Finite Group Databasebeta

← #13171981

Subgroups — #13171981

Order 1728.

1330 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723723C211yesmaximal, characteristic, complemented
2#11723636C211yesmaximal, characteristic
3#11723628C211yesmaximal, characteristic, complemented
4#11723592C211yesmaximal, characteristic, complemented
5C3×#63974C211yesmaximal, characteristic, complemented
6C3×#63956C211yesmaximal, characteristic, complemented
7C3×#63956C211yesmaximal, characteristic, complemented
8#11722999C211yesmaximal, characteristic, complemented
9#11722993C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722937C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic, complemented
14#11722922C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594165—31nomaximal
17#10594094—31nomaximal
18#10594093—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6289C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C32×#217C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38#88804C2211yescharacteristic, complemented
39#88804C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic, complemented
44C3×#3724C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64094—31no—
55#64092—31no—
56#64091—31no—
57C3×D3×C22⋊C4—31no—
58C3×D3×C22⋊C4—31no—
59C3×#879—31no—
60C3×#879—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63977—31no—
64#63977—31no—
65#63977—61no—
66#63975—31no—
67#63975—31no—
68#63975—61no—
69#63974—31no—
70#63974D311yescharacteristic, complemented
71D3×#217—31no—
72D3×#217—31no—
73#63956D311yescharacteristic, complemented
74#63956D311yescharacteristic, complemented
75#63953—31no—
76#63953—31no—
77#63953—61no—
78#63904—31no—
79C4×#626—31no—
80#63897—31no—
81#63897—31no—
82#63896—31no—
83#63895—31no—
84#63895—31no—
85#63894—31no—
86#63894—31no—
87#63893—31no—
88#63890—31no—
89#63890—31no—
90#63881—31no—
91#63880—31no—
92#63878—31no—
93#63877—31no—
94#63857—31no—
95#63855—31no—
96#63851—31no—
97#63850—31no—
98#63850—31no—
99#63841—31no—
100#63836—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—41no—
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6294—22no—
122#6294—41no—
123#6293—41no—
124#6292—22no—
125#6292—22no—
126#6289—41no—
127C3×#624—22no—
128C3×#624—41no—
129#5705—91no—
130#5705—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—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4×C3⋊D3—31no—
146C2×#634—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×#627—31no—
152C2×#627—31no—
153C2×#627—61no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—61no—
159C2×#626—61no—
160C2×#624—31no—
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—31no—
164C2×#624—61no—
165C2×#624C2×D311yescharacteristic
166C2×#624C2×D311yescharacteristic
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174#3757C2×D311yescharacteristic
175#3757C2×D311yescharacteristic
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181C4⋊(C3⋊Dic3)—31no—
182#3750—31no—
183C4×C3⋊Dic3—31no—
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—21no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—61no—
192C3×#217—61no—
193C3×#217C2×D311yescharacteristic
194C3×#217C2×D311yescharacteristic
195C3×#217C2×D311yescharacteristic
196C3×#217C2×D311yescharacteristic
197C3×#217C2×D311yescharacteristic
198C3×#217C2×D311yescharacteristic
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219#3724C2×D311yescharacteristic, complemented
220#3724C2×D311yescharacteristic, complemented
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229Dic3⋊Dic3C2×D311yescharacteristic, complemented
