Finite Group Databasebeta

← #13172340

Subgroups — #13172340

Order 1728.

1378 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic, complemented
2#11723643C211yesmaximal, characteristic, complemented
3#11723633C211yesmaximal, characteristic, complemented
4#11723608C211yesmaximal, characteristic, complemented
5C3×#63980C211yesmaximal, characteristic, complemented
6C3×#63971C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723022C211yesmaximal, characteristic, complemented
10#11722993C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722956C211yesmaximal, characteristic, complemented
14#11722950C211yesmaximal, characteristic, complemented
15#11722949C211yesmaximal, characteristic, complemented
16#10595312—31nomaximal
17#10595264—31nomaximal
18#10594310—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C2×#6295C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6290C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C2×C3×#625C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64149—31no—
55#64146—31no—
56#64095—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—31no—
60C3×#938—31no—
61C3×#884—31no—
62C3×#884—31no—
63#63983—31no—
64#63983—31no—
65#63983—31no—
66#63983—61no—
67#63981—31no—
68#63981—31no—
69#63980—31no—
70#63980D311yescharacteristic, complemented
71#63979—31no—
72#63979—31no—
73#63979—61no—
74#63978—31no—
75#63978—31no—
76#63978—31no—
77#63971D311yescharacteristic, complemented
78#63970—31no—
79#63966—31no—
80#63966—31no—
81#63966—31no—
82#63966—61no—
83#63958—31no—
84#63958D311yescharacteristic, complemented
85#63956—31no—
86#63923—31no—
87#63922—31no—
88#63922—31no—
89#63908—31no—
90#63908—31no—
91#63906—31no—
92#63897—31no—
93#63890—31no—
94#63862—31no—
95#63862—31no—
96#63861—31no—
97#63861—31no—
98#63850—31no—
99#63850—31no—
100#63850—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110C2×D3×C3⋊D3—41no—
111#6312—41no—
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—41no—
114C3×#638—41no—
115C2×C3×C3⋊Dic3—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C32×#67—41no—
121C32×#67—41no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6295—41no—
127#6292—41no—
128#6291—41no—
129#6290—41no—
130C3×#626—41no—
131C3×#626—41no—
132C3×#625—41no—
133C3×#624—41no—
134C3×D3×Dic3—41no—
135#5620—91no—
136#5620—91no—
137#5620—91no—
138C23×C3⋊D3—31no—
139C22×D32—31no—
140C22×D32—31no—
141C22×D32—61no—
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638—61no—
150C2×#638—61no—
151C2×#638—61no—
152C2×#638—121no—
153C2×#638C2×D311yescharacteristic
154C2×#638C2×D311yescharacteristic, complemented
155C22×C3⋊Dic3C2×D311yescharacteristic, complemented
156C2×C4⋊(C3⋊D3)—31no—
157C2×C3×#67—21no—
158C2×C3×#67—21no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—61no—
168C2×C3×#67—61no—
169C2×C3×#67C2×D311yescharacteristic
170C2×C3×#67C2×D311yescharacteristic
171C2×C3×#67C2×D311yescharacteristic, complemented
172C2×C3×#67C2×D311yescharacteristic, complemented
173C22×C3×Dic3—31no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—31no—
176C22×C3×Dic3—61no—
177C2×C3×D12—31no—
178C2×C3×D12—31no—
179C2×C3×C4×D3—31no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—61no—
189C2×#626—61no—
190C2×#626C2×D311yescharacteristic
191C2×#626C2×D311yescharacteristic
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—61no—
196C2×#625C2×D311yescharacteristic
197C2×#624C2×D311yescharacteristic, complemented
198C2×D3×Dic3C2×D311yescharacteristic, complemented
199C32×C22⋊C4—31no—
200#3757—31no—
201#3752—31no—
202#3752—31no—
