Finite Group Databasebeta

← #13172854

Subgroups — #13172854

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#88960C211yesmaximal, characteristic, complemented
3#11723725C211yesmaximal, characteristic, complemented
4#11723624C211yesmaximal, characteristic, complemented
5#11723592C211yesmaximal, characteristic, complemented
6C3×#63977C211yesmaximal, characteristic, complemented
7C3×#63975C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11722987C211yesmaximal, characteristic, complemented
10#11722980C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722950C211yesmaximal, characteristic, complemented
13#11722936C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10594274—31nomaximal
18#10594272—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×#6295C2211yescharacteristic, complemented
25C2×#6294C2211yescharacteristic, complemented
26D3×#638—24no—
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic, complemented
29C2×#6291C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×D3×C3⋊Dic3C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88960—24no—
39C3×#3757C2211yescharacteristic, complemented
40C32×#217C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×#67—61no—
60C2×#3804—31no—
61C2×#3798—31no—
62C2×#3795—31no—
63#64094—31no—
64#64093—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#883—31no—
68C3×#883—31no—
69C3×#882—31no—
70C3×D3×C22⋊C4—31no—
71#63982—31no—
72#63981—31no—
73#63978—31no—
74#63977D311yescharacteristic, complemented
75#63975D311yescharacteristic, complemented
76#63974—31no—
77#67⋊Dic3—31no—
78#63971—31no—
79#63971—31no—
80#63971—31no—
81#63971—61no—
82#63970—31no—
83D3×#217D311yescharacteristic, complemented
84#63966—31no—
85#63958—31no—
86#63953—31no—
87#63953—31no—
88#63953—61no—
89#63952—31no—
90#63923—31no—
91#63922—31no—
92D3×(C2×D3)⋊C4—31no—
93D3×(C2×D3)⋊C4—31no—
94#63909—31no—
95#63902—31no—
96#63899—31no—
97#63898—31no—
98#63896—31no—
99#63890—31no—
100#63886—31no—
101#63881—31no—
102#63879—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3—22no—
109C22×C32×D3—22no—
110C22×C32×D3—41no—
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—41no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6295—22no—
129#6294—41no—
130#6293—22no—
131#6292—41no—
132#6291—22no—
133#6290D414yescomplemented
134Dic3×C3⋊D3—22no—
135D3×C3⋊Dic3—22no—
136C3×#626—22no—
137C3×#626—22no—
138C3×#624—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5654—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3—31no—
146C23×C3×D3—21no—
147C23×C3×D3C2×D311yescharacteristic
148C23×C3×D3C2×D311yescharacteristic
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×#638—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—64no—
158C2×#638—61no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—121no—
162C2×#638C2×D311yescharacteristic
163C2×#638C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3—31no—
165C2×C4⋊(C3⋊D3)—31no—
166C2×C4×C3⋊D3—31no—
167C2×#634—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—61no—
175C2×C3×#67—61no—
176C22×C3×Dic3—31no—
177C22×C3×Dic3—31no—
178C2×C3×D12—31no—
179C2×C3×D12—31no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×C3×C4×D3—31no—
183C2×C3×C4×D3—31no—
184D3×#67—64no—
185D3×#67—64no—
186D3×#67—68no—
187C2×#627—31no—
188C2×#627—31no—
189C2×#627—61no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—61no—
197C2×#626—61no—
198C2×#626C2×D311yescharacteristic
199C2×#626C2×D311yescharacteristic, complemented
200C2×#625—31no—
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—61no—
204C2×#624—31no—
205C2×#624C2×D311yescharacteristic, complemented
206#3804—64no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—61no—
