Finite Group Databasebeta

← #13172905

Subgroups — #13172905

Order 1728.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6289C211yesmaximal, characteristic, complemented
2C2×#88962C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63964C211yesmaximal, characteristic, complemented
9#11723000C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722963C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14#11722935C211yesmaximal, characteristic, complemented
15#11722920C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10594922—31nomaximal
18#10594066—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6294C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6289—24no—
30C2×#6289C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×C3×#627C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37#88962—24no—
38C3×#3757C2211yescharacteristic
39C32×#217C2211yescharacteristic
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88813C2211yescharacteristic, complemented
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×C4×C3⋊D3—31no—
57C22×#624—31no—
58C22×#624—31no—
59C22×#624—61no—
60C2×#3804—31no—
61C2×#3799—31no—
62C2×#3796—31no—
63#64146—31no—
64#64091—31no—
65C3×#939—31no—
66C3×D4×Dic3—31no—
67C3×#930—31no—
68C3×#924—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63981—31no—
72#63981—31no—
73#63981—31no—
74#63981—31no—
75#63981—61no—
76#63981—61no—
77#63978D311yescharacteristic, complemented
78#63975—31no—
79#67⋊Dic3—31no—
80#67⋊Dic3D311yescharacteristic, complemented
81Dic3×#67—31no—
82#63964D311yescharacteristic, complemented
83#63958—31no—
84#63952—31no—
85#63952—31no—
86#63916—31no—
87#63910—31no—
88#63904—31no—
89#63897—31no—
90#63895—31no—
91#63894—31no—
92#63888—31no—
93#63881—31no—
94#63881—31no—
95#63880—31no—
96#63871—31no—
97#63854—31no—
98#63854—31no—
99#63853—31no—
100#63853—31no—
101#63849—31no—
102#63836—31no—
103#63836—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)—22no—
106C22×C3⋊(C3⋊D3)—22no—
107C22×C3⋊(C3⋊D3)—22no—
108C22×C3⋊(C3⋊D3)C2311yescharacteristic
109C22×C3⋊(C3⋊D3)C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C3×#638—22no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—22no—
120C2×C32×Dic3—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6294—22no—
127#6292—22no—
128#6292—22no—
129#6291—22no—
130#6291—22no—
131#6289—22no—
132#6289—22no—
133#6289—22no—
134#6289D414yescomplemented
135C3×#627—22no—
136C3×#626—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5606—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C23×C3⋊D3—31no—
143C23×C3⋊D3—31no—
144C23×C3⋊D3—61no—
145C23×C3⋊D3—61no—
146C23×C3⋊D3—61no—
147C23×C3⋊D3—121no—
148C2×C32×D4—31no—
149C22×C32×C4—31no—
150C2×#638—31no—
151C2×#638—31no—
152C2×#638C2×D311yescharacteristic
153C22×C3⋊Dic3C2×D311yescharacteristic
154C2×C4⋊(C3⋊D3)—31no—
155C2×C4⋊(C3⋊D3)—31no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—31no—
160C2×C4×C3⋊D3—64no—
161C2×C3×#67—21no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—61no—
