Finite Group Databasebeta

← #13172889

Subgroups — #13172889

Order 1728.

1968 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6292C211yesmaximal, characteristic, complemented
2C2×#88962C211yesmaximal, characteristic, complemented
3#11723723C211yesmaximal, characteristic, complemented
4#11723638C211yesmaximal, characteristic, complemented
5#11723627C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×Dic3×#67C211yesmaximal, characteristic, complemented
8C3×#63964C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722999C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722963C211yesmaximal, characteristic, complemented
14#11722959C211yesmaximal, characteristic, complemented
15#11722937C211yesmaximal, characteristic, complemented
16#10595135—31nomaximal
17#10595018—31nomaximal
18#10594063—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C23×C3×C3⋊D3C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6294C2211yescharacteristic, complemented
25C2×#6292—24no—
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic, complemented
31C2×#6291C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×#6289C2211yescharacteristic, complemented
34C2×C3×#627C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88962—24no—
39C3×#3757C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×C4⋊(C3⋊D3)—31no—
57C22×#626—31no—
58C22×#626—31no—
59C22×#626—61no—
60C2×#3804—31no—
61C2×#3799—31no—
62C2×#3796—31no—
63#64146—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#937—31no—
66C3×D4×Dic3—31no—
67C3×C4×#67—31no—
68C3×#924—31no—
69C3×#882—31no—
70C3×#878—31no—
71#63981—31no—
72#63981—31no—
73#63981—61no—
74#63981D311yescharacteristic, complemented
75#63978—31no—
76#63974—31no—
77#63974—31no—
78#63974—31no—
79#63974—61no—
80Dic3×#67D311yescharacteristic, complemented
81#63971—31no—
82D3×#217—31no—
83D3×#217—31no—
84#63964D311yescharacteristic, complemented
85#63958—31no—
86#63916—31no—
87#63910—31no—
88#63910—31no—
89#63909—31no—
90#63907—31no—
91#63897—31no—
92#63897—31no—
93#63894—31no—
94#63890—31no—
95#63890—31no—
96#63886—31no—
97#63886—31no—
98#63881—31no—
99#63880—31no—
100#63864—31no—
101#63854—31no—
102#63853—31no—
103#63852—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)—22no—
106C22×C3⋊(C3⋊D3)—22no—
107C22×C3⋊(C3⋊D3)—41no—
108C22×C3⋊(C3⋊D3)C2311yescharacteristic
109C22×C3⋊(C3⋊D3)C2311yescharacteristic
110C22×C3×C3⋊D3—22no—
111C22×C3×C3⋊D3—22no—
112C22×C3×C3⋊D3—41no—
113C22×C3×C3⋊D3C2311yescharacteristic
114C22×C3×C3⋊D3C2311yescharacteristic
115C22×C32×D3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C32×#67—22no—
121C2×C32×Dic3—22no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6294—22no—
128#6294—41no—
129#6292—22no—
130#6292—22no—
131#6292—22no—
132#6292D414yescomplemented
133#6291—22no—
134#6291—41no—
135#6289—22no—
136#6289—41no—
137C3×#627—22no—
138C3×#626—22no—
139C3×#626—41no—
140C3×D3×Dic3—22no—
141#5630—91no—
142#5591—91no—
143#5550—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3—31no—
146C23×C3⋊D3—31no—
147C23×C3⋊D3—61no—
148C23×C3⋊D3—61no—
