Finite Group Databasebeta

← #13172314

Subgroups — #13172314

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
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3#11723639C211yesmaximal, characteristic, complemented
4C2×#88804C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×#63962C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723008C211yesmaximal, characteristic, complemented
9#11722999C211yesmaximal, characteristic, complemented
10#11722982C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722961C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10595163—31nomaximal
17#10595075—31nomaximal
18#10594293—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6296C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic, complemented
28#89046—24no—
29C2×#6294C2211yescharacteristic, complemented
30C2×#6294C2211yescharacteristic, complemented
31#89039—24no—
32C2×#6292C2211yescharacteristic
33C2×#6292C2211yescharacteristic
34C2×#6292C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic
36C2×#6289C2211yescharacteristic
37C2×C3×#626C2211yescharacteristic, complemented
38C2×C3×#624C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C2×#3811—31no—
58C2×#3811—31no—
59C2×#3811—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3804—31no—
63C2×#3752—31no—
64#64091—31no—
65C3×#939—31no—
66C3×#935—31no—
67C3×#930—31no—
68C3×C4×#67—31no—
69C3×#886—31no—
70C3×#67⋊C4—31no—
71#63981—31no—
72#63981—31no—
73#63981—31no—
74#63981—61no—
75#63978D311yescharacteristic, complemented
76#63974—31no—
77#63971—31no—
78C2×#3722—31no—
79C2×#3722—31no—
80C2×#3722—61no—
81#63962D311yescharacteristic, complemented
82#63953—31no—
83#63952D311yescharacteristic, complemented
84#63923—31no—
85#63922—31no—
86D3×(C2×D3)⋊C4—31no—
87D3×(C2×D3)⋊C4—31no—
88#63910—31no—
89#63910—31no—
90#63909—31no—
91#63906—31no—
92#63897—31no—
93#63895—31no—
94#63895—31no—
95#63894—31no—
96#63890—31no—
97#63890—31no—
98#63886—31no—
99#63881—31no—
100#63880—31no—
101#63865—31no—
102#63852—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⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116C3×#638—22no—
117C3×#638D414yescomplemented
118C2×C3×C3⋊Dic3—22no—
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C32×#67—22no—
124C2×C32×Dic3—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6296—22no—
131#6295—22no—
132#6294—22no—
133#6294—22no—
134#6292—22no—
135#6292—22no—
136#6292—41no—
137#6291—22no—
138#6289—22no—
139C3×#626—41no—
140C3×#624—41no—
141#5654—91no—
142#5610—91no—
143#5554—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3—31no—
146C23×C3⋊D3—31no—
147C23×C3⋊D3—31no—
148C23×C3⋊D3—61no—
149C23×C3⋊D3—61no—
150C23×C3⋊D3—61no—
151C23×C3⋊D3—121no—
152C22×D32—31no—
153C22×D32—31no—
154C22×D32—61no—
155C2×C32×D4—31no—
156C22×C32×C4—31no—
157C2×#638—31no—
158C2×#638C2×D311yescharacteristic
159C2×#638C2×D311yescharacteristic, complemented
160C22×C3⋊Dic3C2×D311yescharacteristic, complemented
161D4×C3⋊D3—64no—
162C2×C4⋊(C3⋊D3)—31no—
163C2×C4⋊(C3⋊D3)—31no—
164C2×C4⋊(C3⋊D3)—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—21no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—61no—
173C2×C3×#67—61no—
174C2×C3×#67C2×D311yescharacteristic
175C2×C3×#67C2×D311yescharacteristic
176C22×C3×Dic3—21no—
177C22×C3×Dic3—31no—
178C22×C3×Dic3—31no—
179C22×C3×Dic3—61no—
180C22×C3×Dic3C2×D311yescharacteristic, complemented
