Finite Group Databasebeta

← #13172901

Subgroups — #13172901

Order 1728.

1968 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6292C211yesmaximal, characteristic, complemented
2C2×#88965C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723627C211yesmaximal, characteristic, complemented
6C3×#63974C211yesmaximal, characteristic, complemented
7C3×#63964C211yesmaximal, characteristic, complemented
8C3×#63952C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722993C211yesmaximal, characteristic, complemented
12#11722968C211yesmaximal, characteristic, complemented
13#11722961C211yesmaximal, characteristic, complemented
14#11722961C211yesmaximal, characteristic, complemented
15#11722933C211yesmaximal, characteristic, complemented
16#10595018—31nomaximal
17#10594187—31nomaximal
18#10594186—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C23×C3×C3⋊D3C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6295C2211yescharacteristic, complemented
24C2×#6295C2211yescharacteristic, complemented
25C2×#6292—24no—
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6292C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×#6289C2211yescharacteristic, complemented
34C2×C3×#627C2211yescharacteristic, complemented
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×#624C2211yescharacteristic, complemented
38#88965—24no—
39C3×#3757C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×C4⋊(C3⋊D3)—31no—
57C22×#626—31no—
58C22×#626—31no—
59C22×#626—61no—
60C2×#3799—31no—
61C2×#3799—31no—
62C2×#3798—31no—
63#64091—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×C4×#67—31no—
66C3×#924—31no—
67C3×#67⋊C4—31no—
68C3×D3×C22⋊C4—31no—
69C3×D3×C22⋊C4—31no—
70C3×#878—31no—
71#63981—31no—
72#63981—31no—
73#63981—31no—
74#63981—61no—
75#63977—31no—
76#63976—31no—
77#63974—31no—
78#63974—31no—
79#63974—61no—
80#63974D311yescharacteristic, complemented
81#63964D311yescharacteristic, complemented
82#63952D311yescharacteristic, complemented
83#63912—31no—
84#63910—31no—
85#63910—31no—
86#63910—31no—
87#63910—31no—
88#63909—31no—
89#63909—31no—
90#63907—31no—
91#63906—31no—
92#63906—31no—
93#63904—31no—
94C4×#626—31no—
95#63897—31no—
96#63897—31no—
97#63894—31no—
98#63864—31no—
99#63854—31no—
100#63853—31no—
101#63852—31no—
102#63850—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)—22no—
106C22×C3⋊(C3⋊D3)—22no—
107C22×C3⋊(C3⋊D3)—41no—
108C22×C3⋊(C3⋊D3)C2311yescharacteristic
109C22×C3⋊(C3⋊D3)C2311yescharacteristic
110C22×C3×C3⋊D3—22no—
111C22×C3×C3⋊D3—22no—
112C22×C3×C3⋊D3—41no—
113C22×C3×C3⋊D3C2311yescharacteristic
114C22×C3×C3⋊D3C2311yescharacteristic
115C22×C3×C3⋊D3C2311yescharacteristic
116C3×#638—22no—
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C32×Dic3—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6295—22no—
128#6295—41no—
129#6292—22no—
130#6292—22no—
131#6292—22no—
132#6292—22no—
133#6292—41no—
134#6292D414yescomplemented
135#6289—22no—
136#6289—41no—
137C3×#627—22no—
138C3×#624—22no—
139C3×#624—22no—
140C3×#624—41no—
141#5630—91no—
142#5550—91no—
143#5490—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3—31no—
146C23×C3⋊D3—31no—
147C23×C3⋊D3—61no—
148C23×C3⋊D3—61no—
149C23×C3⋊D3—61no—
150C23×C3⋊D3—121no—
151C23×C3⋊D3C2×D311yescharacteristic
152C23×C3×D3—31no—
153C23×C3×D3—31no—
154C23×C3×D3—61no—
155C22×C32×C4—31no—
