Finite Group Databasebeta

← #13172703

Subgroups — #13172703

Order 1728.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89028C211yesmaximal, characteristic, complemented
2C2×#88952C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723599C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#63980C211yesmaximal, characteristic, complemented
8C3×#63970C211yesmaximal, characteristic, complemented
9#11723004C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722989C211yesmaximal, characteristic, complemented
12#11722984C211yesmaximal, characteristic, complemented
13#11722935C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595296—31nomaximal
18#10595294—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×#6294C2211yescharacteristic
28C2×#6293C2211yescharacteristic, complemented
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33#89028—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
35C2×C3×#625C2211yescharacteristic
36C2×C3×#625C2211yescharacteristic
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88952—24no—
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic
42#88813C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3830—31no—
57C2×#3811—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×#3804—31no—
61C2×#3804—31no—
62C2×#3804—61no—
63#64147—31no—
64#64146—31no—
65C3×#939—31no—
66C3×#939—31no—
67C3×#939—31no—
68C3×#938—31no—
69C3×#937—31no—
70C3×#937—31no—
71#63983—31no—
72#63983—31no—
73#63983—61no—
74#63983D311yescharacteristic, complemented
75#63980D311yescharacteristic, complemented
76#63975—31no—
77#63974—31no—
78#67⋊Dic3—31no—
79Dic3×#67—31no—
80#63970D311yescharacteristic, complemented
81#63969—31no—
82D3×#217—31no—
83#63962—31no—
84C2×(C2×D3)⋊Dic3—31no—
85#63959—31no—
86#63959—31no—
87#63958—31no—
88#63958—31no—
89#63958—61no—
90#63952—31no—
91#63952—31no—
92#63921—31no—
93#63921—31no—
94D3×(C2×D3)⋊C4—31no—
95#63913—31no—
96#63904—31no—
97#63896—31no—
98#63895—31no—
99#63893—31no—
100#63891—31no—
101#63881—31no—
102#63854—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×D3×C3⋊D3—41no—
113C2×C3×D32—22no—
114C2×C3×D32—22no—
115C2×C3×D32—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C2×C3×C3⋊Dic3—22no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C32×#67—41no—
127C32×#67—41no—
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6294—22no—
132#6293—22no—
133#6291—22no—
134#6291D414yescomplemented
135#6289—22no—
136#6289—41no—
137D3×C3⋊Dic3—22no—
138C3×#625—22no—
139C3×#625—22no—
140C3×D3×Dic3—41no—
141#5612—91no—
142#5610—91no—
143#5591—91no—
144C23×C3⋊D3—31no—
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32—61no—
150C22×D32C2×D311yescharacteristic
151C2×C32×D4—31no—
152C2×C32×D4—31no—
153C2×C32×D4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—61no—
162C2×#638—121no—
163C2×#638C2×D311yescharacteristic
164C22×C3⋊Dic3—31no—
165C22×C3⋊Dic3C2×D311yescharacteristic, complemented
166#3830—64no—
167C2×C4×C3⋊D3—31no—
168C2×C4×C3⋊D3—31no—
169C2×#634—31no—
170C2×C3×#67—21no—
171C2×C3×#67—21no—
172C2×C3×#67—21no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—61no—
180C2×C3×#67C2×D311yescharacteristic, complemented
181C2×C3×#67C2×D311yescharacteristic, complemented
182C2×C3×#67C2×D311yescharacteristic, complemented
183C2×C3×#67C2×D311yescharacteristic, complemented
184C2×C3×#67C2×D311yescharacteristic, complemented
185C2×C3×#67C2×D311yescharacteristic, complemented
186C22×C3×Dic3—31no—
187C22×C3×Dic3—31no—
188C22×C3×Dic3—31no—
189C22×C3×Dic3—61no—
190C2×C3×C4×D3—31no—
191#3811—64no—
192D3×#67—64no—
193D3×#67—64no—
194C2×#627—31no—
195C2×#627—31no—
