Finite Group Databasebeta

← #13172187

Subgroups — #13172187

Order 1728.

1520 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723720C211yesmaximal, characteristic, complemented
2#11723639C211yesmaximal, characteristic
3#11723627C211yesmaximal, characteristic, complemented
4C2×#88804C211yesmaximal, characteristic, complemented
5C3×#63964C211yesmaximal, characteristic, complemented
6C3×#63957C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723021C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11723000C211yesmaximal, characteristic, complemented
12#11722993C211yesmaximal, characteristic, complemented
13#11722977C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722918C211yesmaximal, characteristic, complemented
16#10595035—31nomaximal
17#10594166—31nomaximal
18#10594040—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#624C2211yescharacteristic, complemented
29C3×#3757C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic, complemented
33#88815C2211yescharacteristic, complemented
34#88814C2211yescharacteristic, complemented
35#88814C2211yescharacteristic, complemented
36#88804C2211yescharacteristic
37#88804C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44C3×#3724C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×Dic32C2211yescharacteristic, complemented
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C2×#3752—31no—
55#64091—31no—
56C22⋊C4×C3⋊D3—31no—
57C3×C4×#67—31no—
58C3×#924—31no—
59C3×#67⋊C4—31no—
60C3×#878—31no—
61C3×#877—31no—
62C3×#877—31no—
63#63981—31no—
64#63981—31no—
65#63981—61no—
66#63974—31no—
67#63974—31no—
68#63974—61no—
69#63966—31no—
70#63964D311yescharacteristic, complemented
71C2×#3722—31no—
72C2×#3722—31no—
73C2×#3722—61no—
74#63962—31no—
75#63961—31no—
76#63957D311yescharacteristic, complemented
77#63952D311yescharacteristic, complemented
78#63907—31no—
79#63904—31no—
80C4×#626—31no—
81#63897—31no—
82#63897—31no—
83#63894—31no—
84#63888—31no—
85#63888—31no—
86#63874—31no—
87#63868—31no—
88#63868—31no—
89#63868—31no—
90#63868—31no—
91#63865—31no—
92#63864—31no—
93#63854—31no—
94#63853—31no—
95#63852—31no—
96#63850—31no—
97#63850—31no—
98#63848—31no—
99#63848—31no—
100#63836—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)—22no—
104C22×C3⋊(C3⋊D3)—22no—
105C22×C3⋊(C3⋊D3)—41no—
106C22×C3⋊(C3⋊D3)C2311yescharacteristic
107C22×C3⋊(C3⋊D3)C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C3×#638—22no—
110C2×C3×C3⋊Dic3—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C32×Dic3—41no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6292—22no—
124#6292—41no—
125#6289—22no—
126#6289—41no—
127C3×#627—41no—
128C3×#624—41no—
129#5637—91no—
130#5556—91no—
131#5527—91no—
132C23×C3⋊D3—31no—
133C23×C3⋊D3—31no—
134C23×C3⋊D3—31no—
135C23×C3⋊D3—61no—
136C23×C3⋊D3—61no—
137C23×C3⋊D3—61no—
138C23×C3⋊D3—121no—
139C22×C32×C4—31no—
140C2×#638C2×D311yescharacteristic
141C22×C3⋊Dic3C2×D311yescharacteristic
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—61no—
149C22×C3×Dic3—21no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—61no—
153C22×C3×Dic3C2×D311yescharacteristic
154C22×C3×Dic3C2×D311yescharacteristic
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×Dic6—31no—
158C2×C3×Dic6—31no—
159C2×#627C2×D311yescharacteristic, complemented
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—61no—