181C22×C3×Dic3C2×D311yescharacteristic, complemented
182C2×C3×D12—31no—
183C2×C3×C4×D3—31no—
184C2×C3×C4×D3—31no—
185#3811—64no—
186#3811—64no—
187#3811—68no—
188C2×#627—31no—
189C2×#627—31no—
190C2×#627—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—61no—
202C2×#626—61no—
203C2×#626—61no—
204C2×#626—61no—
205C2×#626C2×D311yescharacteristic, complemented
206C2×#625—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—61no—
212C2×#624C2×D311yescharacteristic, complemented
213#3805—64no—
214#3804—64no—
215#3804—64no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—31no—
220C32×C22⋊C4—31no—
221#3752—31no—
222#3752—31no—
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×#217C2×D311yescharacteristic, complemented
232C3×#217C2×D311yescharacteristic, complemented
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
241C3×C4⋊Dic3—31no—
242C3×C4⋊Dic3—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250#3724C2×D311yescharacteristic, complemented
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252Dic3⋊Dic3C2×D311yescharacteristic, complemented
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269#3722—61no—
270#3722—61no—
271#3722—61no—
272#3722C2×D311yescharacteristic, complemented
273#3722C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2×D412yes—
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)#4112yescomplemented
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⋊D3C2×D412yes—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298D3×C3⋊D3—44no—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3C2×D412yes—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C2×#237—91no—
309C2×#237—91no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×D3×D4—91no—
313C2×D3×D4—181no—
314C2×#235—91no—
315C3×#123—91no—
316C3×#121—91no—
317C3×C4×D4—91no—
318#939—31no—
319#939—91no—
320#937—91no—
321#937—91no—
322#935—31no—
323#930—31no—
324#930—91no—
325C4×#67—31no—
326C2×(C2×D3)⋊C4—91no—
327C2×(C2×D3)⋊C4—91no—
328C2×(C2×D3)⋊C4—91no—
329C2×(C2×D3)⋊C4—91no—
330C2×(C2×D3)⋊C4—181no—
331#897—91no—
332#896—91no—
333#896—91no—
334#895—91no—
335#895—91no—
336#894—91no—
337#894—91no—
338#893—91no—
339#886—31no—
340#886—91no—
341#885—91no—
342#885—91no—
343#884—91no—
344#884—91no—
345#882—91no—
346#882—91no—
347#882—91no—
348#882—91no—
349#882—181no—
350#67⋊C4—31no—
351#67⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
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—31no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—61no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—61no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—62no—
378C22×C3⋊D3—62no—
379C22×C3⋊D3—62no—
380C22×C3⋊D3—62no—
381C22×C3⋊D3—62no—
382C22×C3⋊D3—64no—
383C22×C3⋊D3—64no—
384C22×C3⋊D3—62no—
385C22×C3⋊D3—62no—
386C22×C3⋊D3—121no—
387C22×C3⋊D3—121no—
388C22×C3⋊D3—122no—
389C22×C3⋊D3—122no—
390C22×C3⋊D3—122no—
391C22×C3⋊D3—122no—
392C22×C3⋊D3—124no—
393C22×C3⋊D3—124no—
394C22×C3⋊D3—121no—
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×D3C22×D311yescharacteristic
412C22×C3×D3C22×D311yescharacteristic
413C2×D32—62no—
414C2×D32—62no—
415C2×D32—62no—
416C2×D32—62no—
417C2×D32—64no—
418C2×D32—122no—
419C2×D32—121no—
420C2×D32—121no—
421C2×D32—122no—
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—121no—
429#638—22no—
430#638—62no—
431#638D1214yescomplemented
432C2×C3⋊Dic3—22no—
