Finite Group Databasebeta

← #13171979

Subgroups — #13171979

Order 1728.

1348 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88814C211yesmaximal, characteristic, complemented
2#11723636C211yesmaximal, characteristic
3#11723622C211yesmaximal, characteristic, complemented
4#11723608C211yesmaximal, characteristic, complemented
5C3×#63982C211yesmaximal, characteristic, complemented
6C3×#63974C211yesmaximal, characteristic, complemented
7C3×#63957C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11723000C211yesmaximal, characteristic, complemented
12#11722993C211yesmaximal, characteristic, complemented
13#11722970C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594214—31nomaximal
17#10594166—31nomaximal
18#10594037—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6289C2211yescharacteristic, complemented
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C32×#217C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88806C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#88804C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64095—31no—
55#64091—31no—
56#64090—31no—
57C3×D3×C22⋊C4—31no—
58C3×D3×C22⋊C4—31no—
59C3×#878—31no—
60C3×#878—31no—
61C3×#877—31no—
62C3×#877—31no—
63#63982D311yescharacteristic, complemented
64#63977—31no—
65#63977—31no—
66#63977—61no—
67#63974D311yescharacteristic, complemented
68#63966—31no—
69#63966—31no—
70#63966—61no—
71C2×#3722—31no—
72C2×(C2×D3)⋊Dic3—31no—
73C2×(C2×D3)⋊Dic3—31no—
74#63957D311yescharacteristic, complemented
75#63952—31no—
76#63952—31no—
77#63952—61no—
78#63907—31no—
79#63904—31no—
80C4×#626—31no—
81#63897—31no—
82#63897—31no—
83#63894—31no—
84#63888—31no—
85#63868—31no—
86#63864—31no—
87#63862—31no—
88#63861—31no—
89#63861—31no—
90#63859—31no—
91#63856—31no—
92#63855—31no—
93#63854—31no—
94#63853—31no—
95#63852—31no—
96#63851—31no—
97#63850—31no—
98#63850—31no—
99#63848—31no—
100#63841—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109#6312—22no—
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3—22no—
112C2×C3×C3⋊Dic3—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
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—41no—
126C3×#627—41no—
127C3×#624—22no—
128C3×#624—41no—
129#5637—91no—
130#5527—91no—
131#5495—91no—
132C23×C3⋊D3C2×D311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—61no—
140C2×#638—61no—
141C2×#638—61no—
142C2×#638—121no—
143C22×C3⋊Dic3C2×D311yescharacteristic
144C22×C3⋊Dic3C2×D311yescharacteristic
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4×C3⋊D3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—61no—
153C22×C3×Dic3—61no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×Dic6—31no—
159C2×C3×Dic6—31no—
160C2×#627C2×D311yescharacteristic, complemented
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—61no—
166C2×#626—61no—
167C2×#624—31no—
168C2×#624—31no—
169C2×#624—61no—
170C2×#624C2×D311yescharacteristic
171C2×#624C2×D311yescharacteristic
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180C4⋊(C3⋊Dic3)—31no—
181C4⋊(C3⋊Dic3)—31no—
182#3750—31no—
183C4×C3⋊Dic3—31no—
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—21no—
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×#217C2×D311yescharacteristic
190C3×#217C2×D311yescharacteristic
191C3×#217C2×D311yescharacteristic
192C3×#217C2×D311yescharacteristic
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—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—
211#3724—31no—
212#3724—31no—
213#3724—61no—
214#3724C2×D311yescharacteristic, complemented
215#3724C2×D311yescharacteristic, complemented
216#3724C2×D311yescharacteristic, complemented
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
