Finite Group Databasebeta

← #13170766

Subgroups — #13170766

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×#89018C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723684C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723498C211yesmaximal, characteristic, complemented
6C3×#63888C211yesmaximal, characteristic, complemented
7C3×#63887C211yesmaximal, characteristic, complemented
8C3×#63881C211yesmaximal, characteristic, complemented
9#11723000C211yesmaximal, characteristic, complemented
10#11722961C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722950C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14#11722935C211yesmaximal, characteristic, complemented
15#11722920C211yesmaximal, characteristic, complemented
16#10595430—31nomaximal
17#10594623—31nomaximal
18#10594066—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×Dic6C2211yescharacteristic, complemented
23C2×#6295C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic, complemented
28C2×#6291C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32#89018—24no—
33C2×C3×#626C2211yescharacteristic
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#88814C2211yescharacteristic, complemented
43#88813C2211yescharacteristic, complemented
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3832—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×#946—31no—
66C3×#946—31no—
67C3×#896—31no—
68C3×#893—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63981—31no—
72#63978—31no—
73#63952—31no—
74#63923—31no—
75#63923—31no—
76#63923—31no—
77#63923—61no—
78#63922—31no—
79#63910—31no—
80#63909—31no—
81#63909—31no—
82#63906—31no—
83#63904—31no—
84#63904—31no—
85#63897—31no—
86#63897—31no—
87#63897—31no—
88#63897—61no—
89#63894—31no—
90#63888D311yescharacteristic, complemented
91#63887D311yescharacteristic, complemented
92#63886—31no—
93#63881—31no—
94#63881—31no—
95#63881—31no—
96#63881D311yescharacteristic, complemented
97#63880—31no—
98#63879—31no—
99#63854—31no—
100#63853—31no—
101#63849—31no—
102#63836—31no—
103#63836—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊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
118C3×C4×C3⋊D3—22no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×Dic6—22no—
125#6295—22no—
126#6294—22no—
127#6292—22no—
128#6292—22no—
129#6292—22no—
130#6291—22no—
131#6289—22no—
132#6289—22no—
133#6289D414yescomplemented
134C3×#626—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5627—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×C32×Q8—31no—
146C2×#638—31no—
147#3832—64no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
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×C4×C3⋊D3C2×D311yescharacteristic, complemented
162C2×C3×#67—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C2×C3×D12—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—61no—
173C2×C3×Dic6—21no—
174C2×C3×Dic6C2×D311yescharacteristic, complemented
175C2×C3×Dic6C2×D311yescharacteristic, complemented
176C2×#626—31no—
177C2×#626—31no—
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×#625—31no—
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×(C2×D3)⋊C4—21no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
235C3×C4⋊Dic3—31no—
236C3×Dic3⋊C4—21no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×Dic3⋊C4C2×D311yescharacteristic, complemented
246C3×Dic3⋊C4C2×D311yescharacteristic, complemented
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3C2×D311yescharacteristic, complemented