230Dic3⋊Dic3C2×D311yescharacteristic, complemented
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—61no—
240#3722—61no—
241#3722—61no—
242#3722C2×D311yescharacteristic
243#3722C2×D311yescharacteristic
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—21no—
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—44no—
271C2×C3×C3⋊D3#4112yes—
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×#126—91no—
285C3×#126—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#929—91no—
290C4×#67—91no—
291#926—91no—
292#924—91no—
293#897—91no—
294#897—91no—
295#896—91no—
296#896—91no—
297#894—91no—
298#894—91no—
299#894—91no—
300#894—91no—
301#893—91no—
302#893—91no—
303#892—91no—
304#892—91no—
305#886—91no—
306#885—91no—
307#885—91no—
308#885—91no—
309#885—181no—
310#883—91no—
311#883—91no—
312#883—91no—
313#883—181no—
314#882—91no—
315#882—91no—
316#882—181no—
317#67⋊C4—91no—
318D3×C22⋊C4—31no—
319D3×C22⋊C4—31no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322#879—31no—
323#879—31no—
324#879—31no—
325#879—31no—
326#878—91no—
327#877—91no—
328C4×D12—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—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—121no—
373#638—121no—
374#638—121no—
375#638—122no—
376#638—122no—
377#638—122no—
378#638—124no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—61no—
383C2×C3⋊Dic3—61no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—121no—
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C4⋊(C3⋊D3)—62no—
391C4⋊(C3⋊D3)—62no—
392C4×C3⋊D3—121no—
393#634—121no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—31no—
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—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C3×C4×D3—62no—
425C3×C4×D3—62no—
426C3×C4×D3—121no—
427C3×C4×D3—121no—
428#627—121no—
429#627—121no—
430#627—122no—
431#626—62no—
432#626—62no—
433#626—62no—
434#626—62no—
435#626—122no—
436#626—122no—
437#624—22no—
438#624—41no—
439#624—62no—
440#624—121no—
441#624—121no—
442#624—122no—
443#624—121no—
444D3×Dic3—62no—
445D3×Dic3—62no—
446D3×Dic3—121no—
447D3×Dic3—121no—
448#551—271noSylow
449C2×C33—41no—
450C2×C33C2×#4111yescharacteristic
451C2×C33C2×#4111yescharacteristic
452C2×C33H(5,𝔽2)11yescharacteristic
453C3⋊(C3⋊D3)—41no—
454C3×C3⋊D3—22no—
455C3×C3⋊D3—22no—
456C24×C3—91no—
457C23×D3—31no—
458C23×D3—31no—
459C23×D3—61no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—181no—
468C2×#67—181no—
469C2×#67—181no—
470C2×#67—361no—
471C22×Dic3—91no—
472C22×Dic3—91no—
473C2×D12—91no—
474C2×D12—91no—
475C2×D12—91no—
476C2×D12—91no—
477C2×D12—181no—
478C2×D12—181no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—31no—
482C2×C4×D3—31no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—181no—
491C2×Dic6—91no—
492C2×Dic6—91no—
493C2×Dic6—91no—
494C2×Dic6—181no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C4⋊C4—91no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—31no—
503C3×C22⋊C4—31no—
504C3×C22⋊C4—31no—
505C3×C22⋊C4—31no—
506C3×C22⋊C4—31no—
507C3×C22⋊C4—61no—
508C3×C22⋊C4—61no—
509C3×C22⋊C4—61no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C42—91no—
515C3×C42—91no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—31no—
520#217—61no—
521#217—61no—
522#217—91no—
523#217—91no—
524#217—91no—
525#217—91no—
526#217D3211yescharacteristic
527#217D3211yescharacteristic
528#217D3211yescharacteristic
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
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—181no—
