Finite Group Databasebeta

← #13172115

Subgroups — #13172115

Order 1728.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3#11723609C211yesmaximal, characteristic, complemented
4C2×#88803C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723010C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722957C211yesmaximal, characteristic, complemented
12#11722955C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722928C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595075—31nomaximal
18#10594292—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26#89049—24no—
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6293C2211yescharacteristic, complemented
31C2×#6290C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33#89029—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×#626C2211yescharacteristic, complemented
38C2×C3×#624C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3830—31no—
57C2×#3811—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×#3805—31no—
61C2×#3805—31no—
62C2×#3805—61no—
63C2×#3752—31no—
64#64095—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#930—31no—
68C3×C4×#67—31no—
69C3×#882—31no—
70C3×#67⋊C4—31no—
71#63983—31no—
72#63981D311yescharacteristic, complemented
73#63980—31no—
74#63978D311yescharacteristic, complemented
75#67⋊Dic3—31no—
76#63962—31no—
77#63962—31no—
78#63962—61no—
79C2×(C2×D3)⋊Dic3—31no—
80C2×(C2×D3)⋊Dic3—31no—
81C2×(C2×D3)⋊Dic3—61no—
82#63958—31no—
83#63952D311yescharacteristic, complemented
84#63922—31no—
85#63922—31no—
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63913—31no—
90#63908—31no—
91#63906—31no—
92#63896—31no—
93#63895—31no—
94#63893—31no—
95Dic3×D12—31no—
96#63891—31no—
97#63890—31no—
98#63886—31no—
99#63886—31no—
100#63880—31no—
101#63853—31no—
102#63852—31no—
103#63852—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C2×C3⋊(C3⋊Dic3)—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638D414yescomplemented
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C32×#67—22no—
124C2×C32×Dic3—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6295—22no—
131#6295—22no—
132#6294—22no—
133#6293—22no—
134#6290—22no—
135Dic3×C3⋊D3—22no—
136D3×C3⋊Dic3—22no—
137C3×#626—22no—
138C3×#626—41no—
139C3×#626—41no—
140C3×#624—41no—
141#5610—91no—
142#5591—91no—
143#5554—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×C32×D4—31no—
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638C2×D311yescharacteristic
155C2×#638C2×D311yescharacteristic
156C22×C3⋊Dic3—31no—
157C22×C3⋊Dic3—31no—
158C22×C3⋊Dic3—31no—
159C22×C3⋊Dic3—31no—
160C22×C3⋊Dic3—61no—
161C22×C3⋊Dic3—61no—
162C22×C3⋊Dic3—61no—
163C22×C3⋊Dic3—121no—
164#3830—64no—
165C2×C4×C3⋊D3—31no—
166C2×#634—31no—
167C2×C3×#67—21no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—61no—
176C2×C3×#67—61no—
177C2×C3×#67C2×D311yescharacteristic, complemented
178C2×C3×#67C2×D311yescharacteristic, complemented
179C22×C3×Dic3—21no—
180C22×C3×Dic3C2×D311yescharacteristic, complemented
181C22×C3×Dic3C2×D311yescharacteristic, complemented
182C2×C3×D12—31no—
183C2×C3×D12—31no—
184C2×C3×D12—31no—
185C2×C3×C4×D3—31no—
186C2×C3×C4×D3—31no—
187#3811—64no—
188D3×#67—64no—
189D3×#67—64no—
190C2×#627—31no—