203#3752—31no—
204#3752—31no—
205C4⋊(C3⋊Dic3)—31no—
206C4⋊(C3⋊Dic3)—31no—
207C4×C3⋊Dic3—31no—
208C3×#217—21no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—31no—
212C3×#217C2×D311yescharacteristic, complemented
213C3×#217C2×D311yescharacteristic, complemented
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×C4⋊Dic3—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225#3724—31no—
226#3724C2×D311yescharacteristic, complemented
227#3724C2×D311yescharacteristic, complemented
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—61no—
246#3722—61no—
247#3722—61no—
248#3722C2×D311yescharacteristic
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260(C2×D3)⋊Dic3C2×D311yescharacteristic
261(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
262Dic32—31no—
263Dic32—31no—
264Dic32—61no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3⋊(C3⋊D3)—21no—
270C2×C3⋊(C3⋊D3)—21no—
271C2×C3⋊(C3⋊D3)—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C32×D3—21no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284D3×C3⋊D3—44no—
285C3⋊(C3⋊Dic3)—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C3×#121—91no—
295C3×#121—91no—
296C3×#121—91no—
297#940—91no—
298#940—91no—
299#940—91no—
300#940—181no—
301#939—31no—
302#939—31no—
303#939—31no—
304#939—91no—
305#939—91no—
306#939—91no—
307#938—31no—
308#938—91no—
309#938—91no—
310#937—91no—
311#937—91no—
312#937—91no—
313#937—91no—
314#937—91no—
315#937—91no—
316#937—181no—
317#930—91no—
318#930—91no—
319#930—91no—
320#929—91no—
321#929—91no—
322#929—91no—
323#898—91no—
324#898—91no—
325#898—91no—
326#894—91no—
327#894—91no—
328#894—91no—
329#886—91no—
330#886—91no—
331#886—91no—
332#886—181no—
333#884—31no—
334#884—31no—
335#884—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#879—91no—
340#879—91no—
341#879—91no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—31no—
346C23×C32—31no—
347C23×C32—41no—
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—121no—
358C22×C3⋊D3—121no—
359C22×C3⋊D3—121no—
360C22×C3⋊D3—121no—
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—21no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—61no—
370C22×C3×D3—61no—
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—121no—
376C2×D32—121no—
377C2×D32—121no—
378C2×D32—121no—
379C2×D32—121no—
380C2×D32—121no—
381C2×D32—122no—
382C2×D32—122no—
383C2×D32—122no—
384C32×D4—121no—
385C32×D4—121no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390#638—41no—
391#638—41no—
392#638—121no—
393#638—121no—
394#638—121no—
395#638—121no—
396#638—121no—
397#638—122no—
398#638—122no—
399#638—122no—
400#638—124no—
401C2×C3⋊Dic3—31no—
402C2×C3⋊Dic3—31no—
403C2×C3⋊Dic3—31no—
404C2×C3⋊Dic3—41no—
405C2×C3⋊Dic3—61no—
406C2×C3⋊Dic3—61no—
407C2×C3⋊Dic3—61no—
408C2×C3⋊Dic3—121no—
409C2×C3⋊Dic3C22×D311yescharacteristic
410C2×C3⋊Dic3C22×D311yescharacteristic
411C2×C3⋊Dic3C22×D311yescharacteristic
412C2×C3⋊Dic3C22×D311yescharacteristic
413C4⋊(C3⋊D3)—121no—
414C3×#67—41no—
415C3×#67—41no—
416C3×#67—41no—
417C3×#67—41no—
418C3×#67—42no—
419C3×#67—42no—
420C3×#67—121no—
421C3×#67—121no—
422C3×#67—121no—
423C3×#67—121no—
424C3×#67—121no—
425C3×#67—121no—
426C3×#67—121no—
427C3×#67—121no—
428C3×#67—122no—
429C3×#67—122no—
430C2×C3×Dic3—21no—
431C2×C3×Dic3—21no—
432C2×C3×Dic3—21no—
433C2×C3×Dic3—21no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—61no—
443C2×C3×Dic3—61no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—61no—
446C2×C3×Dic3—121no—
447C2×C3×Dic3—121no—
448C2×C3×Dic3—121no—
449C2×C3×Dic3—122no—