156C2×#638C2×D311yescharacteristic
157C2×C4⋊(C3⋊D3)—31no—
158C2×C4⋊(C3⋊D3)—31no—
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4⋊(C3⋊D3)—31no—
161C2×C4⋊(C3⋊D3)—31no—
162C2×C4⋊(C3⋊D3)—31no—
163C2×C4⋊(C3⋊D3)—64no—
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—61no—
169C22×C3×Dic3—21no—
170C22×C3×Dic3C2×D311yescharacteristic
171C22×C3×Dic3C2×D311yescharacteristic
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×C3×Dic6—31no—
179C2×C3×Dic6—31no—
180C2×#627C2×D311yescharacteristic, complemented
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—64no—
198C2×#626—64no—
199C2×#626—61no—
200C2×#626—61no—
201C2×#626—61no—
202C2×#626—61no—
203C2×#626—68no—
204C2×#626—61no—
205C2×#626—61no—
206C2×#625—31no—
207C2×#625—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—31no—
212C2×#624—61no—
213C2×#624—61no—
214C2×#624C2×D311yescharacteristic, complemented
215C2×#624C2×D311yescharacteristic, complemented
216C2×#624C2×D311yescharacteristic, complemented
217#3799—64no—
218#3799—64no—
219#3798—64no—
220C32×C22⋊C4—31no—
221C32×C22⋊C4—31no—
222#3757C2×D311yescharacteristic
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3752—31no—
227C3×#217—21no—
228C3×#217—21no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—61no—
232C3×#217C2×D311yescharacteristic
233C3×#217C2×D311yescharacteristic
234C3×#217C2×D311yescharacteristic
235C3×#217C2×D311yescharacteristic
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×C4⋊Dic3—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250C3×C4×Dic3—31no—
251C3×C4×Dic3—31no—
252#3724C2×D311yescharacteristic, complemented
253#3724C2×D311yescharacteristic, complemented
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269#3722—61no—
270#3722C2×D311yescharacteristic, complemented
271#3722C2×D311yescharacteristic, complemented
272#3722C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—31no—
276(C2×D3)⋊Dic3—31no—
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33#4112yescomplemented
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3⋊(C3⋊D3)—21no—
286C2×C3⋊(C3⋊D3)—21no—
287C2×C3⋊(C3⋊D3)—44no—
288C2×C3⋊(C3⋊D3)C2×D412yes—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—21no—
296C2×C3×C3⋊D3—21no—
297C2×C3×C3⋊D3—44no—
298C2×C3×C3⋊D3C2×D412yes—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C32×Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3C2×D412yes—
308C22×#67—91no—
309C2×#239—91no—
310C2×#235—91no—
311C2×#235—91no—
312C22×D12—91no—
313C22×D12—91no—
314C22×D12—181no—
315C3×C22⋊Q8—91no—
316C3×C4×D4—91no—
317C2×C3×C22⋊C4—91no—
318#953—91no—
319#947—91no—
320#937—91no—
321#937—91no—
322#930—91no—
323#930—91no—
324#929—91no—
325C4×#67—31no—
326C4×#67—91no—
327#924—31no—
328#895—91no—
329#895—91no—
330#895—91no—
331#894—91no—
332#894—91no—
333#894—91no—
334#894—91no—
335#893—91no—
336#885—91no—
337#884—91no—
338#884—91no—
339#884—91no—
340#884—91no—
341#883—91no—
342#882—91no—
343#882—91no—
344#882—91no—
345#882—181no—
346#67⋊C4—31no—
347D3×C22⋊C4—31no—
348D3×C22⋊C4—31no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—181no—
353#878—31no—
354#875—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—41no—
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C22×C3⋊D3—22no—
364C22×C3⋊D3—22no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—41no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—61no—
