Finite Group Databasebeta

← #13172176

Subgroups — #13172176

Order 1728.

1582 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89031C211yesmaximal, characteristic
2#11723726C211yesmaximal, characteristic, complemented
3#11723622C211yesmaximal, characteristic, complemented
4#11723618C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63955C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11722943C211yesmaximal, characteristic, complemented
9#11722942C211yesmaximal, characteristic, complemented
10#11722937C211yesmaximal, characteristic, complemented
11#11722933C211yesmaximal, characteristic, complemented
12#11722921C211yesmaximal, characteristic, complemented
13#11722920C211yesmaximal, characteristic, complemented
14#11722912C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10594990—31nomaximal
17#10594874—31nomaximal
18#10594049—31nomaximal
19C2×#6312C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30#89031C418yescomplemented
31C2×Dic3×C3⋊D3C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C32×#217C2211yescharacteristic
35#88815C2211yescharacteristic
36#88814C2211yescharacteristic
37#88813C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C3×Dic32C2211yescharacteristic
55C2×#3828—31no—
56C2×#3804—31no—
57C2×#3804—31no—
58C2×#3804—61no—
59C4×#638—31no—
60#64090—31no—
61C3×C4×#67—31no—
62C3×#926—31no—
63C2×C3×C4⋊Dic3—31no—
64C2×C3×Dic3⋊C4—31no—
65C3×#67⋊C4—31no—
66C3×#877—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69C2×Dic3⋊Dic3D311yescharacteristic, complemented
70#63955D311yescharacteristic, complemented
71#63952—31no—
72#63952—31no—
73#63952—31no—
74#63952—31no—
75#63952—31no—
76#63952—61no—
77#63952—61no—
78#63952D311yescharacteristic, complemented
79C4×#627—31no—
80#63904—31no—
81C4×#626—31no—
82#63900—31no—
83#63900—31no—
84#63894—31no—
85#63894—31no—
86#63883—31no—
87#63883—31no—
88#63881—31no—
89#63880—31no—
90#63878—31no—
91#63878—31no—
92D3×Dic3⋊C4—31no—
93D3×Dic3⋊C4—31no—
94#63849—31no—
95#63849—31no—
96#63844—31no—
97#63844—31no—
98#63838—31no—
99#63837—31no—
100#63837—31no—
101#63836—31no—
102#63836—31no—
103C23×C33C2311yescharacteristic
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106#6312C2×C414yescomplemented
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638C2×C414yescomplemented
109C2×C3×C3⋊Dic3—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C32×Dic3—41no—
116C2×C32×Dic3C2×C414yescomplemented
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294—41no—
124#6293C2×C414yescomplemented
125#6292C2×C414yescomplemented
126#6289—41no—
127#6289—41no—
128#6289C2×C414yescomplemented
129Dic3×C3⋊D3C2×C414yescomplemented
130C3×#624—41no—
131#5546—91no—
132#5523—91no—
133#5504—91no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—61no—
140C2×#638—61no—
141C2×#638—61no—
142C2×#638—121no—
143C2×#638C2×D311yescharacteristic
144C22×C3⋊Dic3C2×D311yescharacteristic
145#3828—38no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×#634—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—61no—
155C22×C3×Dic3—21no—
156C22×C3×Dic3—21no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—61no—
160C22×C3×Dic3C2×D311yescharacteristic
161C22×C3×Dic3C2×D311yescharacteristic
162C22×C3×Dic3C2×D311yescharacteristic
163C22×C3×Dic3C2×D311yescharacteristic
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×#627—31no—
