176C2×C4—182no—
1177C2×C4—274no—
1178C2×C4—542no—
1179C2×C4—542no—
1180C2×C4—542no—
1181C2×C4D3311yescharacteristic
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—21no—
1186C2×C3—21no—
1187C2×C3—21no—
1188C2×C3—21no—
1189C2×C3—21no—
1190C2×C3—21no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—41no—
1194C2×C3—62no—
1195C2×C3—62no—
1196C2×C3—122no—
1197C2×C3—122no—
1198C2×C3—121no—
1199C2×C3—121no—
1200C2×C3—182no—
1201C2×C3C2×#379911yescharacteristic
1202C2×C3D3×#23511yescharacteristic
1203C2×C3D3×#23511yescharacteristic
1204C2×C3D3×#23511yescharacteristic
1205C2×C3D32×D411yescharacteristic
1206C2×C3D32×D411yescharacteristic
1207C2×C3#6431211yescharacteristic
1208C2×C3D3×#23911yescharacteristic
1209C2×C3C2×#381111yescharacteristic
1210D3—22no—
1211D3—41no—
1212D3—62no—
1213D3—62no—
1214D3—122no—
1215D3—182no—
1216D3—182no—
1217D3—182no—
1218D3—362no—
1219D3—362no—
1220D3—362no—
1221D3—362no—
1222D3—361no—
1223D3—361no—
1224D3—361no—
1225D3—722no—
1226D3—721no—
1227D3—721no—
1228D3—722no—
1229C22—32no—
1230C22—61no—
1231C22—61no—
1232C22—61no—
1233C22—61no—
1234C22—61no—
1235C22—92no—
1236C22—181no—
1237C22—181no—
1238C22—272no—
1239C22—548no—
1240C22—541no—
1241C22—541no—
1242C22—541no—
1243C22—541no—
1244C22—541no—
1245C22C2×D3311yescharacteristic
1246C4—21no—
1247C4—32no—
1248C4—61no—
1249C4—61no—
1250C4—61no—
1251C4—92no—
1252C4—181no—
1253C4—181no—
1254C4—181no—
1255C4—181no—
1256C3—21no—
1257C3—21no—
1258C3—21no—
1259C3—41no—
1260C3#1059406611yescharacteristic, complemented
1261C3#1059462311yescharacteristic, complemented
1262C3#1059507611yescharacteristic, complemented
1263C2—62no—
1264C2—121no—
1265C2—182no—
1266C2—542no—
1267C2—1081no—
1268C2D3×#379911yescharacteristic
1269C2#1172438811yescharacteristic
1270C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89022C2semidirect
2. C2×D3×#624C2semidirect
3. #11723688C2semidirect
4. #11723542C2semidirect
5. #11723498C2semidirect
6. C3×#63904C2semidirect
7. C3×#63896C2semidirect
8. C3×#63879C2semidirect
9. #11722996C2semidirect
10. #11722966C2semidirect
11. #11722958C2semidirect
12. #11722949C2semidirect
13. #11722933C2semidirect
14. #11722932C2semidirect
15. #11722918C2semidirect
21. C2×C3×#634C22semidirect
22. C2×C32×C4×D3C22semidirect
27. C2×#6291C22semidirect
30. C2×#6289C22semidirect
39. C3×#3750C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×Dic32C22semidirect
55. C3×Dic32C22semidirect
85. #63904D3semidirect
92. #63896D3semidirect
98. #63879D3semidirect
132. #6289D4semidirect
161. C2×#634C2×D3semidirect
173. C2×C3×C4×D3C2×D3semidirect
174. C2×C3×C4×D3C2×D3semidirect
220. #3750C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
242. C3×Dic3⋊C4C2×D3semidirect
249. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
274. Dic32C2×D3semidirect
284. C2×C3×C3⋊D3#41semidirect
290. C2×C32×D3#41semidirect
569. C2×C4×D3D32semidirect
630. Dic3⋊C4D32semidirect
693. C2×C3⋊D3#235semidirect
719. C2×C3×D3#235semidirect
720. C2×C3×D3#239semidirect
782. C33#525semidirect
1097. C2×D3#3799semidirect
1145. C32#5547semidirect
1146. C32#5547semidirect
1147. C32#5627semidirect
1260. C3#10594066semidirect
1261. C3#10594623semidirect
1262. C3#10595076semidirect

Maximal subgroups

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

subgroupindex
C2×#890222
C2×D3×#6242
#117236882
#117235422
#117234982
C3×#639042
C3×#638962
C3×#638792
#117229962
#117229662
#117229582
#117229492
#117229332
#117229322
#117229182
#105950763
#105946233
#105940663