376C22×C3⋊D3—61no—
377C22×C3⋊D3—61no—
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—122no—
398C22×C3⋊D3—122no—
399C22×C3⋊D3—122no—
400C22×C3⋊D3—124no—
401C22×C3⋊D3C22×D311yescharacteristic
402C22×C3⋊D3C22×D311yescharacteristic
403C22×C3⋊D3C22×D311yescharacteristic
404C22×C3×D3—31no—
405C22×C3×D3—31no—
406C22×C3×D3—31no—
407C22×C3×D3—31no—
408C22×C3×D3—31no—
409C22×C3×D3—31no—
410C22×C3×D3—61no—
411C22×C3×D3—61no—
412C22×C3×D3—61no—
413C22×C3×D3—62no—
414C22×C3×D3—62no—
415C22×C3×D3—64no—
416C22×C3×D3—62no—
417C22×C3×D3—62no—
418C22×C3×D3—122no—
419C22×C3×D3—121no—
420C22×C3×D3—121no—
421C22×C3×D3—122no—
422C2×C32×C4—31no—
423C2×C32×C4—31no—
424C2×C32×C4—31no—
425C2×C32×C4—31no—
426C2×C32×C4—31no—
427C2×C32×C4—31no—
428C2×C32×C4—62no—
429#638—22no—
430C2×C3⋊Dic3C22×D311yescharacteristic
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C4⋊(C3⋊D3)—34no—
434C4⋊(C3⋊D3)—62no—
435C4⋊(C3⋊D3)—62no—
436C4⋊(C3⋊D3)—62no—
437C4⋊(C3⋊D3)—62no—
438C4⋊(C3⋊D3)—121no—
439C4×C3⋊D3—62no—
440C4×C3⋊D3—121no—
441C3×#67—62no—
442C3×#67—62no—
443C3×#67—122no—
444C2×C3×Dic3—24no—
445C2×C3×Dic3—22no—
446C2×C3×Dic3—22no—
447C2×C3×Dic3—21no—
448C2×C3×Dic3—21no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
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—61no—
460C2×C3×Dic3—61no—
461C2×C3×Dic3—61no—
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
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×C4×D3—62no—
475C3×C4×D3—62no—
476C3×C4×D3—62no—
477C3×C4×D3—62no—
478C3×C4×D3—121no—
479C3×C4×D3—121no—
480C3×Dic6—62no—
481C3×Dic6—62no—
482#627—22no—
483#626—34no—
484#626—34no—
485#626—64no—
486#626—62no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—62no—
491#626—62no—
492#626—64no—
493#626—64no—
494#626—64no—
495#626—62no—
496#626—62no—
497#626—62no—
498#626—62no—
499#626—122no—
500#626—121no—
501#626—121no—
502#626—122no—
503#626—121no—
504#626—121no—
505#625—62no—
506#625—121no—
507#624—22no—
508#624—22no—
509#624—41no—
510#624—62no—
511#624—62no—
512#624—122no—
513#624—121no—
514#624—121no—
515#624—122no—
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—
525C3×C3⋊D3—41no—
526C24×C3—91no—
527C23×D3—31no—
528C23×D3—31no—
529C23×D3—61no—
530C23×D3—91no—
531C23×D3—91no—
532C23×D3—91no—
533C23×D3—181no—
534C23×D3—181no—
535C23×D3—181no—
536C23×D3—361no—
537C2×C3×Q8—91no—
538C2×C3×D4—91no—
539C22×C3×C4—31no—
540C22×C3×C4—31no—
541C22×C3×C4—61no—
542C22×C3×C4—91no—
543C22×C3×C4—91no—
544C22×C3×C4—91no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—61no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—184no—
559C22×Dic3D3211yescharacteristic
560#239—184no—
561#235—184no—
562#235—184no—
563C2×D12—91no—
564C2×D12—91no—
565C2×D12—91no—
566C2×D12—91no—
567C2×D12—91no—
568C2×D12—91no—
569C2×D12—91no—
570C2×D12—91no—
571C2×D12—91no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—91no—
575C2×D12—91no—
576C2×D12—91no—
577C2×D12—181no—
578C2×D12—181no—
579C2×D12—181no—
580C2×D12—181no—
581C2×D12—181no—
582C2×D12—181no—
583C2×D12—184no—
584C2×D12—184no—
585C2×D12—188no—
586C2×C4×D3—31no—
587C2×C4×D3—31no—
588C2×C4×D3—31no—
589C2×C4×D3—31no—
590C2×C4×D3—31no—
591C2×C4×D3—31no—
592C2×C4×D3—91no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—91no—
598C2×C4×D3—181no—
599C2×C4×D3—181no—
600C2×Dic6—31no—