167C2×#627—31no—
168C2×#627—61no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—61no—
172C2×#624—31no—
173C2×#624—31no—
174C2×#624—31no—
175C2×#624—31no—
176C2×#624—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—61no—
180C2×#624—61no—
181C2×#624—61no—
182C2×#624C2×D311yescharacteristic
183#3804—38no—
184#3804—38no—
185#3804—68no—
186C2×D3×Dic3—31no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—61no—
191C32×C22⋊C4—31no—
192#3757C2×D311yescharacteristic
193#3752—31no—
194#3752—31no—
195#3750—31no—
196#3750—31no—
197C4×C3⋊Dic3—31no—
198C4×C3⋊Dic3—31no—
199C3×#217—21no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—61no—
203C3×#217C2×D311yescharacteristic
204C3×#217C2×D311yescharacteristic
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊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—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227#3724—31no—
228#3724—31no—
229#3724—31no—
230#3724—31no—
231#3724—31no—
232#3724—61no—
233#3724—61no—
234#3724C2×D311yescharacteristic
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic3⋊Dic3C2×D311yescharacteristic
243#3722—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—61no—
249#3722—61no—
250#3722C2×D311yescharacteristic
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32—61no—
262Dic32C2×D311yescharacteristic
263Dic32C2×D311yescharacteristic
264Dic32C2×D311yescharacteristic
265C22×C33—21no—
266C22×C33—21no—
267C22×C33C22×C412yes—
268C22×C33C2411yescharacteristic
269C2×C3⋊(C3⋊D3)—21no—
270C2×C3⋊(C3⋊D3)—21no—
271C2×C3⋊(C3⋊D3)C22×C412yes—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3C22×C412yes—
275C3⋊(C3⋊Dic3)C22×C412yes—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3C22×C412yes—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3C22×C412yes—
286C32×Dic3C22×C412yes—
287C2×#237—91no—
288C2×#235—91no—
289C2×#235—91no—
290C2×#235—181no—
291C3×C4×D4—91no—
292C3×#117—91no—
293C2×C3×C4⋊C4—91no—
294D4×Dic3—91no—
295C4×#67—31no—
296C4×#67—91no—
297C4×#67—91no—
298C4×#67—91no—
299C4×#67—91no—
300C4×#67—91no—
301C4×#67—181no—
302#926—31no—
303C2×C4⋊Dic3—31no—
304C2×Dic3⋊C4—31no—
305C2×Dic3⋊C4—91no—
306#893—91no—
307#893—91no—
308#892—91no—
309#892—91no—
310#892—91no—
311#892—91no—
312D3×C4⋊C4—91no—
313D3×C4⋊C4—91no—
314D3×C4⋊C4—91no—
315D3×C4⋊C4—91no—
316D3×C4⋊C4—91no—
317#887—91no—
318#887—91no—
319#887—91no—
320#67⋊C4—31no—
321#67⋊C4—91no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326#67⋊C4—181no—
327#877—31no—
328#877—91no—
329C4×D12—91no—
330C4×D12—91no—
331#872—91no—
332C4×Dic6—91no—
333C4×Dic6—91no—
334C4×Dic6—91no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—41no—
339C23×C32C22×D311yescharacteristic
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
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—121no—
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—61no—
353C2×C32×C4—34no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—31no—
357C2×C32×C4—31no—
358C2×C32×C4—31no—
359C2×C32×C4—31no—
360C2×C32×C4—121no—
361#638—34no—
362#638—34no—
363#638—34no—
364#638—64no—
365#638—64no—
366#638—64no—
367#638—124no—
368#638C4×D314yescomplemented
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—41no—
373C2×C3⋊Dic3—61no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—121no—