166C2×C3×#67C2×D311yescharacteristic
167C2×C3×#67C2×D311yescharacteristic
168C22×C3×Dic3—21no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—61no—
173C22×C3×Dic3C2×D311yescharacteristic
174C22×C3×Dic3C2×D311yescharacteristic
175C2×C3×D12—31no—
176C2×C3×C4×D3—31no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—31no—
179C2×#627C2×D311yescharacteristic, complemented
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—61no—
189C2×#626—61no—
190C2×#626—61no—
191C2×#626—61no—
192C2×#626C2×D311yescharacteristic, complemented
193C2×#624—31no—
194C2×#624—31no—
195C2×#624—31no—
196C2×#624—31no—
197C2×#624—31no—
198C2×#624—31no—
199C2×#624—31no—
200C2×#624—31no—
201C2×#624—31no—
202C2×#624—64no—
203C2×#624—64no—
204C2×#624—61no—
205C2×#624—61no—
206C2×#624—61no—
207C2×#624—61no—
208C2×#624—68no—
209#3804—64no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3C2×D311yescharacteristic, complemented
213#3799—64no—
214#3796—64no—
215C32×C22⋊C4—31no—
216#3757C2×D311yescharacteristic
217#3752—31no—
218#3752—31no—
219#3752—31no—
220#3752—31no—
221C3×#217—21no—
222C3×#217—31no—
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—31no—
226C3×#217—61no—
227C3×#217C2×D311yescharacteristic
228C3×#217C2×D311yescharacteristic
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3—31no—
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
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×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245#3724—31no—
246#3724C2×D311yescharacteristic, complemented
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3C2×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, complemented
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—31no—
274Dic32C2×D311yescharacteristic, complemented
275C22×C33—21no—
276C22×C33—21no—
277C22×C33#4112yescomplemented
278C22×C33C2411yescharacteristic
279C2×C3⋊(C3⋊D3)—28no—
280C2×C3⋊(C3⋊D3)—21no—
281C2×C3⋊(C3⋊D3)—21no—
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)C2×D412yes—
285C2×C3⋊(C3⋊D3)#4112yescomplemented
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C3×C3⋊Dic3—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×#237—91no—
304C2×#235—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C22×C4×D3—91no—
308C22×C4×D3—181no—
309C3×C22⋊Q8—91no—
310C3×#121—91no—
311C3×C4×D4—91no—
312#946—91no—
313#939—31no—
314#938—91no—
315#937—91no—
316#937—91no—
317#937—91no—
318#937—181no—
319D4×Dic3—31no—
320D4×Dic3—91no—
321#930—31no—
322C4×#67—91no—
323C4×#67—91no—
324#924—31no—
325#897—91no—
326#896—91no—
327#895—91no—
328#894—91no—
329#894—91no—
330#894—91no—
331#893—91no—
332#893—91no—
333#892—91no—
334#892—91no—
335#884—91no—
336#883—91no—
337#883—91no—
338#883—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—21no—
351C23×C32—21no—
352C23×C32—21no—
353C23×C32—31no—
354C23×C32—41no—
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C23×C32C22×D311yescharacteristic
358C22×C3⋊D3—31no—