214C2×D3×Dic3—61no—
215C2×D3×Dic3C2×D311yescharacteristic, complemented
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217#3798—64no—
218#3795—64no—
219C32×C22⋊C4—31no—
220C32×C22⋊C4—31no—
221#3757C2×D311yescharacteristic, complemented
222#3752—31no—
223#3752—31no—
224#3752—31no—
225#3750—31no—
226C4×C3⋊Dic3—31no—
227C3×#217—21no—
228C3×#217—21no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—61no—
236C3×#217C2×D311yescharacteristic, complemented
237C3×#217C2×D311yescharacteristic, complemented
238C3×#217C2×D311yescharacteristic, complemented
239C3×#217C2×D311yescharacteristic, complemented
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×C4⋊Dic3—31no—
247C3×C4⋊Dic3—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250#3724—31no—
251#3724—31no—
252#3724—31no—
253#3724—61no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3C2×D311yescharacteristic, complemented
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—61no—
266#3722—61no—
267#3722—61no—
268#3722C2×D311yescharacteristic, complemented
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273(C2×D3)⋊Dic3C2×D311yescharacteristic
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—61no—
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)—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3C2×D412yes—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—44no—
296C2×C32×D3C2×D412yes—
297C2×C32×D3#4112yescomplemented
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)C2×D412yes—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C22×#67—91no—
310C22×#67—181no—
311C2×#237—91no—
312C2×D3×D4—91no—
313C2×#235—91no—
314C2×#235—91no—
315C3×#123—91no—
316C3×#120—91no—
317C2×C3×C22⋊C4—91no—
318#953—31no—
319C2×#217—31no—
320#939—91no—
321#939—91no—
322#939—91no—
323#938—91no—
324#937—91no—
325D4×Dic3—91no—
326#930—91no—
327#929—91no—
328C4×#67—91no—
329C2×(C2×D3)⋊C4—91no—
330#896—91no—
331#895—91no—
332#894—91no—
333#893—91no—
334#886—91no—
335#885—91no—
336#885—91no—
337#885—91no—
338#885—181no—
339#884—91no—
340#884—91no—
341#884—91no—
342#884—181no—
343#883—31no—
344#883—31no—
345#882—31no—
346#882—91no—
347#882—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351D3×C22⋊C4—31no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32—62no—
363C23×C32—62no—
364C23×C32—121no—
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—62no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—24no—
381C22×C3×D3—22no—
382C22×C3×D3—22no—
383C22×C3×D3—22no—
384C22×C3×D3—22no—
385C22×C3×D3—21no—
386C22×C3×D3—21no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—31no—
391C22×C3×D3—42no—
392C22×C3×D3—41no—
393C22×C3×D3—41no—
394C22×C3×D3—42no—
395C22×C3×D3—61no—
396C22×C3×D3—61no—
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—64no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—122no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—122no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414#638—22no—
415#638—34no—
416#638—41no—
417#638—62no—
418#638—62no—
419#638—62no—
420#638—62no—
421#638—64no—
422#638—122no—
423#638—122no—
424#638—124no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—62no—
432C2×C3⋊Dic3—121no—
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C4⋊(C3⋊D3)—121no—
438C4×C3⋊D3—62no—
439#634—62no—
440C3×#67—62no—
441C3×#67—62no—
442C3×#67—62no—
443C3×#67—62no—
444C3×#67—64no—
445C3×#67—121no—
446C3×#67—121no—
447C3×#67—122no—
448C2×C3×Dic3—21no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
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—61no—
461C2×C3×Dic3—61no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—62no—