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C4⋊(C3⋊D3)—34no—
383C4×C3⋊D3—34no—
384C4×C3⋊D3—34no—
385C4×C3⋊D3—121no—
386C4×C3⋊D3—121no—
387#634—34no—
388C3×#67—34no—
389C3×#67—34no—
390C3×#67—64no—
391C2×C3×Dic3—24no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
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—41no—
409C2×C3×Dic3—41no—
410C2×C3×Dic3—42no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—121no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3—122no—
419C2×C3×Dic3C4×D314yescomplemented
420C2×C3×Dic3C4×D314yescomplemented
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
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C3×C4×D3—121no—
434C3×C4×D3—121no—
435#627—34no—
436#627—34no—
437#627—64no—
438#626—34no—
439#626—34no—
440#626—64no—
441#624—34no—
442#624—34no—
443#624—41no—
444#624—64no—
445#624—121no—
446#624—121no—
447#624—121no—
448#624—121no—
449#624—122no—
450#624—122no—
451#624—121no—
452D3×Dic3—34no—
453D3×Dic3—34no—
454D3×Dic3—64no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457#520—271noSylow
458C2×C33—22no—
459C2×C33C23×C411yescharacteristic
460C2×C33H(5,𝔽2)11yescharacteristic
461C2×C332−1+411yescharacteristic
462C3⋊(C3⋊D3)—22no—
463C3×C3⋊D3—22no—
464C2×C3×D4—91no—
465C22×C3×C4—31no—
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—31no—
469C22×C3×C4—61no—
470C22×C3×C4—61no—
471C22×C3×C4—91no—
472C22×C3×C4—91no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—61no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—181no—
481C2×#67—181no—
482C2×#67—181no—
483C2×#67—361no—
484C22×Dic3—31no—
485C22×Dic3—31no—
486C22×Dic3—61no—
487C22×Dic3—91no—
488C22×Dic3—91no—
489C22×Dic3D3211yescharacteristic
490C22×Dic3D3211yescharacteristic
491#237—98no—
492#235—98no—
493#235—98no—
494#235—188no—
495C2×D12—91no—
496C2×D12—91no—
497C2×D12—181no—
498C2×C4×D3—31no—
499C2×C4×D3—31no—
500C2×C4×D3—91no—
501C2×C4×D3—91no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—181no—
514C2×C4×D3—181no—
515C2×C4×D3—181no—
516C2×C4×D3—181no—
517C2×Dic6—91no—
518C2×Dic6—91no—
519C2×Dic6—91no—
520C2×Dic6—181no—
521C3×C4⋊C4—91no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C4⋊C4—91no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—61no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C42—91no—
534C3×C42—91no—
535C3×C42—91no—
536#217—31no—
537#217—31no—
538#217—61no—
539#217—91no—
540#217D3211yescharacteristic
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
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—181no—
552(C2×D3)⋊C4—181no—
553C4⋊Dic3—31no—
554C4⋊Dic3—31no—
555C4⋊Dic3—31no—
556C4⋊Dic3—31no—
557C4⋊Dic3—31no—
558C4⋊Dic3—31no—
559C4⋊Dic3—91no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574Dic3⋊C4—91no—
575Dic3⋊C4—91no—
576Dic3⋊C4—181no—
577Dic3⋊C4—181no—
578C4×Dic3—31no—
579C4×Dic3—31no—
580C4×Dic3—31no—
581C4×Dic3—31no—
582C4×Dic3—31no—
583C4×Dic3—31no—
584C4×Dic3—91no—
585C4×Dic3—91no—
586C4×Dic3—91no—
587C4×Dic3—91no—
588C4×Dic3—91no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—181no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—22no—
605C22×C32—22no—
606C22×C32—22no—
607C22×C32—41no—
608C22×C32—42no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—81no—
616C22×C32—81no—
617C22×C32C2×C4×D312yes—
618C22×C32C2×C4×D312yes—
619C22×C32C2×C4×D312yes—
620C22×C32C23×D311yescharacteristic
