Finite Group Databasebeta

← #13172025

Subgroups — #13172025

Order 1728.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723720C211yesmaximal, characteristic, complemented
4#11723618C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722980C211yesmaximal, characteristic, complemented
11#11722964C211yesmaximal, characteristic, complemented
12#11722954C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722925C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595307—31nomaximal
18#10595083—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26D3×#638—24no—
27C2×#6293C2211yescharacteristic, complemented
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33#89028—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×#625C2211yescharacteristic
38C2×C3×#625C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88815C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C2×#3830—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×D3×#67—61no—
61C2×#3804—31no—
62C2×#3804—31no—
63C2×#3804—61no—
64C4×#638—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#939—31no—
68C3×#937—31no—
69C3×#930—31no—
70C2×C3×(C2×D3)⋊C4—31no—
71#63983—31no—
72#63982—31no—
73#63981—31no—
74#63980—31no—
75#63978D311yescharacteristic, complemented
76#63976D311yescharacteristic, complemented
77#63975—31no—
78#63974—31no—
79#67⋊Dic3—31no—
80#67⋊Dic3—31no—
81#63971—31no—
82#63966—31no—
83#63962—31no—
84#63961—31no—
85C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
86#63958—31no—
87#63958—31no—
88#63953—31no—
89#63952—31no—
90#63952—31no—
91#63952—61no—
92#63922—31no—
93#63921—31no—
94#63921—31no—
95#63915—31no—
96#63913—31no—
97#63912—31no—
98#63902—31no—
99#63899—31no—
100#63896—31no—
101#63885—31no—
102#63854—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3—22no—
108C22×C32×D3—22no—
109C22×C32×D3—41no—
110C22×C32×D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312D414yescomplemented
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—
126C2×C32×Dic3—41no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6293—22no—
131#6291—22no—
132#6291—22no—
133#6290—22no—
134#6289—22no—
135#6289—41no—
136D3×C3⋊Dic3—22no—
137D3×C3⋊Dic3—22no—
138C3×#626—41no—
139C3×#625—22no—
140C3×#625—41no—
141#5610—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×C32×D4—31no—
153C22×C32×C4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—64no—
161C2×#638—61no—
162C2×#638—61no—
163C2×#638—61no—
164C2×#638—121no—
165C2×#638C2×D311yescharacteristic
166C22×C3⋊Dic3—31no—
167C22×C3⋊Dic3—31no—
168C22×C3⋊Dic3C2×D311yescharacteristic, complemented
169#3830—64no—
170C2×C4×C3⋊D3—31no—
171C2×C4×C3⋊D3—31no—
172C2×#634—31no—
173C2×C3×#67—21no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—31no—
180C2×C3×#67—31no—
181C2×C3×#67—61no—
182C2×C3×#67C2×D311yescharacteristic, complemented
183C2×C3×#67C2×D311yescharacteristic, complemented
184C22×C3×Dic3—21no—
185C22×C3×Dic3—31no—
186C22×C3×Dic3—31no—
187C22×C3×Dic3—61no—