191C2×#627—31no—
192C2×#627—61no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626C2×D311yescharacteristic
198C2×#626C2×D311yescharacteristic, complemented
199C2×#626C2×D311yescharacteristic, complemented
200C2×#625—31no—
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—31no—
204C2×#625—61no—
205C2×#624—31no—
206C2×#624C2×D311yescharacteristic, complemented
207#3805—64no—
208#3805—64no—
209#3805—68no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—61no—
217C2×D3×Dic3—61no—
218C32×C22⋊C4—31no—
219#3752—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3752—31no—
225C4⋊(C3⋊Dic3)—31no—
226C4⋊(C3⋊Dic3)—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217C2×D311yescharacteristic, complemented
230C3×#217C2×D311yescharacteristic, complemented
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×C4⋊Dic3—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246#3724C2×D311yescharacteristic, complemented
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—61no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254#3722C2×D311yescharacteristic
255#3722C2×D311yescharacteristic, complemented
256#3722C2×D311yescharacteristic, complemented
257#3722C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2×D412yes—
281C22×C33C2411yescharacteristic
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—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—44no—
293C2×C3×C3⋊D3C2×D412yes—
294C2×C3×C3⋊D3#4112yescomplemented
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298#1113—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3⋊(C3⋊Dic3)—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3C2×D412yes—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C2×#237—91no—
310C2×#237—91no—
311C2×#237—91no—
312C2×#237—181no—
313C2×D3×D4—91no—
314C2×D3×D4—91no—
315C3×#121—91no—
316C3×#120—91no—
317C3×C4×D4—91no—
318C2×#217—91no—
319#939—31no—
320#939—91no—
321#939—91no—
322#938—91no—
323#937—31no—
324#937—91no—
325#937—91no—
326#935—91no—
327D4×Dic3—91no—
328#930—31no—
329#930—91no—
330C4×#67—31no—
331C2×(C2×D3)⋊C4—91no—
332C2×(C2×D3)⋊C4—91no—
333C2×(C2×D3)⋊C4—91no—
334C2×(C2×D3)⋊C4—181no—
335#897—91no—
336#896—91no—
337#895—91no—
338#894—91no—
339#886—91no—
340#886—91no—
341#886—91no—
342#886—181no—
343#885—91no—
344#885—91no—
345#884—91no—
346#883—91no—
347#882—31no—
348#882—91no—
349#67⋊C4—31no—
350#67⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353#878—91no—
354#875—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—41no—
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C22×C3⋊D3—22no—
365C22×C3⋊D3—22no—
366C22×C3⋊D3—41no—
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3⋊D3C22×D311yescharacteristic
371C22×C3×D3—21no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—62no—
385C22×C3×D3—62no—
386C22×C3×D3—64no—
387C22×C3×D3—62no—
388C22×C3×D3—62no—
389C22×C3×D3—122no—
390C22×C3×D3—121no—
391C22×C3×D3—121no—
392C22×C3×D3—122no—
393C22×C3×D3C22×D311yescharacteristic
394C22×C3×D3C22×D311yescharacteristic
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—121no—
402C2×D32—121no—
403C2×D32—121no—
404C32×D4—62no—
405C2×C32×C4—31no—
406C2×C32×C4—31no—
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—121no—