149C23×C3⋊D3—61no—
150C23×C3⋊D3—121no—
151C23×C3⋊D3C2×D311yescharacteristic
152C23×C3×D3—31no—
153C23×C3×D3—31no—
154C23×C3×D3—61no—
155C2×C32×D4—31no—
156C22×C32×C4—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4⋊(C3⋊D3)—31no—
161C2×C4⋊(C3⋊D3)—31no—
162C2×C4⋊(C3⋊D3)—31no—
163C2×C4⋊(C3⋊D3)—64no—
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—21no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67C2×D311yescharacteristic
170C2×C3×#67C2×D311yescharacteristic
171C22×C3×Dic3—21no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3C2×D311yescharacteristic
174C22×C3×Dic3C2×D311yescharacteristic
175C2×C3×D12—31no—
176C2×C3×D12—31no—
177C2×C3×C4×D3—31no—
178C2×C3×Dic6—31no—
179C2×C3×Dic6—31no—
180C2×#627C2×D311yescharacteristic, complemented
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—64no—
194C2×#626—64no—
195C2×#626—61no—
196C2×#626—61no—
197C2×#626—61no—
198C2×#626—61no—
199C2×#626—68no—
200C2×#626—61no—
201C2×#626—61no—
202C2×#626C2×D311yescharacteristic, complemented
203C2×#626C2×D311yescharacteristic, complemented
204C2×#624—31no—
205C2×#624—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—61no—
211C2×#624—61no—
212#3804—64no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3C2×D311yescharacteristic, complemented
218#3799—64no—
219#3796—64no—
220C32×C22⋊C4—31no—
221#3757C2×D311yescharacteristic
222#3757C2×D311yescharacteristic
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3752—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—61no—
234C3×#217—61no—
235C3×#217C2×D311yescharacteristic
236C3×#217C2×D311yescharacteristic
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×C4⋊Dic3—31no—
243C3×C4⋊Dic3—31no—
244C3×C4⋊Dic3—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250C3×C4×Dic3—31no—
251C3×C4×Dic3—31no—
252#3724C2×D311yescharacteristic, complemented
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269#3722—61no—
270#3722C2×D311yescharacteristic, complemented
271#3722C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—31no—
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33#4112yescomplemented
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)—44no—
288C2×C3⋊(C3⋊D3)C2×D412yes—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—44no—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3C2×D412yes—
308C22×#67—91no—
309C2×#239—91no—
310C2×#237—91no—
311C2×#235—91no—
312C22×D12—91no—
313C22×D12—91no—
314C22×D12—181no—
315C3×C22⋊Q8—91no—
316C3×#120—91no—
317C3×C4×D4—91no—
318C2×#217—91no—
319#947—91no—
320#939—91no—
321#939—91no—
322#938—91no—
323#937—31no—
324#937—91no—
325#937—91no—
326#937—181no—
327D4×Dic3—31no—
328#930—91no—
329C4×#67—31no—
330#924—31no—
331#895—91no—
332#895—91no—
333#895—91no—
334#894—91no—
335#894—91no—
336#894—91no—
337#894—91no—
338#893—91no—
339#886—91no—
340#885—91no—
341#884—91no—
342#884—91no—
343#883—91no—
344#882—31no—
345#882—91no—
346#67⋊C4—91no—
347D3×C22⋊C4—91no—
348D3×C22⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—181no—
353#878—31no—