359C22×C3⋊D3—31no—
360C22×C3⋊D3—31no—
361C22×C3⋊D3—31no—
362C22×C3⋊D3—31no—
363C22×C3⋊D3—31no—
364C22×C3⋊D3—61no—
365C22×C3⋊D3—61no—
366C22×C3⋊D3—61no—
367C22×C3⋊D3—61no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—62no—
371C22×C3⋊D3—62no—
372C22×C3⋊D3—62no—
373C22×C3⋊D3—62no—
374C22×C3⋊D3—62no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—64no—
378C22×C3⋊D3—64no—
379C22×C3⋊D3—64no—
380C22×C3⋊D3—62no—
381C22×C3⋊D3—62no—
382C22×C3⋊D3—121no—
383C22×C3⋊D3—121no—
384C22×C3⋊D3—122no—
385C22×C3⋊D3—122no—
386C22×C3⋊D3—122no—
387C22×C3⋊D3—122no—
388C22×C3⋊D3—122no—
389C22×C3⋊D3—122no—
390C22×C3⋊D3—124no—
391C22×C3⋊D3—124no—
392C22×C3⋊D3—124no—
393C22×C3⋊D3C22×D311yescharacteristic
394C22×C3×D3—21no—
395C22×C3×D3—31no—
396C22×C3×D3—31no—
397C22×C3×D3—61no—
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C32×D4—62no—
401C2×C32×C4—31no—
402C2×C32×C4—31no—
403C2×C32×C4—31no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—62no—
407#638—22no—
408#638—62no—
409#638—62no—
410C2×C3⋊Dic3—22no—
411C2×C3⋊Dic3C22×D311yescharacteristic
412C2×C3⋊Dic3C22×D311yescharacteristic
413C2×C3⋊Dic3C22×D311yescharacteristic
414C2×C3⋊Dic3C22×D311yescharacteristic
415C2×C3⋊Dic3C22×D311yescharacteristic
416C4⋊(C3⋊D3)—62no—
417C4⋊(C3⋊D3)—62no—
418C4×C3⋊D3—34no—
419C4×C3⋊D3—62no—
420C4×C3⋊D3—62no—
421C4×C3⋊D3—62no—
422C3×#67—22no—
423C3×#67—22no—
424C3×#67—42no—
425C3×#67—62no—
426C3×#67—62no—
427C3×#67—62no—
428C3×#67—122no—
429C2×C3×Dic3—24no—
430C2×C3×Dic3—22no—
431C2×C3×Dic3—22no—
432C2×C3×Dic3—21no—
433C2×C3×Dic3—21no—
434C2×C3×Dic3—21no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—61no—
448C2×C3×Dic3—61no—
449C2×C3×Dic3—61no—
450C2×C3×Dic3—61no—
451C2×C3×Dic3—61no—
452C2×C3×Dic3—62no—
453C2×C3×Dic3—62no—
454C2×C3×Dic3—62no—
455C2×C3×Dic3—64no—
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C2×C3×Dic3C22×D311yescharacteristic
459C2×C3×Dic3C22×D311yescharacteristic
460C2×C3×Dic3C22×D311yescharacteristic
461C2×C3×Dic3C22×D311yescharacteristic
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C3×D12—62no—
467C3×C4×D3—62no—
468C3×Dic6—62no—
469C3×Dic6—62no—
470#627—22no—
471#626—22no—
472#626—62no—
473#626—62no—
474#626—62no—
475#626—62no—
476#626—62no—
477#626—62no—
478#626—62no—
479#626—62no—
480#626—122no—
481#626—122no—
482#626—122no—
483#626—122no—
484#624—34no—
485#624—34no—
486#624—64no—
487#624—62no—
488#624—62no—
489#624—62no—
490#624—62no—
491#624—64no—
492#624—64no—
493#624—64no—
494#624—62no—
495#624—62no—
496#624—62no—
497D3×Dic3—22no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500#525—271noSylow
501C2×C33—22no—
502C2×C33C22×D411yescharacteristic
503C2×C33C2×#4111yescharacteristic
504C2×C33C2×#4111yescharacteristic
505C3⋊(C3⋊D3)—22no—
506C3⋊(C3⋊D3)—22no—
507C3×C3⋊D3—41no—
508C32×D3—41no—
509C23×D3—91no—
510C23×D3—91no—
511C23×D3—91no—
512C23×D3—181no—
513C23×D3—181no—
514C23×D3—181no—
515C23×D3—361no—
516C2×C3×Q8—91no—
517C2×C3×D4—31no—
518C2×C3×D4—31no—
519C2×C3×D4—61no—