411#638—22no—
412#638—62no—
413#638D1214yescomplemented
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—31no—
419C2×C3⋊Dic3—31no—
420C2×C3⋊Dic3—61no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—61no—
426C2×C3⋊Dic3—62no—
427C2×C3⋊Dic3—62no—
428C2×C3⋊Dic3—64no—
429C2×C3⋊Dic3—62no—
430C2×C3⋊Dic3—62no—
431C2×C3⋊Dic3—121no—
432C2×C3⋊Dic3—121no—
433C2×C3⋊Dic3—122no—
434C2×C3⋊Dic3—122no—
435C2×C3⋊Dic3—124no—
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4×C3⋊D3—62no—
439#634—62no—
440C3×#67—24no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—34no—
444C3×#67—34no—
445C3×#67—64no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—122no—
450C3×#67—121no—
451C3×#67—121no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—41no—
462C2×C3×Dic3—41no—
463C2×C3×Dic3—42no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3C22×D311yescharacteristic
467C2×C3×Dic3C22×D311yescharacteristic
468C2×C3×Dic3C22×D311yescharacteristic
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C3×D12—62no—
477C3×D12—121no—
478C3×D12—121no—
479C3×C4×D3—121no—
480C3×C4×D3—121no—
481#627—62no—
482#627—62no—
483#627—64no—
484#626—22no—
485#626—41no—
486#626—41no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—62no—
491#625—62no—
492#625—62no—
493#625—62no—
494#625—64no—
495#625—62no—
496#624—41no—
497#624—62no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—64no—
501D3×Dic3—62no—
502D3×Dic3—62no—
503D3×Dic3—62no—
504D3×Dic3—64no—
505D3×Dic3—62no—
506#546—271noSylow
507C2×C33—22no—
508C2×C33C22×D411yescharacteristic
509C2×C33C2×#4111yescharacteristic
510C2×C33H(5,𝔽2)11yescharacteristic
511C3×C3⋊D3—22no—
512C3×C3⋊D3—22no—
513C3×C3⋊D3—41no—
514C3×C3⋊D3—41no—
515C32×D3—41no—
516C24×C3—91no—
517C23×D3—31no—
518C23×D3—31no—
519C23×D3—61no—
520C23×D3—91no—
521C23×D3—91no—
522C23×D3—91no—
523C2×C3×D4—31no—
524C2×C3×D4—31no—
525C2×C3×D4—61no—
526C2×C3×D4—91no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C22×C3×C4—31no—
532C22×C3×C4—31no—
533C22×C3×C4—61no—
534C22×C3×C4—91no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—61no—
543C2×#67—61no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—181no—
552C2×#67—184no—
553C2×#67D3211yescharacteristic, complemented
554C22×Dic3—91no—
555C22×Dic3—91no—
556C22×Dic3—91no—
557C22×Dic3—91no—
558C22×Dic3—91no—
559C22×Dic3—91no—
560C22×Dic3—91no—
561C22×Dic3—181no—
562C22×Dic3—181no—
563C22×Dic3—181no—
564C22×Dic3—181no—
565C22×Dic3—361no—
566C22×Dic3D3211yescharacteristic, complemented
567#237—184no—
568#237—184no—
569#237—184no—
570#237—188no—
571D3×D4—184no—
572D3×D4—184no—
573C2×D12—31no—
574C2×D12—31no—
575C2×D12—31no—
576C2×D12—91no—
577C2×D12—91no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—91no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—181no—
586C2×Dic6—91no—
587C2×Dic6—91no—
588C2×Dic6—91no—
589C2×Dic6—181no—
590C3×C4⋊C4—91no—
591C3×C4⋊C4—91no—
592C3×C22⋊C4—31no—
593C3×C22⋊C4—31no—
594C3×C22⋊C4—61no—
595C3×C22⋊C4—91no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C42—91no—
601#217—31no—
602#217—91no—
603#217—91no—
604#217—91no—
605#217—91no—
606#217—91no—
607#217—91no—
608#217D3211yescharacteristic, complemented