465C2×C3×Dic3—121no—
466C2×C3×Dic3C22×D311yescharacteristic
467C2×C3×Dic3C22×D311yescharacteristic
468C2×C3×Dic3C22×D311yescharacteristic
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C3×D12—62no—
475C3×D12—62no—
476C3×C4×D3—62no—
477C3×C4×D3—62no—
478C3×C4×D3—62no—
479C3×C4×D3—121no—
480#627—62no—
481#627—62no—
482#627—122no—
483#626—22no—
484#626—22no—
485#626—64no—
486#626—62no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—121no—
491#626—121no—
492#626—122no—
493#625—34no—
494#625—34no—
495#625—64no—
496#625—62no—
497#624—22no—
498#624—121no—
499D3×Dic3—22no—
500D3×Dic3—41no—
501D3×Dic3—62no—
502D3×Dic3—62no—
503D3×Dic3—62no—
504D3×Dic3—62no—
505D3×Dic3—64no—
506D3×Dic3—122no—
507D3×Dic3—121no—
508D3×Dic3—121no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—41no—
515C3×C3⋊D3—22no—
516C3×C3⋊D3—41no—
517C32×D3—22no—
518C32×D3—22no—
519C24×C3—31no—
520C24×C3—31no—
521C24×C3—61no—
522C23×D3—91no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—181no—
526C23×D3D3211yescharacteristic
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C22×C3×C4—91no—
532C22×C3×C4—91no—
533C22×C3×C4—91no—
534C2×#67—31no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—61no—
541C2×#67—61no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—181no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—184no—
559C2×#67—184no—
560C2×#67—188no—
561C2×#67—361no—
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—91no—
565C22×Dic3—91no—
566C22×Dic3—91no—
567C22×Dic3—91no—
568C22×Dic3—181no—
569#237—184no—
570D3×D4—184no—
571#235—184no—
572#235—184no—
573C2×D12—31no—
574C2×D12—31no—
575C2×D12—91no—
576C2×D12—91no—
577C2×D12—91no—
578C2×D12—91no—
579C2×D12—181no—
580C2×C4×D3—31no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
583C2×C4×D3—31no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—181no—
590C2×Dic6—91no—
591C2×Dic6—91no—
592C2×Dic6—91no—
593C2×Dic6—181no—
594C3×C4⋊C4—91no—
595C3×C4⋊C4—91no—
596C3×C22⋊C4—31no—
597C3×C22⋊C4—31no—
598C3×C22⋊C4—31no—
599C3×C22⋊C4—31no—
600C3×C22⋊C4—61no—
601C3×C22⋊C4—61no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C22⋊C4—91no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—31no—
612#217—31no—
613#217—31no—
614#217—61no—
615#217—91no—
616#217D3211yescharacteristic, complemented
617#217D3211yescharacteristic, complemented
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—31no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—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—181no—
636(C2×D3)⋊C4—181no—
637(C2×D3)⋊C4—181no—
638C4⋊Dic3—31no—
639C4⋊Dic3—31no—
640C4⋊Dic3—91no—
641Dic3⋊C4—31no—
642Dic3⋊C4—31no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—91no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—181no—
649C4×Dic3—91no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—181no—
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—32no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—42no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—81no—
683C22×C32—81no—
684C22×C32—124no—
685C22×C32C23×D311yescharacteristic
686C22×C32C23×D311yescharacteristic
687C22×C32C23×D311yescharacteristic
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—62no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—61no—
697C2×C3⋊D3—61no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—122no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—121no—
712C2×C3⋊D3—124no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3—241no—
715C2×C3⋊D3D3×D412yes—
716C2×C3×D3—22no—
717C2×C3×D3—22no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
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—22no—