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—31no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—41no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—61no—
376C22×C3⋊D3—61no—
377C22×C3⋊D3—61no—
378C22×C3⋊D3—61no—
379C22×C3⋊D3—62no—
380C22×C3⋊D3—62no—
381C22×C3⋊D3—62no—
382C22×C3⋊D3—62no—
383C22×C3⋊D3—64no—
384C22×C3⋊D3—64no—
385C22×C3⋊D3—62no—
386C22×C3⋊D3—62no—
387C22×C3⋊D3—121no—
388C22×C3⋊D3—121no—
389C22×C3⋊D3—122no—
390C22×C3⋊D3—122no—
391C22×C3⋊D3—122no—
392C22×C3⋊D3—122no—
393C22×C3⋊D3—124no—
394C22×C3⋊D3—124no—
395C22×C3⋊D3—121no—
396C22×C3⋊D3—121no—
397C22×C3⋊D3—121no—
398C22×C3⋊D3—122no—
399C22×C3⋊D3—122no—
400C22×C3⋊D3—122no—
401C22×C3⋊D3—124no—
402C22×C3⋊D3C22×D311yescharacteristic
403C22×C3⋊D3C22×D311yescharacteristic
404C22×C3×D3—21no—
405C22×C3×D3—31no—
406C22×C3×D3—31no—
407C22×C3×D3—31no—
408C22×C3×D3—31no—
409C22×C3×D3—61no—
410C22×C3×D3—61no—
411C22×C3×D3—62no—
412C22×C3×D3—62no—
413C22×C3×D3—64no—
414C22×C3×D3—62no—
415C22×C3×D3—62no—
416C22×C3×D3—122no—
417C22×C3×D3—121no—
418C22×C3×D3—121no—
419C22×C3×D3—122no—
420C22×C3×D3C22×D311yescharacteristic
421C22×C3×D3C22×D311yescharacteristic
422C32×D4—62no—
423C2×C32×C4—31no—
424C2×C32×C4—31no—
425C2×C32×C4—31no—
426C2×C32×C4—31no—
427C2×C32×C4—31no—
428C2×C32×C4—62no—
429#638—62no—
430#638—121no—
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C4⋊(C3⋊D3)—34no—
436C4⋊(C3⋊D3)—62no—
437C4⋊(C3⋊D3)—62no—
438C4⋊(C3⋊D3)—62no—
439C4×C3⋊D3—62no—
440C4×C3⋊D3—121no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—42no—
444C3×#67—62no—
445C3×#67—121no—
446C2×C3×Dic3—24no—
447C2×C3×Dic3—22no—
448C2×C3×Dic3—22no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—62no—
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
476C2×C3×Dic3C22×D311yescharacteristic
477C3×D12—62no—
478C3×D12—121no—
479C3×C4×D3—62no—
480C3×Dic6—62no—
481C3×Dic6—62no—
482#627—22no—
483#626—22no—
484#626—34no—
485#626—34no—
486#626—41no—
487#626—64no—
488#626—62no—
489#626—62no—
490#626—62no—
491#626—62no—
492#626—64no—
493#626—64no—
494#626—64no—
495#626—62no—
496#626—62no—
497#626—62no—
498#626—62no—
499#626—122no—
500#626—121no—
501#626—121no—
502#626—122no—
503#624—62no—
504#624—62no—
505#624—62no—
506#624—122no—
507#624—121no—
508#624—121no—
509#624—122no—
510#624—121no—
511D3×Dic3—22no—
512D3×Dic3—62no—
513D3×Dic3—62no—
514D3×Dic3—121no—
515D3×Dic3—121no—
516#546—271noSylow
517C2×C33—22no—
518C2×C33C22×D411yescharacteristic
519C2×C33C2×#4111yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C3⋊(C3⋊D3)—22no—
522C3⋊(C3⋊D3)—41no—
523C3×C3⋊D3—22no—
524C3×C3⋊D3—41no—
525C32×D3—41no—
526C24×C3—91no—
527C23×D3—31no—
528C23×D3—31no—
529C23×D3—61no—
530C23×D3—91no—
531C23×D3—91no—
532C23×D3—91no—
533C23×D3—181no—
534C23×D3—181no—
535C23×D3—181no—
536C23×D3—361no—
537C2×C3×Q8—91no—
538C2×C3×D4—31no—
539C2×C3×D4—31no—
540C2×C3×D4—61no—
541C2×C3×D4—91no—
542C2×C3×D4—91no—
543C22×C3×C4—31no—
544C22×C3×C4—31no—
545C22×C3×C4—61no—
546C22×C3×C4—91no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—181no—
558C2×#67—181no—
559C2×#67—184no—
560C2×#67D3211yescharacteristic