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—31no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—181no—
631(C2×D3)⋊C4—181no—
632(C2×D3)⋊C4—181no—
633(C2×D3)⋊C4—181no—
634(C2×D3)⋊C4—181no—
635(C2×D3)⋊C4—181no—
636C4⋊Dic3—31no—
637C4⋊Dic3—91no—
638C4⋊Dic3—91no—
639C4⋊Dic3—91no—
640C4⋊Dic3—91no—
641C4⋊Dic3—181no—
642C4⋊Dic3—181no—
643Dic3⋊C4—31no—
644Dic3⋊C4—31no—
645Dic3⋊C4—31no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648C4×Dic3—31no—
649C4×Dic3—31no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—22no—
653C22×C32—22no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—22no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—42no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—42no—
671C22×C32—42no—
672C22×C32—61no—
673C22×C32—61no—
674C22×C32—61no—
675C22×C32C2×D1212yes—
676C22×C32D3×D412yes—
677C22×C32D3×D412yes—
678C22×C32C23×D311yescharacteristic
679C22×C32C23×D311yescharacteristic
680C22×C32C23×D311yescharacteristic
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—44no—
692C2×C3⋊D3C2×D1212yes—
693C2×C3⋊D3#23712yescomplemented
694C2×C3×D3—22no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—32no—
702C2×C3×D3—32no—
703C2×C3×D3—32no—
704C2×C3×D3—32no—
705C2×C3×D3—41no—
706C2×C3×D3—41no—
707C2×C3×D3—62no—
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—61no—
716C2×C3×D3—61no—
717C2×C3×D3—62no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—121no—
734C2×C3×D3—121no—
735C2×C3×D3—121no—
736C2×C3×D3—121no—
737C2×C3×D3—121no—
738C2×C3×D3—121no—
739C2×C3×D3—124no—
740C2×C3×D3—124no—
741C2×C3×D3—128no—
742D32—124no—
743D32—124no—
744D32—124no—
745C32×C4—61no—
746C32×C4—61no—
747C32×C4—61no—
748C32×C4—61no—
749C32×C4—61no—
750C3⋊Dic3—21no—
751C3⋊Dic3—61no—
752C3⋊Dic3—61no—
753C3⋊Dic3—62no—
754C3⋊Dic3—62no—
755C3⋊Dic3—61no—
756C3⋊Dic3—61no—
757C3⋊Dic3—61no—
758C3⋊Dic3—61no—
759C3⋊Dic3—121no—
760C3⋊Dic3—121no—
761C3⋊Dic3—121no—
762C3⋊Dic3—121no—
763C3⋊Dic3—122no—
764C3⋊Dic3—122no—
765C3⋊Dic3C2×D1212yes—
766C3×Dic3—22no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—32no—
778C3×Dic3—32no—
779C3×Dic3—41no—
780C3×Dic3—41no—
781C3×Dic3—41no—
782C3×Dic3—41no—
783C3×Dic3—62no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—121no—
787C2×#41—271no—
788C22×D4—271no—
789#124—271no—
790#123—271no—
791#123—271no—
792C22⋊Q8—271no—
793#121—91no—
794#121—271no—
795#121—271no—
796#120—91no—
797#120—271no—
798C4×D4—91no—
799C4×D4—271no—
800C2×C22⋊C4—271no—
801C2×C22⋊C4—271no—
802C33#54611yescharacteristic, complemented, Sylow
803C23×C3—21no—
804C23×C3—21no—
805C23×C3—21no—
806C23×C3—31no—
807C23×C3—31no—
808C23×C3—41no—
809C23×C3—61no—
810C23×C3—91no—
811C23×C3—91no—
812C23×C3—91no—
813C23×C3—91no—
814C23×C3—182no—
815C23×C3—182no—
816C23×C3—361no—
817C23×C3C2×D3211yescharacteristic
818C23×C3C2×D3211yescharacteristic
819C23×C3C2×D3211yescharacteristic
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—61no—
829C22×D3—61no—
830C22×D3—61no—
831C22×D3—61no—
832C22×D3—62no—
833C22×D3—62no—
834C22×D3—64no—
835C22×D3—62no—
836C22×D3—62no—
837C22×D3—122no—
838C22×D3—121no—
839C22×D3—121no—
840C22×D3—122no—
841C22×D3—182no—
842C22×D3—182no—
843C22×D3—182no—
844C22×D3—182no—
845C22×D3—182no—
846C22×D3—182no—
847C22×D3—361no—