601C2×Dic6—31no—
602C3×C4⋊C4—91no—
603C3×C4⋊C4—91no—
604C3×C4⋊C4—91no—
605C3×C4⋊C4—91no—
606C3×C22⋊C4—31no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—31no—
609C3×C22⋊C4—31no—
610C3×C22⋊C4—61no—
611C3×C22⋊C4—61no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4—91no—
614C3×C22⋊C4—91no—
615C3×C22⋊C4—91no—
616C3×C42—91no—
617#217—31no—
618#217—31no—
619#217—61no—
620#217—91no—
621#217—91no—
622#217D3211yescharacteristic
623#217D3211yescharacteristic
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—31no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—181no—
647(C2×D3)⋊C4—181no—
648(C2×D3)⋊C4—181no—
649(C2×D3)⋊C4—181no—
650C4⋊Dic3—31no—
651C4⋊Dic3—31no—
652Dic3⋊C4—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#23512yescomplemented
683C22×C32#23512yescomplemented
684C22×C32#23912yescomplemented
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—21no—
694C2×C3⋊D3—21no—
695C2×C3⋊D3—21no—
696C2×C3⋊D3—32no—
697C2×C3⋊D3—32no—
698C2×C3⋊D3—32no—
699C2×C3⋊D3—44no—
700C2×C3⋊D3—62no—
701C2×C3⋊D3—62no—
702C2×C3⋊D3—62no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—62no—
709C2×C3⋊D3—62no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—61no—
714C2×C3⋊D3—62no—
715C2×C3⋊D3—62no—
716C2×C3⋊D3—62no—
717C2×C3⋊D3—61no—
718C2×C3⋊D3—61no—
719C2×C3⋊D3—61no—
720C2×C3⋊D3—61no—
721C2×C3⋊D3—61no—
722C2×C3⋊D3—61no—
723C2×C3⋊D3—122no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—121no—
727C2×C3⋊D3—121no—
728C2×C3⋊D3—121no—
729C2×C3⋊D3—121no—
730C2×C3⋊D3—121no—
731C2×C3⋊D3—121no—
732C2×C3⋊D3—121no—
733C2×C3⋊D3—121no—
734C2×C3⋊D3—122no—
735C2×C3⋊D3—122no—
736C2×C3⋊D3—122no—
737C2×C3⋊D3—122no—
738C2×C3⋊D3—122no—
739C2×C3⋊D3—124no—
740C2×C3⋊D3—124no—
741C2×C3⋊D3—124no—
742C2×C3⋊D3—128no—
743C2×C3⋊D3—128no—
744C2×C3⋊D3—128no—
745C2×C3⋊D3—1216no—
746C2×C3⋊D3D3×D412yes—
747C2×C3×D3—32no—
748C2×C3×D3—32no—
749C2×C3×D3—62no—
750C2×C3×D3—61no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—62no—
755C2×C3×D3—61no—
756C2×C3×D3—61no—
757C2×C3×D3—61no—
758C2×C3×D3—61no—
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—121no—
768C2×C3×D3—121no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774C2×C3×D3—124no—
775C2×C3×D3—124no—
776C2×C3×D3—128no—
777C32×C4—32no—
778C32×C4—61no—
779C32×C4—61no—
780C32×C4—61no—
781C32×C4—61no—
782C32×C4—61no—
783C3⋊Dic3—21no—
784C3⋊Dic3—21no—
785C3⋊Dic3—21no—
786C3×Dic3—22no—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—21no—
790C3×Dic3—21no—
791C3×Dic3—21no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—21no—
795C3×Dic3—21no—
796C3×Dic3—21no—
797C3×Dic3—22no—
798C3×Dic3—41no—
799C3×Dic3—41no—
800C3×Dic3—41no—
801C3×Dic3—41no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—121no—
809C3×Dic3—121no—
810C3×Dic3—121no—
811C3×Dic3D3×D412yes—
812C3×Dic3D3×D412yes—
813C2×#41—271no—
814C22×D4—271no—
815#124—271no—
816#123—271no—
817#123—271no—
818C22⋊Q8—91no—
819#121—271no—
820#121—271no—
821#121—271no—
822#120—271no—
823#120—271no—
824C4×D4—91no—
825C4×D4—271no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—271no—
828C33#54611yescharacteristic, complemented, Sylow
829C23×C3—21no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—41no—
833C23×C3—91no—
834C23×C3—91no—
835C23×C3—91no—
836C23×C3—182no—
837C23×C3—182no—
838C23×C3—361no—
839C23×C3C2×D3211yescharacteristic