188C22×C3×Dic3C2×D311yescharacteristic, complemented
189C22×C3×Dic3C2×D311yescharacteristic, complemented
190C2×C3×D12—31no—
191D3×#67—64no—
192D3×#67—64no—
193D3×#67—68no—
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×#626C2×D311yescharacteristic, complemented
204C2×#625—31no—
205C2×#625—31no—
206C2×#625—61no—
207C2×#625C2×D311yescharacteristic
208C2×#625C2×D311yescharacteristic, complemented
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—31no—
212C2×#624—31no—
213C2×#624—61no—
214C2×#624—61no—
215#3804—64no—
216#3804—64no—
217#3804—68no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—31no—
220C2×D3×Dic3—31no—
221C2×D3×Dic3—31no—
222C2×D3×Dic3—61no—
223C2×D3×Dic3—61no—
224#3757C2×D311yescharacteristic, complemented
225#3752—31no—
226#3750—31no—
227C4×C3⋊Dic3—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—31no—
236C3×#217—31no—
237C3×#217—61no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
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×(C2×D3)⋊C4—31no—
247C3×C4⋊Dic3—31no—
248C3×Dic3⋊C4—31no—
249#3724—31no—
250#3724—31no—
251#3724—31no—
252#3724—31no—
253#3724—61no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722C2×D311yescharacteristic, complemented
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276Dic32—31no—
277Dic32—31no—
278Dic32—61no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2×D412yes—
282C22×C33C2411yescharacteristic
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3⋊(C3⋊D3)C2×D412yes—
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—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—44no—
298C2×C32×D3#4112yescomplemented
299D3×C3⋊D3—44no—
300C3⋊(C3⋊Dic3)C2×D412yes—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C32×Dic3—21no—
309C22×#67—91no—
310C22×#67—91no—
311C22×#67—181no—
312C2×#237—91no—
313C2×#237—91no—
314C2×#237—181no—
315C2×D3×D4—91no—
316C2×#235—91no—
317C3×#121—91no—
318C3×#120—91no—
319C2×C3×C22⋊C4—91no—
320#953—31no—
321C2×#217—31no—
322#939—31no—
323#939—91no—
324#939—91no—
325#938—91no—
326#937—31no—
327#937—91no—
328#937—91no—
329#935—91no—
330D4×Dic3—91no—
331#930—31no—
332#929—91no—
333C4×#67—91no—
334C4×#67—91no—
335C4×#67—181no—
336C2×(C2×D3)⋊C4—31no—
337#896—91no—
338#894—91no—
339#886—91no—
340#885—91no—
341#885—91no—
342#885—91no—
343#884—91no—
344#884—91no—
345#884—91no—
346#883—91no—
347#883—91no—
348#882—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—91no—
355#878—91no—
356#878—91no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—21no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—31no—
363C23×C32—41no—
364C23×C32—62no—
365C23×C32—62no—
366C23×C32—121no—
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—31no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—61no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—62no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3—121no—
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3×D3—24no—
382C22×C3×D3—22no—
383C22×C3×D3—22no—