848C22×D3—361no—
849C22×D3—361no—
850C22×D3C2×D3211yescharacteristic
851C3×D4—64no—
852C3×D4—62no—
853C3×D4—62no—
854C3×D4—94no—
855C3×D4—182no—
856C3×D4—182no—
857C3×D4—361no—
858C3×D4—361no—
859C2×C3×C4—31no—
860C2×C3×C4—31no—
861C2×C3×C4—31no—
862C2×C3×C4—31no—
863C2×C3×C4—31no—
864C2×C3×C4—31no—
865C2×C3×C4—31no—
866C2×C3×C4—31no—
867C2×C3×C4—31no—
868C2×C3×C4—31no—
869C2×C3×C4—61no—
870C2×C3×C4—61no—
871C2×C3×C4—61no—
872C2×C3×C4—61no—
873C2×C3×C4—61no—
874C2×C3×C4—91no—
875C2×C3×C4—91no—
876C2×C3×C4—121no—
877C2×C3×C4—121no—
878C2×C3×C4—122no—
879C2×C3×C4—361no—
880#67—22no—
881#67—34no—
882#67—34no—
883#67—64no—
884#67—62no—
885#67—62no—
886#67—62no—
887#67—122no—
888#67—121no—
889#67—121no—
890#67—182no—
891#67—182no—
892#67—182no—
893#67—182no—
894#67—182no—
895#67—182no—
896#67—182no—
897#67—184no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—41no—
903C2×Dic3—61no—
904C2×Dic3—61no—
905C2×Dic3—91no—
906C2×Dic3—91no—
907C2×Dic3—91no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—91no—
911C2×Dic3—181no—
912C2×Dic3—181no—
913C2×Dic3—181no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—182no—
918C2×Dic3—182no—
919C2×Dic3—182no—
920C2×Dic3—182no—
921C2×Dic3—184no—
922C2×Dic3—184no—
923C2×Dic3—182no—
924C2×Dic3—182no—
925C2×Dic3—182no—
926C2×Dic3—361no—
927C2×Dic3—361no—
928C2×Dic3—362no—
929C2×Dic3—362no—
930C2×Dic3—364no—
931C2×Dic3C2×D3211yescharacteristic
932C2×Dic3C2×D3211yescharacteristic
933C2×Dic3C2×D3211yescharacteristic
934C2×Dic3C2×D3211yescharacteristic
935C2×Dic3C2×D3211yescharacteristic
936D12—62no—
937D12—121no—
938D12—121no—
939D12—182no—
940D12—182no—
941C4×D3—121no—
942C4×D3—121no—
943C4×D3—182no—
944C4×D3—182no—
945C4×D3—182no—
946C4×D3—182no—
947C4×D3—184no—
948C4×D3—182no—
949Dic6—182no—
950Dic6—182no—
951Dic6—182no—
952Dic6—184no—
953C2×C32—22no—
954C2×C32—24no—
955C2×C32—22no—
956C2×C32—22no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—41no—
967C2×C32—41no—
968C2×C32—41no—
969C2×C32—42no—
970C2×C32—42no—
971C2×C32—44no—
972C2×C32—121no—
973C2×C32C22×D1211yescharacteristic
974C2×C32C2×D3×D411yescharacteristic
975C2×C32C2×D3×D411yescharacteristic
976C2×C32C2×#23711yescharacteristic
977C2×C32#100411yescharacteristic
978C2×C32#100411yescharacteristic
979C2×C32#100411yescharacteristic
980C2×C32D3×#4111yescharacteristic
981C2×C32D3×#4111yescharacteristic
982C3⋊D3—22no—
983C3⋊D3—22no—
984C3⋊D3—41no—
985C3⋊D3—41no—
986C3×D3—42no—
987C3×D3—41no—
988C3×D3—41no—
989C3×D3—62no—
990C3×D3—62no—
991C3×D3—62no—
992C3×D3—62no—
993C3×D3—122no—
994C3×D3—122no—
995C3×D3—122no—
996C3×D3—121no—
997C3×D3—121no—
998C3×D3—121no—
999C3×D3—121no—
1000C3×D3—241no—
1001C24—91no—
1002C24—271no—
1003#41—544no—
1004C2×Q8—271no—
1005C2×D4—31no—
1006C2×D4—91no—
1007C2×D4—91no—
1008C2×D4—91no—
1009C2×D4—91no—
1010C2×D4—91no—
1011C2×D4—271no—
1012C2×D4—271no—
1013C2×D4—271no—
1014C2×D4—544no—
1015C22×C4—31no—
1016C22×C4—91no—
1017C22×C4—271no—
1018C22×C4—271no—
1019C22×C4—271no—
1020C22×C4—271no—
1021C4⋊C4—91no—
1022C4⋊C4—91no—
1023C4⋊C4—271no—
1024C4⋊C4—271no—
1025C22⋊C4—31no—
1026C22⋊C4—91no—
1027C22⋊C4—91no—
1028C22⋊C4—91no—
1029C22⋊C4—91no—
1030C22⋊C4—91no—
1031C22⋊C4—271no—
1032C22⋊C4—271no—
1033C22⋊C4—271no—