165C2×#626—61no—
166C2×#624—31no—
167C2×#624—31no—
168C2×#624—31no—
169C2×#624—31no—
170C2×#624—61no—
171C2×#624—61no—
172C2×#624C2×D311yescharacteristic, complemented
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175#3757C2×D311yescharacteristic
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—61no—
189C3×#217C2×D311yescharacteristic
190C3×#217C2×D311yescharacteristic
191C3×#217C2×D311yescharacteristic
192C3×#217C2×D311yescharacteristic
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213#3724—31no—
214#3724—31no—
215#3724C2×D311yescharacteristic, complemented
216#3724C2×D311yescharacteristic, complemented
217#3724C2×D311yescharacteristic, complemented
218#3724C2×D311yescharacteristic, complemented
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3C2×D311yescharacteristic, complemented
224Dic3⋊Dic3C2×D311yescharacteristic, complemented
225#3722—31no—
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—61no—
244#3722—61no—
245#3722—61no—
246#3722—61no—
247#3722—61no—
248#3722—61no—
249#3722—61no—
250#3722—61no—
251#3722C2×D311yescharacteristic, complemented
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256Dic32C2×D311yescharacteristic, complemented
257Dic32C2×D311yescharacteristic, complemented
258Dic32C2×D311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C3⋊(C3⋊D3)—21no—
267C2×C3⋊(C3⋊D3)—21no—
268C2×C3⋊(C3⋊D3)—44no—
269C2×C3⋊(C3⋊D3)#4112yes—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×C22⋊Q8—91no—
285C3×C4×D4—91no—
286C3×#117—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290#935—91no—
291#929—91no—
292#929—91no—
293C4×#67—31no—
294C4×#67—91no—
295C2×(C2×D3)⋊C4—91no—
296C2×(C2×D3)⋊C4—91no—
297C2×(C2×D3)⋊C4—91no—
298C2×(C2×D3)⋊C4—181no—
299#924—31no—
300#898—91no—
301#898—91no—
302#898—91no—
303#898—91no—
304#896—91no—
305#896—91no—
306#894—91no—
307#894—91no—
308#894—91no—
309#894—91no—
310#893—91no—
311#892—91no—
312#886—91no—
313#885—91no—
314#883—91no—
315#882—91no—
316#882—91no—
317#882—181no—
318#67⋊C4—31no—
319D3×C22⋊C4—91no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322D3×C22⋊C4—181no—
323#878—31no—
324#877—31no—
325#877—31no—
326#876—91no—
327#876—91no—
328#875—91no—
329C4×D12—91no—
330#872—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—31no—
344C22×C3⋊D3—31no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—61no—
347C22×C3⋊D3—61no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—62no—
353C22×C3⋊D3—62no—
354C22×C3⋊D3—62no—
355C22×C3⋊D3—64no—
356C22×C3⋊D3—64no—
357C22×C3⋊D3—62no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—121no—
360C22×C3⋊D3—121no—
361C22×C3⋊D3—122no—
362C22×C3⋊D3—122no—
363C22×C3⋊D3—122no—
364C22×C3⋊D3—122no—
365C22×C3⋊D3—124no—
366C22×C3⋊D3—124no—
367C22×C3⋊D3—121no—
368C22×C3⋊D3—121no—
369C22×C3⋊D3—121no—
370C22×C3⋊D3—122no—
371C22×C3⋊D3—122no—
372C22×C3⋊D3—122no—
373C22×C3⋊D3—124no—
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—61no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—121no—
385#638—22no—
386C2×C3⋊Dic3—22no—
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C4⋊(C3⋊D3)—62no—
393C4⋊(C3⋊D3)—121no—
394C4×C3⋊D3—62no—
395C4×C3⋊D3—121no—
396C3×#67—62no—
397C3×#67—62no—
398C3×#67—122no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—41no—
416C2×C3×Dic3—41no—
417C2×C3×Dic3—42no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—62no—