384C22×C3×D3—22no—
385C22×C3×D3—22no—
386C22×C3×D3—21no—
387C22×C3×D3—21no—
388C22×C3×D3—21no—
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×D3C22×D311yescharacteristic
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C22×C3×D3C22×D311yescharacteristic
402C2×D32—62no—
403C2×D32—62no—
404C2×D32—64no—
405C2×D32—62no—
406C2×D32—62no—
407C2×D32—122no—
408C2×D32—121no—
409C2×D32—121no—
410C2×D32—122no—
411C32×D4—62no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—121no—
416#638—22no—
417#638—34no—
418#638—34no—
419#638—34no—
420#638—64no—
421#638—64no—
422#638—64no—
423#638—62no—
424#638—62no—
425#638—62no—
426#638—124no—
427C2×C3⋊Dic3—22no—
428C2×C3⋊Dic3—31no—
429C2×C3⋊Dic3—31no—
430C2×C3⋊Dic3—31no—
431C2×C3⋊Dic3—61no—
432C2×C3⋊Dic3—61no—
433C2×C3⋊Dic3—61no—
434C2×C3⋊Dic3—62no—
435C2×C3⋊Dic3—62no—
436C2×C3⋊Dic3—121no—
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C2×C3⋊Dic3C22×D311yescharacteristic
441C2×C3⋊Dic3C22×D311yescharacteristic
442C4×C3⋊D3—62no—
443C4×C3⋊D3—121no—
444#634—62no—
445C3×#67—24no—
446C3×#67—22no—
447C3×#67—22no—
448C3×#67—62no—
449C3×#67—64no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—62no—
453C3×#67—121no—
454C3×#67—121no—
455C3×#67—121no—
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—41no—
470C2×C3×Dic3—41no—
471C2×C3×Dic3—42no—
472C2×C3×Dic3—61no—
473C2×C3×Dic3—61no—
474C2×C3×Dic3—61no—
475C2×C3×Dic3—61no—
476C2×C3×Dic3—61no—
477C2×C3×Dic3—64no—
478C2×C3×Dic3—62no—
479C2×C3×Dic3—62no—
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C2×C3×Dic3C22×D311yescharacteristic
484C2×C3×Dic3C22×D311yescharacteristic
485C2×C3×Dic3C22×D311yescharacteristic
486C3×D12—121no—
487#627—62no—
488#627—62no—
489#627—64no—
490#626—41no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—64no—
496#626—64no—
497#625—22no—
498#625—41no—
499#625—62no—
500#625—62no—
501#625—64no—
502#624—62no—
503#624—62no—
504#624—64no—
505#624—121no—
506#624—121no—
507#624—122no—
508D3×Dic3—62no—
509D3×Dic3—62no—
510D3×Dic3—62no—
511D3×Dic3—62no—
512D3×Dic3—64no—
513D3×Dic3—64no—
514#546—271noSylow
515C2×C33—22no—
516C2×C33C22×D411yescharacteristic
517C2×C33C2×#4111yescharacteristic
518C2×C33H(5,𝔽2)11yescharacteristic
519C3⋊(C3⋊D3)—22no—
520C3×C3⋊D3—41no—
521C32×D3—22no—
522C32×D3—41no—
523C32×D3—41no—
524C24×C3—31no—
525C24×C3—31no—
526C24×C3—61no—
527C23×D3—91no—
528C23×D3—91no—
529C23×D3—91no—
530C23×D3—181no—
531C23×D3D3211yescharacteristic
532C2×C3×D4—31no—
533C2×C3×D4—31no—
534C2×C3×D4—61no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C2×C3×D4—91no—
538C2×C3×D4—91no—
539C22×C3×C4—31no—
540C22×C3×C4—31no—
541C22×C3×C4—61no—
542C22×C3×C4—91no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—61no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—91no—
560C2×#67—91no—
561C2×#67—181no—
562C2×#67—181no—
563C2×#67—181no—
564C2×#67—181no—
565C2×#67—181no—
566C2×#67—181no—
567C2×#67—184no—
568C2×#67—184no—
569C2×#67—188no—
570C2×#67—361no—
571C2×#67D3211yescharacteristic, complemented