727C2×C3×D3—22no—
728C2×C3×D3—32no—
729C2×C3×D3—32no—
730C2×C3×D3—41no—
731C2×C3×D3—41no—
732C2×C3×D3—44no—
733C2×C3×D3—44no—
734C2×C3×D3—48no—
735C2×C3×D3—62no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—62no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
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—121no—
750C2×C3×D3—121no—
751C2×C3×D3#23512yescomplemented
752C2×C3×D3D3×D412yes—
753C2×C3×D3D3×D412yes—
754C2×C3×D3#23712yescomplemented
755D32—124no—
756D32—124no—
757D32—128no—
758C32×C4—61no—
759C32×C4—61no—
760C32×C4—61no—
761C32×C4—61no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—21no—
766C3⋊Dic3—32no—
767C3⋊Dic3—32no—
768C3⋊Dic3—32no—
769C3⋊Dic3—62no—
770C3⋊Dic3—62no—
771C3⋊Dic3—62no—
772C3⋊Dic3—122no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—21no—
781C3×Dic3—41no—
782C3×Dic3—41no—
783C3×Dic3—41no—
784C3×Dic3—41no—
785C3×Dic3—62no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C3×Dic3—121no—
797C2×#41—271no—
798C22×D4—271no—
799#124—271no—
800#123—91no—
801#123—271no—
802C22⋊Q8—271no—
803#121—271no—
804#121—271no—
805#121—271no—
806#120—91no—
807#120—271no—
808C4×D4—271no—
809C4×D4—271no—
810C2×C22⋊C4—91no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—31no—
820C23×C3—41no—
821C23×C3—61no—
822C23×C3—61no—
823C23×C3—62no—
824C23×C3—62no—
825C23×C3—62no—
826C23×C3—62no—
827C23×C3—64no—
828C23×C3—91no—
829C23×C3—91no—
830C23×C3—122no—
831C23×C3—121no—
832C23×C3—121no—
833C23×C3—122no—
834C23×C3C2×D3211yescharacteristic
835C23×C3C2×D3211yescharacteristic
836C23×C3C2×D3211yescharacteristic
837C22×D3—22no—
838C22×D3—22no—
839C22×D3—31no—
840C22×D3—31no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—41no—
844C22×D3—61no—
845C22×D3—61no—
846C22×D3—91no—
847C22×D3—91no—
848C22×D3—91no—
849C22×D3—181no—
850C22×D3—181no—
851C22×D3—181no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—182no—
857C22×D3—184no—
858C22×D3—182no—
859C22×D3—361no—
860C22×D3—362no—
861C22×D3—361no—
862C22×D3—361no—
863C22×D3—361no—
864C22×D3—362no—
865C22×D3C2×D3211yescharacteristic
866C22×D3C2×D3211yescharacteristic
867C3×D4—182no—
868C3×D4—182no—
869C3×D4—182no—
870C3×D4—361no—
871C2×C3×C4—31no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—61no—
880C2×C3×C4—61no—
881C2×C3×C4—61no—
882C2×C3×C4—61no—
883C2×C3×C4—91no—
884C2×C3×C4—91no—
885C2×C3×C4—91no—
886C2×C3×C4—91no—
887C2×C3×C4—182no—
888C2×C3×C4—182no—
889C2×C3×C4—361no—
890#67—62no—
891#67—62no—
892#67—62no—
893#67—62no—
894#67—64no—
895#67—94no—
896#67—94no—
897#67—94no—
898#67—121no—
899#67—121no—
900#67—122no—
901#67—184no—
902#67—182no—
903#67—182no—
904#67—182no—
905#67—182no—
906#67—184no—
907#67—182no—
908#67—182no—
909#67—182no—
910#67—184no—
911#67—362no—
912#67—362no—
913#67—364no—
914#67—361no—
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—61no—
924C2×Dic3—61no—
925C2×Dic3—61no—
926C2×Dic3—61no—
927C2×Dic3—62no—
928C2×Dic3—91no—
929C2×Dic3—91no—
930C2×Dic3—91no—
931C2×Dic3—121no—
932C2×Dic3—181no—
933C2×Dic3—181no—
934C2×Dic3—181no—
935C2×Dic3—182no—
936C2×Dic3—182no—
937C2×Dic3—182no—
938C2×Dic3—184no—
939C2×Dic3—361no—
940C2×Dic3—361no—
941C2×Dic3C2×D3211yescharacteristic
942C2×Dic3C2×D3211yescharacteristic
943C2×Dic3C2×D3211yescharacteristic
944C2×Dic3C2×D3211yescharacteristic
945D12—62no—
946D12—62no—
947D12—182no—
948D12—182no—
949D12—361no—
950D12—361no—
951D12—362no—
952C4×D3—62no—
953C4×D3—62no—
954C4×D3—62no—
955C4×D3—121no—
956C4×D3—182no—
957C4×D3—182no—
958C4×D3—182no—
959C4×D3—362no—
960C4×D3—361no—
961C4×D3—361no—
962Dic6—182no—
963Dic6—182no—
964Dic6—182no—
965Dic6—362no—
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—21no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—41no—