840C23×C3C2×D3211yescharacteristic
841C23×C3C2×D3211yescharacteristic
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—31no—
847C22×D3—31no—
848C22×D3—61no—
849C22×D3—61no—
850C22×D3—61no—
851C22×D3—62no—
852C22×D3—62no—
853C22×D3—64no—
854C22×D3—62no—
855C22×D3—62no—
856C22×D3—91no—
857C22×D3—91no—
858C22×D3—91no—
859C22×D3—91no—
860C22×D3—91no—
861C22×D3—91no—
862C22×D3—122no—
863C22×D3—121no—
864C22×D3—121no—
865C22×D3—122no—
866C22×D3—181no—
867C22×D3—181no—
868C22×D3—181no—
869C22×D3—181no—
870C22×D3—181no—
871C22×D3—181no—
872C22×D3—182no—
873C22×D3—182no—
874C22×D3—182no—
875C22×D3—184no—
876C22×D3—184no—
877C22×D3—182no—
878C22×D3—182no—
879C22×D3—182no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—362no—
883C22×D3—362no—
884C22×D3—362no—
885C22×D3—362no—
886C22×D3—364no—
887C22×D3—364no—
888C22×D3—361no—
889C22×D3—361no—
890C22×D3—361no—
891C22×D3—362no—
892C22×D3—362no—
893C22×D3—362no—
894C22×D3—364no—
895C3×Q8—182no—
896C3×D4—182no—
897C2×C3×C4—31no—
898C2×C3×C4—31no—
899C2×C3×C4—31no—
900C2×C3×C4—31no—
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—61no—
910C2×C3×C4—61no—
911C2×C3×C4—61no—
912C2×C3×C4—61no—
913C2×C3×C4—61no—
914C2×C3×C4—61no—
915C2×C3×C4—62no—
916C2×C3×C4—62no—
917C2×C3×C4—64no—
918C2×C3×C4—91no—
919C2×C3×C4—91no—
920C2×C3×C4—91no—
921C2×C3×C4—182no—
922C2×C3×C4—182no—
923C2×C3×C4—361no—
924#67—62no—
925#67—62no—
926#67—94no—
927#67—122no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—182no—
934#67—361no—
935#67—361no—
936#67—361no—
937C2×Dic3—22no—
938C2×Dic3—31no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—61no—
945C2×Dic3—61no—
946C2×Dic3—61no—
947C2×Dic3C2×D3211yescharacteristic
948C2×Dic3C2×D3211yescharacteristic
949C2×Dic3C2×D3211yescharacteristic
950C2×Dic3C2×D3211yescharacteristic
951C2×Dic3C2×D3211yescharacteristic
952C2×Dic3C2×D3211yescharacteristic
953D12—94no—
954D12—94no—
955D12—184no—
956D12—182no—
957D12—182no—
958D12—182no—
959D12—182no—
960D12—182no—
961D12—182no—
962D12—182no—
963D12—182no—
964D12—184no—
965D12—184no—
966D12—184no—
967D12—182no—
968D12—362no—
969D12—361no—
970D12—361no—
971D12—362no—
972D12—361no—
973C4×D3—62no—
974C4×D3—62no—
975C4×D3—62no—
976C4×D3—62no—
977C4×D3—121no—
978C4×D3—121no—
979C4×D3—182no—
980C4×D3—182no—
981C4×D3—182no—
982C4×D3—362no—
983C4×D3—361no—
984C4×D3—361no—
985C4×D3—361no—
986C4×D3—362no—
987Dic6—62no—
988Dic6—62no—
989C2×C32—22no—
990C2×C32—24no—
991C2×C32—22no—
992C2×C32—22no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—42no—
1006C2×C32—42no—
1007C2×C32—44no—
1008C2×C32C2×#23511yescharacteristic
1009C2×C32C2×#23511yescharacteristic
1010C2×C32C2×D3×D411yescharacteristic
1011C2×C32C2×D3×D411yescharacteristic
1012C2×C32C2×D3×D411yescharacteristic
1013C2×C32#100411yescharacteristic
1014C2×C32C2×#23911yescharacteristic
1015C2×C32#100911yescharacteristic
1016C2×C32#100911yescharacteristic
1017C3⋊D3—22no—
1018C3⋊D3—41no—
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—62no—
1035C3×D3—62no—
1036C3×D3—122no—
1037C3×D3—122no—
1038C3×D3—121no—
1039C3×D3—121no—
1040C3×D3—121no—
1041C3×D3—121no—
1042C3×D3—241no—
1043C24—91no—
1044C24—271no—
1045#41—544no—
1046C2×Q8—91no—
1047C2×D4—91no—
1048C2×D4—271no—
1049C2×D4—271no—
1050C2×D4—271no—
1051C2×D4—271no—
1052C2×D4—271no—
1053C2×D4—271no—
1054C2×D4—271no—
1055C2×D4—271no—
1056C2×D4—544no—