196C2×#627—61no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—61no—
202C2×#626—61no—
203C2×#625C2×D311yescharacteristic
204C2×#625C2×D311yescharacteristic
205C2×#624—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—61no—
211C2×#624—61no—
212#3804—64no—
213#3804—64no—
214#3804—68no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—61no—
220C2×D3×Dic3C2×D311yescharacteristic, complemented
221#3757—31no—
222#3757—31no—
223#3757C2×D311yescharacteristic, complemented
224#3752—31no—
225#3752—31no—
226C4⋊(C3⋊Dic3)—31no—
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—61no—
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×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×C4⋊Dic3—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246#3724—31no—
247#3724C2×D311yescharacteristic, complemented
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—61no—
258#3722C2×D311yescharacteristic
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—61no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)C2×D412yes—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3#4112yescomplemented
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3C2×D412yes—
297D3×C3⋊D3—44no—
298C3×D32—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3C2×D412yes—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C2×#237—91no—
310C2×#237—91no—
311C2×#237—181no—
312C2×D3×D4—91no—
313C2×D3×D4—91no—
314C2×#235—91no—
315C3×#121—91no—
316C3×#121—91no—
317C3×#120—91no—
318C2×#217—91no—
319#939—31no—
320#939—31no—
321#939—31no—
322#938—31no—
323#938—91no—
324#938—91no—
325#938—181no—
326#937—31no—
327#937—31no—
328#937—91no—
329#937—91no—
330#937—91no—
331#937—181no—
332#936—91no—
333#935—91no—
334D4×Dic3—91no—
335C4×#67—91no—
336C4×#67—91no—
337C2×(C2×D3)⋊C4—91no—
338#897—91no—
339#896—91no—
340#894—91no—
341#893—91no—
342#886—91no—
343#885—91no—
344#885—91no—
345#884—91no—
346#883—91no—
347#883—91no—
348#883—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C23×C32C22×D311yescharacteristic
366C22×C3⋊D3—31no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—61no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—62no—
373C22×C3⋊D3—62no—
374C22×C3⋊D3—121no—
375C22×C3⋊D3—121no—
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—21no—
378C22×C3×D3—21no—
379C22×C3×D3—21no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—61no—
383C22×C3×D3—62no—
384C22×C3×D3—62no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—121no—
388C22×C3×D3—121no—
389C22×C3×D3C22×D311yescharacteristic
390C22×C3×D3C22×D311yescharacteristic
391C22×C3×D3C22×D311yescharacteristic
392C22×C3×D3C22×D311yescharacteristic
393C22×C3×D3C22×D311yescharacteristic
394C22×C3×D3C22×D311yescharacteristic
395C2×D32—22no—
396C2×D32—22no—
397C2×D32—41no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—62no—
402C2×D32—122no—
403C2×D32—122no—
404C2×D32—121no—
405C2×D32—121no—
406C2×D32—122no—
407C32×D4—62no—
408C32×D4—121no—
409C32×D4—121no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413#638—22no—
414#638—34no—
415#638—62no—
416#638—62no—
417#638—62no—
418#638—62no—
419#638—64no—
420#638—122no—
421#638—122no—
422#638—124no—
423C2×C3⋊Dic3—22no—
424C2×C3⋊Dic3—31no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—61no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—62no—
431C2×C3⋊Dic3—121no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C4×C3⋊D3—62no—
438C4×C3⋊D3—121no—
439#634—62no—
440C3×#67—24no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—41no—
444C3×#67—41no—
445C3×#67—41no—
446C3×#67—41no—
447C3×#67—42no—
448C3×#67—42no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—62no—