424C2×C3×Dic3—62no—
425C2×C3×Dic3—122no—
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C3×C4×D3—121no—
439C3×C4×D3—121no—
440C3×Dic6—121no—
441C3×Dic6—121no—
442#627—41no—
443#626—62no—
444#626—62no—
445#626—122no—
446#626—121no—
447#626—121no—
448#626—122no—
449#624—41no—
450#624—62no—
451#624—62no—
452#624—122no—
453#624—121no—
454#624—121no—
455#624—122no—
456#551—271noSylow
457C2×C33—22no—
458C2×C33C2×#4111yescharacteristic
459C2×C33C2×#4111yescharacteristic
460C2×C33H(5,𝔽2)11yescharacteristic
461C3⋊(C3⋊D3)—22no—
462C3⋊(C3⋊D3)—41no—
463C3×C3⋊D3—41no—
464C23×D3—91no—
465C23×D3—91no—
466C23×D3—91no—
467C23×D3—181no—
468C23×D3—181no—
469C23×D3—181no—
470C23×D3—361no—
471C2×C3×Q8—91no—
472C2×C3×D4—91no—
473C22×C3×C4—31no—
474C22×C3×C4—31no—
475C22×C3×C4—61no—
476C22×C3×C4—91no—
477C22×C3×C4—91no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—61no—
481C2×#67—91no—
482C2×#67—91no—
483C22×Dic3—31no—
484C22×Dic3—31no—
485C22×Dic3—61no—
486C22×Dic3D3211yescharacteristic
487C2×D12—91no—
488C2×D12—91no—
489C2×D12—91no—
490C2×D12—91no—
491C2×D12—181no—
492C2×D12—181no—
493C2×C4×D3—31no—
494C2×C4×D3—31no—
495C2×C4×D3—91no—
496C2×C4×D3—91no—
497C2×C4×D3—91no—
498C2×C4×D3—91no—
499C2×C4×D3—91no—
500C2×C4×D3—91no—
501C2×C4×D3—181no—
502C2×C4×D3—181no—
503C2×Dic6—31no—
504C2×Dic6—31no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C4⋊C4—91no—
508C3×C4⋊C4—91no—
509C3×C4⋊C4—91no—
510C3×C4⋊C4—91no—
511C3×C22⋊C4—31no—
512C3×C22⋊C4—31no—
513C3×C22⋊C4—31no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—61no—
516C3×C22⋊C4—61no—
517C3×C22⋊C4—91no—
518C3×C22⋊C4—91no—
519C3×C42—91no—
520C3×C42—91no—
521C3×C42—91no—
522#217—31no—
523#217—31no—
524#217—61no—
525#217—91no—
526#217—91no—
527#217D3211yescharacteristic
528#217D3211yescharacteristic
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548(C2×D3)⋊C4—91no—
549(C2×D3)⋊C4—91no—
550(C2×D3)⋊C4—91no—
551(C2×D3)⋊C4—91no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—181no—
560(C2×D3)⋊C4—181no—
561(C2×D3)⋊C4—181no—
562(C2×D3)⋊C4—181no—
563(C2×D3)⋊C4—181no—
564(C2×D3)⋊C4—181no—
565(C2×D3)⋊C4—181no—
566(C2×D3)⋊C4—181no—
567C4⋊Dic3—31no—
568C4⋊Dic3—31no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585C4×Dic3—31no—
586C4×Dic3—31no—
587C4×Dic3—31no—
588C4×Dic3—31no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—22no—
594C22×C32—22no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—22no—
603C22×C32—22no—
604C22×C32—22no—
605C22×C32—42no—
606C22×C32—41no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—42no—
612C22×C32—42no—
613C22×C32#23512yes—
614C22×C32#23512yes—
615C22×C32#23912yes—
616C22×C32C23×D311yescharacteristic
617C22×C32C23×D311yescharacteristic
618C22×C32C23×D311yescharacteristic
619C2×C3⋊D3—21no—
620C2×C3⋊D3—21no—
621C2×C3⋊D3—21no—
622C2×C3⋊D3—32no—
623C2×C3⋊D3—32no—
624C2×C3⋊D3—32no—
625C2×C3⋊D3—62no—
626C2×C3⋊D3—62no—
627C2×C3⋊D3—62no—
628C2×C3⋊D3—61no—
629C2×C3⋊D3—61no—
630C2×C3⋊D3—61no—
631C2×C3⋊D3—61no—
632C2×C3⋊D3—61no—
633C2×C3⋊D3—62no—
634C2×C3⋊D3—62no—
635C2×C3⋊D3—61no—
636C2×C3⋊D3—61no—
637C2×C3⋊D3—61no—
638C2×C3⋊D3—61no—
639C2×C3⋊D3—62no—
640C2×C3⋊D3—62no—
641C2×C3⋊D3—62no—
642C2×C3⋊D3—61no—
643C2×C3⋊D3—61no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—61no—
646C2×C3⋊D3—61no—
647C2×C3⋊D3—61no—
648C2×C3⋊D3—122no—