561C22×Dic3—31no—
562C22×Dic3—91no—
563C22×Dic3—91no—
564C22×Dic3D3211yescharacteristic
565#239—184no—
566#237—184no—
567#235—184no—
568C2×D12—31no—
569C2×D12—31no—
570C2×D12—91no—
571C2×D12—91no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—91no—
575C2×D12—91no—
576C2×D12—91no—
577C2×D12—91no—
578C2×D12—91no—
579C2×D12—91no—
580C2×D12—181no—
581C2×D12—181no—
582C2×D12—181no—
583C2×D12—181no—
584C2×D12—184no—
585C2×D12—184no—
586C2×D12—188no—
587C2×C4×D3—31no—
588C2×C4×D3—91no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×C4×D3—91no—
592C2×C4×D3—91no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—91no—
598C2×C4×D3—181no—
599C2×C4×D3—181no—
600C2×Dic6—31no—
601C2×Dic6—31no—
602C3×C4⋊C4—91no—
603C3×C4⋊C4—91no—
604C3×C4⋊C4—91no—
605C3×C4⋊C4—91no—
606C3×C22⋊C4—31no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—61no—
609C3×C22⋊C4—91no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4—91no—
614C3×C42—91no—
615#217—31no—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—61no—
621#217—61no—
622#217—91no—
623#217—91no—
624#217D3211yescharacteristic
625(C2×D3)⋊C4—31no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—181no—
647(C2×D3)⋊C4—181no—
648(C2×D3)⋊C4—181no—
649(C2×D3)⋊C4—181no—
650C4⋊Dic3—31no—
651C4⋊Dic3—31no—
652C4⋊Dic3—31no—
653Dic3⋊C4—31no—
654Dic3⋊C4—31no—
655Dic3⋊C4—31no—
656Dic3⋊C4—31no—
657Dic3⋊C4—31no—
658C4×Dic3—31no—
659C4×Dic3—31no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—22no—
672C22×C32—22no—
673C22×C32—22no—
674C22×C32—42no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—42no—
681C22×C32—42no—
682C22×C32—61no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32#23512yescomplemented
686C22×C32#23712yescomplemented
687C22×C32#23912yescomplemented
688C22×C32C23×D311yescharacteristic
689C22×C32C23×D311yescharacteristic
690C22×C32C23×D311yescharacteristic
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—44no—
700C2×C3⋊D3—62no—
701C2×C3⋊D3—62no—
702C2×C3⋊D3—62no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—62no—
709C2×C3⋊D3—62no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—61no—
714C2×C3⋊D3—62no—
715C2×C3⋊D3—62no—
716C2×C3⋊D3—62no—
717C2×C3⋊D3—61no—
718C2×C3⋊D3—61no—
719C2×C3⋊D3—61no—
720C2×C3⋊D3—61no—
721C2×C3⋊D3—61no—
722C2×C3⋊D3—61no—
723C2×C3⋊D3—122no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—121no—
727C2×C3⋊D3—121no—
728C2×C3⋊D3—121no—
729C2×C3⋊D3—121no—
730C2×C3⋊D3—121no—
731C2×C3⋊D3—121no—
732C2×C3⋊D3—121no—
733C2×C3⋊D3—121no—
734C2×C3⋊D3—122no—
735C2×C3⋊D3—122no—
736C2×C3⋊D3—122no—
737C2×C3⋊D3—122no—
738C2×C3⋊D3—122no—
739C2×C3⋊D3—124no—
740C2×C3⋊D3—124no—
741C2×C3⋊D3—124no—
742C2×C3⋊D3—128no—
743C2×C3⋊D3—128no—
744C2×C3⋊D3—128no—
745C2×C3⋊D3—1216no—
746C2×C3⋊D3D3×D412yes—
747C2×C3×D3—21no—
748C2×C3×D3—21no—
749C2×C3×D3—21no—
750C2×C3×D3—21no—
751C2×C3×D3—21no—
752C2×C3×D3—21no—
753C2×C3×D3—32no—
754C2×C3×D3—32no—
755C2×C3×D3—41no—
756C2×C3×D3—41no—
757C2×C3×D3—41no—
758C2×C3×D3—62no—
759C2×C3×D3—61no—
760C2×C3×D3—61no—
761C2×C3×D3—61no—
762C2×C3×D3—61no—
763C2×C3×D3—62no—
764C2×C3×D3—61no—
