Finite Group Databasebeta

← #13172924

Subgroups — #13172924

Order 1728.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6294C211yesmaximal, characteristic, complemented
2C2×#88962C211yesmaximal, characteristic, complemented
3#11723636C211yesmaximal, characteristic, complemented
4#11723635C211yesmaximal, characteristic, complemented
5#11723622C211yesmaximal, characteristic, complemented
6C3×#63982C211yesmaximal, characteristic, complemented
7C3×#63981C211yesmaximal, characteristic, complemented
8C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
9#11722999C211yesmaximal, characteristic, complemented
10#11722994C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722922C211yesmaximal, characteristic, complemented
16#10595129—31nomaximal
17#10594066—31nomaximal
18#10594055—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6294—24no—
25C2×#6294C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C2×#6294C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6292C2211yescharacteristic
31C2×#6291C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×C3×#627C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37#88962—24no—
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C22×D3×Dic3—31no—
59C22×D3×Dic3—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64148—31no—
63#64091—31no—
64#64090—31no—
65C3×#937—31no—
66C3×D4×Dic3—31no—
67C3×#882—31no—
68C3×#67⋊C4—31no—
69C3×#878—31no—
70C3×#878—31no—
71#63982D311yescharacteristic, complemented
72#63981D311yescharacteristic, complemented
73#63978—31no—
74#63978—31no—
75#63978—61no—
76#63977—31no—
77#63977—31no—
78#63977—61no—
79#67⋊Dic3D311yescharacteristic, complemented
80Dic3×#67—31no—
81#63971—31no—
82#63969—31no—
83#63952—31no—
84#63952—31no—
85#63952—61no—
86#63910—31no—
87#63904—31no—
88#63899—31no—
89#63898—31no—
90#63897—31no—
91#63894—31no—
92#63890—31no—
93#63890—31no—
94#63888—31no—
95#63887—31no—
96#63886—31no—
97#63884—31no—
98#63881—31no—
99#63880—31no—
100#63878—31no—
101#63877—31no—
102#63854—31no—
103#63836—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—22no—
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112#6312—22no—
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3—22no—
115C2×C3×C3⋊Dic3—22no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C32×#67—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6294—22no—
127#6294—22no—
128#6294—22no—
129#6294D414yescomplemented
130#6292—22no—
131#6292—22no—
132#6291—22no—
133#6289—22no—
134C3×#627—22no—
135C3×#626—22no—
136C3×#626—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5586—91no—
140#5547—91no—
141C23×C3⋊D3C2×D311yescharacteristic
142C23×C3×D3—31no—
143C23×C3×D3—31no—
144C23×C3×D3—61no—
145C2×C32×D4—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638—31no—
150C2×#638—61no—
151C2×#638—61no—
152C2×#638—61no—
153C2×#638—121no—
154C22×C3⋊Dic3C2×D311yescharacteristic
155C22×C3⋊Dic3C2×D311yescharacteristic
156C2×C4⋊(C3⋊D3)—31no—
157C2×C4⋊(C3⋊D3)—31no—
158C2×C4×C3⋊D3—31no—
159C2×C3×#67—21no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67C2×D311yescharacteristic
163C2×C3×#67C2×D311yescharacteristic
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C22×C3×Dic3—31no—
168C22×C3×Dic3—31no—