455C3×#67—122no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—31no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3—61no—
473C2×C3×Dic3—61no—
474C2×C3×Dic3—62no—
475C2×C3×Dic3—62no—
476C2×C3×Dic3—64no—
477C2×C3×Dic3—121no—
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C2×C3×Dic3C22×D311yescharacteristic
484C3×C4×D3—121no—
485#627—62no—
486#627—62no—
487#627—64no—
488#626—34no—
489#626—34no—
490#626—64no—
491#626—62no—
492#626—62no—
493#626—122no—
494#625—22no—
495#625—22no—
496#624—62no—
497#624—62no—
498#624—64no—
499#624—62no—
500#624—121no—
501#624—121no—
502#624—122no—
503D3×Dic3—41no—
504D3×Dic3—62no—
505D3×Dic3—64no—
506D3×Dic3—62no—
507D3×Dic3—62no—
508D3×Dic3—62no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—22no—
515C3×C3⋊D3—22no—
516C32×D3—22no—
517C32×D3—41no—
518C32×D3—41no—
519C24×C3—91no—
520C23×D3—31no—
521C23×D3—31no—
522C23×D3—91no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—181no—
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—31no—
529C2×C3×D4—31no—
530C2×C3×D4—31no—
531C2×C3×D4—31no—
532C2×C3×D4—61no—
533C2×C3×D4—61no—
534C2×C3×D4—61no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C2×C3×D4—91no—
538C22×C3×C4—91no—
539C22×C3×C4—91no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—61no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—181no—
559C2×#67—184no—
560C2×#67—361no—
561C2×#67D3211yescharacteristic, complemented
562C2×#67D3211yescharacteristic, complemented
563C2×#67D3211yescharacteristic, complemented
564C22×Dic3—31no—
565C22×Dic3—31no—
566C22×Dic3—31no—
567C22×Dic3—61no—
568C22×Dic3—91no—
569C22×Dic3—91no—
570C22×Dic3—91no—
571C22×Dic3—181no—
572#237—184no—
573#237—184no—
574#237—188no—
575D3×D4—184no—
576D3×D4—184no—
577#235—184no—
578C2×D12—91no—
579C2×D12—91no—
580C2×C4×D3—31no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—91no—
590C2×C4×D3—181no—
591C2×C4×D3—181no—
592C2×Dic6—91no—
593C2×Dic6—91no—
594C2×Dic6—91no—
595C2×Dic6—181no—
596C3×C4⋊C4—91no—
597C3×C4⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—31no—
612#217—61no—
613#217—91no—
614#217—91no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—181no—
620#217—181no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—31no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
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—181no—
638(C2×D3)⋊C4—181no—
639C4⋊Dic3—31no—
640C4⋊Dic3—91no—
641C4⋊Dic3—91no—
642C4⋊Dic3—91no—
643C4⋊Dic3—181no—
644Dic3⋊C4—31no—
645Dic3⋊C4—31no—
646Dic3⋊C4—31no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—91no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—32no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—42no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—61no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—81no—
686C22×C32—81no—
687C22×C32C23×D311yescharacteristic
688C22×C32C23×D311yescharacteristic
689C22×C32C23×D311yescharacteristic
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—32no—
693C2×C3⋊D3—32no—
694C2×C3⋊D3—32no—
695C2×C3⋊D3—62no—
696C2×C3⋊D3—62no—
697C2×C3⋊D3—62no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—122no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—124no—
712C2×C3⋊D3—241no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3#23712yescomplemented
715C2×C3×D3—21no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—22no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
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—22no—
733C2×C3×D3—32no—
734C2×C3×D3—32no—
735C2×C3×D3—41no—
736C2×C3×D3—41no—
737C2×C3×D3—41no—
738C2×C3×D3—41no—
739C2×C3×D3—41no—
740C2×C3×D3—41no—
741C2×C3×D3—41no—