621C22×C32C23×D311yescharacteristic
622C22×C32C23×D311yescharacteristic
623C2×C3⋊D3—21no—
624C2×C3⋊D3—21no—
625C2×C3⋊D3—32no—
626C2×C3⋊D3—32no—
627C2×C3⋊D3—32no—
628C2×C3⋊D3—62no—
629C2×C3⋊D3—62no—
630C2×C3⋊D3—62no—
631C2×C3⋊D3—61no—
632C2×C3⋊D3—61no—
633C2×C3⋊D3—61no—
634C2×C3⋊D3—61no—
635C2×C3⋊D3—61no—
636C2×C3⋊D3—61no—
637C2×C3⋊D3—122no—
638C2×C3⋊D3—121no—
639C2×C3⋊D3—121no—
640C2×C3⋊D3—121no—
641C2×C3⋊D3—121no—
642C2×C3⋊D3—121no—
643C2×C3⋊D3—121no—
644C2×C3⋊D3—241no—
645C2×C3⋊D3—241no—
646C2×C3⋊D3C2×C4×D312yes—
647C2×C3×D3—32no—
648C2×C3×D3—32no—
649C2×C3×D3—62no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C32×C4—32no—
657C32×C4—32no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—61no—
661C32×C4—61no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—32no—
667C3⋊Dic3—32no—
668C3⋊Dic3—32no—
669C3⋊Dic3—62no—
670C3⋊Dic3—62no—
671C3⋊Dic3—62no—
672C3⋊Dic3—122no—
673C3⋊Dic3C2×C4×D312yes—
674C3×Dic3—22no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—21no—
683C3×Dic3—22no—
684C3×Dic3—22no—
685C3×Dic3—32no—
686C3×Dic3—32no—
687C3×Dic3—41no—
688C3×Dic3—41no—
689C3×Dic3—41no—
690C3×Dic3—62no—
691C3×Dic3—62no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—121no—
701C3×Dic3—121no—
702C3×Dic3—121no—
703C3×Dic3C2×C4×D312yes—
704C3×Dic3C2×C4×D312yes—
705C3×Dic3C2×C4×D312yes—
706C3×Dic3C2×C4×D312yes—
707C2×#41—271no—
708C4×Q8—271no—
709C4×Q8—271no—
710C4×D4—91no—
711C4×D4—271no—
712C4×D4—271no—
713C4×D4—271no—
714C4×D4—271no—
715C4×D4—271no—
716#117—91no—
717#117—271no—
718#117—271no—
719C2×C4⋊C4—91no—
720C2×C4⋊C4—271no—
721C2×C4⋊C4—271no—
722C33#52011yescharacteristic, complemented, Sylow
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—21no—
726C23×C3—41no—
727C23×C3—91no—
728C23×C3C2×D3211yescharacteristic
729C23×C3C2×D3211yescharacteristic
730C23×C3C2×D3211yescharacteristic
731C22×D3—31no—
732C22×D3—31no—
733C22×D3—61no—
734C22×D3—91no—
735C22×D3—91no—
736C22×D3—91no—
737C22×D3—181no—
738C22×D3—181no—
739C22×D3—181no—
740C22×D3—361no—
741C3×D4—94no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—34no—
747C2×C3×C4—34no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—61no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—64no—
760C2×C3×C4—61no—
761C2×C3×C4—61no—
762C2×C3×C4—61no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—91no—
768C2×C3×C4—121no—
769C2×C3×C4—121no—
770C2×C3×C4—122no—
771C2×C3×C4—361no—
772C2×C3×C4—361no—
773#67—34no—
774#67—34no—
775#67—64no—
776#67—94no—
777#67—94no—
778#67—94no—
779#67—94no—
780#67—184no—
781#67—184no—
782#67—184no—
783#67—364no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—41no—
795C2×Dic3—61no—
796C2×Dic3—61no—
797C2×Dic3—61no—
798C2×Dic3—61no—
799C2×Dic3—61no—
800C2×Dic3—91no—
801C2×Dic3—91no—
802C2×Dic3—91no—
803C2×Dic3—94no—
804C2×Dic3—121no—
805C2×Dic3—121no—
806C2×Dic3—122no—
807C2×Dic3—181no—
808C2×Dic3—181no—
809C2×Dic3—181no—
810C2×Dic3—361no—
811C2×Dic3—361no—
812C2×Dic3#62414yescomplemented
813C2×Dic3C2×D3211yescharacteristic
814C2×Dic3C2×D3211yescharacteristic
815C2×Dic3C2×D3211yescharacteristic
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C2×Dic3C2×D3211yescharacteristic
819D12—94no—
820D12—94no—
821D12—184no—
822C4×D3—94no—
823C4×D3—94no—
824C4×D3—94no—
825C4×D3—94no—
826C4×D3—94no—
827C4×D3—121no—
828C4×D3—121no—
829C4×D3—184no—