169C22×C3×Dic3—61no—
170C22×C3×Dic3—61no—
171C2×C3×D12—31no—
172C2×C3×D12—31no—
173C2×C3×C4×D3—31no—
174C2×C3×Dic6—31no—
175C2×C3×Dic6—31no—
176C2×#627C2×D311yescharacteristic, complemented
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—61no—
184C2×#626—61no—
185C2×#626—61no—
186C2×#626C2×D311yescharacteristic
187C2×#626C2×D311yescharacteristic
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—31no—
193C2×#624—31no—
194C2×#624—64no—
195C2×#624—61no—
196#3804—64no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—64no—
206C2×D3×Dic3—64no—
207C2×D3×Dic3C2×D311yescharacteristic, complemented
208#3799—64no—
209#3796—64no—
210C32×C22⋊C4—31no—
211C32×C22⋊C4—31no—
212#3757—31no—
213#3752—31no—
214#3752—31no—
215#3752—31no—
216#3752—31no—
217#3750—31no—
218#3750—31no—
219C4×C3⋊Dic3—31no—
220C3×#217—21no—
221C3×#217—21no—
222C3×#217—31no—
223C3×#217C2×D311yescharacteristic
224C3×#217C2×D311yescharacteristic
225C3×#217C2×D311yescharacteristic
226C3×#217C2×D311yescharacteristic
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×C4⋊Dic3—31no—
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242#3724—31no—
243#3724—31no—
244#3724—61no—
245#3724C2×D311yescharacteristic, complemented
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3C2×D311yescharacteristic, complemented
250Dic3⋊Dic3C2×D311yescharacteristic, complemented
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—61no—
257#3722—61no—
258#3722C2×D311yescharacteristic
259#3722C2×D311yescharacteristic
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—61no—
267(C2×D3)⋊Dic3—61no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270Dic32—31no—
271Dic32—31no—
272Dic32—61no—
273Dic32C2×D311yescharacteristic, complemented
274C22×C33—21no—
275C22×C33—21no—
276C22×C33#4112yescomplemented
277C22×C33C2411yescharacteristic
278C2×C3⋊(C3⋊D3)—21no—
279C2×C3⋊(C3⋊D3)—21no—
280C2×C3⋊(C3⋊D3)—21no—
281C2×C3×C3⋊D3—28no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3C2×D412yes—
287C2×C3×C3⋊D3#4112yescomplemented
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C3⋊(C3⋊Dic3)—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3C2×D412yes—
295C3×C3⋊Dic3C2×D412yes—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C23×Dic3—91no—
302C2×#239—91no—
303C2×#237—91no—
304C2×#235—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×#120—91no—
309C3×C4×D4—91no—
310#953—91no—
311#946—91no—
312#939—91no—
313#939—91no—
314#939—91no—
315#939—181no—
316#937—31no—
317#935—91no—
318D4×Dic3—31no—
319D4×Dic3—91no—
320#930—91no—
321C4×#67—91no—
322C4×#67—91no—
323#896—91no—
324#895—91no—
325#894—91no—
326#894—91no—
327#894—91no—
328#893—91no—
329#893—91no—
330#892—91no—
331#886—91no—
332#884—91no—
333#883—91no—
334#882—31no—
335#882—91no—
336#882—91no—
337#882—181no—
338#67⋊C4—31no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—181no—
343#878—31no—
344#878—31no—
345#878—91no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—21no—
350C23×C32—21no—
351C23×C32—21no—
352C23×C32—31no—
353C23×C32—41no—
354C23×C32C22×D311yescharacteristic
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C22×C3⋊D3—22no—
358C22×C3⋊D3—22no—
359C22×C3⋊D3—22no—
360C22×C3⋊D3—31no—
361C22×C3⋊D3—31no—