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C4⋊(C3⋊D3)—62no—
438C4⋊(C3⋊D3)—62no—
439C4⋊(C3⋊D3)—121no—
440C4×C3⋊D3—62no—
441C3×#67—24no—
442C3×#67—22no—
443C3×#67—22no—
444C3×#67—34no—
445C3×#67—34no—
446C3×#67—64no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—122no—
450C3×#67—121no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
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—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—41no—
465C2×C3×Dic3—41no—
466C2×C3×Dic3—42no—
467C2×C3×Dic3—61no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—62no—
472C2×C3×Dic3—62no—
473C2×C3×Dic3—122no—
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
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×D12—121no—
485C3×C4×D3—121no—
486C3×C4×D3—121no—
487#627—62no—
488#627—62no—
489#627—62no—
490#626—41no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—64no—
496#626—62no—
497#626—62no—
498#626—64no—
499#626—62no—
500#626—62no—
501#626—122no—
502#626—121no—
503#626—121no—
504#626—122no—
505#625—62no—
506#624—41no—
507#624—62no—
508#624—62no—
509#624—64no—
510#624—62no—
511#624—62no—
512D3×Dic3—62no—
513D3×Dic3—62no—
514D3×Dic3—62no—
515D3×Dic3—62no—
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—
526C23×D3—91no—
527C23×D3—91no—
528C23×D3—91no—
529C23×D3—91no—
530C23×D3—91no—
531C23×D3—91no—
532C23×D3—181no—
533C23×D3—181no—
534C23×D3—181no—
535C23×D3—181no—
536C23×D3—361no—
537C2×C3×D4—31no—
538C2×C3×D4—31no—
539C2×C3×D4—61no—
540C2×C3×D4—91no—
541C2×C3×D4—91no—
542C2×C3×D4—91no—
543C22×C3×C4—31no—
544C22×C3×C4—31no—
545C22×C3×C4—61no—
546C22×C3×C4—91no—
547C22×C3×C4—91no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—61no—
554C2×#67—61no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—91no—
560C2×#67—91no—
561C2×#67—91no—
562C2×#67—181no—
563C2×#67D3211yescharacteristic
564C22×Dic3—31no—
565C22×Dic3—31no—
566C22×Dic3—61no—
567C22×Dic3—91no—
568C22×Dic3—91no—
569C22×Dic3D3211yescharacteristic, complemented
570#237—184no—
571#237—184no—
572D3×D4—184no—
573D3×D4—184no—
574D3×D4—184no—
575D3×D4—188no—
576#235—184no—
577C2×D12—31no—
578C2×D12—91no—
579C2×D12—91no—
580C2×D12—91no—
581C2×D12—91no—
582C2×D12—91no—
583C2×D12—91no—
584C2×D12—91no—
585C2×D12—91no—
586C2×D12—181no—
587C2×D12—181no—
588C2×D12—181no—
589C2×C4×D3—31no—
590C2×C4×D3—31no—
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×Dic6—91no—
600C2×Dic6—91no—
601C2×Dic6—91no—
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#217D3211yescharacteristic, complemented
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—31no—
625(C2×D3)⋊C4—31no—
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—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—181no—
645(C2×D3)⋊C4—181no—
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×C32C2×D1212yes—
686C22×C32D3×D412yes—
687C22×C32D3×D412yes—
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—62no—
700C2×C3⋊D3—62no—
701C2×C3⋊D3—62no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—62no—
708C2×C3⋊D3—62no—
709C2×C3⋊D3—61no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—62no—
714C2×C3⋊D3—62no—
715C2×C3⋊D3—62no—
716C2×C3⋊D3—61no—
717C2×C3⋊D3—61no—
718C2×C3⋊D3—61no—
719C2×C3⋊D3—61no—
720C2×C3⋊D3—61no—
721C2×C3⋊D3—61no—
722C2×C3⋊D3—122no—
723C2×C3⋊D3—121no—
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—122no—
734C2×C3⋊D3—122no—
735C2×C3⋊D3—122no—
736C2×C3⋊D3—122no—