765C2×C3×D3—61no—
766C2×C3×D3—61no—
767C2×C3×D3—61no—
768C2×C3×D3—61no—
769C2×C3×D3—61no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774C2×C3×D3—124no—
775C2×C3×D3—124no—
776C2×C3×D3—128no—
777C32×C4—32no—
778C32×C4—61no—
779C32×C4—61no—
780C32×C4—61no—
781C32×C4—61no—
782C3⋊Dic3—21no—
783C3⋊Dic3—21no—
784C3⋊Dic3—21no—
785C3⋊Dic3—21no—
786C3×Dic3—22no—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—21no—
790C3×Dic3—21no—
791C3×Dic3—21no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—21no—
795C3×Dic3—22no—
796C3×Dic3—41no—
797C3×Dic3—41no—
798C3×Dic3—41no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—61no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—121no—
808C3×Dic3—121no—
809C3×Dic3—121no—
810C3×Dic3—121no—
811C3×Dic3D3×D412yes—
812C3×Dic3D3×D412yes—
813C2×#41—271no—
814C22×D4—271no—
815#124—271no—
816#123—271no—
817#123—271no—
818C22⋊Q8—91no—
819#121—271no—
820#121—271no—
821#121—271no—
822#120—91no—
823#120—271no—
824C4×D4—91no—
825C4×D4—271no—
826C2×C22⋊C4—271no—
827C2×C22⋊C4—271no—
828C33#54611yescharacteristic, complemented, Sylow
829C23×C3—21no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—31no—
833C23×C3—31no—
834C23×C3—41no—
835C23×C3—61no—
836C23×C3—91no—
837C23×C3—91no—
838C23×C3—182no—
839C23×C3—182no—
840C23×C3—361no—
841C23×C3C2×D3211yescharacteristic
842C23×C3C2×D3211yescharacteristic
843C23×C3C2×D3211yescharacteristic
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—31no—
847C22×D3—31no—
848C22×D3—61no—
849C22×D3—61no—
850C22×D3—62no—
851C22×D3—62no—
852C22×D3—64no—
853C22×D3—62no—
854C22×D3—62no—
855C22×D3—91no—
856C22×D3—91no—
857C22×D3—91no—
858C22×D3—91no—
859C22×D3—91no—
860C22×D3—91no—
861C22×D3—122no—
862C22×D3—121no—
863C22×D3—121no—
864C22×D3—122no—
865C22×D3—181no—
866C22×D3—181no—
867C22×D3—181no—
868C22×D3—181no—
869C22×D3—181no—
870C22×D3—181no—
871C22×D3—182no—
872C22×D3—182no—
873C22×D3—182no—
874C22×D3—184no—
875C22×D3—184no—
876C22×D3—182no—
877C22×D3—182no—
878C22×D3—182no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—362no—
882C22×D3—362no—
883C22×D3—362no—
884C22×D3—362no—
885C22×D3—364no—
886C22×D3—364no—
887C22×D3—361no—
888C22×D3—361no—
889C22×D3—361no—
890C22×D3—362no—
891C22×D3—362no—
892C22×D3—362no—
893C22×D3—364no—
894C22×D3C2×D3211yescharacteristic
895C3×Q8—182no—
896C3×D4—62no—
897C3×D4—62no—
898C3×D4—122no—
899C3×D4—182no—
900C3×D4—361no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—31no—
906C2×C3×C4—31no—
907C2×C3×C4—31no—
908C2×C3×C4—31no—
909C2×C3×C4—31no—
910C2×C3×C4—31no—
911C2×C3×C4—61no—
912C2×C3×C4—61no—
913C2×C3×C4—61no—
914C2×C3×C4—61no—
915C2×C3×C4—61no—
916C2×C3×C4—62no—
917C2×C3×C4—62no—
918C2×C3×C4—64no—
919C2×C3×C4—91no—
920C2×C3×C4—91no—
921C2×C3×C4—91no—
922C2×C3×C4—91no—
923C2×C3×C4—182no—
924#67—22no—
925#67—62no—
926#67—94no—
927#67—121no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—362no—
934#67—361no—
935#67—361no—
936#67—362no—
937C2×Dic3—22no—
938C2×Dic3—31no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—31no—
946C2×Dic3—61no—
947C2×Dic3—61no—