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252Dic3⋊Dic3C2×D311yescharacteristic, complemented
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—61no—
263#3722—61no—
264#3722—61no—
265#3722—61no—
266#3722C2×D311yescharacteristic
267#3722C2×D311yescharacteristic, complemented
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271Dic32—31no—
272Dic32—31no—
273Dic32—31no—
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—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3#4112yescomplemented
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⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3C2×D412yes—
302C2×#239—91no—
303C2×#239—91no—
304C2×#239—181no—
305C2×#235—91no—
306C22×C4×D3—91no—
307C22×C4×D3—91no—
308C22×C4×D3—91no—
309C3×C22⋊Q8—91no—
310C3×C22⋊Q8—91no—
311C3×C4×D4—91no—
312#946—31no—
313#946—31no—
314#939—91no—
315#937—91no—
316#930—91no—
317#930—91no—
318C4×#67—91no—
319C4×#67—91no—
320#896—31no—
321#895—91no—
322#895—91no—
323#894—91no—
324#894—91no—
325#894—91no—
326#894—91no—
327#894—91no—
328#894—181no—
329#893—31no—
330#893—91no—
331#893—91no—
332#893—91no—
333#892—91no—
334#892—91no—
335#884—91no—
336#883—91no—
337#882—91no—
338#882—91no—
339#882—91no—
340#882—91no—
341#882—91no—
342#882—181no—
343#67⋊C4—31no—
344#67⋊C4—91no—
345#67⋊C4—91no—
346#67⋊C4—91no—
347#878—31no—
348C4×D12—91no—
349#872—91no—
350C23×C32—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—31no—
356C22×C3⋊D3—31no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—61no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—61no—
363C22×C3⋊D3—62no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—62no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3—121no—
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—21no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—61no—
376C22×C3×D3—61no—
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—
388C32×Q8—62no—
389C2×C32×C4—21no—
390C2×C32×C4—21no—
391C2×C32×C4—21no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—31no—
395C2×C32×C4—31no—
396C2×C32×C4—31no—
397C2×C32×C4—41no—
398C2×C32×C4C22×D311yescharacteristic
399C2×C32×C4C22×D311yescharacteristic
400C2×C32×C4C22×D311yescharacteristic
401#638—62no—
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C4⋊(C3⋊D3)—62no—
407C4⋊(C3⋊D3)—62no—
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—22no—
417C4×C3⋊D3—34no—
418C4×C3⋊D3—62no—
419C4×C3⋊D3—62no—
420C3×#67—62no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—31no—
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—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—62no—
439C2×C3×Dic3—62no—
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C3×D12—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×C4×D3—62no—
455C3×C4×D3—64no—
456C3×C4×D3—62no—
457C3×C4×D3—62no—
458C3×Dic6—24no—
459C3×Dic6—22no—
460C3×Dic6—22no—
461#626—22no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—62no—
466#626—64no—
467#626—64no—
468#626—62no—
469#626—62no—
470#626—62no—
471#626—62no—
472#626—62no—
473#626—62no—
474#626—122no—
475#626—122no—
476#625—62no—
477#624—22no—
478#624—34no—
479#624—34no—
480#624—64no—
481#624—62no—
482#624—62no—
483#624—62no—
484#624—62no—
485#624—64no—
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—
499C3×C3⋊D3—41no—
500C32×D3—22no—
501C23×D3—91no—
502C23×D3—91no—
503C23×D3—91no—
504C23×D3—181no—
505C2×C3×Q8—31no—
506C2×C3×Q8—31no—
507C2×C3×Q8—61no—
508C2×C3×D4—91no—
509C22×C3×C4—91no—
510C22×C3×C4—91no—
511C22×C3×C4—91no—