362C22×C3⋊D3—31no—
363C22×C3⋊D3—61no—
364C22×C3⋊D3—61no—
365C22×C3⋊D3—61no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3×D3—21no—
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—61no—
375C22×C3×D3—61no—
376C22×C3×D3—62no—
377C22×C3×D3—62no—
378C22×C3×D3—62no—
379C22×C3×D3—62no—
380C22×C3×D3—62no—
381C22×C3×D3—62no—
382C22×C3×D3—122no—
383C22×C3×D3—122no—
384C22×C3×D3—122no—
385C22×C3×D3C22×D311yescharacteristic
386C22×C3×D3C22×D311yescharacteristic
387C32×D4—62no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393#638—62no—
394#638—64no—
395#638—62no—
396#638—62no—
397#638—62no—
398#638—122no—
399#638—122no—
400#638—124no—
401C2×C3⋊Dic3—22no—
402C2×C3⋊Dic3—22no—
403C2×C3⋊Dic3—31no—
404C2×C3⋊Dic3—31no—
405C2×C3⋊Dic3—31no—
406C2×C3⋊Dic3—61no—
407C2×C3⋊Dic3—61no—
408C2×C3⋊Dic3—61no—
409C2×C3⋊Dic3—121no—
410C2×C3⋊Dic3C22×D311yescharacteristic
411C2×C3⋊Dic3C22×D311yescharacteristic
412C2×C3⋊Dic3C22×D311yescharacteristic
413C2×C3⋊Dic3C22×D311yescharacteristic
414C4⋊(C3⋊D3)—62no—
415C4⋊(C3⋊D3)—62no—
416C4×C3⋊D3—62no—
417C3×#67—22no—
418C3×#67—22no—
419C3×#67—42no—
420C3×#67—62no—
421C3×#67—62no—
422C2×C3×Dic3—21no—
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—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—62no—
440C2×C3×Dic3—62no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3—122no—
445C2×C3×Dic3—122no—
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C3×D12—62no—
457C3×D12—62no—
458C3×C4×D3—62no—
459C3×Dic6—62no—
460C3×Dic6—62no—
461#627—22no—
462#626—22no—
463#626—22no—
464#626—62no—
465#626—62no—
466#626—62no—
467#626—62no—
468#626—62no—
469#626—62no—
470#626—122no—
471#626—122no—
472#626—122no—
473#624—34no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—122no—
480D3×Dic3—22no—
481D3×Dic3—34no—
482D3×Dic3—34no—
483D3×Dic3—62no—
484D3×Dic3—62no—
485D3×Dic3—62no—
486D3×Dic3—62no—
487D3×Dic3—62no—
488D3×Dic3—62no—
489#525—271noSylow
490C2×C33—22no—
491C2×C33C22×D411yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C2×C33C2×#4111yescharacteristic
494C3⋊(C3⋊D3)—41no—
495C3×C3⋊D3—22no—
496C3×C3⋊D3—22no—
497C32×D3—41no—
498C24×C3—91no—
499C23×D3—31no—
500C23×D3—31no—
501C23×D3—61no—
502C2×C3×Q8—91no—
503C2×C3×D4—31no—
504C2×C3×D4—31no—
505C2×C3×D4—61no—
506C2×C3×D4—91no—
507C2×C3×D4—91no—
508C22×C3×C4—91no—
509C22×C3×C4—91no—
510C22×C3×C4—91no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—181no—
521C2×#67—181no—
522C2×#67—181no—
523C2×#67—181no—
524C2×#67—361no—
525C2×#67D3211yescharacteristic
526C22×Dic3—31no—
527C22×Dic3—31no—
528C22×Dic3—31no—
529C22×Dic3—31no—
530C22×Dic3—31no—
531C22×Dic3—61no—
532C22×Dic3—61no—
533C22×Dic3—91no—
534C22×Dic3—91no—
535C22×Dic3—91no—
536C22×Dic3—91no—
537C22×Dic3—184no—
538#239—184no—
539#237—184no—
540#235—184no—
541C2×D12—31no—
542C2×D12—31no—
543C2×D12—91no—
544C2×D12—91no—
545C2×D12—91no—
546C2×D12—91no—
547C2×D12—91no—
548C2×D12—181no—
549C2×D12—181no—
550C2×C4×D3—31no—
551C2×C4×D3—91no—
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—181no—
563C2×C4×D3—184no—
564C2×C4×D3—184no—
565C2×Dic6—31no—
566C2×Dic6—31no—
567C3×C4⋊C4—91no—
568C3×C4⋊C4—91no—
569C3×C4⋊C4—91no—
570C3×C4⋊C4—91no—
571C3×C22⋊C4—31no—
572C3×C22⋊C4—31no—
573C3×C22⋊C4—31no—