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—61no—
236#3722—61no—
237#3722—61no—
238#3722C2×D311yescharacteristic
239#3722C2×D311yescharacteristic
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
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—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—44no—
272C2×C3×C3⋊D3#4112yes—
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×#117—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#947—91no—
290#946—91no—
291#929—91no—
292#929—91no—
293C4×#67—91no—
294C4×#67—91no—
295C2×(C2×D3)⋊C4—91no—
296C2×(C2×D3)⋊C4—91no—
297#926—91no—
298#924—91no—
299#898—91no—
300#898—91no—
301#898—91no—
302#896—91no—
303#894—91no—
304#894—91no—
305#894—91no—
306#894—91no—
307#893—91no—
308#892—91no—
309#886—91no—
310#886—91no—
311#886—181no—
312#885—91no—
313#883—91no—
314#882—91no—
315#882—91no—
316#882—181no—
317#67⋊C4—91no—
318#67⋊C4—91no—
319#67⋊C4—181no—
320D3×C22⋊C4—31no—
321D3×C22⋊C4—31no—
322#879—91no—
323#879—91no—
324#878—31no—
325#878—31no—
326#877—31no—
327#877—31no—
328#876—91no—
329#875—91no—
330C4×D12—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—22no—
340C22×C3⋊D3—22no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—31no—
344C22×C3⋊D3—41no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—61no—
347C22×C3⋊D3—61no—
348C22×C3⋊D3—121no—
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—61no—
356C22×C3×D3—61no—
357C22×C3×D3—62no—
358C22×C3×D3—62no—
359C22×C3×D3—62no—
360C22×C3×D3—62no—
361C22×C3×D3—122no—
362C22×C3×D3—122no—
363C22×C3×D3—121no—
364C22×C3×D3—121no—
365C22×C3×D3—122no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372#638—62no—
373#638—64no—
374#638—62no—
375#638—62no—
376#638—122no—
377#638—122no—
378#638—124no—
379C2×C3⋊Dic3—22no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—41no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—121no—
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—121no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3—122no—
416C2×C3×Dic3—121no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3—122no—
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C3×C4×D3—62no—
432C3×C4×D3—62no—
433C3×C4×D3—121no—
434C3×C4×D3—121no—
435C3×Dic6—121no—
436C3×Dic6—121no—
437#627—41no—
438#626—62no—
439#626—62no—
440#626—122no—
441#626—121no—
442#626—121no—
443#626—122no—
444#624—22no—
445#624—41no—
446#624—121no—
447#624—121no—
448#624—122no—
449#551—271noSylow
450C2×C33—22no—
451C2×C33C2×#4111yescharacteristic
452C2×C33C2×#4111yescharacteristic
453C2×C33H(5,𝔽2)11yescharacteristic
454C3⋊(C3⋊D3)—41no—
455C3×C3⋊D3—22no—
456C3×C3⋊D3—41no—
457C24×C3—91no—
458C23×D3—31no—
459C23×D3—31no—
460C23×D3—61no—
461C2×C3×Q8—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C22×C3×C4—91no—
465C22×C3×C4—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—181no—
472C2×#67—181no—
473C2×#67—181no—
474C2×#67—361no—
475C22×Dic3—31no—
476C22×Dic3—31no—
477C22×Dic3—31no—
478C22×Dic3—31no—
479C22×Dic3—61no—
480C22×Dic3—61no—
481C2×D12—91no—
482C2×D12—91no—
483C2×D12—91no—
484C2×D12—91no—
485C2×D12—181no—
486C2×D12—181no—
487C2×C4×D3—31no—
488C2×C4×D3—31no—
489C2×C4×D3—31no—
490C2×C4×D3—31no—
491C2×C4×D3—91no—
492C2×C4×D3—91no—
493C2×C4×D3—91no—
494C2×C4×D3—181no—
495C2×Dic6—31no—
496C2×Dic6—31no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C4⋊C4—91no—
501C3×C4⋊C4—91no—
502C3×C22⋊C4—31no—
503C3×C22⋊C4—31no—
504C3×C22⋊C4—31no—
505C3×C22⋊C4—31no—
506C3×C22⋊C4—31no—
507C3×C22⋊C4—31no—
508C3×C22⋊C4—61no—
509C3×C22⋊C4—61no—
510C3×C22⋊C4—61no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C42—91no—
514C3×C42—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217D3211yescharacteristic
522#217D3211yescharacteristic