979C2×C32—42no—
980C2×C32—41no—
981C2×C32—41no—
982C2×C32—62no—
983C2×C32—62no—
984C2×C32—81no—
985C2×C32—81no—
986C2×C32—82no—
987C2×C32C2×#23511yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×D3×D411yescharacteristic
991C2×C32C2×#23711yescharacteristic
992C2×C32#100411yescharacteristic
993C2×C32#100411yescharacteristic
994C2×C32D3×#4111yescharacteristic
995C2×C32#100911yescharacteristic
996C3⋊D3—22no—
997C3⋊D3—41no—
998C3⋊D3—121no—
999C3⋊D3—122no—
1000C3⋊D3—121no—
1001C3⋊D3—121no—
1002C3⋊D3—241no—
1003C3⋊D3—241no—
1004C3⋊D3—242no—
1005C3×D3—24no—
1006C3×D3—22no—
1007C3×D3—22no—
1008C3×D3—22no—
1009C3×D3—22no—
1010C3×D3—42no—
1011C3×D3—62no—
1012C3×D3—62no—
1013C3×D3—122no—
1014C3×D3—122no—
1015C3×D3—121no—
1016C3×D3—121no—
1017C24—31no—
1018C24—271no—
1019#41—544no—
1020C2×Q8—271no—
1021C2×D4—91no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—271no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4—544no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C22×C4—271no—
1037C4⋊C4—91no—
1038C4⋊C4—91no—
1039C4⋊C4—271no—
1040C4⋊C4—271no—
1041C22⋊C4—31no—
1042C22⋊C4—31no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—91no—
1048C22⋊C4—91no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—271no—
1054C22×C3—22no—
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—21no—
1067C22×C3—32no—
1068C22×C3—32no—
1069C22×C3—32no—
1070C22×C3—32no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—42no—
1080C22×C3—41no—
1081C22×C3—62no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—62no—
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—81no—
1094C22×C3—81no—
1095C22×C3—92no—
1096C22×C3—121no—
1097C22×C3—121no—
1098C22×C3—124no—
1099C22×C3—124no—
1100C22×C3—128no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—181no—
1104C22×C3—181no—
1105C22×C3—181no—
1106C22×C3C22×D3211yescharacteristic
1107C22×C3C22×D3211yescharacteristic
1108C22×C3C22×D3211yescharacteristic
1109C2×D3—21no—
1110C2×D3—21no—
1111C2×D3—21no—
1112C2×D3—21no—
1113C2×D3—32no—
1114C2×D3—32no—
1115C2×D3—44no—
1116C2×D3—62no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—62no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—121no—
1131C2×D3—121no—
1132C2×D3—182no—
1133C2×D3—181no—
1134C2×D3—181no—
1135C2×D3—181no—
1136C2×D3—181no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—361no—
1143C2×D3—361no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—362no—
1151C2×D3—364no—
1152C2×D3—364no—
1153C2×D3—364no—
1154C2×D3—368no—
1155C2×D3—721no—
1156C2×D3—721no—
1157C2×D3#380412yescomplemented
1158C2×D3#381112yes—
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4—121no—
1168C3×C4—121no—
1169C3×C4—121no—
1170C3×C4—121no—
1171C3×C4—181no—
1172C3×C4—181no—
1173C3×C4—181no—
1174C3×C4—181no—
1175Dic3—21no—
1176Dic3—21no—
1177Dic3—21no—
1178Dic3—21no—
1179Dic3—62no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—61no—
1188Dic3—92no—
1189Dic3—92no—
1190Dic3—92no—
1191Dic3—121no—
1192Dic3—121no—
1193Dic3—121no—
1194Dic3—182no—
1195Dic3—182no—
1196Dic3—182no—
1197Dic3—362no—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#549011yescharacteristic, complemented
1203C32#559111yescharacteristic, complemented
1204C32#565411yescharacteristic, complemented
1205C23—31no—
1206C23—31no—
1207C23—62no—
1208C23—62no—
1209C23—91no—
1210C23—91no—
1211C23—121no—
1212C23—271no—
1213C23—542no—
1214C23—542no—
1215C23—1081no—
1216C23D3311yescharacteristic
1217Q8—542no—
1218D4—182no—
1219D4—182no—
1220D4—182no—
1221D4—274no—
1222D4—361no—
1223D4—542no—
1224D4—542no—
1225D4—542no—