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C3×D12—121no—
459C3×D12—121no—
460C3×C4×D3—121no—
461C3×C4×D3—121no—
462C3×C4×D3—121no—
463#626—41no—
464#626—41no—
465#626—121no—
466#626—121no—
467#626—122no—
468#626—121no—
469#626—121no—
470#626—122no—
471#626—121no—
472#626—121no—
473#625—41no—
474#625—121no—
475#625—121no—
476#625—121no—
477#625—122no—
478#624—41no—
479D3×Dic3—41no—
480#560—271noSylow
481C2×C33—41no—
482C2×C33H(5,𝔽2)11yescharacteristic
483C2×C33H(5,𝔽2)11yescharacteristic
484C2×C33H(5,𝔽2)11yescharacteristic
485C3⋊(C3⋊D3)—41no—
486C3×C3⋊D3—41no—
487C3×C3⋊D3—41no—
488C32×D3—41no—
489C32×D3—41no—
490C23×D3—91no—
491C23×D3—91no—
492C23×D3—91no—
493C23×D3—181no—
494C2×C3×D4—31no—
495C2×C3×D4—31no—
496C2×C3×D4—31no—
497C2×C3×D4—31no—
498C2×C3×D4—61no—
499C2×C3×D4—61no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C2×C3×D4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—31no—
515C2×#67—31no—
516C2×#67—61no—
517C2×#67—61no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—91no—
522C2×#67—91no—
523C2×#67—91no—
524C2×#67—91no—
525C2×#67—91no—
526C2×#67—91no—
527C2×#67—91no—
528C2×#67—91no—
529C2×#67—181no—
530C2×#67—181no—
531C2×#67—181no—
532C2×#67—181no—
533C2×#67—181no—
534C2×#67—361no—
535C2×#67D3211yescharacteristic
536C2×#67D3211yescharacteristic, complemented
537C22×Dic3—31no—
538C22×Dic3—31no—
539C22×Dic3—31no—
540C22×Dic3—61no—
541C2×D12—31no—
542C2×D12—31no—
543C2×D12—91no—
544C2×D12—91no—
545C2×D12—91no—
546C2×D12—91no—
547C2×D12—181no—
548C2×C4×D3—31no—
549C2×C4×D3—31no—
550C2×C4×D3—31no—
551C3×C4⋊C4—91no—
552C3×C4⋊C4—91no—
553C3×C4⋊C4—91no—
554C3×C22⋊C4—31no—
555C3×C22⋊C4—31no—
556C3×C22⋊C4—61no—
557C3×C22⋊C4—91no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561#217—31no—
562#217—31no—
563#217—31no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—91no—
569#217—181no—
570#217D3211yescharacteristic, complemented
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—91no—
577(C2×D3)⋊C4—91no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—91no—
582(C2×D3)⋊C4—91no—
583(C2×D3)⋊C4—91no—
584(C2×D3)⋊C4—91no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—91no—
592(C2×D3)⋊C4—181no—
593(C2×D3)⋊C4—181no—
594(C2×D3)⋊C4—181no—
595(C2×D3)⋊C4—181no—
596C4⋊Dic3—31no—
597C4⋊Dic3—91no—
598C4⋊Dic3—91no—
599C4⋊Dic3—91no—
600C4⋊Dic3—91no—
601C4⋊Dic3—91no—
602C4⋊Dic3—181no—
603C4⋊Dic3—181no—
604Dic3⋊C4—31no—
605Dic3⋊C4—31no—
606Dic3⋊C4—31no—
607Dic3⋊C4—31no—
608Dic3⋊C4—31no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613C4×Dic3—91no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C4×Dic3—181no—
617C22×C32—21no—
618C22×C32—22no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—42no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—61no—
645C22×C32—61no—
646C22×C32—81no—
647C22×C32—81no—
648C22×C32C23×D311yescharacteristic
649C22×C32C23×D311yescharacteristic
650C22×C32C23×D311yescharacteristic
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3⋊D3—21no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—62no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—61no—
661C2×C3⋊D3—61no—
662C2×C3⋊D3—61no—
663C2×C3⋊D3—61no—
664C2×C3⋊D3—61no—
665C2×C3⋊D3—61no—
666C2×C3⋊D3—61no—
667C2×C3⋊D3—121no—
668C2×C3⋊D3—121no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—121no—
671C2×C3⋊D3—121no—
672C2×C3⋊D3—121no—
673C2×C3⋊D3—121no—
674C2×C3⋊D3—121no—
675C2×C3⋊D3—121no—
676C2×C3⋊D3—124no—
677C2×C3⋊D3—241no—
678C2×C3⋊D3—241no—
679C2×C3×D3—22no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—21no—
683C2×C3×D3—21no—
684C2×C3×D3—21no—