523#217D3211yescharacteristic
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—91no—
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—181no—
550(C2×D3)⋊C4—181no—
551(C2×D3)⋊C4—181no—
552(C2×D3)⋊C4—181no—
553(C2×D3)⋊C4—181no—
554C4⋊Dic3—31no—
555C4⋊Dic3—31no—
556C4⋊Dic3—91no—
557C4⋊Dic3—91no—
558C4⋊Dic3—91no—
559C4⋊Dic3—91no—
560C4⋊Dic3—181no—
561C4⋊Dic3—181no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574Dic3⋊C4—91no—
575Dic3⋊C4—181no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—31no—
579C4×Dic3—31no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—91no—
583C4×Dic3—181no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—22no—
594C22×C32—22no—
595C22×C32—22no—
596C22×C32—41no—
597C22×C32—42no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—81no—
605C22×C32—81no—
606C22×C32#23512yes—
607C22×C32#23512yes—
608C22×C32#23912yes—
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—44no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—62no—
620C2×C3⋊D3—61no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—61no—
626C2×C3⋊D3—61no—
627C2×C3⋊D3—61no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—122no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—121no—
634C2×C3⋊D3—121no—
635C2×C3⋊D3—121no—
636C2×C3⋊D3—121no—
637C2×C3⋊D3—241no—
638C2×C3⋊D3—241no—
639C2×C3⋊D3#23712yes—
640C2×C3×D3—32no—
641C2×C3×D3—32no—
642C2×C3×D3—62no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—62no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658C2×C3×D3—124no—
659C2×C3×D3—124no—
660C2×C3×D3—128no—
661C32×C4—61no—
662C32×C4—61no—
663C32×C4—61no—
664C32×C4—61no—
665C32×C4—61no—
666C32×C4—61no—
667C3⋊Dic3—21no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3⋊Dic3—61no—
672C3⋊Dic3—62no—
673C3⋊Dic3—61no—
674C3⋊Dic3—61no—
675C3⋊Dic3—121no—
676C3⋊Dic3—121no—
677C3⋊Dic3—122no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—21no—
683C3×Dic3—21no—
684C3×Dic3—21no—
685C3×Dic3—21no—
686C3×Dic3—21no—
687C3×Dic3—21no—
688C3×Dic3—21no—
689C3×Dic3—21no—
690C3×Dic3—41no—
691C3×Dic3—41no—
692C3×Dic3—41no—
693C3×Dic3—41no—
694C3×Dic3—41no—
695C3×Dic3—41no—
696C3×Dic3—62no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—121no—
706C3×Dic3—121no—
707C3×Dic3—121no—
708#126—271no—
709#126—271no—
710#124—271no—
711#123—271no—
712#123—271no—
713#123—271no—
714C22⋊Q8—91no—
715C22⋊Q8—271no—
716#120—271no—
717C4×D4—271no—
718C4×D4—271no—
719#117—91no—
720#117—271no—
721C2×C22⋊C4—91no—
722C2×C22⋊C4—271no—
723C33#55111yescharacteristic, complemented, Sylow
724C23×C3—21no—
725C23×C3—21no—
726C23×C3—21no—
727C23×C3—41no—
728C23×C3—91no—
729C23×C3—91no—
730C23×C3—182no—
731C23×C3—182no—
732C23×C3—361no—
733C23×C3C2×D3211yescharacteristic
734C23×C3C2×D3211yescharacteristic
735C23×C3C2×D3211yescharacteristic
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—31no—
740C22×D3—61no—
741C22×D3—61no—
742C22×D3—62no—
743C22×D3—62no—
744C22×D3—62no—
745C22×D3—62no—
746C22×D3—91no—
747C22×D3—91no—
748C22×D3—91no—
749C22×D3—122no—
750C22×D3—122no—
751C22×D3—121no—
752C22×D3—121no—
753C22×D3—122no—
754C22×D3—181no—
755C22×D3—181no—
756C22×D3—181no—
757C22×D3—361no—
758C3×Q8—361no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—31no—
762C2×C3×C4—31no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—61no—
772C2×C3×C4—61no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—182no—
782C2×C3×C4—182no—
783C2×C3×C4—361no—
784C2×C3×C4—361no—
785#67—182no—
786#67—184no—
787#67—182no—
788#67—182no—
789#67—182no—
790#67—362no—
791#67—362no—
792#67—364no—
793#67—361no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—62no—
807C2×Dic3—62no—
808C2×Dic3—91no—
809C2×Dic3—91no—
810C2×Dic3—91no—