520C2×C3×D4—91no—
521C2×C3×D4—91no—
522C22×C3×C4—31no—
523C22×C3×C4—31no—
524C22×C3×C4—61no—
525C22×C3×C4—91no—
526C22×C3×C4—91no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—61no—
531C2×#67—91no—
532C2×#67—91no—
533C2×#67—91no—
534C2×#67—91no—
535C2×#67—91no—
536C2×#67—91no—
537C2×#67—181no—
538C2×#67—181no—
539C2×#67D3211yescharacteristic
540C22×Dic3—31no—
541C22×Dic3—31no—
542C22×Dic3—31no—
543C22×Dic3—61no—
544C22×Dic3—91no—
545C22×Dic3D3211yescharacteristic
546#239—184no—
547#237—184no—
548#235—184no—
549C2×D12—31no—
550C2×D12—91no—
551C2×D12—91no—
552C2×D12—91no—
553C2×D12—91no—
554C2×D12—91no—
555C2×D12—91no—
556C2×D12—181no—
557C2×D12—181no—
558C2×C4×D3—31no—
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—91no—
567C2×C4×D3—91no—
568C2×C4×D3—91no—
569C2×C4×D3—91no—
570C2×C4×D3—91no—
571C2×C4×D3—91no—
572C2×C4×D3—91no—
573C2×C4×D3—181no—
574C2×C4×D3—181no—
575C2×C4×D3—181no—
576C2×C4×D3—181no—
577C2×C4×D3—184no—
578C2×C4×D3—184no—
579C2×C4×D3—184no—
580C2×C4×D3—188no—
581C2×Dic6—31no—
582C2×Dic6—31no—
583C3×C4⋊C4—91no—
584C3×C4⋊C4—91no—
585C3×C4⋊C4—91no—
586C3×C4⋊C4—91no—
587C3×C4⋊C4—91no—
588C3×C22⋊C4—31no—
589C3×C22⋊C4—31no—
590C3×C22⋊C4—61no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593C3×C22⋊C4—91no—
594C3×C22⋊C4—91no—
595C3×C42—91no—
596#217—31no—
597#217—31no—
598#217—31no—
599#217—31no—
600#217—61no—
601#217—91no—
602#217D3211yescharacteristic
603(C2×D3)⋊C4—31no—
604(C2×D3)⋊C4—31no—
605(C2×D3)⋊C4—31no—
606(C2×D3)⋊C4—31no—
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—91no—
614(C2×D3)⋊C4—91no—
615(C2×D3)⋊C4—91no—
616(C2×D3)⋊C4—91no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—181no—
622(C2×D3)⋊C4—181no—
623(C2×D3)⋊C4—181no—
624(C2×D3)⋊C4—181no—
625C4⋊Dic3—31no—
626C4⋊Dic3—31no—
627C4⋊Dic3—31no—
628C4⋊Dic3—31no—
629C4⋊Dic3—91no—
630Dic3⋊C4—31no—
631Dic3⋊C4—31no—
632Dic3⋊C4—31no—
633Dic3⋊C4—31no—
634Dic3⋊C4—31no—
635Dic3⋊C4—31no—
636Dic3⋊C4—91no—
637Dic3⋊C4—91no—
638C4×Dic3—31no—
639C4×Dic3—31no—
640C4×Dic3—91no—
641C4×Dic3—91no—
642C4×Dic3—91no—
643C22×C32—21no—
644C22×C32—21no—
645C22×C32—22no—
646C22×C32—22no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—22no—
656C22×C32—22no—
657C22×C32—42no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—42no—
664C22×C32—42no—
665C22×C32—61no—
666C22×C32—61no—
667C22×C32—61no—
668C22×C32#23512yescomplemented
669C22×C32#23712yescomplemented
670C22×C32#23912yescomplemented
671C22×C32C23×D311yescharacteristic
672C22×C32C23×D311yescharacteristic
673C22×C32C23×D311yescharacteristic
674C2×C3⋊D3—21no—
675C2×C3⋊D3—21no—
676C2×C3⋊D3—21no—
677C2×C3⋊D3—32no—
678C2×C3⋊D3—32no—
679C2×C3⋊D3—32no—
680C2×C3⋊D3—32no—
681C2×C3⋊D3—32no—
682C2×C3⋊D3—32no—
683C2×C3⋊D3—62no—
684C2×C3⋊D3—62no—
685C2×C3⋊D3—62no—
686C2×C3⋊D3—62no—
687C2×C3⋊D3—62no—
688C2×C3⋊D3—62no—
689C2×C3⋊D3—68no—
690C2×C3⋊D3—61no—
691C2×C3⋊D3—61no—
692C2×C3⋊D3—61no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—62no—
695C2×C3⋊D3—616no—
696C2×C3⋊D3—68no—