649C2×C3⋊D3—121no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—121no—
657C2×C3⋊D3—121no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—122no—
660C2×C3⋊D3—122no—
661C2×C3⋊D3—122no—
662C2×C3⋊D3—122no—
663C2×C3⋊D3—122no—
664C2×C3⋊D3—124no—
665C2×C3⋊D3—124no—
666C2×C3⋊D3—124no—
667C2×C3⋊D3—128no—
668C2×C3⋊D3—128no—
669C2×C3⋊D3—128no—
670C2×C3⋊D3—1216no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—121no—
678C2×C3×D3—121no—
679C2×C3×D3—121no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—41no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722C3×Dic3—121no—
723C3×Dic3—121no—
724#126—271no—
725#126—271no—
726#124—271no—
727#123—271no—
728#123—271no—
729#123—271no—
730C22⋊Q8—91no—
731C22⋊Q8—271no—
732#120—271no—
733C4×D4—91no—
734C4×D4—271no—
735#117—91no—
736#117—271no—
737C2×C22⋊C4—271no—
738C2×C22⋊C4—271no—
739C33#55111yescharacteristic, complemented, Sylow
740C23×C3—21no—
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—41no—
744C23×C3—91no—
745C23×C3C2×D3211yescharacteristic
746C23×C3C2×D3211yescharacteristic
747C23×C3C2×D3211yescharacteristic
748C22×D3—31no—
749C22×D3—31no—
750C22×D3—61no—
751C22×D3—91no—
752C22×D3—91no—
753C22×D3—91no—
754C22×D3—91no—
755C22×D3—91no—
756C22×D3—91no—
757C22×D3—181no—
758C22×D3—181no—
759C22×D3—181no—
760C22×D3—181no—
761C22×D3—181no—
762C22×D3—181no—
763C22×D3—182no—
764C22×D3—182no—
765C22×D3—182no—
766C22×D3—184no—
767C22×D3—184no—
768C22×D3—182no—
769C22×D3—182no—
770C22×D3—182no—
771C22×D3—361no—
772C22×D3—361no—
773C22×D3—362no—
774C22×D3—362no—
775C22×D3—362no—
776C22×D3—362no—
777C22×D3—364no—
778C22×D3—364no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C22×D3—362no—
783C22×D3—362no—
784C22×D3—362no—
785C22×D3—364no—
786C3×Q8—361no—
787C3×D4—182no—
788C2×C3×C4—31no—
789C2×C3×C4—31no—
790C2×C3×C4—31no—
791C2×C3×C4—31no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—61no—
801C2×C3×C4—61no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—91no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—121no—
812C2×C3×C4—121no—
813C2×C3×C4—122no—
814C2×C3×C4—182no—
815C2×C3×C4—361no—
816#67—62no—
817#67—62no—
818#67—122no—
819#67—182no—
820#67—361no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—41no—
832C2×Dic3—61no—
833C2×Dic3—61no—
834C2×Dic3—61no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—62no—
838C2×Dic3—62no—
839C2×Dic3—122no—
840C2×Dic3C2×D3211yescharacteristic
841C2×Dic3C2×D3211yescharacteristic
842C2×Dic3C2×D3211yescharacteristic
843C2×Dic3C2×D3211yescharacteristic
844C2×Dic3C2×D3211yescharacteristic
845C2×Dic3C2×D3211yescharacteristic
846D12—182no—
847D12—182no—
848D12—362no—
849D12—361no—
850D12—361no—
851D12—362no—
852C4×D3—121no—
853C4×D3—121no—
854C4×D3—182no—
855C4×D3—182no—
856C4×D3—182no—
857C4×D3—362no—
858C4×D3—361no—
859C4×D3—361no—
860C4×D3—361no—
861C4×D3—362no—
862Dic6—121no—
863Dic6—121no—
864C2×C32—22no—
865C2×C32—24no—
866C2×C32—22no—
867C2×C32—22no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—41no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—42no—
881C2×C32—42no—
882C2×C32—44no—
883C2×C32C2×#23511yescharacteristic
884C2×C32C2×#23511yescharacteristic
885C2×C32#100411yescharacteristic
886C2×C32#100411yescharacteristic
887C2×C32C2×#23911yescharacteristic
888C2×C32D3×#4111yescharacteristic
889C2×C32D3×#4111yescharacteristic