512C22×C3×C4—91no—
513C2×#67—31no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—181no—
522C22×Dic3—31no—
523C22×Dic3—31no—
524C22×Dic3—91no—
525#239—184no—
526#239—184no—
527#239—188no—
528#235—184no—
529C2×D12—31no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—91no—
538C2×D12—91no—
539C2×D12—91no—
540C2×D12—91no—
541C2×D12—181no—
542C2×D12—181no—
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—31no—
553C2×C4×D3—31no—
554C2×C4×D3—61no—
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—91no—
564C2×C4×D3—91no—
565C2×C4×D3—91no—
566C2×C4×D3—181no—
567C2×C4×D3—181no—
568C2×C4×D3—181no—
569C2×C4×D3—184no—
570C2×C4×D3—184no—
571C2×C4×D3—184no—
572C2×Dic6D3211yescharacteristic, complemented
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×C4⋊C4—91no—
580C3×C4⋊C4—91no—
581C3×C22⋊C4—31no—
582C3×C22⋊C4—31no—
583C3×C22⋊C4—61no—
584C3×C22⋊C4—91no—
585C3×C22⋊C4—91no—
586C3×C22⋊C4—91no—
587C3×C22⋊C4—91no—
588C3×C42—91no—
589#217—31no—
590#217—91no—
591(C2×D3)⋊C4—31no—
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—31no—
598(C2×D3)⋊C4—61no—
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—91no—
613(C2×D3)⋊C4—181no—
614(C2×D3)⋊C4—181no—
615(C2×D3)⋊C4—181no—
616(C2×D3)⋊C4—181no—
617(C2×D3)⋊C4D3211yescharacteristic
618C4⋊Dic3—31no—
619C4⋊Dic3—31no—
620C4⋊Dic3—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—31no—
624Dic3⋊C4—31no—
625Dic3⋊C4—31no—
626Dic3⋊C4—31no—
627Dic3⋊C4—31no—
628Dic3⋊C4—61no—
629Dic3⋊C4D3211yescharacteristic, complemented
630C4×Dic3—31no—
631C4×Dic3—31no—
632C4×Dic3—91no—
633C4×Dic3—91no—
634C4×Dic3—91no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—32no—
639C22×C32—41no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32C23×D311yescharacteristic
643C22×C32C23×D311yescharacteristic
644C22×C32C23×D311yescharacteristic
645C2×C3⋊D3—21no—
646C2×C3⋊D3—21no—
647C2×C3⋊D3—21no—
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#23912yescomplemented
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—22no—
699C2×C3×D3—32no—
700C2×C3×D3—32no—
701C2×C3×D3—41no—
702C2×C3×D3—41no—
703C2×C3×D3—62no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—62no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—121no—
716C2×C3×D3—121no—
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—
735C32×C4—61no—
736C3⋊Dic3—21no—
737C3⋊Dic3—21no—
738C3⋊Dic3—21no—
739C3⋊Dic3D3×D412yes—
740C3×Dic3—22no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—21no—
747C3×Dic3—21no—
748C3×Dic3—21no—
749C3×Dic3—22no—
750C3×Dic3—32no—
751C3×Dic3—32no—
752C3×Dic3—41no—
753C3×Dic3—41no—
754C3×Dic3—41no—
755C3×Dic3—62no—
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—91no—
773#121—271no—
774#121—271no—
775#120—271no—
776#120—271no—
777C4×D4—91no—
778C4×D4—271no—
779C4×D4—271no—
780C4×D4—271no—
781#117—271no—
782C33#52511yescharacteristic, complemented, Sylow
783C23×C3—31no—
784C23×C3—31no—
785C23×C3—61no—
786C23×C3—91no—
787C23×C3—91no—
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—61no—
793C22×D3—61no—
794C22×D3—91no—
795C22×D3—91no—
796C22×D3—91no—
797C22×D3—91no—
798C22×D3—91no—
799C22×D3—91no—
800C22×D3—181no—
801C22×D3—181no—
802C22×D3—181no—
803C22×D3—181no—
804C22×D3—181no—
805C22×D3—181no—
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—182no—
815C22×D3—361no—
816C22×D3—361no—
817C22×D3—362no—
818C22×D3—362no—
819C22×D3—362no—
820C22×D3C2×D3211yescharacteristic
821C3×Q8—62no—
822C3×Q8—62no—
823C3×Q8—64no—
824C3×D4—182no—
825C2×C3×C4—21no—
826C2×C3×C4—21no—
827C2×C3×C4—21no—