697C2×C3⋊D3—68no—
698C2×C3⋊D3—62no—
699C2×C3⋊D3—62no—
700C2×C3⋊D3—62no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—122no—
710C2×C3⋊D3—122no—
711C2×C3⋊D3—121no—
712C2×C3⋊D3—121no—
713C2×C3⋊D3—121no—
714C2×C3⋊D3—121no—
715C2×C3⋊D3—121no—
716C2×C3⋊D3—121no—
717C2×C3⋊D3—121no—
718C2×C3⋊D3—121no—
719C2×C3⋊D3—122no—
720C2×C3⋊D3—122no—
721C2×C3⋊D3—122no—
722C2×C3⋊D3—122no—
723C2×C3⋊D3—128no—
724C2×C3⋊D3—128no—
725C2×C3⋊D3—1216no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—21no—
729C2×C3×D3—21no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—41no—
733C2×C3×D3—41no—
734C2×C3×D3—41no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C32×C4—32no—
745C32×C4—61no—
746C32×C4—61no—
747C32×C4—61no—
748C32×C4—61no—
749C3⋊Dic3—21no—
750C3⋊Dic3—21no—
751C3⋊Dic3—21no—
752C3⋊Dic3—21no—
753C3⋊Dic3D3×D412yes—
754C3×Dic3—22no—
755C3×Dic3—21no—
756C3×Dic3—21no—
757C3×Dic3—21no—
758C3×Dic3—21no—
759C3×Dic3—21no—
760C3×Dic3—21no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—22no—
764C3×Dic3—32no—
765C3×Dic3—32no—
766C3×Dic3—41no—
767C3×Dic3—41no—
768C3×Dic3—41no—
769C3×Dic3—62no—
770C3×Dic3—62no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—61no—
774C3×Dic3—61no—
775C3×Dic3—61no—
776C3×Dic3—61no—
777C3×Dic3—61no—
778C3×Dic3—61no—
779C3×Dic3—121no—
780C3×Dic3—121no—
781C3×Dic3—121no—
782C3×Dic3D3×D412yes—
783C3×Dic3D3×D412yes—
784C2×#41—271no—
785C23×C4—271no—
786#123—271no—
787#123—271no—
788C22⋊Q8—91no—
789C22⋊Q8—271no—
790#121—91no—
791#121—271no—
792#120—271no—
793#120—271no—
794C4×D4—91no—
795C4×D4—271no—
796C4×D4—271no—
797C4×D4—271no—
798#117—271no—
799C33#52511yescharacteristic, complemented, Sylow
800C23×C3—21no—
801C23×C3—21no—
802C23×C3—21no—
803C23×C3—31no—
804C23×C3—31no—
805C23×C3—41no—
806C23×C3—61no—
807C23×C3—91no—
808C23×C3C2×D3211yescharacteristic
809C23×C3C2×D3211yescharacteristic
810C23×C3C2×D3211yescharacteristic
811C22×D3—31no—
812C22×D3—31no—
813C22×D3—61no—
814C22×D3—91no—
815C22×D3—91no—
816C22×D3—91no—
817C22×D3—91no—
818C22×D3—91no—
819C22×D3—91no—
820C22×D3—181no—
821C22×D3—181no—
822C22×D3—181no—
823C22×D3—181no—
824C22×D3—181no—
825C22×D3—181no—
826C22×D3—182no—
827C22×D3—182no—
828C22×D3—182no—
829C22×D3—182no—
830C22×D3—182no—
831C22×D3—182no—
832C22×D3—184no—
833C22×D3—184no—
834C22×D3—184no—
835C22×D3—182no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—361no—
839C22×D3—361no—
840C22×D3—362no—
841C22×D3—362no—
842C22×D3—362no—
843C22×D3—362no—
844C22×D3—362no—
845C22×D3—362no—
846C22×D3—364no—
847C22×D3—364no—
848C22×D3—364no—
849C22×D3C2×D3211yescharacteristic
850C3×Q8—182no—
851C3×D4—62no—
852C3×D4—62no—
853C3×D4—122no—
854C3×D4—182no—
855C3×D4—182no—
856C2×C3×C4—31no—
857C2×C3×C4—31no—
858C2×C3×C4—31no—
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—61no—
867C2×C3×C4—61no—
868C2×C3×C4—61no—
869C2×C3×C4—61no—
870C2×C3×C4—61no—
871C2×C3×C4—62no—
872C2×C3×C4—62no—
873C2×C3×C4—64no—
874C2×C3×C4—91no—
875C2×C3×C4—91no—
876C2×C3×C4—91no—
877C2×C3×C4—91no—