1034C22⋊C4—271no—
1035C22⋊C4—271no—
1036C22⋊C4—271no—
1037C42—91no—
1038C22×C3—22no—
1039C22×C3—22no—
1040C22×C3—21no—
1041C22×C3—21no—
1042C22×C3—21no—
1043C22×C3—21no—
1044C22×C3—21no—
1045C22×C3—21no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—22no—
1050C22×C3—22no—
1051C22×C3—22no—
1052C22×C3—41no—
1053C22×C3—41no—
1054C22×C3—41no—
1055C22×C3—41no—
1056C22×C3—42no—
1057C22×C3—42no—
1058C22×C3—41no—
1059C22×C3—42no—
1060C22×C3—62no—
1061C22×C3—61no—
1062C22×C3—61no—
1063C22×C3—61no—
1064C22×C3—61no—
1065C22×C3—61no—
1066C22×C3—61no—
1067C22×C3—92no—
1068C22×C3—92no—
1069C22×C3—121no—
1070C22×C3—121no—
1071C22×C3—181no—
1072C22×C3—181no—
1073C22×C3—181no—
1074C22×C3—181no—
1075C22×C3—181no—
1076C22×C3—181no—
1077C22×C3—181no—
1078C22×C3—181no—
1079C22×C3—181no—
1080C22×C3—181no—
1081C22×C3—364no—
1082C22×C3D3×D1212yes—
1083C22×C3D3×D1212yes—
1084C22×C3#381112yes—
1085C22×C3C22×D3211yescharacteristic
1086C22×C3C22×D3211yescharacteristic
1087C22×C3C22×D3211yescharacteristic
1088C2×D3—21no—
1089C2×D3—21no—
1090C2×D3—21no—
1091C2×D3—32no—
1092C2×D3—32no—
1093C2×D3—32no—
1094C2×D3—32no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—62no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—121no—
1122C2×D3—121no—
1123C2×D3—121no—
1124C2×D3—121no—
1125C2×D3—121no—
1126C2×D3—121no—
1127C2×D3—124no—
1128C2×D3—124no—
1129C2×D3—128no—
1130C2×D3—364no—
1131C2×D3—364no—
1132C2×D3—364no—
1133C3×C4—62no—
1134C3×C4—61no—
1135C3×C4—61no—
1136C3×C4—61no—
1137C3×C4—61no—
1138C3×C4—61no—
1139C3×C4—61no—
1140C3×C4—61no—
1141C3×C4—61no—
1142C3×C4—61no—
1143C3×C4—61no—
1144C3×C4—92no—
1145C3×C4—121no—
1146C3×C4—121no—
1147C3×C4—121no—
1148C3×C4—121no—
1149C3×C4—181no—
1150Dic3—21no—
1151Dic3—21no—
1152Dic3—21no—
1153Dic3—21no—
1154Dic3—21no—
1155Dic3—32no—
1156Dic3—32no—
1157Dic3—62no—
1158Dic3—61no—
1159Dic3—61no—
1160Dic3—121no—
1161Dic3—182no—
1162Dic3—182no—
1163Dic3—181no—
1164Dic3—181no—
1165Dic3—181no—
1166Dic3—181no—
1167Dic3—181no—
1168Dic3—181no—
1169Dic3—361no—
1170Dic3—361no—
1171Dic3—361no—
1172Dic3—361no—
1173Dic3—362no—
1174Dic3—362no—
1175C32—21no—
1176C32—21no—
1177C32—21no—
1178C32—41no—
1179C32#555411yescharacteristic, complemented
1180C32#559111yescharacteristic, complemented
1181C32#561011yescharacteristic, complemented
1182C23—31no—
1183C23—91no—
1184C23—91no—
1185C23—91no—
1186C23—91no—
1187C23—182no—
1188C23—182no—
1189C23—361no—
1190C23—542no—
1191C23—542no—
1192C23—1081no—
1193C23D3311yescharacteristic
1194Q8—542no—
1195D4—62no—
1196D4—94no—
1197D4—182no—
1198D4—182no—
1199D4—361no—
1200D4—361no—
1201D4—542no—
1202D4—542no—
1203D4—542no—
1204C2×C4—31no—
1205C2×C4—31no—
1206C2×C4—31no—
1207C2×C4—31no—
1208C2×C4—31no—
1209C2×C4—91no—
1210C2×C4—91no—
1211C2×C4—121no—
1212C2×C4—271no—
1213C2×C4—271no—
1214C2×C4—361no—
1215C2×C4—542no—
1216C2×C4—542no—
1217C2×C4—542no—
1218C2×C4—542no—
1219C2×C3—24no—
1220C2×C3—22no—
1221C2×C3—22no—
1222C2×C3—22no—
1223C2×C3—21no—
1224C2×C3—21no—
1225C2×C3—21no—
1226C2×C3—21no—
1227C2×C3—21no—
1228C2×C3—21no—
1229C2×C3—21no—
1230C2×C3—21no—
1231C2×C3—21no—
1232C2×C3—42no—
1233C2×C3—42no—
1234C2×C3—44no—
1235C2×C3—41no—
1236C2×C3—41no—
1237C2×C3—41no—
1238C2×C3—122no—