572C22×Dic3—31no—
573C22×Dic3—31no—
574C22×Dic3—61no—
575C22×Dic3—91no—
576C22×Dic3—91no—
577C22×Dic3—91no—
578C22×Dic3—91no—
579C22×Dic3—181no—
580C22×Dic3—181no—
581C22×Dic3D3211yescharacteristic, complemented
582#237—184no—
583#237—184no—
584#237—188no—
585D3×D4—184no—
586#235—184no—
587C2×D12—31no—
588C2×D12—91no—
589C2×D12—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—91no—
601C2×Dic6—91no—
602C2×Dic6—91no—
603C2×Dic6—181no—
604C3×C4⋊C4—91no—
605C3×C22⋊C4—91no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608C3×C22⋊C4—91no—
609C3×C22⋊C4—91no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4—91no—
614#217—31no—
615#217—31no—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—31no—
622#217—31no—
623#217—61no—
624#217—91no—
625#217—91no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—31no—
634(C2×D3)⋊C4—31no—
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—181no—
643C4⋊Dic3—31no—
644C4⋊Dic3—91no—
645C4⋊Dic3—91no—
646Dic3⋊C4—31no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—91no—
651Dic3⋊C4—91no—
652Dic3⋊C4—91no—
653Dic3⋊C4—91no—
654Dic3⋊C4—181no—
655C4×Dic3—91no—
656C4×Dic3—91no—
657C4×Dic3—91no—
658C4×Dic3—181no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—22no—
669C22×C32—22no—
670C22×C32—22no—
671C22×C32—32no—
672C22×C32—41no—
673C22×C32—42no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—61no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—61no—
686C22×C32—61no—
687C22×C32—61no—
688C22×C32—81no—
689C22×C32—81no—
690C22×C32—124no—
691C22×C32D3×D412yes—
692C22×C32D3×D412yes—
693C22×C32D3×D412yes—
694C22×C32C23×D311yescharacteristic
695C22×C32C23×D311yescharacteristic
696C22×C32C23×D311yescharacteristic
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3—21no—
700C2×C3⋊D3—32no—
701C2×C3⋊D3—32no—
702C2×C3⋊D3—32no—
703C2×C3⋊D3—62no—
704C2×C3⋊D3—62no—
705C2×C3⋊D3—62no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—61no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—122no—
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—124no—
720C2×C3⋊D3—241no—
721C2×C3⋊D3—241no—
722C2×C3×D3—22no—
723C2×C3×D3—22no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—22no—
729C2×C3×D3—22no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—21no—
733C2×C3×D3—21no—
734C2×C3×D3—21no—
735C2×C3×D3—21no—
736C2×C3×D3—21no—
737C2×C3×D3—21no—
738C2×C3×D3—21no—
739C2×C3×D3—21no—
740C2×C3×D3—21no—
741C2×C3×D3—21no—
742C2×C3×D3—22no—
743C2×C3×D3—41no—
744C2×C3×D3—41no—
745C2×C3×D3—41no—
746C2×C3×D3—41no—
747C2×C3×D3—44no—
748C2×C3×D3—44no—
749C2×C3×D3—48no—
750C2×C3×D3—62no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—61no—
755C2×C3×D3—61no—
756C2×C3×D3—61no—
757C2×C3×D3—121no—
758C2×C3×D3—121no—
759C2×C3×D3#23512yescomplemented
760C2×C3×D3#23712yescomplemented
761D32—124no—
762D32—124no—
763D32—128no—
764C32×C4—61no—
765C32×C4—61no—
766C32×C4—61no—
767C3⋊Dic3—21no—
768C3⋊Dic3—21no—
769C3⋊Dic3—21no—
770C3⋊Dic3—21no—
771C3⋊Dic3—21no—