878C2×C3×C4—91no—
879C2×C3×C4—182no—
880C2×C3×C4—182no—
881#67—22no—
882#67—62no—
883#67—62no—
884#67—62no—
885#67—122no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—362no—
893#67—362no—
894C2×Dic3—22no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—31no—
903C2×Dic3—31no—
904C2×Dic3—31no—
905C2×Dic3—61no—
906C2×Dic3—61no—
907C2×Dic3—61no—
908C2×Dic3—61no—
909C2×Dic3—61no—
910C2×Dic3—62no—
911C2×Dic3—62no—
912C2×Dic3—62no—
913C2×Dic3—64no—
914C2×Dic3—182no—
915C2×Dic3C2×D3211yescharacteristic
916C2×Dic3C2×D3211yescharacteristic
917C2×Dic3C2×D3211yescharacteristic
918C2×Dic3C2×D3211yescharacteristic
919C2×Dic3C2×D3211yescharacteristic
920D12—62no—
921D12—182no—
922D12—182no—
923D12—182no—
924D12—182no—
925D12—182no—
926D12—182no—
927D12—362no—
928D12—362no—
929C4×D3—62no—
930C4×D3—94no—
931C4×D3—94no—
932C4×D3—94no—
933C4×D3—184no—
934C4×D3—182no—
935C4×D3—182no—
936C4×D3—182no—
937C4×D3—182no—
938C4×D3—182no—
939C4×D3—182no—
940C4×D3—182no—
941C4×D3—182no—
942C4×D3—182no—
943C4×D3—184no—
944C4×D3—184no—
945C4×D3—184no—
946C4×D3—182no—
947C4×D3—182no—
948Dic6—62no—
949Dic6—62no—
950C2×C32—22no—
951C2×C32—24no—
952C2×C32—22no—
953C2×C32—22no—
954C2×C32—21no—
955C2×C32—21no—
956C2×C32—21no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—21no—
963C2×C32—41no—
964C2×C32—41no—
965C2×C32—41no—
966C2×C32—42no—
967C2×C32—42no—
968C2×C32—44no—
969C2×C32—121no—
970C2×C32C2×#23511yescharacteristic
971C2×C32C2×D3×D411yescharacteristic
972C2×C32C2×D3×D411yescharacteristic
973C2×C32C2×D3×D411yescharacteristic
974C2×C32C2×#23711yescharacteristic
975C2×C32C2×#23911yescharacteristic
976C2×C32D3×#4111yescharacteristic
977C2×C32D3×#4111yescharacteristic
978C2×C32D3×#4111yescharacteristic
979C3⋊D3—41no—
980C3⋊D3—62no—
981C3⋊D3—62no—
982C3⋊D3—64no—
983C3⋊D3—64no—
984C3⋊D3—62no—
985C3⋊D3—62no—
986C3⋊D3—62no—
987C3⋊D3—62no—
988C3⋊D3—122no—
989C3⋊D3—122no—
990C3⋊D3—122no—
991C3⋊D3—122no—
992C3⋊D3—124no—
993C3⋊D3—124no—
994C3×D3—41no—
995C3×D3—41no—
996C3×D3—81no—
997C3×D3—121no—
998C3×D3—121no—
999C3×D3—241no—
1000C24—271no—
1001#41—544no—
1002C2×Q8—91no—
1003C2×D4—31no—
1004C2×D4—91no—
1005C2×D4—91no—
1006C2×D4—271no—
1007C2×D4—271no—
1008C2×D4—271no—
1009C2×D4—271no—
1010C22×C4—31no—
1011C22×C4—91no—
1012C22×C4—91no—
1013C22×C4—271no—
1014C22×C4—271no—
1015C22×C4—271no—
1016C22×C4—271no—
1017C22×C4—271no—
1018C22×C4—544no—
1019C4⋊C4—91no—
1020C4⋊C4—91no—
1021C4⋊C4—91no—
1022C4⋊C4—91no—
1023C4⋊C4—91no—
1024C4⋊C4—271no—
1025C22⋊C4—31no—
1026C22⋊C4—91no—
1027C22⋊C4—91no—
1028C22⋊C4—91no—
1029C22⋊C4—91no—
1030C22⋊C4—271no—
1031C22⋊C4—271no—
1032C22⋊C4—271no—
1033C22⋊C4—271no—
1034C22⋊C4—271no—
1035C42—91no—
1036C42—271no—
1037C22×C3—22no—
1038C22×C3—22no—
1039C22×C3—21no—
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—22no—
1049C22×C3—22no—
1050C22×C3—22no—
1051C22×C3—41no—
1052C22×C3—41no—
1053C22×C3—41no—
1054C22×C3—41no—
1055C22×C3—42no—
1056C22×C3—42no—
1057C22×C3—41no—
1058C22×C3—42no—
1059C22×C3—61no—