551(C2×D3)⋊C4—181no—
552(C2×D3)⋊C4—181no—
553(C2×D3)⋊C4—181no—
554(C2×D3)⋊C4—181no—
555C4⋊Dic3—31no—
556C4⋊Dic3—31no—
557C4⋊Dic3—31no—
558C4⋊Dic3—31no—
559C4⋊Dic3—91no—
560C4⋊Dic3—91no—
561C4⋊Dic3—91no—
562C4⋊Dic3—181no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574Dic3⋊C4—181no—
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—31no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—181no—
583C22×C32—21no—
584C22×C32—22no—
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—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—42no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—41no—
605C22×C32—41no—
606C22×C32—81no—
607C22×C32—81no—
608C22×C32C23×D311yescharacteristic
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—44no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—62no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—61no—
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—121no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—122no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—121no—
634C2×C3⋊D3—121no—
635C2×C3⋊D3—241no—
636C2×C3⋊D3—241no—
637C2×C3⋊D3#23512yes—
638C2×C3⋊D3#23712yes—
639C2×C3×D3—32no—
640C2×C3×D3—32no—
641C2×C3×D3—32no—
642C2×C3×D3—32no—
643C2×C3×D3—62no—
644C2×C3×D3—62no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—124no—
658C2×C3×D3—124no—
659C2×C3×D3—128no—
660C32×C4—61no—
661C32×C4—61no—
662C32×C4—61no—
663C32×C4—61no—
664C32×C4—61no—
665C32×C4—61no—
666C3⋊Dic3—21no—
667C3⋊Dic3—21no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—61no—
671C3⋊Dic3—62no—
672C3⋊Dic3—61no—
673C3⋊Dic3—61no—
674C3⋊Dic3—121no—
675C3⋊Dic3—121no—
676C3⋊Dic3—122no—
677C3×Dic3—21no—
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—41no—
690C3×Dic3—41no—
691C3×Dic3—41no—
692C3×Dic3—41no—
693C3×Dic3—41no—
694C3×Dic3—41no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—121no—
704C3×Dic3—121no—
705C3×Dic3—121no—
706C3×Dic3—121no—
707#126—91no—
708#126—91no—
709#124—271no—
710#123—271no—
711#123—271no—
712#123—271no—
713C22⋊Q8—271no—
714C22⋊Q8—271no—
715#120—271no—
716C4×D4—271no—
717C4×D4—271no—
718#117—271no—
719#117—271no—
720C2×C22⋊C4—91no—
721C2×C22⋊C4—271no—
722C33#55111yescharacteristic, complemented, Sylow
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—21no—
726C23×C3—41no—
727C23×C3—91no—
728C23×C3—91no—
729C23×C3—182no—
730C23×C3—182no—
731C23×C3—361no—
732C23×C3C2×D3211yescharacteristic
733C23×C3C2×D3211yescharacteristic
734C23×C3C2×D3211yescharacteristic
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—61no—
740C22×D3—61no—
741C22×D3—62no—
742C22×D3—62no—
743C22×D3—62no—
744C22×D3—62no—
745C22×D3—91no—
746C22×D3—91no—
747C22×D3—91no—
748C22×D3—122no—
749C22×D3—122no—
750C22×D3—121no—
751C22×D3—121no—
752C22×D3—122no—
753C22×D3—181no—
754C22×D3—181no—
755C22×D3—181no—
756C22×D3—361no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
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—61no—
770C2×C3×C4—61no—
771C2×C3×C4—61no—
772C2×C3×C4—61no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—91no—
776C2×C3×C4—91no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—182no—
780C2×C3×C4—361no—
781#67—182no—
782#67—182no—
783#67—361no—
784#67—361no—
785#67—361no—
786#67—362no—
787#67—362no—
788#67—362no—
789#67—364no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—61no—
799C2×Dic3—61no—
800C2×Dic3—61no—
801C2×Dic3—61no—
802C2×Dic3—91no—
803C2×Dic3—91no—
804C2×Dic3—91no—
805C2×Dic3—181no—
806C2×Dic3—181no—
807C2×Dic3—181no—