890C2×C32D3×#4111yescharacteristic
891C2×C32#100911yescharacteristic
892C3⋊D3—41no—
893C3⋊D3—62no—
894C3⋊D3—64no—
895C3⋊D3—62no—
896C3⋊D3—62no—
897C3⋊D3—122no—
898C3⋊D3—122no—
899C3⋊D3—124no—
900C3⋊D3—122no—
901C3⋊D3—122no—
902C3⋊D3—122no—
903C3⋊D3—124no—
904C3⋊D3—121no—
905C3⋊D3—121no—
906C3⋊D3—121no—
907C3×D3—121no—
908C3×D3—121no—
909C3×D3—241no—
910C24—271no—
911C2×Q8—91no—
912C2×D4—91no—
913C2×D4—271no—
914C2×D4—271no—
915C22×C4—31no—
916C22×C4—91no—
917C22×C4—91no—
918C22×C4—271no—
919C22×C4—271no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C4⋊C4—91no—
926C4⋊C4—271no—
927C4⋊C4—271no—
928C22⋊C4—31no—
929C22⋊C4—31no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C22⋊C4—271no—
940C22⋊C4—271no—
941C22⋊C4—271no—
942C42—91no—
943C42—91no—
944C42—91no—
945C22×C3—22no—
946C22×C3—22no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—22no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—41no—
966C22×C3—42no—
967C22×C3—181no—
968C22×C3—181no—
969C22×C3—181no—
970C22×C3#379812yes—
971C22×C3#379912yes—
972C22×C3#379912yes—
973C22×C3C22×D3211yescharacteristic
974C22×C3C22×D3211yescharacteristic
975C22×C3C22×D3211yescharacteristic
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—92no—
983C2×D3—92no—
984C2×D3—92no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—182no—
989C2×D3—182no—
990C2×D3—182no—
991C2×D3—182no—
992C2×D3—182no—
993C2×D3—181no—
994C2×D3—181no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—182no—
1000C2×D3—182no—
1001C2×D3—182no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—181no—
1005C2×D3—181no—
1006C2×D3—181no—
1007C2×D3—181no—
1008C2×D3—181no—
1009C2×D3—181no—
1010C2×D3—181no—
1011C2×D3—362no—
1012C2×D3—361no—
1013C2×D3—361no—
1014C2×D3—361no—
1015C2×D3—361no—
1016C2×D3—361no—
1017C2×D3—361no—
1018C2×D3—361no—
1019C2×D3—361no—
1020C2×D3—361no—
1021C2×D3—361no—
1022C2×D3—362no—
1023C2×D3—362no—
1024C2×D3—362no—
1025C2×D3—362no—
1026C2×D3—362no—
1027C2×D3—364no—
1028C2×D3—364no—
1029C2×D3—364no—
1030C2×D3—368no—
1031C2×D3—368no—
1032C2×D3—368no—
1033C2×D3—3616no—
1034C3×C4—61no—
1035C3×C4—61no—
1036C3×C4—61no—
1037C3×C4—61no—
1038C3×C4—61no—
1039C3×C4—61no—
1040C3×C4—61no—
1041C3×C4—61no—
1042C3×C4—61no—
1043C3×C4—61no—
1044C3×C4—61no—
1045C3×C4—61no—
1046C3×C4—121no—
1047C3×C4—121no—
1048C3×C4—121no—
1049C3×C4—121no—
1050C3×C4—121no—
1051C3×C4—121no—
1052C3×C4—181no—
1053C3×C4—181no—
1054C3×C4—181no—
1055C3×C4—181no—
1056C3×C4—181no—
1057Dic3—21no—
1058Dic3—21no—
1059Dic3—21no—
1060Dic3—21no—
1061Dic3—21no—
1062Dic3—21no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—61no—
1066Dic3—61no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—121no—
1074Dic3—121no—
1075Dic3—121no—
1076Dic3—121no—
1077Dic3—121no—
1078C32—21no—
1079C32—21no—
1080C32—21no—
1081C32—41no—
1082C32#552711yescharacteristic, complemented
1083C32#555611yescharacteristic, complemented
1084C32#563711yescharacteristic, complemented
1085C23—91no—
1086C23—271no—
1087C23—271no—
1088C23—542no—
1089C23—542no—
1090C23—1081no—
1091C23D3311yescharacteristic
1092Q8—361no—
1093D4—182no—
1094D4—542no—
1095D4—1081no—
1096C2×C4—31no—
1097C2×C4—31no—
1098C2×C4—31no—
1099C2×C4—31no—
1100C2×C4—31no—
1101C2×C4—31no—
1102C2×C4—91no—
1103C2×C4—91no—
1104C2×C4—91no—
1105C2×C4—91no—
1106C2×C4—91no—
1107C2×C4—121no—
1108C2×C4—182no—