772C3⋊Dic3—32no—
773C3⋊Dic3—32no—
774C3⋊Dic3—32no—
775C3⋊Dic3—62no—
776C3⋊Dic3—62no—
777C3⋊Dic3—62no—
778C3⋊Dic3—122no—
779C3×Dic3—22no—
780C3×Dic3—22no—
781C3×Dic3—21no—
782C3×Dic3—21no—
783C3×Dic3—21no—
784C3×Dic3—21no—
785C3×Dic3—21no—
786C3×Dic3—21no—
787C3×Dic3—41no—
788C3×Dic3—62no—
789C3×Dic3—62no—
790C3×Dic3—62no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—61no—
795C3×Dic3—61no—
796C3×Dic3—61no—
797C3×Dic3—61no—
798C3×Dic3—61no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—121no—
802C3×Dic3—121no—
803C2×#41—271no—
804C22×D4—271no—
805#124—271no—
806#123—271no—
807#123—271no—
808C22⋊Q8—271no—
809#121—91no—
810#121—271no—
811#121—271no—
812#120—91no—
813#120—271no—
814C4×D4—271no—
815C4×D4—271no—
816C2×C22⋊C4—91no—
817C2×C22⋊C4—271no—
818C33#54611yescharacteristic, complemented, Sylow
819C23×C3—21no—
820C23×C3—21no—
821C23×C3—21no—
822C23×C3—31no—
823C23×C3—31no—
824C23×C3—31no—
825C23×C3—31no—
826C23×C3—31no—
827C23×C3—31no—
828C23×C3—41no—
829C23×C3—61no—
830C23×C3—61no—
831C23×C3—61no—
832C23×C3—62no—
833C23×C3—62no—
834C23×C3—64no—
835C23×C3—62no—
836C23×C3—62no—
837C23×C3—91no—
838C23×C3—122no—
839C23×C3—121no—
840C23×C3—121no—
841C23×C3—122no—
842C23×C3C2×D3211yescharacteristic
843C23×C3C2×D3211yescharacteristic
844C23×C3C2×D3211yescharacteristic
845C22×D3—22no—
846C22×D3—22no—
847C22×D3—31no—
848C22×D3—31no—
849C22×D3—41no—
850C22×D3—61no—
851C22×D3—91no—
852C22×D3—91no—
853C22×D3—91no—
854C22×D3—181no—
855C22×D3—181no—
856C22×D3—181no—
857C22×D3—182no—
858C22×D3—182no—
859C22×D3—182no—
860C22×D3—182no—
861C22×D3—182no—
862C22×D3—184no—
863C22×D3—182no—
864C22×D3—361no—
865C22×D3—362no—
866C22×D3—361no—
867C22×D3—361no—
868C22×D3—361no—
869C22×D3—362no—
870C22×D3C2×D3211yescharacteristic
871C22×D3C2×D3211yescharacteristic
872C22×D3C2×D3211yescharacteristic
873C3×D4—64no—
874C3×D4—62no—
875C3×D4—62no—
876C3×D4—182no—
877C3×D4—182no—
878C3×D4—361no—
879C3×D4—361no—
880C2×C3×C4—31no—
881C2×C3×C4—31no—
882C2×C3×C4—31no—
883C2×C3×C4—31no—
884C2×C3×C4—31no—
885C2×C3×C4—31no—
886C2×C3×C4—61no—
887C2×C3×C4—61no—
888C2×C3×C4—61no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—91no—
892C2×C3×C4—91no—
893C2×C3×C4—91no—
894C2×C3×C4—121no—
895C2×C3×C4—121no—
896C2×C3×C4—122no—
897C2×C3×C4—182no—
898#67—22no—
899#67—62no—
900#67—64no—
901#67—62no—
902#67—62no—
903#67—62no—
904#67—94no—
905#67—94no—
906#67—94no—
907#67—121no—
908#67—121no—
909#67—121no—
910#67—184no—
911#67—184no—
912#67—184no—
913#67—182no—
914#67—182no—
915#67—182no—
916#67—182no—
917#67—184no—
918#67—184no—
919#67—182no—
920#67—182no—
921#67—182no—
922#67—184no—
923#67—364no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—31no—
928C2×Dic3—31no—
929C2×Dic3—31no—
930C2×Dic3—31no—
931C2×Dic3—31no—
932C2×Dic3—31no—
933C2×Dic3—31no—
934C2×Dic3—41no—
935C2×Dic3—61no—
936C2×Dic3—61no—
937C2×Dic3—61no—
938C2×Dic3—61no—
939C2×Dic3—61no—
940C2×Dic3—64no—
941C2×Dic3—62no—
942C2×Dic3—62no—
943C2×Dic3—91no—
944C2×Dic3—91no—