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—31no—
836C2×C3×C4—31no—
837C2×C3×C4—31no—
838C2×C3×C4—41no—
839C2×C3×C4—61no—
840C2×C3×C4—61no—
841C2×C3×C4—61no—
842C2×C3×C4—61no—
843C2×C3×C4—61no—
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×C4—182no—
852C2×C3×C4C2×D3211yescharacteristic
853C2×C3×C4C2×D3211yescharacteristic
854C2×C3×C4C2×D3211yescharacteristic
855#67—62no—
856#67—182no—
857#67—182no—
858#67—182no—
859#67—182no—
860#67—182no—
861#67—182no—
862#67—182no—
863#67—362no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—31no—
867C2×Dic3—31no—
868C2×Dic3—31no—
869C2×Dic3—31no—
870C2×Dic3—31no—
871C2×Dic3—31no—
872C2×Dic3—61no—
873C2×Dic3—61no—
874C2×Dic3—61no—
875C2×Dic3—61no—
876C2×Dic3—62no—
877C2×Dic3—62no—
878C2×Dic3—182no—
879C2×Dic3C2×D3211yescharacteristic
880C2×Dic3C2×D3211yescharacteristic
881C2×Dic3C2×D3211yescharacteristic
882C2×Dic3C2×D3211yescharacteristic
883C2×Dic3C2×D3211yescharacteristic
884D12—62no—
885D12—182no—
886D12—182no—
887D12—182no—
888D12—184no—
889D12—182no—
890D12—182no—
891D12—182no—
892D12—182no—
893D12—182no—
894D12—182no—
895D12—184no—
896D12—184no—
897D12—182no—
898D12—182no—
899D12—362no—
900D12—362no—
901D12—364no—
902D12—362no—
903C4×D3—62no—
904C4×D3—62no—
905C4×D3—62no—
906C4×D3—62no—
907C4×D3—64no—
908C4×D3—62no—
909C4×D3—62no—
910C4×D3—94no—
911C4×D3—94no—
912C4×D3—94no—
913C4×D3—184no—
914C4×D3—182no—
915C4×D3—182no—
916C4×D3—182no—
917C4×D3—182no—
918C4×D3—182no—
919C4×D3—182no—
920C4×D3—182no—
921C4×D3—184no—
922C4×D3—182no—
923C4×D3—362no—
924Dic6—22no—
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×C32C2×#23511yescharacteristic
939C2×C32C2×D3×D411yescharacteristic
940C2×C32C2×D3×D411yescharacteristic
941C2×C32C2×D3×D411yescharacteristic
942C2×C32C2×#23911yescharacteristic
943C2×C32C2×#23911yescharacteristic
944C2×C32D3×#4111yescharacteristic
945C2×C32D3×#4111yescharacteristic
946C2×C32D3×#4111yescharacteristic
947C3⋊D3—22no—
948C3⋊D3—41no—
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—62no—
967C3×D3—62no—
968C3×D3—122no—
969C3×D3—122no—
970C3×D3—121no—
971C3×D3—121no—
972C24—271no—
973#41—544no—
974C2×Q8—31no—
975C2×D4—91no—
976C2×D4—271no—
977C2×D4—271no—
978C2×D4—271no—
979C2×D4—271no—
980C2×D4—271no—
981C2×D4—271no—
982C22×C4—91no—
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—91no—
996C4⋊C4—91no—
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—271no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—32no—
1013C22×C3—32no—
1014C22×C3—41no—
1015C22×C3—62no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—92no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—181no—
1024C22×C3—181no—
1025C22×C3—181no—
1026C22×C3—181no—
1027C22×C3—181no—
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C22×D3211yescharacteristic
1030C22×C3C22×D3211yescharacteristic
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—32no—
1034C2×D3—32no—
1035C2×D3—62no—
1036C2×D3—61no—
1037C2×D3—61no—
1038C2×D3—61no—
1039C2×D3—61no—
1040C2×D3—62no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—61no—
1044C2×D3—61no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—92no—
1048C2×D3—92no—
1049C2×D3—92no—
1050C2×D3—121no—
1051C2×D3—121no—
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—62no—
1109C3×C4—61no—
1110C3×C4—61no—
1111C3×C4—61no—
1112C3×C4—61no—
1113C3×C4—61no—
1114C3×C4—61no—
1115C3×C4—61no—
1116C3×C4—61no—
1117C3×C4—92no—
1118C3×C4—121no—
1119C3×C4—121no—
1120C3×C4—121no—
1121C3×C4—181no—
1122C3×C4—181no—