830C4×D3—184no—
831C4×D3—361no—
832C4×D3—361no—
833C4×D3—361no—
834C4×D3—361no—
835C4×D3—361no—
836C4×D3—361no—
837C4×D3—362no—
838C4×D3—361no—
839C4×D3—361no—
840C4×D3—362no—
841Dic6—94no—
842Dic6—94no—
843Dic6—94no—
844Dic6—184no—
845C2×C32—22no—
846C2×C32—22no—
847C2×C32—22no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—21no—
854C2×C32—21no—
855C2×C32—21no—
856C2×C32—21no—
857C2×C32—41no—
858C2×C32—41no—
859C2×C32—41no—
860C2×C32—42no—
861C2×C32—42no—
862C2×C32—42no—
863C2×C32—82no—
864C2×C32C22×C4×D311yescharacteristic
865C2×C32C22×C4×D311yescharacteristic
866C2×C32C22×C4×D311yescharacteristic
867C2×C32#100411yescharacteristic
868C2×C32#100411yescharacteristic
869C2×C32#100711yescharacteristic
870C2×C32#100911yescharacteristic
871C2×C32#101011yescharacteristic
872C2×C32#101011yescharacteristic
873C3⋊D3—22no—
874C3⋊D3—62no—
875C3⋊D3—62no—
876C3⋊D3—62no—
877C3⋊D3—122no—
878C3⋊D3—122no—
879C3⋊D3—122no—
880C3⋊D3—242no—
881C3×D3—62no—
882C3×D3—62no—
883C3×D3—122no—
884#41—278no—
885C2×Q8—271no—
886C2×D4—91no—
887C2×D4—271no—
888C2×D4—271no—
889C22×C4—31no—
890C22×C4—31no—
891C22×C4—91no—
892C22×C4—91no—
893C22×C4—271no—
894C22×C4—271no—
895C22×C4—271no—
896C22×C4—271no—
897C22×C4—271no—
898C4⋊C4—91no—
899C4⋊C4—91no—
900C4⋊C4—91no—
901C4⋊C4—91no—
902C4⋊C4—91no—
903C4⋊C4—91no—
904C4⋊C4—91no—
905C4⋊C4—271no—
906C4⋊C4—271no—
907C4⋊C4—271no—
908C22⋊C4—31no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—271no—
912C22⋊C4—271no—
913C22⋊C4—271no—
914C42—91no—
915C42—91no—
916C42—91no—
917C42—271no—
918C42—271no—
919C42—271no—
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—22no—
930C22×C3—22no—
931C22×C3—22no—
932C22×C3—41no—
933C22×C3—41no—
934C22×C3—41no—
935C22×C3—41no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3—42no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—92no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3C4×D3212yes—
946C22×C3C4×D3212yes—
947C22×C3C2×#62412yes—
948C22×C3C22×D3211yescharacteristic
949C22×C3C22×D3211yescharacteristic
950C22×C3C22×D3211yescharacteristic
951C2×D3—32no—
952C2×D3—32no—
953C2×D3—62no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—92no—
959C2×D3—92no—
960C2×D3—92no—
961C2×D3—121no—
962C2×D3—121no—
963C2×D3—182no—
964C2×D3—182no—
965C2×D3—182no—
966C2×D3—181no—
967C2×D3—181no—
968C2×D3—181no—
969C2×D3—181no—
970C2×D3—181no—
971C2×D3—181no—
972C2×D3—362no—
973C2×D3—361no—
974C2×D3—361no—
975C2×D3—361no—
976C2×D3—361no—
977C2×D3—361no—
978C2×D3—361no—
979C2×D3—721no—
980C2×D3—721no—
981C3×C4—32no—
982C3×C4—32no—
983C3×C4—32no—
984C3×C4—32no—
985C3×C4—62no—
986C3×C4—62no—
987C3×C4—62no—
988C3×C4—61no—
989C3×C4—61no—
990C3×C4—61no—
991C3×C4—61no—
992C3×C4—61no—
993C3×C4—61no—
994C3×C4—61no—
995C3×C4—61no—
996C3×C4—92no—
997C3×C4—121no—
998C3×C4—121no—
999C3×C4—121no—
1000C3×C4—181no—
1001C3×C4—181no—
1002C3×C4—181no—
1003C3×C4—181no—
1004Dic3—21no—
1005Dic3—21no—
1006Dic3—21no—
1007Dic3—21no—
1008Dic3—32no—
1009Dic3—32no—
1010Dic3—62no—
1011Dic3—62no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—92no—
1021Dic3—92no—
1022Dic3—92no—
1023Dic3—121no—
1024Dic3—121no—
1025Dic3—121no—
1026Dic3—182no—
1027Dic3—182no—
1028Dic3—182no—
1029Dic3—362no—
1030Dic3C2×#62412yes—
1031Dic3C2×#62412yes—
1032C32—21no—
1033C32—21no—
1034C32—21no—
1035C32—41no—
1036C32#550411yescharacteristic, complemented