945C2×Dic3—91no—
946C2×Dic3—181no—
947C2×Dic3—181no—
948C2×Dic3—181no—
949C2×Dic3—182no—
950C2×Dic3—182no—
951C2×Dic3—182no—
952C2×Dic3—182no—
953C2×Dic3—184no—
954C2×Dic3—184no—
955C2×Dic3—361no—
956C2×Dic3C2×D3211yescharacteristic
957C2×Dic3C2×D3211yescharacteristic
958C2×Dic3C2×D3211yescharacteristic
959D12—121no—
960D12—182no—
961D12—182no—
962C4×D3—182no—
963C4×D3—182no—
964C4×D3—182no—
965C4×D3—184no—
966C4×D3—182no—
967C4×D3—182no—
968C4×D3—361no—
969C4×D3—361no—
970C4×D3—361no—
971C4×D3—362no—
972Dic6—182no—
973Dic6—182no—
974Dic6—182no—
975Dic6—184no—
976C2×C32—22no—
977C2×C32—22no—
978C2×C32—22no—
979C2×C32—21no—
980C2×C32—21no—
981C2×C32—21no—
982C2×C32—21no—
983C2×C32—21no—
984C2×C32—21no—
985C2×C32—21no—
986C2×C32—21no—
987C2×C32—21no—
988C2×C32—41no—
989C2×C32—41no—
990C2×C32—41no—
991C2×C32—42no—
992C2×C32—42no—
993C2×C32—42no—
994C2×C32—62no—
995C2×C32—82no—
996C2×C32—121no—
997C2×C32—121no—
998C2×C32C2×#23511yescharacteristic
999C2×C32C2×D3×D411yescharacteristic
1000C2×C32C2×D3×D411yescharacteristic
1001C2×C32C2×D3×D411yescharacteristic
1002C2×C32C2×#23711yescharacteristic
1003C2×C32#100411yescharacteristic
1004C2×C32#100411yescharacteristic
1005C2×C32#100411yescharacteristic
1006C2×C32D3×#4111yescharacteristic
1007C3⋊D3—41no—
1008C3⋊D3—62no—
1009C3⋊D3—62no—
1010C3⋊D3—62no—
1011C3⋊D3—122no—
1012C3⋊D3—122no—
1013C3⋊D3—122no—
1014C3⋊D3—242no—
1015C3×D3—24no—
1016C3×D3—22no—
1017C3×D3—22no—
1018C3×D3—42no—
1019C3×D3—42no—
1020C3×D3—41no—
1021C3×D3—41no—
1022C3×D3—41no—
1023C3×D3—41no—
1024C3×D3—122no—
1025C3×D3—121no—
1026C3×D3—121no—
1027C24—31no—
1028C24—271no—
1029#41—544no—
1030C2×Q8—271no—
1031C2×D4—31no—
1032C2×D4—91no—
1033C2×D4—91no—
1034C2×D4—91no—
1035C2×D4—91no—
1036C2×D4—271no—
1037C2×D4—271no—
1038C2×D4—271no—
1039C2×D4—271no—
1040C2×D4—544no—
1041C22×C4—31no—
1042C22×C4—91no—
1043C22×C4—271no—
1044C22×C4—271no—
1045C22×C4—271no—
1046C22×C4—271no—
1047C4⋊C4—91no—
1048C4⋊C4—271no—
1049C4⋊C4—271no—
1050C4⋊C4—271no—
1051C22⋊C4—91no—
1052C22⋊C4—91no—
1053C22⋊C4—91no—
1054C22⋊C4—91no—
1055C22⋊C4—91no—
1056C22⋊C4—91no—
1057C22⋊C4—91no—
1058C22⋊C4—91no—
1059C22⋊C4—91no—
1060C22⋊C4—271no—
1061C22⋊C4—271no—
1062C22⋊C4—271no—
1063C42—271no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—21no—
1067C22×C3—21no—
1068C22×C3—21no—
1069C22×C3—21no—
1070C22×C3—21no—
1071C22×C3—21no—
1072C22×C3—21no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—32no—
1077C22×C3—32no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—42no—
1086C22×C3—62no—
1087C22×C3—62no—
1088C22×C3—62no—
1089C22×C3—62no—
1090C22×C3—62no—
1091C22×C3—61no—
1092C22×C3—61no—
1093C22×C3—61no—
1094C22×C3—61no—
1095C22×C3—61no—
1096C22×C3—61no—
1097C22×C3—61no—
1098C22×C3—61no—
1099C22×C3—61no—
1100C22×C3—61no—
1101C22×C3—61no—
1102C22×C3—61no—
1103C22×C3—61no—
1104C22×C3—61no—
1105C22×C3—61no—
1106C22×C3—61no—
1107C22×C3—81no—
1108C22×C3—81no—
1109C22×C3—121no—
1110C22×C3—121no—
1111C22×C3—121no—
1112C22×C3—121no—