1123C3×C4—181no—
1124Dic3—21no—
1125Dic3—21no—
1126Dic3—21no—
1127Dic3—21no—
1128Dic3—32no—
1129Dic3—32no—
1130Dic3—62no—
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#562711yescharacteristic, complemented
1147C32#562711yescharacteristic, complemented
1148C23—31no—
1149C23—91no—
1150C23—91no—
1151C23—271no—
1152C23—271no—
1153C23—542no—
1154C23—542no—
1155C23—542no—
1156Q8—62no—
1157D4—182no—
1158D4—542no—
1159D4—542no—
1160D4—542no—
1161D4—542no—
1162D4—542no—
1163D4—542no—
1164C2×C4—31no—
1165C2×C4—31no—
1166C2×C4—31no—
1167C2×C4—31no—
1168C2×C4—31no—
1169C2×C4—91no—
1170C2×C4—91no—
1171C2×C4—91no—
1172C2×C4—91no—
1173C2×C4—182no—
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—182no—
1198C2×C3—361no—
1199C2×C3C2×#379911yescharacteristic
1200C2×C3D3×#23511yescharacteristic
1201C2×C3D32×D411yescharacteristic
1202C2×C3D32×D411yescharacteristic
1203C2×C3#6431211yescharacteristic
1204C2×C3D3×#23911yescharacteristic
1205C2×C3D3×#23911yescharacteristic
1206C2×C3D3×#23911yescharacteristic
1207C2×C3C2×#381111yescharacteristic
1208D3—22no—
1209D3—62no—
1210D3—62no—
1211D3—122no—
1212D3—122no—
1213D3—121no—
1214D3—121no—
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—92no—
1233C22—181no—
1234C22—181no—
1235C22—181no—
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—61no—
1252C4—92no—
1253C4—181no—
1254C4—181no—
1255C4—181no—
1256C3—21no—
1257C3—21no—
1258C3—21no—
1259C3—41no—
1260C3#1059406611yescharacteristic, complemented
1261C3#1059462311yescharacteristic, complemented
1262C3#1059543011yescharacteristic, complemented
1263C2—62no—
1264C2—182no—
1265C2—361no—
1266C2—542no—
1267C2—1081no—
1268C2#1172437711yescharacteristic
1269C2D3×#379911yescharacteristic
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×#89018C2semidirect
2. C2×D3×#624C2semidirect
3. #11723684C2semidirect
4. #11723542C2semidirect
5. #11723498C2semidirect
6. C3×#63888C2semidirect
7. C3×#63887C2semidirect
8. C3×#63881C2semidirect
9. #11723000C2semidirect
10. #11722961C2semidirect
11. #11722959C2semidirect
12. #11722950C2semidirect
13. #11722937C2semidirect
14. #11722935C2semidirect
15. #11722920C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C32×Dic6C22semidirect
27. C2×#6292C22semidirect
31. C2×#6289C22semidirect
39. C3×#3750C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88814C22semidirect
43. #88813C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
90. #63888D3semidirect
91. #63887D3semidirect
96. #63881D3semidirect
133. #6289D4semidirect
161. C2×C4×C3⋊D3C2×D3semidirect
174. C2×C3×Dic6C2×D3semidirect
175. C2×C3×Dic6C2×D3semidirect
220. #3750C2×D3semidirect
245. C3×Dic3⋊C4C2×D3semidirect
246. C3×Dic3⋊C4C2×D3semidirect
249. #3724C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
267. #3722C2×D3semidirect
274. Dic32C2×D3semidirect
287. C2×C3×C3⋊D3#41semidirect
290. C2×C32×D3#41semidirect
572. C2×Dic6D32semidirect
629. Dic3⋊C4D32semidirect
693. C2×C3⋊D3#239semidirect
719. C2×C3×D3#235semidirect
720. C2×C3×D3#239semidirect
782. C33#525semidirect
1097. C2×D3#3799semidirect
1145. C32#5547semidirect
1146. C32#5627semidirect
1147. C32#5627semidirect
1260. C3#10594066semidirect
1261. C3#10594623semidirect
1262. C3#10595430semidirect

Maximal subgroups

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

subgroupindex
C2×#890182
C2×D3×#6242
#117236842
#117235422
#117234982
C3×#638882
C3×#638872
C3×#638812
#117230002
#117229612
#117229592
#117229502
#117229372
#117229352
#117229202
#105954303
#105946233
#105940663