1060C22×C3—61no—
1061C22×C3—61no—
1062C22×C3—61no—
1063C22×C3—61no—
1064C22×C3—61no—
1065C22×C3—121no—
1066C22×C3—121no—
1067C22×C3—121no—
1068C22×C3—181no—
1069C22×C3—181no—
1070C22×C3—181no—
1071C22×C3#379612yescomplemented
1072C22×C3#379912yescomplemented
1073C22×C3#380412yescomplemented
1074C22×C3C22×D3211yescharacteristic
1075C22×C3C22×D3211yescharacteristic
1076C22×C3C22×D3211yescharacteristic
1077C2×D3—21no—
1078C2×D3—21no—
1079C2×D3—21no—
1080C2×D3—61no—
1081C2×D3—61no—
1082C2×D3—61no—
1083C2×D3—61no—
1084C2×D3—61no—
1085C2×D3—61no—
1086C2×D3—92no—
1087C2×D3—92no—
1088C2×D3—92no—
1089C2×D3—92no—
1090C2×D3—92no—
1091C2×D3—92no—
1092C2×D3—121no—
1093C2×D3—121no—
1094C2×D3—121no—
1095C2×D3—182no—
1096C2×D3—182no—
1097C2×D3—182no—
1098C2×D3—182no—
1099C2×D3—182no—
1100C2×D3—182no—
1101C2×D3—182no—
1102C2×D3—188no—
1103C2×D3—1816no—
1104C2×D3—188no—
1105C2×D3—188no—
1106C2×D3—182no—
1107C2×D3—182no—
1108C2×D3—182no—
1109C2×D3—181no—
1110C2×D3—181no—
1111C2×D3—181no—
1112C2×D3—181no—
1113C2×D3—181no—
1114C2×D3—181no—
1115C2×D3—181no—
1116C2×D3—181no—
1117C2×D3—181no—
1118C2×D3—181no—
1119C2×D3—181no—
1120C2×D3—181no—
1121C2×D3—362no—
1122C2×D3—362no—
1123C2×D3—361no—
1124C2×D3—361no—
1125C2×D3—361no—
1126C2×D3—361no—
1127C2×D3—361no—
1128C2×D3—361no—
1129C2×D3—361no—
1130C2×D3—361no—
1131C2×D3—368no—
1132C2×D3—368no—
1133C2×D3—3616no—
1134C2×D3—362no—
1135C2×D3—362no—
1136C2×D3—362no—
1137C2×D3—362no—
1138C3×C4—32no—
1139C3×C4—32no—
1140C3×C4—62no—
1141C3×C4—62no—
1142C3×C4—61no—
1143C3×C4—61no—
1144C3×C4—61no—
1145C3×C4—61no—
1146C3×C4—61no—
1147C3×C4—61no—
1148C3×C4—61no—
1149C3×C4—61no—
1150C3×C4—92no—
1151C3×C4—121no—
1152C3×C4—121no—
1153C3×C4—121no—
1154C3×C4—181no—
1155C3×C4—181no—
1156C3×C4—181no—
1157C3×C4—181no—
1158Dic3—21no—
1159Dic3—21no—
1160Dic3—21no—
1161Dic3—21no—
1162Dic3—32no—
1163Dic3—32no—
1164Dic3—62no—
1165Dic3—62no—
1166Dic3—61no—
1167Dic3—61no—
1168Dic3—61no—
1169Dic3—61no—
1170Dic3—61no—
1171Dic3—61no—
1172Dic3—61no—
1173Dic3—61no—
1174Dic3—121no—
1175Dic3—121no—
1176Dic3—121no—
1177Dic3#381112yes—
1178C32—21no—
1179C32—21no—
1180C32—21no—
1181C32—41no—
1182C32#554711yescharacteristic, complemented
1183C32#560611yescharacteristic, complemented
1184C32#562711yescharacteristic, complemented
1185C23—31no—
1186C23—91no—
1187C23—271no—
1188C23—271no—
1189C23—542no—
1190C23—542no—
1191C23—542no—
1192C23D3311yescharacteristic
1193Q8—182no—
1194D4—62no—
1195D4—182no—
1196D4—182no—
1197D4—542no—
1198D4—542no—
1199D4—542no—
1200D4—542no—
1201C2×C4—31no—
1202C2×C4—31no—
1203C2×C4—31no—
1204C2×C4—31no—
1205C2×C4—31no—
1206C2×C4—62no—
1207C2×C4—91no—
1208C2×C4—91no—
1209C2×C4—91no—
1210C2×C4—91no—
1211C2×C4—91no—
1212C2×C4—182no—
1213C2×C4—182no—
1214C2×C4—274no—
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—121no—
1239C2×C3—121no—
1240C2×C3—241no—
1241C2×C3—361no—
1242C2×C3C2×#379611yescharacteristic
1243C2×C3C2×#379911yescharacteristic
1244C2×C3#6430611yescharacteristic