737C2×C3⋊D3—122no—
738C2×C3⋊D3—124no—
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⋊D3C2×D1212yes—
747C2×C3×D3—22no—
748C2×C3×D3—21no—
749C2×C3×D3—21no—
750C2×C3×D3—21no—
751C2×C3×D3—21no—
752C2×C3×D3—21no—
753C2×C3×D3—21no—
754C2×C3×D3—32no—
755C2×C3×D3—32no—
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—61no—
764C2×C3×D3—61no—
765C2×C3×D3—61no—
766C2×C3×D3—61no—
767C2×C3×D3—61no—
768C2×C3×D3—61no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774D32—124no—
775D32—124no—
776D32—128no—
777C32×C4—61no—
778C32×C4—61no—
779C32×C4—61no—
780C32×C4—61no—
781C32×C4—61no—
782C3⋊Dic3—21no—
783C3⋊Dic3—21no—
784C3⋊Dic3—21no—
785C3⋊Dic3C2×D1212yes—
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—21no—
796C3×Dic3—21no—
797C3×Dic3—32no—
798C3×Dic3—32no—
799C3×Dic3—41no—
800C3×Dic3—41no—
801C3×Dic3—41no—
802C3×Dic3—41no—
803C3×Dic3—62no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—121no—
811C3×Dic3—121no—
812C3×Dic3—121no—
813C2×#41—271no—
814C22×D4—271no—
815#124—271no—
816#123—91no—
817#123—271no—
818C22⋊Q8—271no—
819#121—91no—
820#121—271no—
821#121—271no—
822#120—271no—
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×C3C2×D3211yescharacteristic
839C23×C3C2×D3211yescharacteristic
840C23×C3C2×D3211yescharacteristic
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—61no—
846C22×D3—61no—
847C22×D3—91no—
848C22×D3—91no—
849C22×D3—91no—
850C22×D3—91no—
851C22×D3—91no—
852C22×D3—91no—
853C22×D3—181no—
854C22×D3—181no—
855C22×D3—181no—
856C22×D3—181no—
857C22×D3—181no—
858C22×D3—181no—
859C22×D3—182no—
860C22×D3—182no—
861C22×D3—182no—
862C22×D3—182no—
863C22×D3—182no—
864C22×D3—182no—
865C22×D3—184no—
866C22×D3—182no—
867C22×D3—182no—
868C22×D3—182no—
869C22×D3—184no—
870C22×D3—184no—
871C22×D3—182no—
872C22×D3—182no—
873C22×D3—182no—
874C22×D3—361no—
875C22×D3—361no—
876C22×D3—362no—
877C22×D3—362no—
878C22×D3—362no—
879C22×D3—362no—
880C22×D3—362no—
881C22×D3—364no—
882C22×D3—364no—
883C22×D3—361no—
884C22×D3—361no—
885C22×D3—361no—
886C22×D3—362no—
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×D4—64no—
896C3×D4—62no—
897C3×D4—62no—
898C3×D4—94no—
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—91no—
917C2×C3×C4—91no—
918C2×C3×C4—91no—
919C2×C3×C4—91no—
920C2×C3×C4—121no—
921C2×C3×C4—121no—
922C2×C3×C4—122no—
923C2×C3×C4—182no—
924C2×C3×C4—361no—
925#67—22no—
926#67—34no—
927#67—34no—
928#67—64no—
929#67—62no—
930#67—62no—
931#67—122no—
932#67—121no—
933#67—182no—
934#67—182no—
935#67—182no—
936#67—182no—
937#67—182no—
938#67—182no—
939#67—184no—
940#67—361no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—31no—
946C2×Dic3—31no—
947C2×Dic3—31no—
948C2×Dic3—31no—
949C2×Dic3—41no—
950C2×Dic3—61no—
951C2×Dic3—61no—
952C2×Dic3—61no—
953C2×Dic3—61no—
954C2×Dic3—62no—
955C2×Dic3—62no—
956C2×Dic3—122no—
957C2×Dic3—182no—
958C2×Dic3—182no—
959C2×Dic3C2×D3211yescharacteristic
960C2×Dic3C2×D3211yescharacteristic
961C2×Dic3C2×D3211yescharacteristic
962C2×Dic3C2×D3211yescharacteristic
963C2×Dic3C2×D3211yescharacteristic
964D12—121no—
965D12—182no—
966D12—182no—
967D12—182no—
968D12—182no—
969D12—184no—
970D12—182no—
971D12—182no—
972D12—362no—
973D12—361no—
974D12—361no—
975D12—362no—
976C4×D3—121no—
977C4×D3—121no—
978C4×D3—182no—
979C4×D3—182no—
980C4×D3—182no—
981C4×D3—182no—
982C4×D3—184no—
983C4×D3—182no—
984C4×D3—182no—
985C4×D3—182no—
986Dic6—182no—
987Dic6—182no—