742C2×C3×D3—62no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—121no—
748C2×C3×D3—121no—
749C2×C3×D3—124no—
750C2×C3×D3—124no—
751C2×C3×D3D3×D412yes—
752C2×C3×D3D3×D412yes—
753D32—44no—
754D32—124no—
755D32—124no—
756D32—128no—
757C32×C4—61no—
758C32×C4—61no—
759C32×C4—61no—
760C3⋊Dic3—21no—
761C3⋊Dic3—21no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—61no—
765C3⋊Dic3—62no—
766C3⋊Dic3—61no—
767C3⋊Dic3—61no—
768C3⋊Dic3—121no—
769C3⋊Dic3—121no—
770C3⋊Dic3—122no—
771C3⋊Dic3D3×D412yes—
772C3×Dic3—22no—
773C3×Dic3—22no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—32no—
781C3×Dic3—32no—
782C3×Dic3—41no—
783C3×Dic3—62no—
784C3×Dic3—62no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—121no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C2×#41—271no—
797C22×D4—271no—
798#124—271no—
799#123—271no—
800#123—271no—
801C22⋊Q8—271no—
802#121—91no—
803#121—91no—
804#121—271no—
805#120—91no—
806#120—271no—
807C4×D4—271no—
808C4×D4—271no—
809C2×C22⋊C4—271no—
810C2×C22⋊C4—271no—
811C33#54611yescharacteristic, complemented, Sylow
812C23×C3—21no—
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—31no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—31no—
820C23×C3—31no—
821C23×C3—41no—
822C23×C3—61no—
823C23×C3—61no—
824C23×C3—61no—
825C23×C3—91no—
826C23×C3—182no—
827C23×C3—182no—
828C23×C3—361no—
829C23×C3C2×D3211yescharacteristic
830C23×C3C2×D3211yescharacteristic
831C23×C3C2×D3211yescharacteristic
832C22×D3—31no—
833C22×D3—31no—
834C22×D3—61no—
835C22×D3—62no—
836C22×D3—62no—
837C22×D3—62no—
838C22×D3—62no—
839C22×D3—91no—
840C22×D3—91no—
841C22×D3—91no—
842C22×D3—121no—
843C22×D3—121no—
844C22×D3—181no—
845C22×D3—181no—
846C22×D3—181no—
847C22×D3—182no—
848C22×D3—182no—
849C22×D3—182no—
850C22×D3—182no—
851C22×D3—182no—
852C22×D3—182no—
853C22×D3—361no—
854C22×D3—362no—
855C22×D3—362no—
856C22×D3—361no—
857C22×D3—361no—
858C22×D3—361no—
859C22×D3—362no—
860C22×D3C2×D3211yescharacteristic
861C22×D3C2×D3211yescharacteristic
862C22×D3C2×D3211yescharacteristic
863C3×D4—62no—
864C3×D4—62no—
865C3×D4—64no—
866C3×D4—121no—
867C3×D4—121no—
868C3×D4—121no—
869C3×D4—121no—
870C3×D4—122no—
871C3×D4—122no—
872C3×D4—182no—
873C3×D4—182no—
874C3×D4—182no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—61no—
882C2×C3×C4—61no—
883C2×C3×C4—61no—
884C2×C3×C4—91no—
885C2×C3×C4—91no—
886C2×C3×C4—91no—
887C2×C3×C4—91no—
888C2×C3×C4—91no—
889C2×C3×C4—182no—
890C2×C3×C4—361no—
891#67—22no—
892#67—41no—
893#67—41no—
894#67—62no—
895#67—62no—
896#67—62no—
897#67—62no—
898#67—62no—
899#67—62no—
900#67—94no—
901#67—94no—
902#67—122no—
903#67—184no—
904#67—182no—
905#67—182no—
906#67—182no—
907#67—182no—
908#67—182no—
909#67—184no—
910#67—362no—
911#67—362no—
912#67—362no—
913#67—364no—
914C2×Dic3—31no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—61no—
925C2×Dic3—61no—
926C2×Dic3—61no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—62no—
930C2×Dic3—62no—
931C2×Dic3—64no—
932C2×Dic3—91no—
933C2×Dic3—91no—
934C2×Dic3—91no—
935C2×Dic3—121no—
936C2×Dic3—181no—
937C2×Dic3—181no—
938C2×Dic3—181no—
939C2×Dic3—182no—
940C2×Dic3—182no—
941C2×Dic3—182no—
942C2×Dic3—184no—
943C2×Dic3—361no—
944C2×Dic3C2×D3211yescharacteristic
945C2×Dic3C2×D3211yescharacteristic
946C2×Dic3C2×D3211yescharacteristic
947D12—94no—
948D12—182no—
949C4×D3—121no—
950C4×D3—182no—
951C4×D3—182no—
952C4×D3—182no—
953C4×D3—182no—
954C4×D3—184no—
955C4×D3—182no—
956C4×D3—182no—
957C4×D3—361no—
958C4×D3—361no—
959C4×D3—361no—
960C4×D3—362no—
961Dic6—182no—
962Dic6—182no—
963Dic6—182no—
964Dic6—184no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—41no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—42no—