1245C2×C3D32×D411yescharacteristic
1246C2×C3D32×D411yescharacteristic
1247C2×C3#6431211yescharacteristic
1248C2×C3#6431211yescharacteristic
1249C2×C3C2×#380411yescharacteristic
1250C2×C3C2×#381111yescharacteristic
1251D3—41no—
1252D3—121no—
1253D3—121no—
1254D3—184no—
1255D3—184no—
1256D3—182no—
1257D3—182no—
1258D3—182no—
1259D3—182no—
1260D3—182no—
1261D3—182no—
1262D3—241no—
1263D3—362no—
1264D3—362no—
1265D3—362no—
1266D3—362no—
1267D3—364no—
1268D3—364no—
1269C22—21no—
1270C22—21no—
1271C22—61no—
1272C22—61no—
1273C22—61no—
1274C22—181no—
1275C22—181no—
1276C22—181no—
1277C22—272no—
1278C22—272no—
1279C22—548no—
1280C22—541no—
1281C22—541no—
1282C22—541no—
1283C22—541no—
1284C22#8896212yescomplemented
1285C22C2×D3311yescharacteristic
1286C4—32no—
1287C4—61no—
1288C4—61no—
1289C4—61no—
1290C4—61no—
1291C4—92no—
1292C4—181no—
1293C4—181no—
1294C4—181no—
1295C4—181no—
1296C3—21no—
1297C3—21no—
1298C3—21no—
1299C3—41no—
1300C3#1059406611yescharacteristic, complemented
1301C3#1059492211yescharacteristic, complemented
1302C3#1059513811yescharacteristic, complemented
1303C2—22no—
1304C2—121no—
1305C2—361no—
1306C2—542no—
1307C2—542no—
1308C2#1172441111yescharacteristic
1309C2C2×#8896211yescharacteristic
1310C2D3×#381111yescharacteristic
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×#6289C2semidirect
2. C2×#88962C2semidirect
3. #11723726C2semidirect
4. #11723639C2semidirect
5. #11723638C2semidirect
6. C3×#63978C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. C3×#63964C2semidirect
9. #11723000C2semidirect
10. #11722996C2semidirect
11. #11722973C2semidirect
12. #11722963C2semidirect
13. #11722937C2semidirect
14. #11722935C2semidirect
15. #11722920C2semidirect
24. C2×#6294C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×D3×Dic3C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88813C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
77. #63978D3semidirect
80. #67⋊Dic3D3semidirect
82. #63964D3semidirect
134. #6289D4semidirect
179. C2×#627C2×D3semidirect
192. C2×#626C2×D3semidirect
212. C2×D3×Dic3C2×D3semidirect
246. #3724C2×D3semidirect
249. Dic3⋊Dic3C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
266. #3722C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
274. Dic32C2×D3semidirect
277. C22×C33#41semidirect
285. C2×C3⋊(C3⋊D3)#41semidirect
668. C22×C32#235semidirect
669. C22×C32#237semidirect
670. C22×C32#239semidirect
799. C33#525semidirect
1071. C22×C3#3796semidirect
1072. C22×C3#3799semidirect
1073. C22×C3#3804semidirect
1182. C32#5547semidirect
1183. C32#5606semidirect
1184. C32#5627semidirect
1284. C22#88962semidirect
1300. C3#10594066semidirect
1301. C3#10594922semidirect
1302. C3#10595138semidirect

Maximal subgroups

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

subgroupindex
C22×#62892
C2×#889622
#117237262
#117236392
#117236382
C3×#639782
C3×#67⋊Dic32
C3×#639642
#117230002
#117229962
#117229732
#117229632
#117229372
#117229352
#117229202
#105951383
#105949223
#105940663