948C2×Dic3—61no—
949C2×Dic3—61no—
950C2×Dic3—62no—
951C2×Dic3—182no—
952C2×Dic3—361no—
953C2×Dic3C2×D3211yescharacteristic
954C2×Dic3C2×D3211yescharacteristic
955C2×Dic3C2×D3211yescharacteristic
956C2×Dic3C2×D3211yescharacteristic
957C2×Dic3C2×D3211yescharacteristic
958D12—62no—
959D12—94no—
960D12—94no—
961D12—121no—
962D12—184no—
963D12—182no—
964D12—182no—
965D12—182no—
966D12—182no—
967D12—182no—
968D12—182no—
969D12—184no—
970D12—184no—
971D12—184no—
972D12—182no—
973D12—361no—
974C4×D3—62no—
975C4×D3—182no—
976C4×D3—182no—
977C4×D3—182no—
978C4×D3—182no—
979C4×D3—182no—
980C4×D3—362no—
981C4×D3—361no—
982C4×D3—361no—
983C4×D3—361no—
984C4×D3—361no—
985C4×D3—361no—
986C4×D3—362no—
987Dic6—62no—
988Dic6—62no—
989C2×C32—22no—
990C2×C32—24no—
991C2×C32—22no—
992C2×C32—22no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—42no—
1006C2×C32—42no—
1007C2×C32—44no—
1008C2×C32—121no—
1009C2×C32C2×#23511yescharacteristic
1010C2×C32C2×D3×D411yescharacteristic
1011C2×C32C2×D3×D411yescharacteristic
1012C2×C32C2×D3×D411yescharacteristic
1013C2×C32C2×#23711yescharacteristic
1014C2×C32#100411yescharacteristic
1015C2×C32C2×#23911yescharacteristic
1016C2×C32#100911yescharacteristic
1017C2×C32#100911yescharacteristic
1018C3⋊D3—22no—
1019C3⋊D3—41no—
1020C3⋊D3—62no—
1021C3⋊D3—64no—
1022C3⋊D3—62no—
1023C3⋊D3—62no—
1024C3⋊D3—122no—
1025C3⋊D3—122no—
1026C3⋊D3—124no—
1027C3⋊D3—122no—
1028C3⋊D3—122no—
1029C3⋊D3—122no—
1030C3⋊D3—124no—
1031C3⋊D3—121no—
1032C3⋊D3—121no—
1033C3⋊D3—121no—
1034C3×D3—41no—
1035C3×D3—41no—
1036C3×D3—62no—
1037C3×D3—62no—
1038C3×D3—81no—
1039C3×D3—122no—
1040C3×D3—122no—
1041C3×D3—121no—
1042C3×D3—121no—
1043C24—91no—
1044C24—271no—
1045#41—544no—
1046C2×Q8—91no—
1047C2×D4—31no—
1048C2×D4—91no—
1049C2×D4—91no—
1050C2×D4—271no—
1051C2×D4—271no—
1052C2×D4—271no—
1053C2×D4—271no—
1054C2×D4—271no—
1055C2×D4—271no—
1056C2×D4—544no—
1057C22×C4—31no—
1058C22×C4—91no—
1059C22×C4—271no—
1060C22×C4—271no—
1061C22×C4—271no—
1062C22×C4—271no—
1063C4⋊C4—91no—
1064C4⋊C4—91no—
1065C4⋊C4—91no—
1066C4⋊C4—91no—
1067C22⋊C4—31no—
1068C22⋊C4—91no—
1069C22⋊C4—91no—
1070C22⋊C4—91no—
1071C22⋊C4—91no—
1072C22⋊C4—91no—
1073C22⋊C4—271no—
1074C22⋊C4—271no—
1075C22⋊C4—271no—
1076C22⋊C4—271no—
1077C22⋊C4—271no—
1078C22⋊C4—271no—
1079C42—91no—
1080C22×C3—22no—
1081C22×C3—22no—
1082C22×C3—21no—
1083C22×C3—21no—
1084C22×C3—21no—
1085C22×C3—21no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—22no—
1092C22×C3—22no—
1093C22×C3—22no—
1094C22×C3—41no—
1095C22×C3—41no—
1096C22×C3—41no—
1097C22×C3—41no—
1098C22×C3—42no—
1099C22×C3—42no—
1100C22×C3—41no—
1101C22×C3—42no—
1102C22×C3—61no—
1103C22×C3—61no—
1104C22×C3—61no—
1105C22×C3—61no—
1106C22×C3—61no—
1107C22×C3—61no—
1108C22×C3—92no—
1109C22×C3—121no—
1110C22×C3—121no—
1111C22×C3—121no—
1112C22×C3—181no—
1113C22×C3—181no—
1114C22×C3—181no—
1115C22×C3—181no—
1116C22×C3—181no—
1117C22×C3—364no—
1118C22×C3#379612yescomplemented
1119C22×C3#379912yescomplemented
1120C22×C3#380412yescomplemented
1121C22×C3C22×D3211yescharacteristic
1122C22×C3C22×D3211yescharacteristic