574C3×C22⋊C4—31no—
575C3×C22⋊C4—61no—
576C3×C22⋊C4—61no—
577C3×C22⋊C4—91no—
578C3×C22⋊C4—91no—
579C3×C22⋊C4—91no—
580C3×C42—91no—
581#217—31no—
582#217—91no—
583#217—91no—
584#217—91no—
585#217—91no—
586#217—181no—
587#217D3211yescharacteristic
588#217D3211yescharacteristic
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
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—181no—
606(C2×D3)⋊C4—181no—
607(C2×D3)⋊C4—181no—
608(C2×D3)⋊C4—181no—
609C4⋊Dic3—31no—
610C4⋊Dic3—31no—
611C4⋊Dic3—31no—
612C4⋊Dic3—91no—
613Dic3⋊C4—31no—
614Dic3⋊C4—31no—
615Dic3⋊C4—31no—
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623Dic3⋊C4—181no—
624Dic3⋊C4—181no—
625C4×Dic3—31no—
626C4×Dic3—31no—
627C4×Dic3—91no—
628C4×Dic3—91no—
629C4×Dic3—91no—
630C4×Dic3—181no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—22no—
641C22×C32—22no—
642C22×C32—22no—
643C22×C32—41no—
644C22×C32—42no—
645C22×C32—41no—
646C22×C32—41no—
647C22×C32—41no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—61no—
652C22×C32—61no—
653C22×C32—61no—
654C22×C32—81no—
655C22×C32—81no—
656C22×C32#23512yescomplemented
657C22×C32#23712yescomplemented
658C22×C32#23912yescomplemented
659C22×C32C23×D311yescharacteristic
660C22×C32C23×D311yescharacteristic
661C22×C32C23×D311yescharacteristic
662C2×C3⋊D3—28no—
663C2×C3⋊D3—21no—
664C2×C3⋊D3—21no—
665C2×C3⋊D3—21no—
666C2×C3⋊D3—21no—
667C2×C3⋊D3—61no—
668C2×C3⋊D3—62no—
669C2×C3⋊D3—61no—
670C2×C3⋊D3—61no—
671C2×C3⋊D3—61no—
672C2×C3⋊D3—61no—
673C2×C3⋊D3—61no—
674C2×C3⋊D3—61no—
675C2×C3⋊D3—61no—
676C2×C3⋊D3—61no—
677C2×C3⋊D3—121no—
678C2×C3⋊D3—121no—
679C2×C3⋊D3—122no—
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—241no—
687C2×C3⋊D3—241no—
688C2×C3⋊D3D3×D412yes—
689C2×C3⋊D3#23712yescomplemented
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—32no—
697C2×C3×D3—32no—
698C2×C3×D3—32no—
699C2×C3×D3—32no—
700C2×C3×D3—41no—
701C2×C3×D3—41no—
702C2×C3×D3—41no—
703C2×C3×D3—62no—
704C2×C3×D3—62no—
705C2×C3×D3—68no—
706C2×C3×D3—68no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
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—128no—
720C32×C4—61no—
721C32×C4—61no—
722C32×C4—61no—
723C32×C4—61no—
724C32×C4—61no—
725C3⋊Dic3—21no—
726C3⋊Dic3—21no—
727C3⋊Dic3—61no—
728C3⋊Dic3—62no—
729C3⋊Dic3—61no—
730C3⋊Dic3—61no—
731C3⋊Dic3—121no—
732C3⋊Dic3—121no—
733C3⋊Dic3—122no—
734C3⋊Dic3D3×D412yes—
735C3⋊Dic3D3×D412yes—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—32no—
747C3×Dic3—32no—
748C3×Dic3—32no—
749C3×Dic3—32no—
750C3×Dic3—41no—
751C3×Dic3—41no—
752C3×Dic3—41no—
753C3×Dic3—41no—
754C3×Dic3—41no—
755C3×Dic3—62no—
756C3×Dic3—62no—
757C3×Dic3—61no—
758C3×Dic3—61no—
759C3×Dic3—61no—
760C3×Dic3—61no—
761C3×Dic3—121no—
762C3×Dic3—121no—
763C2×#41—271no—
764C23×C4—271no—
765#123—271no—
766#123—271no—
767C22⋊Q8—91no—
768C22⋊Q8—271no—
769#121—271no—
770#121—271no—
771#120—91no—
772#120—271no—
773C4×D4—91no—
774C4×D4—271no—
775C4×D4—271no—
776C4×D4—271no—
777#117—271no—
778C33#52511yescharacteristic, complemented, Sylow
779C23×C3—21no—
780C23×C3—21no—
781C23×C3—21no—
782C23×C3—31no—
783C23×C3—31no—
784C23×C3—41no—
785C23×C3—61no—
786C23×C3—91no—
787C23×C3—91no—
788C23×C3—182no—
789C23×C3—182no—
790C23×C3—182no—
791C23×C3C2×D3211yescharacteristic