988Dic6—182no—
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×C32C22×D1211yescharacteristic
1010C2×C32C2×D3×D411yescharacteristic
1011C2×C32C2×D3×D411yescharacteristic
1012C2×C32#100411yescharacteristic
1013C2×C32#100411yescharacteristic
1014C2×C32D3×#4111yescharacteristic
1015C2×C32D3×#4111yescharacteristic
1016C2×C32D3×#4111yescharacteristic
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—42no—
1035C3×D3—41no—
1036C3×D3—41no—
1037C3×D3—62no—
1038C3×D3—62no—
1039C3×D3—122no—
1040C3×D3—121no—
1041C3×D3—121no—
1042C3×D3—241no—
1043C24—271no—
1044C24—271no—
1045#41—544no—
1046C2×Q8—271no—
1047C2×D4—31no—
1048C2×D4—91no—
1049C2×D4—91no—
1050C2×D4—91no—
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—91no—
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—62no—
1103C22×C3—61no—
1104C22×C3—61no—
1105C22×C3—61no—
1106C22×C3—61no—
1107C22×C3—61no—
1108C22×C3—61no—
1109C22×C3—92no—
1110C22×C3—121no—
1111C22×C3—121no—
1112C22×C3—181no—
1113C22×C3—181no—
1114C22×C3—181no—
1115C22×C3—181no—
1116C22×C3—181no—
1117C22×C3D3×D1212yes—
1118C22×C3D3×D1212yes—
1119C22×C3#381112yes—
1120C22×C3C22×D3211yescharacteristic
1121C22×C3C22×D3211yescharacteristic
1122C22×C3C22×D3211yescharacteristic
1123C2×D3—21no—
1124C2×D3—21no—
1125C2×D3—21no—
1126C2×D3—32no—
1127C2×D3—32no—
1128C2×D3—62no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—61no—
1133C2×D3—61no—
1134C2×D3—61no—
1135C2×D3—61no—
1136C2×D3—61no—
1137C2×D3—61no—
1138C2×D3—61no—
1139C2×D3—92no—
1140C2×D3—92no—
1141C2×D3—92no—
1142C2×D3—121no—
1143C2×D3—121no—
1144C2×D3—121no—
1145C2×D3—121no—
1146C2×D3—121no—
1147C2×D3—182no—
1148C2×D3—182no—
1149C2×D3—182no—
1150C2×D3—182no—
1151C2×D3—182no—
1152C2×D3—181no—
1153C2×D3—181no—
1154C2×D3—181no—
1155C2×D3—181no—
1156C2×D3—181no—
1157C2×D3—181no—
1158C2×D3—182no—
1159C2×D3—182no—
1160C2×D3—182no—
1161C2×D3—181no—
1162C2×D3—181no—
1163C2×D3—181no—
1164C2×D3—181no—
1165C2×D3—181no—
1166C2×D3—181no—
1167C2×D3—181no—
1168C2×D3—181no—
1169C2×D3—181no—
1170C2×D3—362no—
1171C2×D3—361no—
1172C2×D3—361no—
1173C2×D3—361no—
1174C2×D3—361no—
1175C2×D3—361no—
1176C2×D3—361no—
1177C2×D3—361no—
1178C2×D3—361no—
1179C2×D3—361no—
1180C2×D3—361no—
1181C2×D3—362no—
1182C2×D3—362no—
1183C2×D3—362no—
1184C2×D3—362no—
1185C2×D3—362no—
1186C2×D3—364no—
1187C2×D3—364no—
1188C2×D3—364no—
1189C2×D3—368no—
1190C2×D3—364no—
1191C2×D3—364no—
1192C2×D3—364no—
1193C2×D3—368no—
1194C2×D3—368no—
1195C2×D3—368no—
1196C2×D3—3616no—
1197C3×C4—62no—
1198C3×C4—61no—
1199C3×C4—61no—
1200C3×C4—61no—
1201C3×C4—61no—
1202C3×C4—61no—
1203C3×C4—61no—
1204C3×C4—61no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—92no—
1209C3×C4—121no—
1210C3×C4—121no—
1211C3×C4—121no—
1212C3×C4—121no—
1213C3×C4—181no—
1214C3×C4—181no—
1215C3×C4—181no—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—21no—
1221Dic3—32no—
1222Dic3—32no—
1223Dic3—62no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—121no—
1231Dic3—121no—
1232Dic3—121no—
1233C32—21no—
1234C32—21no—
1235C32—21no—
1236C32—41no—
1237C32#555411yescharacteristic, complemented
1238C32#561011yescharacteristic, complemented
1239C32#565411yescharacteristic, complemented
1240C23—31no—
1241C23—91no—
1242C23—91no—
1243C23—271no—
1244C23—271no—
1245C23—542no—
1246C23—542no—
1247C23—542no—
1248C23—542no—
1249C23—1081no—
1250C23—1081no—
1251C23D3311yescharacteristic
1252Q8—542no—
1253D4—62no—