1123C22×C3C22×D3211yescharacteristic
1124C2×D3—21no—
1125C2×D3—21no—
1126C2×D3—21no—
1127C2×D3—32no—
1128C2×D3—32no—
1129C2×D3—62no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—61no—
1133C2×D3—61no—
1134C2×D3—62no—
1135C2×D3—61no—
1136C2×D3—61no—
1137C2×D3—61no—
1138C2×D3—61no—
1139C2×D3—61no—
1140C2×D3—61no—
1141C2×D3—92no—
1142C2×D3—92no—
1143C2×D3—92no—
1144C2×D3—121no—
1145C2×D3—121no—
1146C2×D3—121no—
1147C2×D3—121no—
1148C2×D3—124no—
1149C2×D3—124no—
1150C2×D3—128no—
1151C2×D3—182no—
1152C2×D3—182no—
1153C2×D3—182no—
1154C2×D3—182no—
1155C2×D3—182no—
1156C2×D3—181no—
1157C2×D3—181no—
1158C2×D3—181no—
1159C2×D3—181no—
1160C2×D3—181no—
1161C2×D3—181no—
1162C2×D3—182no—
1163C2×D3—182no—
1164C2×D3—182no—
1165C2×D3—181no—
1166C2×D3—181no—
1167C2×D3—181no—
1168C2×D3—181no—
1169C2×D3—181no—
1170C2×D3—181no—
1171C2×D3—181no—
1172C2×D3—181no—
1173C2×D3—181no—
1174C2×D3—362no—
1175C2×D3—361no—
1176C2×D3—361no—
1177C2×D3—361no—
1178C2×D3—361no—
1179C2×D3—361no—
1180C2×D3—361no—
1181C2×D3—361no—
1182C2×D3—361no—
1183C2×D3—361no—
1184C2×D3—361no—
1185C2×D3—362no—
1186C2×D3—362no—
1187C2×D3—362no—
1188C2×D3—362no—
1189C2×D3—362no—
1190C2×D3—364no—
1191C2×D3—364no—
1192C2×D3—364no—
1193C2×D3—368no—
1194C2×D3—368no—
1195C2×D3—368no—
1196C2×D3—3616no—
1197C3×C4—32no—
1198C3×C4—32no—
1199C3×C4—62no—
1200C3×C4—62no—
1201C3×C4—61no—
1202C3×C4—61no—
1203C3×C4—61no—
1204C3×C4—61no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—61no—
1209C3×C4—121no—
1210C3×C4—121no—
1211C3×C4—121no—
1212C3×C4—181no—
1213C3×C4—181no—
1214C3×C4—181no—
1215C3×C4—181no—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—61no—
1221Dic3—61no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—121no—
1229Dic3—121no—
1230Dic3—121no—
1231Dic3—121no—
1232Dic3#381112yes—
1233C32—21no—
1234C32—21no—
1235C32—21no—
1236C32—41no—
1237C32#555011yescharacteristic, complemented
1238C32#559111yescharacteristic, complemented
1239C32#563011yescharacteristic, complemented
1240C23—31no—
1241C23—91no—
1242C23—91no—
1243C23—182no—
1244C23—182no—
1245C23—271no—
1246C23—271no—
1247C23—361no—
1248C23—542no—
1249C23—542no—
1250C23—1081no—
1251C23D3311yescharacteristic
1252Q8—182no—
1253D4—62no—
1254D4—182no—
1255D4—274no—
1256D4—361no—
1257D4—542no—
1258D4—542no—
1259D4—542no—
1260D4—542no—
1261D4—1081no—
1262C2×C4—31no—
1263C2×C4—31no—
1264C2×C4—31no—
1265C2×C4—31no—
1266C2×C4—31no—
1267C2×C4—62no—
1268C2×C4—91no—
1269C2×C4—91no—
1270C2×C4—91no—
1271C2×C4—91no—
1272C2×C4—182no—
1273C2×C4—542no—
1274C2×C4—542no—
1275C2×C4—1081no—
1276C2×C4—1081no—
1277C2×C3—24no—
1278C2×C3—22no—
1279C2×C3—22no—
1280C2×C3—22no—
1281C2×C3—21no—
1282C2×C3—21no—
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—42no—
1291C2×C3—42no—
1292C2×C3—44no—
1293C2×C3—41no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—121no—
1297C2×C3—121no—
1298C2×C3—182no—
1299C2×C3—241no—
1300C2×C3—361no—
1301C2×C3C2×#379611yescharacteristic
1302C2×C3C2×#379911yescharacteristic
1303C2×C3#6430811yescharacteristic
1304C2×C3D32×D411yescharacteristic
1305C2×C3D32×D411yescharacteristic