792C23×C3C2×D3211yescharacteristic
793C23×C3C2×D3211yescharacteristic
794C22×D3—31no—
795C22×D3—31no—
796C22×D3—31no—
797C22×D3—31no—
798C22×D3—61no—
799C22×D3—61no—
800C22×D3—62no—
801C22×D3—62no—
802C22×D3—62no—
803C22×D3—62no—
804C22×D3—62no—
805C22×D3—62no—
806C22×D3—91no—
807C22×D3—91no—
808C22×D3—91no—
809C22×D3—122no—
810C22×D3—122no—
811C22×D3—122no—
812C22×D3—181no—
813C22×D3—181no—
814C22×D3—181no—
815C22×D3—361no—
816C22×D3C2×D3211yescharacteristic
817C3×Q8—182no—
818C3×D4—62no—
819C3×D4—62no—
820C3×D4—122no—
821C3×D4—182no—
822C3×D4—182no—
823C2×C3×C4—31no—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
826C2×C3×C4—31no—
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—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—91no—
842C2×C3×C4—182no—
843C2×C3×C4—182no—
844C2×C3×C4—182no—
845#67—22no—
846#67—62no—
847#67—62no—
848#67—182no—
849#67—182no—
850#67—182no—
851#67—182no—
852#67—184no—
853#67—182no—
854#67—182no—
855#67—182no—
856#67—362no—
857#67—362no—
858#67—362no—
859#67—364no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—31no—
867C2×Dic3—31no—
868C2×Dic3—61no—
869C2×Dic3—61no—
870C2×Dic3—61no—
871C2×Dic3—61no—
872C2×Dic3—62no—
873C2×Dic3—62no—
874C2×Dic3—62no—
875C2×Dic3—62no—
876C2×Dic3—62no—
877C2×Dic3—94no—
878C2×Dic3—91no—
879C2×Dic3—91no—
880C2×Dic3—91no—
881C2×Dic3—122no—
882C2×Dic3—122no—
883C2×Dic3—181no—
884C2×Dic3—181no—
885C2×Dic3—181no—
886C2×Dic3—182no—
887C2×Dic3—182no—
888C2×Dic3—182no—
889C2×Dic3—361no—
890C2×Dic3C2×D3211yescharacteristic
891C2×Dic3C2×D3211yescharacteristic
892C2×Dic3C2×D3211yescharacteristic
893C2×Dic3C2×D3211yescharacteristic
894C2×Dic3C2×D3211yescharacteristic
895D12—62no—
896D12—62no—
897D12—182no—
898D12—182no—
899D12—182no—
900D12—182no—
901D12—182no—
902D12—362no—
903D12—362no—
904C4×D3—62no—
905C4×D3—94no—
906C4×D3—94no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—182no—
910C4×D3—182no—
911C4×D3—182no—
912C4×D3—182no—
913C4×D3—182no—
914C4×D3—182no—
915C4×D3—182no—
916C4×D3—362no—
917Dic6—62no—
918Dic6—62no—
919C2×C32—22no—
920C2×C32—22no—
921C2×C32—22no—
922C2×C32—21no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—21no—
929C2×C32—21no—
930C2×C32—21no—
931C2×C32—41no—
932C2×C32—41no—
933C2×C32—41no—
934C2×C32—42no—
935C2×C32—42no—
936C2×C32—42no—
937C2×C32—82no—
938C2×C32—121no—
939C2×C32C2×#23511yescharacteristic
940C2×C32C2×D3×D411yescharacteristic
941C2×C32C2×D3×D411yescharacteristic
942C2×C32C2×D3×D411yescharacteristic
943C2×C32C2×#23711yescharacteristic
944C2×C32C2×#23711yescharacteristic
945C2×C32C2×#23911yescharacteristic
946C2×C32D3×#4111yescharacteristic
947C2×C32D3×#4111yescharacteristic
948C3⋊D3—22no—
949C3⋊D3—22no—
950C3⋊D3—121no—
951C3⋊D3—122no—
952C3⋊D3—121no—
953C3⋊D3—121no—
954C3⋊D3—241no—
955C3⋊D3—241no—
956C3⋊D3—242no—
957C3×D3—41no—
958C3×D3—41no—
959C3×D3—62no—
960C3×D3—62no—
961C3×D3—62no—
962C3×D3—62no—
963C3×D3—81no—
964C3×D3—122no—
965C3×D3—122no—
966C24—91no—
967#41—544no—
968C2×Q8—91no—
969C2×D4—31no—
970C2×D4—91no—
971C2×D4—91no—
972C2×D4—271no—
973C2×D4—271no—
974C2×D4—271no—
975C2×D4—271no—
976C22×C4—91no—
977C22×C4—91no—
978C22×C4—91no—
979C22×C4—271no—
980C22×C4—271no—
981C22×C4—271no—
982C22×C4—271no—