1254D4—94no—
1255D4—182no—
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—91no—
1268C2×C4—91no—
1269C2×C4—91no—
1270C2×C4—91no—
1271C2×C4—121no—
1272C2×C4—182no—
1273C2×C4—361no—
1274C2×C4—542no—
1275C2×C4—542no—
1276C2×C4—542no—
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—122no—
1297C2×C3—121no—
1298C2×C3—121no—
1299C2×C3—182no—
1300C2×C3—361no—
1301C2×C3C2×D3×D1211yescharacteristic
1302C2×C3C2×D3×D1211yescharacteristic
1303C2×C3#6430611yescharacteristic
1304C2×C3#6431211yescharacteristic
1305C2×C3#6431211yescharacteristic
1306C2×C3#6431411yescharacteristic
1307C2×C3#6431411yescharacteristic
1308C2×C3C2×#381111yescharacteristic
1309C2×C3#6433011yescharacteristic
1310D3—41no—
1311D3—62no—
1312D3—62no—
1313D3—122no—
1314D3—121no—
1315D3—121no—
1316D3—184no—
1317D3—182no—
1318D3—182no—
1319D3—182no—
1320D3—241no—
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—541no—
1344C22—541no—
1345C22—541no—
1346C22—541no—
1347C22—541no—
1348C22—1084no—
1349C22—1084no—
1350C22#8895512yes—
1351C22C2×D3311yescharacteristic
1352C4—61no—
1353C4—61no—
1354C4—61no—
1355C4—61no—
1356C4—61no—
1357C4—92no—
1358C4—181no—
1359C4—181no—
1360C4—181no—
1361C3—21no—
1362C3—21no—
1363C3—21no—
1364C3—41no—
1365C3#1059429311yescharacteristic, complemented
1366C3#1059507511yescharacteristic, complemented
1367C3#1059516311yescharacteristic, complemented
1368C2—22no—
1369C2—121no—
1370C2—182no—
1371C2—361no—
1372C2—542no—
1373C2—1081no—
1374C2#1172441111yescharacteristic
1375C2#1172441911yescharacteristic
1376C2C2×#8895511yescharacteristic
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×#89046C2semidirect
2. C2×#89039C2semidirect
3. #11723639C2semidirect
4. C2×#88804C2semidirect
5. C3×#63978C2semidirect
6. C3×#63962C2semidirect
7. C3×#63952C2semidirect
8. #11723008C2semidirect
9. #11722999C2semidirect
10. #11722982C2semidirect
11. #11722966C2semidirect
12. #11722961C2semidirect
13. #11722950C2semidirect
14. #11722937C2semidirect
15. #11722904C2semidirect
22. C2×C3×#638C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
25. C22×C32×Dic3C22semidirect
26. C2×#6296C22semidirect
27. C2×#6295C22semidirect
29. C2×#6294C22semidirect
30. C2×#6294C22semidirect
34. C2×#6292C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#624C22semidirect
39. C32×#217C22semidirect
43. #88804C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
75. #63978D3semidirect
81. #63962D3semidirect
83. #63952D3semidirect
117. C3×#638D4semidirect
159. C2×#638C2×D3semidirect
160. C22×C3⋊Dic3C2×D3semidirect
180. C22×C3×Dic3C2×D3semidirect
181. C22×C3×Dic3C2×D3semidirect
205. C2×#626C2×D3semidirect
212. C2×#624C2×D3semidirect
231. C3×#217C2×D3semidirect
232. C3×#217C2×D3semidirect
250. #3724C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
272. #3722C2×D3semidirect
273. #3722C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
288. C2×C3⋊(C3⋊D3)#41semidirect
431. #638D12semidirect
569. C22×Dic3D32semidirect
618. #217D32semidirect
828. C33#546semidirect
1237. C32#5554semidirect
1238. C32#5610semidirect
1239. C32#5654semidirect
1365. C3#10594293semidirect
1366. C3#10595075semidirect
1367. C3#10595163semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#890392
#117236392
C2×#888042
C3×#639782
C3×#639622
C3×#639522
#117230082
#117229992
#117229822
#117229662
#117229612
#117229502
#117229372
#117229042
#105951633
#105950753
#105942933