1113C22×C3—124no—
1114C22×C3—124no—
1115C22×C3—128no—
1116C22×C3—181no—
1117C22×C3—181no—
1118C22×C3—181no—
1119C22×C3#380212yes—
1120C22×C3#381112yes—
1121C22×C3#381112yes—
1122C22×C3C22×D3211yescharacteristic
1123C22×C3C22×D3211yescharacteristic
1124C22×C3C22×D3211yescharacteristic
1125C2×D3—21no—
1126C2×D3—21no—
1127C2×D3—21no—
1128C2×D3—21no—
1129C2×D3—21no—
1130C2×D3—21no—
1131C2×D3—21no—
1132C2×D3—21no—
1133C2×D3—44no—
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—182no—
1147C2×D3—182no—
1148C2×D3—182no—
1149C2×D3—181no—
1150C2×D3—181no—
1151C2×D3—181no—
1152C2×D3—181no—
1153C2×D3—181no—
1154C2×D3—181no—
1155C2×D3—362no—
1156C2×D3—361no—
1157C2×D3—361no—
1158C2×D3—361no—
1159C2×D3—361no—
1160C2×D3—361no—
1161C2×D3—361no—
1162C2×D3—364no—
1163C2×D3—364no—
1164C2×D3—364no—
1165C2×D3—368no—
1166C2×D3—721no—
1167C2×D3—721no—
1168C2×D3#380412yescomplemented
1169C3×C4—62no—
1170C3×C4—62no—
1171C3×C4—61no—
1172C3×C4—61no—
1173C3×C4—61no—
1174C3×C4—61no—
1175C3×C4—61no—
1176C3×C4—61no—
1177C3×C4—121no—
1178C3×C4—181no—
1179C3×C4—181no—
1180C3×C4—181no—
1181C3×C4—181no—
1182C3×C4—181no—
1183Dic3—21no—
1184Dic3—21no—
1185Dic3—21no—
1186Dic3—62no—
1187Dic3—62no—
1188Dic3—62no—
1189Dic3—61no—
1190Dic3—61no—
1191Dic3—61no—
1192Dic3—61no—
1193Dic3—61no—
1194Dic3—61no—
1195Dic3—61no—
1196Dic3—61no—
1197Dic3—61no—
1198Dic3—61no—
1199Dic3—92no—
1200Dic3—92no—
1201Dic3—92no—
1202Dic3—121no—
1203Dic3—121no—
1204Dic3—182no—
1205Dic3—182no—
1206Dic3—182no—
1207Dic3—362no—
1208C32—21no—
1209C32—21no—
1210C32—21no—
1211C32—41no—
1212C32#549011yescharacteristic, complemented
1213C32#559111yescharacteristic, complemented
1214C32#561011yescharacteristic, complemented
1215C23—31no—
1216C23—31no—
1217C23—31no—
1218C23—62no—
1219C23—62no—
1220C23—91no—
1221C23—121no—
1222C23—271no—
1223C23—542no—
1224C23—542no—
1225C23—1081no—
1226C23D3311yescharacteristic
1227Q8—542no—
1228D4—62no—
1229D4—182no—
1230D4—182no—
1231D4—274no—
1232D4—361no—
1233D4—361no—
1234D4—542no—
1235D4—542no—
1236D4—542no—
1237C2×C4—31no—
1238C2×C4—31no—
1239C2×C4—31no—
1240C2×C4—91no—
1241C2×C4—91no—
1242C2×C4—91no—
1243C2×C4—91no—
1244C2×C4—91no—
1245C2×C4—121no—
1246C2×C4—182no—
1247C2×C4—271no—
1248C2×C4—542no—
1249C2×C4—542no—
1250C2×C4—542no—
1251C2×C4—1081no—
1252C2×C3—22no—
1253C2×C3—22no—
1254C2×C3—22no—
1255C2×C3—21no—
1256C2×C3—21no—
1257C2×C3—21no—
1258C2×C3—21no—
1259C2×C3—21no—
1260C2×C3—21no—
1261C2×C3—21no—
1262C2×C3—21no—
1263C2×C3—21no—
1264C2×C3—42no—
1265C2×C3—42no—
1266C2×C3—42no—
1267C2×C3—41no—
1268C2×C3—41no—
1269C2×C3—41no—
1270C2×C3—64no—
1271C2×C3—62no—
1272C2×C3—62no—
1273C2×C3—82no—
1274C2×C3—122no—
1275C2×C3—122no—
1276C2×C3—121no—
1277C2×C3—121no—
1278C2×C3—121no—
1279C2×C3—121no—
1280C2×C3—361no—
1281C2×C3C2×#380211yescharacteristic
1282C2×C3D3×#23511yescharacteristic
1283C2×C3D3×#23711yescharacteristic
1284C2×C3#6431311yescharacteristic
1285C2×C3C2×#380411yescharacteristic
1286C2×C3C2×#381111yescharacteristic