811C2×Dic3—122no—
812C2×Dic3—121no—
813C2×Dic3—121no—
814C2×Dic3—122no—
815C2×Dic3—181no—
816C2×Dic3—181no—
817C2×Dic3—181no—
818C2×Dic3—361no—
819C2×Dic3C2×D3211yescharacteristic
820C2×Dic3C2×D3211yescharacteristic
821C2×Dic3C2×D3211yescharacteristic
822C2×Dic3C2×D3211yescharacteristic
823C2×Dic3C2×D3211yescharacteristic
824C2×Dic3C2×D3211yescharacteristic
825D12—182no—
826D12—182no—
827D12—362no—
828D12—361no—
829D12—361no—
830D12—362no—
831C4×D3—62no—
832C4×D3—62no—
833C4×D3—121no—
834C4×D3—121no—
835C4×D3—361no—
836C4×D3—361no—
837C4×D3—361no—
838C4×D3—362no—
839Dic6—121no—
840Dic6—121no—
841C2×C32—22no—
842C2×C32—22no—
843C2×C32—22no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—41no—
854C2×C32—41no—
855C2×C32—41no—
856C2×C32—42no—
857C2×C32—42no—
858C2×C32—42no—
859C2×C32—82no—
860C2×C32C2×#23511yescharacteristic
861C2×C32C2×#23511yescharacteristic
862C2×C32C2×#23711yescharacteristic
863C2×C32#100411yescharacteristic
864C2×C32#100411yescharacteristic
865C2×C32C2×#23911yescharacteristic
866C2×C32D3×#4111yescharacteristic
867C2×C32D3×#4111yescharacteristic
868C2×C32#100911yescharacteristic
869C3⋊D3—22no—
870C3⋊D3—41no—
871C3⋊D3—121no—
872C3⋊D3—122no—
873C3⋊D3—121no—
874C3⋊D3—121no—
875C3⋊D3—241no—
876C3⋊D3—241no—
877C3⋊D3—242no—
878C3×D3—62no—
879C3×D3—62no—
880C3×D3—122no—
881C3×D3—122no—
882C3×D3—121no—
883C3×D3—121no—
884C24—91no—
885C2×Q8—91no—
886C2×D4—271no—
887C2×D4—271no—
888C2×D4—271no—
889C22×C4—91no—
890C22×C4—91no—
891C22×C4—91no—
892C22×C4—91no—
893C22×C4—271no—
894C4⋊C4—91no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—91no—
898C4⋊C4—91no—
899C4⋊C4—271no—
900C4⋊C4—271no—
901C4⋊C4—271no—
902C22⋊C4—31no—
903C22⋊C4—31no—
904C22⋊C4—31no—
905C22⋊C4—91no—
906C22⋊C4—91no—
907C22⋊C4—271no—
908C22⋊C4—271no—
909C22⋊C4—271no—
910C22⋊C4—271no—
911C22⋊C4—271no—
912C22⋊C4—271no—
913C22⋊C4—271no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C42—91no—
917C42—91no—
918C42—271no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—21no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—22no—
929C22×C3—22no—
930C22×C3—22no—
931C22×C3—41no—
932C22×C3—41no—
933C22×C3—41no—
934C22×C3—41no—
935C22×C3—41no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—42no—
939C22×C3—81no—
940C22×C3—81no—
941C22×C3—92no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—364no—
948C22×C3#379812yes—
949C22×C3#379912yes—
950C22×C3#379912yes—
951C22×C3C22×D3211yescharacteristic
952C22×C3C22×D3211yescharacteristic
953C22×C3C22×D3211yescharacteristic
954C2×D3—32no—
955C2×D3—32no—
956C2×D3—62no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—62no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—121no—
969C2×D3—121no—
970C2×D3—121no—
971C2×D3—121no—
972C2×D3—124no—
973C2×D3—124no—
974C2×D3—128no—
975C2×D3—182no—
976C2×D3—181no—
977C2×D3—181no—
978C2×D3—181no—
979C2×D3—181no—
980C2×D3—181no—
981C2×D3—181no—
982C2×D3—181no—
983C2×D3—181no—
984C2×D3—181no—
985C2×D3—361no—
986C2×D3—361no—
987C2×D3—361no—
988C2×D3—361no—
989C2×D3—361no—
990C2×D3—361no—
991C2×D3—361no—
992C2×D3—361no—
993C2×D3—362no—
994C2×D3—721no—
995C2×D3—721no—
996C3×C4—61no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—61no—
1000C3×C4—61no—
1001C3×C4—61no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—121no—
1009C3×C4—121no—
1010C3×C4—121no—
1011C3×C4—121no—
1012C3×C4—121no—
1013C3×C4—121no—
1014C3×C4—181no—
1015C3×C4—181no—
1016C3×C4—181no—
1017C3×C4—181no—
1018Dic3—21no—
1019Dic3—21no—
1020Dic3—21no—
1021Dic3—21no—
1022Dic3—21no—
1023Dic3—21no—
1024Dic3—62no—
1025Dic3—61no—
1026Dic3—61no—
1027Dic3—61no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—121no—
1034Dic3—121no—
1035Dic3—121no—
1036Dic3—182no—
1037Dic3—181no—