1037C32#552311yescharacteristic, complemented
1038C32#554611yescharacteristic, complemented
1039C23—91no—
1040C23—271no—
1041C23D3311yescharacteristic
1042Q8—274no—
1043D4—94no—
1044D4—274no—
1045D4—274no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—34no—
1049C2×C4—31no—
1050C2×C4—31no—
1051C2×C4—31no—
1052C2×C4—31no—
1053C2×C4—91no—
1054C2×C4—91no—
1055C2×C4—91no—
1056C2×C4—91no—
1057C2×C4—91no—
1058C2×C4—121no—
1059C2×C4—274no—
1060C2×C4—274no—
1061C2×C4—271no—
1062C2×C4—361no—
1063C2×C4—361no—
1064C2×C4—1081no—
1065C2×C4—1081no—
1066C2×C4—1081no—
1067C2×C3—22no—
1068C2×C3—22no—
1069C2×C3—22no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—42no—
1080C2×C3—42no—
1081C2×C3—42no—
1082C2×C3—41no—
1083C2×C3—41no—
1084C2×C3—41no—
1085C2×C3—82no—
1086C2×C3—182no—
1087C2×C3#6429711yescharacteristic
1088C2×C3#6429711yescharacteristic
1089C2×C3C2×C4×D3211yescharacteristic
1090C2×C3C2×C4×D3211yescharacteristic
1091C2×C3#6430711yescharacteristic
1092C2×C3#6430911yescharacteristic
1093C2×C3#6431411yescharacteristic
1094C2×C3C22×#62411yescharacteristic
1095C2×C3#6433011yescharacteristic
1096D3—62no—
1097D3—62no—
1098D3—122no—
1099D3—182no—
1100D3—182no—
1101D3—182no—
1102D3—362no—
1103D3—362no—
1104D3—362no—
1105D3—722no—
1106C22—21no—
1107C22—21no—
1108C22—92no—
1109C22—181no—
1110C22—181no—
1111C22—272no—
1112C22—541no—
1113C22—541no—
1114C22D3×#62412yes—
1115C22C2×D3311yescharacteristic
1116C4—32no—
1117C4—32no—
1118C4—61no—
1119C4—61no—
1120C4—61no—
1121C4—61no—
1122C4—92no—
1123C4—181no—
1124C4—181no—
1125C4—181no—
1126C4—181no—
1127C4—272no—
1128C3—21no—
1129C3—21no—
1130C3—21no—
1131C3—41no—
1132C3#1059404911yescharacteristic, complemented
1133C3#1059487411yescharacteristic, complemented
1134C3#1059499011yescharacteristic, complemented
1135C2—22no—
1136C2—182no—
1137C2—542no—
1138C2C2×D3×#62411yescharacteristic
1139C2#1172441811yescharacteristic
1140C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC2×#89031C2
hypercenterC23D33
hypocenterC33#520
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723726C2semidirect
3. #11723622C2semidirect
4. #11723618C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C3×#63955C2semidirect
7. C3×#63952C2semidirect
8. #11722943C2semidirect
9. #11722942C2semidirect
10. #11722937C2semidirect
11. #11722933C2semidirect
12. #11722921C2semidirect
13. #11722920C2semidirect
14. #11722912C2semidirect
15. #11722911C2semidirect
30. #89031C4semidirect
69. C2×Dic3⋊Dic3D3semidirect
70. #63955D3semidirect
78. #63952D3semidirect
106. #6312C2×C4semidirect
108. C3×#638C2×C4semidirect
116. C2×C32×Dic3C2×C4semidirect
124. #6293C2×C4semidirect
125. #6292C2×C4semidirect
128. #6289C2×C4semidirect
129. Dic3×C3⋊D3C2×C4semidirect
368. #638C4×D3semidirect
419. C2×C3×Dic3C4×D3semidirect
420. C2×C3×Dic3C4×D3semidirect
722. C33#520semidirect
812. C2×Dic3#624semidirect
1036. C32#5504semidirect
1037. C32#5523semidirect
1038. C32#5546semidirect
1132. C3#10594049semidirect
1133. C3#10594874semidirect
1134. C3#10594990semidirect

Maximal subgroups

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

subgroupindex
C2×#890312
#117237262
#117236222
#117236182
C2×C3×Dic3⋊Dic32
C3×#639552
C3×#639522
#117229432
#117229422
#117229372
#117229332
#117229212
#117229202
#117229122
#117229112
#105949903
#105948743
#105940493