1306C2×C3#6431411yescharacteristic
1307C2×C3#6431411yescharacteristic
1308C2×C3C2×#380411yescharacteristic
1309C2×C3C2×#381111yescharacteristic
1310D3—41no—
1311D3—62no—
1312D3—62no—
1313D3—122no—
1314D3—122no—
1315D3—121no—
1316D3—121no—
1317D3—184no—
1318D3—182no—
1319D3—182no—
1320D3—182no—
1321D3—362no—
1322D3—362no—
1323D3—364no—
1324D3—362no—
1325D3—362no—
1326D3—362no—
1327D3—364no—
1328D3—361no—
1329D3—361no—
1330D3—361no—
1331C22—21no—
1332C22—21no—
1333C22—61no—
1334C22—61no—
1335C22—61no—
1336C22—92no—
1337C22—181no—
1338C22—181no—
1339C22—181no—
1340C22—181no—
1341C22—181no—
1342C22—272no—
1343C22—364no—
1344C22—541no—
1345C22—541no—
1346C22—541no—
1347C22—541no—
1348C22—541no—
1349C22—1084no—
1350C22#8896212yescomplemented
1351C22C2×D3311yescharacteristic
1352C4—32no—
1353C4—61no—
1354C4—61no—
1355C4—61no—
1356C4—61no—
1357C4—181no—
1358C4—181no—
1359C4—181no—
1360C4—181no—
1361C3—21no—
1362C3—21no—
1363C3—21no—
1364C3—41no—
1365C3#1059406311yescharacteristic, complemented
1366C3#1059501811yescharacteristic, complemented
1367C3#1059513511yescharacteristic, complemented
1368C2—22no—
1369C2—121no—
1370C2—182no—
1371C2—361no—
1372C2—542no—
1373C2—1081no—
1374C2#1172442011yescharacteristic
1375C2C2×#8896211yescharacteristic
1376C2D3×#381111yescharacteristic
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. C22×#6292C2semidirect
2. C2×#88962C2semidirect
3. #11723723C2semidirect
4. #11723638C2semidirect
5. #11723627C2semidirect
6. C3×#63981C2semidirect
7. C3×Dic3×#67C2semidirect
8. C3×#63964C2semidirect
9. #11723003C2semidirect
10. #11723000C2semidirect
11. #11722999C2semidirect
12. #11722966C2semidirect
13. #11722963C2semidirect
14. #11722959C2semidirect
15. #11722937C2semidirect
23. C2×#6294C22semidirect
24. C2×#6294C22semidirect
30. C2×#6291C22semidirect
31. C2×#6291C22semidirect
32. C2×#6289C22semidirect
33. C2×#6289C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×D3×Dic3C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
74. #63981D3semidirect
80. Dic3×#67D3semidirect
84. #63964D3semidirect
132. #6292D4semidirect
180. C2×#627C2×D3semidirect
202. C2×#626C2×D3semidirect
203. C2×#626C2×D3semidirect
217. C2×D3×Dic3C2×D3semidirect
252. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
270. #3722C2×D3semidirect
271. #3722C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
280. C22×C33#41semidirect
685. C22×C32#235semidirect
686. C22×C32#237semidirect
687. C22×C32#239semidirect
828. C33#546semidirect
1118. C22×C3#3796semidirect
1119. C22×C3#3799semidirect
1120. C22×C3#3804semidirect
1237. C32#5550semidirect
1238. C32#5591semidirect
1239. C32#5630semidirect
1350. C22#88962semidirect
1365. C3#10594063semidirect
1366. C3#10595018semidirect
1367. C3#10595135semidirect

Maximal subgroups

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

subgroupindex
C22×#62922
C2×#889622
#117237232
#117236382
#117236272
C3×#639812
C3×Dic3×#672
C3×#639642
#117230032
#117230002
#117229992
#117229662
#117229632
#117229592
#117229372
#105951353
#105950183
#105940633