979C2×C32—41no—
980C2×C32—41no—
981C2×C32—62no—
982C2×C32—81no—
983C2×C32—81no—
984C2×C32—82no—
985C2×C32—121no—
986C2×C32—121no—
987C2×C32C2×D3×D411yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×#23711yescharacteristic
991C2×C32#100411yescharacteristic
992C2×C32#100411yescharacteristic
993C2×C32#100411yescharacteristic
994C2×C32D3×#4111yescharacteristic
995C2×C32D3×#4111yescharacteristic
996C3⋊D3—22no—
997C3⋊D3—62no—
998C3⋊D3—62no—
999C3⋊D3—62no—
1000C3⋊D3—122no—
1001C3⋊D3—122no—
1002C3⋊D3—122no—
1003C3⋊D3—242no—
1004C3×D3—22no—
1005C3×D3—22no—
1006C3×D3—42no—
1007C3×D3—42no—
1008C3×D3—41no—
1009C3×D3—41no—
1010C3×D3—41no—
1011C3×D3—41no—
1012C3×D3—62no—
1013C3×D3—62no—
1014C3×D3—81no—
1015C3×D3—122no—
1016C24—91no—
1017C24—271no—
1018#41—544no—
1019C2×Q8—271no—
1020C2×D4—31no—
1021C2×D4—31no—
1022C2×D4—31no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—544no—
1030C22×C4—91no—
1031C22×C4—91no—
1032C22×C4—271no—
1033C22×C4—271no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C4⋊C4—91no—
1037C4⋊C4—91no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C22⋊C4—91no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—271no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C42—271no—
1053C22×C3—22no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—32no—
1067C22×C3—32no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—42no—
1077C22×C3—41no—
1078C22×C3—62no—
1079C22×C3—62no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—61no—
1091C22×C3—61no—
1092C22×C3—61no—
1093C22×C3—61no—
1094C22×C3—61no—
1095C22×C3—61no—
1096C22×C3—81no—
1097C22×C3—81no—
1098C22×C3—92no—
1099C22×C3—121no—
1100C22×C3—121no—
1101C22×C3—121no—
1102C22×C3—121no—
1103C22×C3—121no—
1104C22×C3—121no—
1105C22×C3—121no—
1106C22×C3—181no—
1107C22×C3—181no—
1108C22×C3—364no—
1109C22×C3C22×D3211yescharacteristic
1110C22×C3C22×D3211yescharacteristic
1111C22×C3C22×D3211yescharacteristic
1112C2×D3—21no—
1113C2×D3—21no—
1114C2×D3—21no—
1115C2×D3—21no—
1116C2×D3—21no—
1117C2×D3—21no—
1118C2×D3—21no—
1119C2×D3—21no—
1120C2×D3—32no—
1121C2×D3—32no—
1122C2×D3—62no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—92no—
1128C2×D3—92no—
1129C2×D3—92no—
1130C2×D3—121no—
1131C2×D3—121no—
1132C2×D3—124no—
1133C2×D3—124no—
1134C2×D3—182no—
1135C2×D3—182no—
1136C2×D3—182no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—362no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—364no—
1151C2×D3—364no—
1152C2×D3—364no—
1153C2×D3—368no—
1154C2×D3—721no—
1155C2×D3—721no—
1156C2×D3#381112yes—
1157C3×C4—62no—
1158C3×C4—62no—
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—92no—
1166C3×C4—121no—
1167C3×C4—181no—
1168C3×C4—181no—
1169C3×C4—181no—
1170C3×C4—181no—
1171Dic3—21no—
1172Dic3—21no—
1173Dic3—21no—
1174Dic3—32no—
1175Dic3—32no—
1176Dic3—62no—
1177Dic3—62no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—121no—
1187Dic3—121no—
1188Dic3—121no—
1189Dic3—182no—
1190Dic3—181no—
1191Dic3—181no—
1192Dic3—181no—
1193Dic3—361no—
1194Dic3—361no—
1195Dic3—362no—
1196C32—21no—
1197C32—21no—
1198C32—21no—
1199C32—41no—
1200C32#559111yescharacteristic, complemented
1201C32#561011yescharacteristic, complemented
1202C32#561211yescharacteristic, complemented
1203C23—31no—
1204C23—31no—
1205C23—31no—
1206C23—91no—
1207C23—182no—
1208C23—182no—
1209C23—271no—
1210C23—361no—
1211C23—542no—
1212C23—542no—
1213C23—1081no—
1214C23D3311yescharacteristic
1215Q8—542no—
1216D4—62no—
1217D4—121no—
1218D4—121no—
1219D4—182no—
1220D4—182no—
1221D4—182no—
1222D4—274no—
1223D4—542no—
1224D4—542no—
1225C2×C4—31no—
1226C2×C4—31no—
1227C2×C4—31no—
1228C2×C4—91no—
1229C2×C4—91no—