1057C22×C4—31no—
1058C22×C4—91no—
1059C22×C4—91no—
1060C22×C4—91no—
1061C22×C4—271no—
1062C22×C4—271no—
1063C4⋊C4—91no—
1064C4⋊C4—91no—
1065C4⋊C4—91no—
1066C4⋊C4—91no—
1067C22⋊C4—31no—
1068C22⋊C4—31no—
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—92no—
1103C22×C3—181no—
1104C22×C3—181no—
1105C22×C3—181no—
1106C22×C3—181no—
1107C22×C3—181no—
1108C22×C3—181no—
1109C22×C3—181no—
1110C22×C3—181no—
1111C22×C3—364no—
1112C22×C3#379812yescomplemented
1113C22×C3#379912yescomplemented
1114C22×C3#379912yescomplemented
1115C22×C3C22×D3211yescharacteristic
1116C22×C3C22×D3211yescharacteristic
1117C22×C3C22×D3211yescharacteristic
1118C2×D3—32no—
1119C2×D3—32no—
1120C2×D3—62no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—62no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
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—92no—
1139C2×D3—92no—
1140C2×D3—92no—
1141C2×D3—121no—
1142C2×D3—121no—
1143C2×D3—121no—
1144C2×D3—121no—
1145C2×D3—121no—
1146C2×D3—121no—
1147C2×D3—121no—
1148C2×D3—124no—
1149C2×D3—124no—
1150C2×D3—128no—
1151C2×D3—182no—
1152C2×D3—182no—
1153C2×D3—182no—
1154C2×D3—182no—
1155C2×D3—182no—
1156C2×D3—181no—
1157C2×D3—181no—
1158C2×D3—181no—
1159C2×D3—181no—
1160C2×D3—181no—
1161C2×D3—181no—
1162C2×D3—182no—
1163C2×D3—182no—
1164C2×D3—182no—
1165C2×D3—181no—
1166C2×D3—181no—
1167C2×D3—181no—
1168C2×D3—181no—
1169C2×D3—181no—
1170C2×D3—181no—
1171C2×D3—181no—
1172C2×D3—181no—
1173C2×D3—181no—
1174C2×D3—362no—
1175C2×D3—361no—
1176C2×D3—361no—
1177C2×D3—361no—
1178C2×D3—361no—
1179C2×D3—361no—
1180C2×D3—361no—
1181C2×D3—361no—
1182C2×D3—361no—
1183C2×D3—361no—
1184C2×D3—361no—
1185C2×D3—362no—
1186C2×D3—362no—
1187C2×D3—362no—
1188C2×D3—362no—
1189C2×D3—362no—
1190C2×D3—364no—
1191C2×D3—364no—
1192C2×D3—364no—
1193C2×D3—368no—
1194C2×D3—368no—
1195C2×D3—368no—
1196C2×D3—3616no—
1197C3×C4—32no—
1198C3×C4—32no—
1199C3×C4—62no—
1200C3×C4—62no—
1201C3×C4—61no—
1202C3×C4—61no—
1203C3×C4—61no—
1204C3×C4—61no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—61no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—121no—
1212C3×C4—121no—
1213C3×C4—121no—
1214C3×C4—121no—
1215C3×C4—181no—
1216C3×C4—181no—
1217C3×C4—181no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—21no—
1221Dic3—21no—
1222Dic3—21no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—121no—
1230Dic3—121no—
1231Dic3—121no—
1232Dic3#381112yes—
1233C32—21no—
1234C32—21no—
1235C32—21no—
1236C32—41no—
1237C32#549011yescharacteristic, complemented
1238C32#555011yescharacteristic, complemented
1239C32#563011yescharacteristic, complemented
1240C23—91no—
1241C23—91no—
1242C23—91no—
1243C23—182no—
1244C23—182no—
1245C23—271no—
1246C23—271no—
1247C23—361no—
1248C23—542no—
1249C23—542no—
1250C23—1081no—
1251C23D3311yescharacteristic
1252Q8—182no—
1253D4—182no—
1254D4—274no—
1255D4—542no—
1256D4—542no—
1257D4—542no—
1258D4—542no—
1259D4—542no—
1260D4—1081no—
1261D4—1081no—
1262C2×C4—31no—
1263C2×C4—31no—
1264C2×C4—31no—
1265C2×C4—31no—
1266C2×C4—31no—
1267C2×C4—31no—
1268C2×C4—62no—
1269C2×C4—91no—
1270C2×C4—91no—
1271C2×C4—91no—
1272C2×C4—182no—
1273C2×C4—182no—
1274C2×C4—361no—
1275C2×C4—542no—
1276C2×C4—1081no—
1277C2×C3—24no—
1278C2×C3—22no—
1279C2×C3—22no—
1280C2×C3—22no—
1281C2×C3—21no—
1282C2×C3—21no—
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—42no—