1239C2×C3—121no—
1240C2×C3—121no—
1241C2×C3—182no—
1242C2×C3—182no—
1243C2×C3—361no—
1244C2×C3—361no—
1245C2×C3C2×D3×D1211yescharacteristic
1246C2×C3C2×D3×D1211yescharacteristic
1247C2×C3#6430611yescharacteristic
1248C2×C3D3×#23711yescharacteristic
1249C2×C3D3×#23711yescharacteristic
1250C2×C3#6431311yescharacteristic
1251C2×C3#6431311yescharacteristic
1252C2×C3C2×#381111yescharacteristic
1253C2×C3#6433011yescharacteristic
1254D3—41no—
1255D3—62no—
1256D3—62no—
1257D3—62no—
1258D3—62no—
1259D3—122no—
1260D3—122no—
1261D3—122no—
1262D3—121no—
1263D3—121no—
1264D3—121no—
1265D3—121no—
1266D3—241no—
1267C22—21no—
1268C22—21no—
1269C22—61no—
1270C22—61no—
1271C22—61no—
1272C22—92no—
1273C22—92no—
1274C22—181no—
1275C22—181no—
1276C22—181no—
1277C22—181no—
1278C22—181no—
1279C22—181no—
1280C22—181no—
1281C22—181no—
1282C22—181no—
1283C22—181no—
1284C22—364no—
1285C22—1084no—
1286C22#8895512yes—
1287C22C2×D3311yescharacteristic
1288C4—61no—
1289C4—61no—
1290C4—61no—
1291C4—61no—
1292C4—61no—
1293C4—92no—
1294C4—181no—
1295C4—541no—
1296C4—541no—
1297C3—21no—
1298C3—21no—
1299C3—21no—
1300C3—41no—
1301C3#1059429211yescharacteristic, complemented
1302C3#1059507511yescharacteristic, complemented
1303C3#1059530711yescharacteristic, complemented
1304C2—22no—
1305C2—121no—
1306C2—182no—
1307C2—182no—
1308C2—361no—
1309C2—361no—
1310C2#1172440711yescharacteristic
1311C2#1172441511yescharacteristic
1312C2C2×#8895511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#89029C2semidirect
3. #11723609C2semidirect
4. C2×#88803C2semidirect
5. C3×#63981C2semidirect
6. C3×#63978C2semidirect
7. C3×#63952C2semidirect
8. #11723010C2semidirect
9. #11722997C2semidirect
10. #11722984C2semidirect
11. #11722957C2semidirect
12. #11722955C2semidirect
13. #11722951C2semidirect
14. #11722928C2semidirect
15. #11722905C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
30. C2×#6293C22semidirect
31. C2×#6290C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#624C22semidirect
39. C32×#217C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88803C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
72. #63981D3semidirect
74. #63978D3semidirect
83. #63952D3semidirect
120. C3×#638D4semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
180. C22×C3×Dic3C2×D3semidirect
181. C22×C3×Dic3C2×D3semidirect
198. C2×#626C2×D3semidirect
199. C2×#626C2×D3semidirect
206. C2×#624C2×D3semidirect
229. C3×#217C2×D3semidirect
230. C3×#217C2×D3semidirect
246. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
255. #3722C2×D3semidirect
256. #3722C2×D3semidirect
257. #3722C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
294. C2×C3×C3⋊D3#41semidirect
413. #638D12semidirect
553. C2×#67D32semidirect
566. C22×Dic3D32semidirect
608. #217D32semidirect
693. C2×C3⋊D3#237semidirect
802. C33#546semidirect
1179. C32#5554semidirect
1180. C32#5591semidirect
1181. C32#5610semidirect
1301. C3#10594292semidirect
1302. C3#10595075semidirect
1303. C3#10595307semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#890292
#117236092
C2×#888032
C3×#639812
C3×#639782
C3×#639522
#117230102
#117229972
#117229842
#117229572
#117229552
#117229512
#117229282
#117229052
#105953073
#105950753
#105942923