1287C2×C3C2×#381111yescharacteristic
1288C2×C3#6433011yescharacteristic
1289C2×C3#6433011yescharacteristic
1290D3—22no—
1291D3—41no—
1292D3—41no—
1293D3—122no—
1294D3—121no—
1295D3—121no—
1296D3—182no—
1297D3—182no—
1298D3—182no—
1299D3—362no—
1300D3—362no—
1301D3—362no—
1302D3—722no—
1303C22—21no—
1304C22—21no—
1305C22—32no—
1306C22—61no—
1307C22—61no—
1308C22—61no—
1309C22—61no—
1310C22—61no—
1311C22—61no—
1312C22—61no—
1313C22—61no—
1314C22—124no—
1315C22—181no—
1316C22—181no—
1317C22—181no—
1318C22—272no—
1319C22—541no—
1320C22—541no—
1321C22—1084no—
1322C22#8895412yes—
1323C22C2×D3311yescharacteristic
1324C4—61no—
1325C4—61no—
1326C4—61no—
1327C4—181no—
1328C4—181no—
1329C4—181no—
1330C4—181no—
1331C4—181no—
1332C4—272no—
1333C3—21no—
1334C3—21no—
1335C3—21no—
1336C3—41no—
1337C3#1059508311yescharacteristic, complemented
1338C3#1059530711yescharacteristic, complemented
1339C3#1059550011yescharacteristic, complemented
1340C2—22no—
1341C2—62no—
1342C2—121no—
1343C2—121no—
1344C2—361no—
1345C2—542no—
1346C2D3×#380411yescharacteristic
1347C2#1172441411yescharacteristic
1348C2C2×#8895411yescharacteristic
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×#89028C2semidirect
3. #11723720C2semidirect
4. #11723618C2semidirect
5. C3×#63978C2semidirect
6. C3×#63976C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11723009C2semidirect
9. #11722996C2semidirect
10. #11722980C2semidirect
11. #11722964C2semidirect
12. #11722954C2semidirect
13. #11722949C2semidirect
14. #11722925C2semidirect
15. #11722906C2semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
27. C2×#6293C22semidirect
29. C2×#6291C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
35. C2×D3×C3⋊Dic3C22semidirect
36. C2×C3×#626C22semidirect
38. C2×C3×#625C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
41. #88815C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88806C22semidirect
45. #88804C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
75. #63978D3semidirect
76. #63976D3semidirect
85. C2×(C2×D3)⋊Dic3D3semidirect
116. #6312D4semidirect
168. C22×C3⋊Dic3C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
183. C2×C3×#67C2×D3semidirect
188. C22×C3×Dic3C2×D3semidirect
189. C22×C3×Dic3C2×D3semidirect
203. C2×#626C2×D3semidirect
208. C2×#625C2×D3semidirect
224. #3757C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
264. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
298. C2×C32×D3#41semidirect
571. C2×#67D32semidirect
581. C22×Dic3D32semidirect
759. C2×C3×D3#235semidirect
760. C2×C3×D3#237semidirect
818. C33#546semidirect
1168. C2×D3#3804semidirect
1212. C32#5490semidirect
1213. C32#5591semidirect
1214. C32#5610semidirect
1337. C3#10595083semidirect
1338. C3#10595307semidirect
1339. 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×#890282
#117237202
#117236182
C3×#639782
C3×#639762
C2×C3×(C2×D3)⋊Dic32
#117230092
#117229962
#117229802
#117229642
#117229542
#117229492
#117229252
#117229062
#105955003
#105953073
#105950833