1291C2×C3—42no—
1292C2×C3—44no—
1293C2×C3—41no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—182no—
1297C2×C3—361no—
1298C2×C3—361no—
1299C2×C3C2×#379811yescharacteristic
1300C2×C3C2×#379911yescharacteristic
1301C2×C3C2×#379911yescharacteristic
1302C2×C3#6430811yescharacteristic
1303C2×C3D32×D411yescharacteristic
1304C2×C3D32×D411yescharacteristic
1305C2×C3#6431411yescharacteristic
1306C2×C3#6431411yescharacteristic
1307C2×C3C2×#381111yescharacteristic
1308D3—62no—
1309D3—62no—
1310D3—122no—
1311D3—122no—
1312D3—121no—
1313D3—121no—
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—92no—
1334C22—181no—
1335C22—181no—
1336C22—181no—
1337C22—181no—
1338C22—181no—
1339C22—181no—
1340C22—181no—
1341C22—181no—
1342C22—272no—
1343C22—364no—
1344C22—541no—
1345C22—541no—
1346C22—541no—
1347C22—541no—
1348C22—541no—
1349C22—1084no—
1350C22#8896512yescomplemented
1351C22C2×D3311yescharacteristic
1352C4—32no—
1353C4—61no—
1354C4—61no—
1355C4—61no—
1356C4—61no—
1357C4—61no—
1358C4—181no—
1359C4—181no—
1360C4—181no—
1361C3—21no—
1362C3—21no—
1363C3—21no—
1364C3—41no—
1365C3#1059418611yescharacteristic, complemented
1366C3#1059418711yescharacteristic, complemented
1367C3#1059501811yescharacteristic, complemented
1368C2—22no—
1369C2—182no—
1370C2—361no—
1371C2—361no—
1372C2—542no—
1373C2—1081no—
1374C2#1172442011yescharacteristic
1375C2C2×#8896511yescharacteristic
1376C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#6292C2semidirect
2. C2×#88965C2semidirect
3. #11723727C2semidirect
4. #11723639C2semidirect
5. #11723627C2semidirect
6. C3×#63974C2semidirect
7. C3×#63964C2semidirect
8. C3×#63952C2semidirect
9. #11723003C2semidirect
10. #11723000C2semidirect
11. #11722993C2semidirect
12. #11722968C2semidirect
13. #11722961C2semidirect
14. #11722961C2semidirect
15. #11722933C2semidirect
23. C2×#6295C22semidirect
24. C2×#6295C22semidirect
30. C2×#6292C22semidirect
31. C2×#6292C22semidirect
32. C2×#6289C22semidirect
33. C2×#6289C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×#624C22semidirect
37. C2×C3×#624C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. C3×#3724C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
54. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
80. #63974D3semidirect
81. #63964D3semidirect
82. #63952D3semidirect
134. #6292D4semidirect
180. C2×#627C2×D3semidirect
214. C2×#624C2×D3semidirect
215. C2×#624C2×D3semidirect
216. C2×#624C2×D3semidirect
252. #3724C2×D3semidirect
253. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
270. #3722C2×D3semidirect
271. #3722C2×D3semidirect
272. #3722C2×D3semidirect
277. Dic32C2×D3semidirect
280. C22×C33#41semidirect
682. C22×C32#235semidirect
683. C22×C32#235semidirect
684. C22×C32#239semidirect
828. C33#546semidirect
1112. C22×C3#3798semidirect
1113. C22×C3#3799semidirect
1114. C22×C3#3799semidirect
1237. C32#5490semidirect
1238. C32#5550semidirect
1239. C32#5630semidirect
1350. C22#88965semidirect
1365. C3#10594186semidirect
1366. C3#10594187semidirect
1367. C3#10595018semidirect

Maximal subgroups

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

subgroupindex
C22×#62922
C2×#889652
#117237272
#117236392
#117236272
C3×#639742
C3×#639642
C3×#639522
#117230032
#117230002
#117229932
#117229682
#117229612
#117229332
#105950183
#105941873
#105941863