808C2×Dic3—182no—
809C2×Dic3—361no—
810C2×Dic3—361no—
811C2×Dic3C2×D3211yescharacteristic
812C2×Dic3C2×D3211yescharacteristic
813C2×Dic3C2×D3211yescharacteristic
814C2×Dic3C2×D3211yescharacteristic
815C2×Dic3C2×D3211yescharacteristic
816C2×Dic3C2×D3211yescharacteristic
817D12—182no—
818D12—182no—
819D12—182no—
820D12—182no—
821D12—362no—
822D12—362no—
823C4×D3—62no—
824C4×D3—62no—
825C4×D3—121no—
826C4×D3—121no—
827C4×D3—182no—
828C4×D3—182no—
829C4×D3—361no—
830C4×D3—361no—
831C4×D3—361no—
832C4×D3—361no—
833C4×D3—361no—
834C4×D3—362no—
835Dic6—361no—
836Dic6—361no—
837Dic6—361no—
838Dic6—362no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—41no—
849C2×C32—41no—
850C2×C32—41no—
851C2×C32—41no—
852C2×C32—42no—
853C2×C32—41no—
854C2×C32—41no—
855C2×C32—81no—
856C2×C32—81no—
857C2×C32—82no—
858C2×C32C2×#23511yescharacteristic
859C2×C32C2×#23711yescharacteristic
860C2×C32#100411yescharacteristic
861C2×C32D3×#4111yescharacteristic
862C2×C32D3×#4111yescharacteristic
863C2×C32D3×#4111yescharacteristic
864C2×C32D3×#4111yescharacteristic
865C2×C32#100911yescharacteristic
866C2×C32#100911yescharacteristic
867C3⋊D3—22no—
868C3⋊D3—22no—
869C3⋊D3—121no—
870C3⋊D3—122no—
871C3⋊D3—121no—
872C3⋊D3—121no—
873C3⋊D3—241no—
874C3⋊D3—241no—
875C3⋊D3—242no—
876C3×D3—62no—
877C3×D3—62no—
878C3×D3—62no—
879C3×D3—62no—
880C3×D3—122no—
881C3×D3—122no—
882C24—91no—
883C2×Q8—271no—
884C2×D4—271no—
885C2×D4—271no—
886C2×D4—271no—
887C22×C4—91no—
888C22×C4—91no—
889C22×C4—271no—
890C22×C4—271no—
891C22×C4—271no—
892C4⋊C4—91no—
893C4⋊C4—91no—
894C4⋊C4—91no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—91no—
898C4⋊C4—271no—
899C4⋊C4—271no—
900C22⋊C4—31no—
901C22⋊C4—31no—
902C22⋊C4—31no—
903C22⋊C4—91no—
904C22⋊C4—91no—
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—
914C42—91no—
915C42—91no—
916C42—271no—
917C22×C3—22no—
918C22×C3—21no—
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—21no—
929C22×C3—21no—
930C22×C3—41no—
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—41no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—92no—
943C22×C3—92no—
944C22×C3—181no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—181no—
948C22×C3—364no—
949C22×C3C22×D3211yescharacteristic
950C22×C3C22×D3211yescharacteristic
951C22×C3C22×D3211yescharacteristic
952C2×D3—32no—
953C2×D3—32no—
954C2×D3—32no—
955C2×D3—32no—
956C2×D3—62no—
957C2×D3—62no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—121no—
967C2×D3—121no—
968C2×D3—121no—
969C2×D3—121no—
970C2×D3—124no—
971C2×D3—124no—
972C2×D3—128no—
973C2×D3—182no—
974C2×D3—181no—
975C2×D3—181no—
976C2×D3—181no—
977C2×D3—181no—
978C2×D3—181no—
979C2×D3—181no—
980C2×D3—181no—
981C2×D3—181no—
982C2×D3—181no—
983C2×D3—361no—
984C2×D3—361no—
985C2×D3—361no—
986C2×D3—361no—
987C2×D3—361no—
988C2×D3—361no—
989C2×D3—361no—
990C2×D3—361no—
991C2×D3—362no—
992C2×D3—721no—
993C2×D3—721no—
994C3×C4—61no—
995C3×C4—61no—
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—121no—
1007C3×C4—121no—
1008C3×C4—121no—
1009C3×C4—121no—
1010C3×C4—121no—
1011C3×C4—121no—
1012C3×C4—181no—
1013C3×C4—181no—
1014C3×C4—181no—
1015C3×C4—181no—
1016Dic3—21no—
1017Dic3—21no—
1018Dic3—21no—
1019Dic3—21no—
1020Dic3—21no—
1021Dic3—21no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—61no—
1025Dic3—61no—
1026Dic3—61no—
1027Dic3—61no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—121no—
1031Dic3—121no—
1032Dic3—121no—
1033Dic3—121no—
1034Dic3—182no—
1035Dic3—181no—
1036Dic3—181no—
1037Dic3—181no—
1038Dic3—361no—
1039Dic3—361no—