983C22×C4—271no—
984C22×C4—544no—
985C4⋊C4—91no—
986C4⋊C4—91no—
987C4⋊C4—91no—
988C4⋊C4—91no—
989C4⋊C4—271no—
990C4⋊C4—271no—
991C22⋊C4—31no—
992C22⋊C4—31no—
993C22⋊C4—91no—
994C22⋊C4—91no—
995C22⋊C4—91no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22⋊C4—271no—
1000C22⋊C4—271no—
1001C42—91no—
1002C42—271no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—22no—
1013C22×C3—22no—
1014C22×C3—22no—
1015C22×C3—41no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—41no—
1019C22×C3—41no—
1020C22×C3—41no—
1021C22×C3—41no—
1022C22×C3—42no—
1023C22×C3—61no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—61no—
1028C22×C3—61no—
1029C22×C3—81no—
1030C22×C3—81no—
1031C22×C3—92no—
1032C22×C3—92no—
1033C22×C3—121no—
1034C22×C3—121no—
1035C22×C3—121no—
1036C22×C3—188no—
1037C22×C3—181no—
1038C22×C3—181no—
1039C22×C3—181no—
1040C22×C3—181no—
1041C22×C3#379612yescomplemented
1042C22×C3#379912yescomplemented
1043C22×C3#380412yescomplemented
1044C22×C3C22×D3211yescharacteristic
1045C22×C3C22×D3211yescharacteristic
1046C22×C3C22×D3211yescharacteristic
1047C2×D3—21no—
1048C2×D3—21no—
1049C2×D3—21no—
1050C2×D3—32no—
1051C2×D3—32no—
1052C2×D3—32no—
1053C2×D3—32no—
1054C2×D3—62no—
1055C2×D3—62no—
1056C2×D3—68no—
1057C2×D3—68no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—61no—
1064C2×D3—61no—
1065C2×D3—61no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C2×D3—128no—
1071C2×D3—182no—
1072C2×D3—181no—
1073C2×D3—181no—
1074C2×D3—181no—
1075C2×D3—181no—
1076C2×D3—181no—
1077C2×D3—181no—
1078C2×D3—181no—
1079C2×D3—181no—
1080C2×D3—181no—
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—362no—
1090C2×D3—721no—
1091C2×D3—721no—
1092C3×C4—61no—
1093C3×C4—61no—
1094C3×C4—61no—
1095C3×C4—61no—
1096C3×C4—61no—
1097C3×C4—61no—
1098C3×C4—61no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—61no—
1102C3×C4—92no—
1103C3×C4—92no—
1104C3×C4—121no—
1105C3×C4—121no—
1106C3×C4—121no—
1107C3×C4—121no—
1108C3×C4—121no—
1109C3×C4—181no—
1110C3×C4—181no—
1111Dic3—21no—
1112Dic3—21no—
1113Dic3—21no—
1114Dic3—21no—
1115Dic3—21no—
1116Dic3—32no—
1117Dic3—32no—
1118Dic3—32no—
1119Dic3—32no—
1120Dic3—62no—
1121Dic3—62no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—121no—
1127Dic3—121no—
1128Dic3—182no—
1129Dic3—181no—
1130Dic3—181no—
1131Dic3—181no—
1132Dic3—361no—
1133Dic3—361no—
1134Dic3—362no—
1135C32—21no—
1136C32—21no—
1137C32—21no—
1138C32—41no—
1139C32#554711yescharacteristic, complemented
1140C32#558611yescharacteristic, complemented
1141C32#562711yescharacteristic, complemented
1142C23—31no—
1143C23—91no—
1144C23—91no—
1145C23—182no—
1146C23—182no—
1147C23—182no—
1148C23—271no—
1149C23D3311yescharacteristic
1150Q8—182no—
1151D4—62no—
1152D4—182no—
1153D4—182no—
1154D4—542no—
1155D4—542no—
1156D4—542no—
1157D4—542no—
1158C2×C4—31no—
1159C2×C4—31no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—31no—
1163C2×C4—91no—
1164C2×C4—91no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—182no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—274no—
1171C2×C4—271no—
1172C2×C4—542no—
1173C2×C4—542no—
1174C2×C4—542no—
1175C2×C4—542no—
1176C2×C3—22no—
1177C2×C3—22no—
1178C2×C3—22no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—21no—