1226D4—1081no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—31no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—182no—
1236C2×C4—182no—
1237C2×C4—271no—
1238C2×C4—361no—
1239C2×C4—542no—
1240C2×C4—542no—
1241C2×C4—1081no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—42no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—41no—
1257C2×C3—41no—
1258C2×C3—64no—
1259C2×C3—62no—
1260C2×C3—62no—
1261C2×C3—62no—
1262C2×C3—62no—
1263C2×C3—81no—
1264C2×C3—81no—
1265C2×C3—82no—
1266C2×C3—122no—
1267C2×C3—182no—
1268C2×C3—361no—
1269C2×C3D3×#23511yescharacteristic
1270C2×C3#6430711yescharacteristic
1271C2×C3D32×D411yescharacteristic
1272C2×C3D32×D411yescharacteristic
1273C2×C3D3×#23711yescharacteristic
1274C2×C3#6431411yescharacteristic
1275C2×C3C2×#380411yescharacteristic
1276C2×C3C2×#381111yescharacteristic
1277C2×C3#6433011yescharacteristic
1278D3—22no—
1279D3—22no—
1280D3—62no—
1281D3—62no—
1282D3—122no—
1283D3—122no—
1284D3—121no—
1285D3—121no—
1286D3—362no—
1287D3—361no—
1288D3—361no—
1289D3—361no—
1290D3—721no—
1291D3—721no—
1292D3—722no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—32no—
1297C22—32no—
1298C22—61no—
1299C22—61no—
1300C22—61no—
1301C22—61no—
1302C22—92no—
1303C22—124no—
1304C22—181no—
1305C22—181no—
1306C22—181no—
1307C22—181no—
1308C22—181no—
1309C22—541no—
1310C22—541no—
1311C22—541no—
1312C22—1084no—
1313C22C2×D3311yescharacteristic
1314C4—61no—
1315C4—61no—
1316C4—61no—
1317C4—61no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—272no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059427211yescharacteristic, complemented
1328C3#1059427411yescharacteristic, complemented
1329C3#1059550011yescharacteristic, complemented
1330C2—41no—
1331C2—62no—
1332C2—62no—
1333C2—182no—
1334C2—361no—
1335C2—1081no—
1336C2D3×#380411yescharacteristic
1337C2#1172441811yescharacteristic
1338C2D3×#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×D3×#638C2semidirect
2. C2×#88960C2semidirect
3. #11723725C2semidirect
4. #11723624C2semidirect
5. #11723592C2semidirect
6. C3×#63977C2semidirect
7. C3×#63975C2semidirect
8. C3×D3×#217C2semidirect
9. #11722987C2semidirect
10. #11722980C2semidirect
11. #11722959C2semidirect
12. #11722950C2semidirect
13. #11722936C2semidirect
14. #11722929C2semidirect
15. #11722904C2semidirect
23. C2×C3×#638C22semidirect
24. C2×#6295C22semidirect
25. C2×#6294C22semidirect
27. C2×#6293C22semidirect
28. C2×#6292C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. C32×#217C22semidirect
41. C32×#217C22semidirect
42. #88815C22semidirect
43. #88814C22semidirect
44. #88806C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
74. #63977D3semidirect
75. #63975D3semidirect
83. D3×#217D3semidirect
133. #6290D4semidirect
163. C2×#638C2×D3semidirect
199. C2×#626C2×D3semidirect
205. C2×#624C2×D3semidirect
215. C2×D3×Dic3C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
221. #3757C2×D3semidirect
236. C3×#217C2×D3semidirect
237. C3×#217C2×D3semidirect
238. C3×#217C2×D3semidirect
239. C3×#217C2×D3semidirect
256. Dic3⋊Dic3C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
268. #3722C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
297. C2×C32×D3#41semidirect
616. #217D32semidirect
617. #217D32semidirect
751. C2×C3×D3#235semidirect
754. C2×C3×D3#237semidirect
812. C33#546semidirect
1157. C2×D3#3804semidirect
1202. C32#5490semidirect
1203. C32#5591semidirect
1204. C32#5654semidirect
1327. C3#10594272semidirect
1328. C3#10594274semidirect
1329. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#889602
#117237252
#117236242
#117235922
C3×#639772
C3×#639752
C3×D3×#2172
#117229872
#117229802
#117229592
#117229502
#117229362
#117229292
#117229042
#105955003
#105942743
#105942723