1040Dic3—362no—
1041C32—21no—
1042C32—21no—
1043C32—21no—
1044C32—41no—
1045C32#549511yescharacteristic, complemented
1046C32#570511yescharacteristic, complemented
1047C32#570511yescharacteristic, complemented
1048C23—91no—
1049C23—91no—
1050C23—182no—
1051C23—182no—
1052C23—271no—
1053C23—361no—
1054C23D3311yescharacteristic
1055Q8—1081no—
1056D4—542no—
1057D4—542no—
1058D4—1081no—
1059C2×C4—31no—
1060C2×C4—31no—
1061C2×C4—31no—
1062C2×C4—31no—
1063C2×C4—31no—
1064C2×C4—31no—
1065C2×C4—91no—
1066C2×C4—91no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—182no—
1070C2×C4—271no—
1071C2×C4—361no—
1072C2×C4—542no—
1073C2×C4—1081no—
1074C2×C4—1081no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—42no—
1085C2×C3—41no—
1086C2×C3—41no—
1087C2×C3—41no—
1088C2×C3—41no—
1089C2×C3—41no—
1090C2×C3—41no—
1091C2×C3—81no—
1092C2×C3—81no—
1093C2×C3—82no—
1094C2×C3—182no—
1095C2×C3—182no—
1096C2×C3D3×#23511yescharacteristic
1097C2×C3D3×#23511yescharacteristic
1098C2×C3#6430811yescharacteristic
1099C2×C3D3×#23711yescharacteristic
1100C2×C3D3×#23711yescharacteristic
1101C2×C3#6431211yescharacteristic
1102C2×C3#6431211yescharacteristic
1103C2×C3#6431411yescharacteristic
1104C2×C3#6431411yescharacteristic
1105D3—62no—
1106D3—62no—
1107D3—62no—
1108D3—62no—
1109D3—122no—
1110D3—122no—
1111D3—362no—
1112D3—361no—
1113D3—361no—
1114D3—361no—
1115D3—721no—
1116D3—721no—
1117D3—722no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—92no—
1122C22—92no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—364no—
1128C22—541no—
1129C22—541no—
1130C22—541no—
1131C22C2×D3311yescharacteristic
1132C4—61no—
1133C4—61no—
1134C4—61no—
1135C4—61no—
1136C4—61no—
1137C4—61no—
1138C4—181no—
1139C4—181no—
1140C4—181no—
1141C4—181no—
1142C4—541no—
1143C3—21no—
1144C3—21no—
1145C3—21no—
1146C3—41no—
1147C3#1059409311yescharacteristic, complemented
1148C3#1059409411yescharacteristic, complemented
1149C3#1059416511yescharacteristic, complemented
1150C2—41no—
1151C2—182no—
1152C2—182no—
1153C2—1081no—
1154C2#1172440811yescharacteristic
1155C2#1172441011yescharacteristic
1156C2#1172442011yescharacteristic
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. #11723723C2semidirect
3. #11723628C2semidirect
4. #11723592C2semidirect
5. C3×#63974C2semidirect
6. C3×#63956C2semidirect
7. C3×#63956C2semidirect
8. #11722999C2semidirect
9. #11722993C2semidirect
10. #11722984C2semidirect
11. #11722972C2semidirect
12. #11722937C2semidirect
13. #11722933C2semidirect
14. #11722922C2semidirect
15. #11722915C2semidirect
23. C2×#6293C22semidirect
26. C2×#6289C22semidirect
36. #88807C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. #88804C22semidirect
39. #88804C22semidirect
40. #88804C22semidirect
43. Dic3×C3⋊Dic3C22semidirect
44. C3×#3724C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
70. #63974D3semidirect
73. #63956D3semidirect
74. #63956D3semidirect
219. #3724C2×D3semidirect
220. #3724C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
230. Dic3⋊Dic3C2×D3semidirect
257. Dic32C2×D3semidirect
258. Dic32C2×D3semidirect
722. C33#551semidirect
1045. C32#5495semidirect
1046. C32#5705semidirect
1047. C32#5705semidirect
1147. C3#10594093semidirect
1148. C3#10594094semidirect
1149. C3#10594165semidirect

Maximal subgroups

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

subgroupindex
#117237232
#117236362
#117236282
#117235922
C3×#639742
C3×#639562
#117229992
#117229932
#117229842
#117229722
#117229372
#117229332
#117229222
#117229152
#105941653
#105940943
#105940933