1109C2×C4—361no—
1110C2×C4—542no—
1111C2×C4—1081no—
1112C2×C3—24no—
1113C2×C3—22no—
1114C2×C3—22no—
1115C2×C3—22no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—21no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—21no—
1123C2×C3—21no—
1124C2×C3—21no—
1125C2×C3—42no—
1126C2×C3—42no—
1127C2×C3—44no—
1128C2×C3—41no—
1129C2×C3—41no—
1130C2×C3—41no—
1131C2×C3—361no—
1132C2×C3C2×#379811yescharacteristic
1133C2×C3C2×#379911yescharacteristic
1134C2×C3C2×#379911yescharacteristic
1135C2×C3#6430611yescharacteristic
1136C2×C3#6431211yescharacteristic
1137C2×C3#6431211yescharacteristic
1138C2×C3#6431411yescharacteristic
1139C2×C3#6431411yescharacteristic
1140C2×C3#6433011yescharacteristic
1141D3—121no—
1142D3—121no—
1143D3—184no—
1144D3—182no—
1145D3—182no—
1146D3—182no—
1147D3—241no—
1148D3—362no—
1149D3—362no—
1150D3—364no—
1151D3—362no—
1152D3—362no—
1153D3—362no—
1154D3—364no—
1155D3—361no—
1156D3—361no—
1157D3—361no—
1158C22—21no—
1159C22—21no—
1160C22—181no—
1161C22—181no—
1162C22—181no—
1163C22—272no—
1164C22—541no—
1165C22—541no—
1166C22—541no—
1167C22—541no—
1168C22—541no—
1169C22—1084no—
1170C22#8896512yes—
1171C22C2×D3311yescharacteristic
1172C4—61no—
1173C4—61no—
1174C4—61no—
1175C4—61no—
1176C4—61no—
1177C4—61no—
1178C4—181no—
1179C4—181no—
1180C4—181no—
1181C4—181no—
1182C4—181no—
1183C3—21no—
1184C3—21no—
1185C3—21no—
1186C3—41no—
1187C3#1059404011yescharacteristic, complemented
1188C3#1059416611yescharacteristic, complemented
1189C3#1059503511yescharacteristic, complemented
1190C2—22no—
1191C2—361no—
1192C2—542no—
1193C2—1081no—
1194C2#1172441111yescharacteristic
1195C2#1172441911yescharacteristic
1196C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723639C2
hypercenterC23D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723720C2semidirect
3. #11723627C2semidirect
4. C2×#88804C2semidirect
5. C3×#63964C2semidirect
6. C3×#63957C2semidirect
7. C3×#63952C2semidirect
8. #11723021C2semidirect
9. #11723021C2semidirect
10. #11723003C2semidirect
11. #11723000C2semidirect
12. #11722993C2semidirect
13. #11722977C2semidirect
14. #11722933C2semidirect
15. #11722918C2semidirect
27. C2×C3×#627C22semidirect
28. C2×C3×#624C22semidirect
32. #88815C22semidirect
33. #88815C22semidirect
34. #88814C22semidirect
35. #88814C22semidirect
44. C3×#3724C22semidirect
45. C3×#3724C22semidirect
46. C3×#3724C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×Dic32C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
70. #63964D3semidirect
76. #63957D3semidirect
77. #63952D3semidirect
159. C2×#627C2×D3semidirect
172. C2×#624C2×D3semidirect
215. #3724C2×D3semidirect
216. #3724C2×D3semidirect
217. #3724C2×D3semidirect
218. #3724C2×D3semidirect
223. Dic3⋊Dic3C2×D3semidirect
224. Dic3⋊Dic3C2×D3semidirect
251. #3722C2×D3semidirect
256. Dic32C2×D3semidirect
257. Dic32C2×D3semidirect
258. Dic32C2×D3semidirect
739. C33#551semidirect
1082. C32#5527semidirect
1083. C32#5556semidirect
1084. C32#5637semidirect
1187. C3#10594040semidirect
1188. C3#10594166semidirect
1189. C3#10595035semidirect

Maximal subgroups

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

subgroupindex
#117237202
#117236392
#117236272
C2×#888042
C3×#639642
C3×#639572
C3×#639522
#117230212
#117230032
#117230002
#117229932
#117229772
#117229332
#117229182
#105950353
#105941663
#105940403