1186C2×C3—21no—
1187C2×C3—21no—
1188C2×C3—42no—
1189C2×C3—42no—
1190C2×C3—42no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—41no—
1194C2×C3—82no—
1195C2×C3—121no—
1196C2×C3—121no—
1197C2×C3—182no—
1198C2×C3—182no—
1199C2×C3—241no—
1200C2×C3C2×#379611yescharacteristic
1201C2×C3C2×#379911yescharacteristic
1202C2×C3D32×D411yescharacteristic
1203C2×C3D32×D411yescharacteristic
1204C2×C3D32×D411yescharacteristic
1205C2×C3D3×#23711yescharacteristic
1206C2×C3D3×#23711yescharacteristic
1207C2×C3#6431211yescharacteristic
1208C2×C3C2×#380411yescharacteristic
1209D3—41no—
1210D3—62no—
1211D3—62no—
1212D3—62no—
1213D3—62no—
1214D3—122no—
1215D3—122no—
1216D3—362no—
1217D3—361no—
1218D3—361no—
1219D3—361no—
1220D3—721no—
1221D3—721no—
1222D3—722no—
1223C22—21no—
1224C22—21no—
1225C22—61no—
1226C22—61no—
1227C22—61no—
1228C22—92no—
1229C22—92no—
1230C22—188no—
1231C22—181no—
1232C22—181no—
1233C22—181no—
1234C22—181no—
1235C22—541no—
1236C22—541no—
1237C22—541no—
1238C22#8896212yescomplemented
1239C22C2×D3311yescharacteristic
1240C4—61no—
1241C4—61no—
1242C4—61no—
1243C4—61no—
1244C4—61no—
1245C4—92no—
1246C4—92no—
1247C4—181no—
1248C4—181no—
1249C4—541no—
1250C3—21no—
1251C3—21no—
1252C3—21no—
1253C3—41no—
1254C3#1059405511yescharacteristic, complemented
1255C3#1059406611yescharacteristic, complemented
1256C3#1059512911yescharacteristic, complemented
1257C2—22no—
1258C2—121no—
1259C2—182no—
1260C2—182no—
1261C2—1081no—
1262C2#1172440811yescharacteristic
1263C2C2×#8896211yescharacteristic
1264C2#1172444011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6294C2semidirect
2. C2×#88962C2semidirect
3. #11723636C2semidirect
4. #11723635C2semidirect
5. #11723622C2semidirect
6. C3×#63982C2semidirect
7. C3×#63981C2semidirect
8. C3×#67⋊Dic3C2semidirect
9. #11722999C2semidirect
10. #11722994C2semidirect
11. #11722979C2semidirect
12. #11722966C2semidirect
13. #11722937C2semidirect
14. #11722927C2semidirect
15. #11722922C2semidirect
31. C2×#6291C22semidirect
32. C2×#6289C22semidirect
33. C2×C3×#627C22semidirect
36. C2×C3×D3×Dic3C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. #88804C22semidirect
43. #88804C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
71. #63982D3semidirect
72. #63981D3semidirect
79. #67⋊Dic3D3semidirect
129. #6294D4semidirect
176. C2×#627C2×D3semidirect
207. C2×D3×Dic3C2×D3semidirect
245. #3724C2×D3semidirect
249. Dic3⋊Dic3C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
276. C22×C33#41semidirect
287. C2×C3×C3⋊D3#41semidirect
656. C22×C32#235semidirect
657. C22×C32#237semidirect
658. C22×C32#239semidirect
689. C2×C3⋊D3#237semidirect
778. C33#525semidirect
1041. C22×C3#3796semidirect
1042. C22×C3#3799semidirect
1043. C22×C3#3804semidirect
1139. C32#5547semidirect
1140. C32#5586semidirect
1141. C32#5627semidirect
1238. C22#88962semidirect
1254. C3#10594055semidirect
1255. C3#10594066semidirect
1256. C3#10595129semidirect

Maximal subgroups

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

subgroupindex
C22×#62942
C2×#889622
#117236362
#117236352
#117236222
C3×#639822
C3×#639812
C3×#67⋊Dic32
#117229992
#117229942
#117229792
#117229662
#117229372
#117229272
#117229222
#105951293
#105940663
#105940553