1230C2×C4—91no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—182no—
1234C2×C4—271no—
1235C2×C4—361no—
1236C2×C4—542no—
1237C2×C4—542no—
1238C2×C4—542no—
1239C2×C4—1081no—
1240C2×C3—21no—
1241C2×C3—21no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—42no—
1250C2×C3—41no—
1251C2×C3—41no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—62no—
1257C2×C3—62no—
1258C2×C3—81no—
1259C2×C3—81no—
1260C2×C3—82no—
1261C2×C3—122no—
1262C2×C3—122no—
1263C2×C3—121no—
1264C2×C3—121no—
1265C2×C3—121no—
1266C2×C3—121no—
1267C2×C3—182no—
1268C2×C3—241no—
1269C2×C3D32×D411yescharacteristic
1270C2×C3D32×D411yescharacteristic
1271C2×C3D3×#23711yescharacteristic
1272C2×C3D3×#23711yescharacteristic
1273C2×C3#6431211yescharacteristic
1274C2×C3#6431311yescharacteristic
1275C2×C3C2×#381111yescharacteristic
1276C2×C3#6433011yescharacteristic
1277C2×C3#6433011yescharacteristic
1278D3—22no—
1279D3—41no—
1280D3—41no—
1281D3—62no—
1282D3—62no—
1283D3—122no—
1284D3—182no—
1285D3—182no—
1286D3—182no—
1287D3—362no—
1288D3—362no—
1289D3—362no—
1290D3—722no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—32no—
1295C22—61no—
1296C22—61no—
1297C22—61no—
1298C22—61no—
1299C22—61no—
1300C22—61no—
1301C22—61no—
1302C22—61no—
1303C22—92no—
1304C22—181no—
1305C22—181no—
1306C22—272no—
1307C22—364no—
1308C22—541no—
1309C22—541no—
1310C22—1084no—
1311C22C2×D3311yescharacteristic
1312C4—61no—
1313C4—61no—
1314C4—61no—
1315C4—92no—
1316C4—181no—
1317C4—181no—
1318C4—181no—
1319C4—181no—
1320C4—541no—
1321C3—21no—
1322C3—21no—
1323C3—21no—
1324C3—41no—
1325C3#1059529411yescharacteristic, complemented
1326C3#1059529611yescharacteristic, complemented
1327C3#1059530711yescharacteristic, complemented
1328C2—41no—
1329C2—62no—
1330C2—121no—
1331C2—121no—
1332C2—182no—
1333C2—542no—
1334C2#1172440811yescharacteristic
1335C2#1172441411yescharacteristic
1336C2D3×#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. C2×#89028C2semidirect
2. C2×#88952C2semidirect
3. #11723726C2semidirect
4. #11723643C2semidirect
5. #11723599C2semidirect
6. C3×#63983C2semidirect
7. C3×#63980C2semidirect
8. C3×#63970C2semidirect
9. #11723004C2semidirect
10. #11722996C2semidirect
11. #11722989C2semidirect
12. #11722984C2semidirect
13. #11722935C2semidirect
14. #11722906C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×#6312C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×#67C22semidirect
28. C2×#6293C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
42. #88813C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88804C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
74. #63983D3semidirect
75. #63980D3semidirect
80. #63970D3semidirect
134. #6291D4semidirect
165. C22×C3⋊Dic3C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
181. C2×C3×#67C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
183. C2×C3×#67C2×D3semidirect
184. C2×C3×#67C2×D3semidirect
185. C2×C3×#67C2×D3semidirect
220. C2×D3×Dic3C2×D3semidirect
223. #3757C2×D3semidirect
247. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
287. C2×C3×C3⋊D3#41semidirect
561. C2×#67D32semidirect
562. C2×#67D32semidirect
563. C2×#67D32semidirect
714. C2×C3⋊D3#237semidirect
811. C33#546semidirect
1200. C32#5591semidirect
1201. C32#5610semidirect
1202. C32#5612semidirect
1325. C3#10595294semidirect
1326. C3#10595296semidirect
1327. C3#10595307semidirect

Maximal subgroups

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

subgroupindex
C2×#890282
C2×#889522
#117237262
#117236432
#117235992
C3×#639832
C3×#639802
C3×#639702
#117230042
#117229962
#117229892
#117229842
#117229352
#117229062
D3×(C2×D3)⋊Dic32
#105953073
#105952963
#105952943