1038Dic3—181no—
1039Dic3—181no—
1040Dic3—361no—
1041Dic3—361no—
1042Dic3—362no—
1043C32—21no—
1044C32—21no—
1045C32—21no—
1046C32—41no—
1047C32#549511yescharacteristic, complemented
1048C32#552711yescharacteristic, complemented
1049C32#563711yescharacteristic, complemented
1050C23—91no—
1051C23—91no—
1052C23—182no—
1053C23—182no—
1054C23—271no—
1055C23—361no—
1056C23D3311yescharacteristic
1057Q8—361no—
1058D4—542no—
1059D4—542no—
1060D4—1081no—
1061C2×C4—31no—
1062C2×C4—31no—
1063C2×C4—31no—
1064C2×C4—31no—
1065C2×C4—31no—
1066C2×C4—31no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—91no—
1070C2×C4—91no—
1071C2×C4—182no—
1072C2×C4—182no—
1073C2×C4—271no—
1074C2×C4—361no—
1075C2×C4—361no—
1076C2×C4—1081no—
1077C2×C3—22no—
1078C2×C3—22no—
1079C2×C3—22no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—42no—
1090C2×C3—42no—
1091C2×C3—42no—
1092C2×C3—41no—
1093C2×C3—41no—
1094C2×C3—41no—
1095C2×C3—82no—
1096C2×C3—182no—
1097C2×C3—361no—
1098C2×C3C2×#379811yescharacteristic
1099C2×C3C2×#379911yescharacteristic
1100C2×C3C2×#379911yescharacteristic
1101C2×C3D3×#23711yescharacteristic
1102C2×C3D3×#23711yescharacteristic
1103C2×C3#6431211yescharacteristic
1104C2×C3#6431311yescharacteristic
1105C2×C3#6431411yescharacteristic
1106C2×C3#6431411yescharacteristic
1107D3—62no—
1108D3—62no—
1109D3—122no—
1110D3—122no—
1111D3—121no—
1112D3—121no—
1113D3—362no—
1114D3—361no—
1115D3—361no—
1116D3—361no—
1117D3—721no—
1118D3—721no—
1119D3—722no—
1120C22—21no—
1121C22—21no—
1122C22—92no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—181no—
1128C22—364no—
1129C22—541no—
1130C22—541no—
1131C22—541no—
1132C22#8896512yes—
1133C22C2×D3311yescharacteristic
1134C4—61no—
1135C4—61no—
1136C4—61no—
1137C4—61no—
1138C4—61no—
1139C4—61no—
1140C4—181no—
1141C4—181no—
1142C4—181no—
1143C4—181no—
1144C4—541no—
1145C3—21no—
1146C3—21no—
1147C3—21no—
1148C3—41no—
1149C3#1059403711yescharacteristic, complemented
1150C3#1059416611yescharacteristic, complemented
1151C3#1059421411yescharacteristic, complemented
1152C2—22no—
1153C2—182no—
1154C2—361no—
1155C2—1081no—
1156C2#1172440811yescharacteristic
1157C2#1172441611yescharacteristic
1158C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723636C2
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. C2×#88814C2semidirect
3. #11723622C2semidirect
4. #11723608C2semidirect
5. C3×#63982C2semidirect
6. C3×#63974C2semidirect
7. C3×#63957C2semidirect
8. #11723027C2semidirect
9. #11723023C2semidirect
10. #11723003C2semidirect
11. #11723000C2semidirect
12. #11722993C2semidirect
13. #11722970C2semidirect
14. #11722933C2semidirect
15. #11722915C2semidirect
25. C2×#6289C22semidirect
26. C2×C3×#627C22semidirect
36. #88806C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
39. #88804C22semidirect
40. #88804C22semidirect
41. #88804C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×#3724C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
63. #63982D3semidirect
67. #63974D3semidirect
74. #63957D3semidirect
160. C2×#627C2×D3semidirect
214. #3724C2×D3semidirect
215. #3724C2×D3semidirect
216. #3724C2×D3semidirect
223. Dic3⋊Dic3C2×D3semidirect
224. Dic3⋊Dic3C2×D3semidirect
257. Dic32C2×D3semidirect
258. Dic32C2×D3semidirect
723. C33#551semidirect
1047. C32#5495semidirect
1048. C32#5527semidirect
1049. C32#5637semidirect
1149. C3#10594037semidirect
1150. C3#10594166semidirect
1151. C3#10594214semidirect

Maximal subgroups

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

subgroupindex
C2×#888142
#117236362
#117236222
#117236082
C3×#639822
C3×#639742
C3×#639572
#117230272
#117230232
#117230032
#117230002
#117229932
#117229702
#117229332
#117229152
#105942143
#105941663
#105940373