685C2×C3×D3—21no—
686C2×C3×D3—21no—
687C2×C3×D3—21no—
688C2×C3×D3—21no—
689C2×C3×D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—41no—
693C2×C3×D3—41no—
694C2×C3×D3—41no—
695C2×C3×D3—41no—
696C2×C3×D3—41no—
697C2×C3×D3—62no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—121no—
711C2×C3×D3—121no—
712C2×C3×D3—121no—
713C2×C3×D3—121no—
714C2×C3×D3—121no—
715D32—128no—
716D32—124no—
717D32—124no—
718C32×C4—61no—
719C32×C4—61no—
720C32×C4—61no—
721C32×C4—61no—
722C3⋊Dic3—21no—
723C3⋊Dic3—21no—
724C3⋊Dic3—21no—
725C3⋊Dic3—21no—
726C3⋊Dic3—61no—
727C3⋊Dic3—62no—
728C3⋊Dic3—61no—
729C3⋊Dic3—61no—
730C3⋊Dic3—121no—
731C3⋊Dic3—121no—
732C3⋊Dic3—122no—
733C3×Dic3—22no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—41no—
743C3×Dic3—41no—
744C3×Dic3—41no—
745C3×Dic3—62no—
746C3×Dic3—61no—
747C3×Dic3—61no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—121no—
755C3×Dic3—121no—
756C3×Dic3—121no—
757#127—271no—
758#126—271no—
759#126—271no—
760#123—271no—
761#123—271no—
762#123—271no—
763#121—91no—
764#121—91no—
765#121—91no—
766#121—271no—
767#121—271no—
768#121—271no—
769#120—271no—
770#120—271no—
771#120—271no—
772C33#56011yescharacteristic, complemented, Sylow
773C23×C3—21no—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3—31no—
777C23×C3—31no—
778C23×C3—31no—
779C23×C3—31no—
780C23×C3—41no—
781C23×C3—61no—
782C23×C3—61no—
783C23×C3—91no—
784C23×C3—91no—
785C23×C3C2×D3211yescharacteristic
786C23×C3C2×D3211yescharacteristic
787C23×C3C2×D3211yescharacteristic
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—61no—
793C22×D3—61no—
794C22×D3—91no—
795C22×D3—91no—
796C22×D3—91no—
797C22×D3—181no—
798C22×D3—181no—
799C22×D3—181no—
800C22×D3—361no—
801C22×D3—361no—
802C22×D3—361no—
803C22×D3—361no—
804C22×D3—361no—
805C22×D3—361no—
806C22×D3—361no—
807C22×D3—361no—
808C22×D3—361no—
809C22×D3—361no—
810C22×D3—362no—
811C22×D3—362no—
812C22×D3—362no—
813C22×D3C2×D3211yescharacteristic
814C22×D3C2×D3211yescharacteristic
815C3×D4—121no—
816C3×D4—121no—
817C3×D4—121no—
818C3×D4—121no—
819C3×D4—122no—
820C3×D4—122no—
821C3×D4—361no—
822C3×D4—361no—
823C3×D4—361no—
824C3×D4—361no—
825C3×D4—361no—
826C2×C3×C4—31no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—91no—
842C2×C3×C4—361no—
843C2×C3×C4—361no—
844C2×C3×C4—361no—
845#67—41no—
846#67—41no—
847#67—121no—
848#67—121no—
849#67—121no—
850#67—121no—
851#67—121no—
852#67—121no—
853#67—121no—
854#67—121no—
855#67—122no—
856#67—122no—
857#67—361no—
858#67—361no—
859#67—361no—
860#67—361no—
861#67—361no—
862#67—362no—
863#67—361no—
864#67—361no—
865#67—361no—
866#67—362no—
867#67—361no—
868#67—361no—
869#67—361no—
870#67—362no—
871#67—362no—
872#67—362no—
873#67—364no—
874C2×Dic3—31no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—31no—
878C2×Dic3—31no—
879C2×Dic3—31no—
880C2×Dic3—31no—
881C2×Dic3—31no—
882C2×Dic3—61no—
883C2×Dic3—61no—
884C2×Dic3—61no—
885C2×Dic3—61no—
886C2×Dic3—91no—
887C2×Dic3—91no—
888C2×Dic3—91no—
889C2×Dic3—121no—
890C2×Dic3—121no—
891C2×Dic3—121no—
892C2×Dic3—122no—
893C2×Dic3—181no—
894C2×Dic3—181no—
895C2×Dic3—181no—
896C2×Dic3—361no—
897C2×Dic3C2×D3211yescharacteristic
898C2×Dic3C2×D3211yescharacteristic
899C2×Dic3C2×D3211yescharacteristic
900C2×Dic3C2×D3211yescharacteristic
901D12—121no—
902D12—121no—
903D12—361no—
904D12—361no—
905D12—362no—
906D12—361no—
907D12—361no—
908C4×D3—121no—
909C4×D3—121no—
910C4×D3—121no—
911C2×C32—21no—
912C2×C32—21no—
913C2×C32—21no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—21no—
917C2×C32—21no—
918C2×C32—21no—
919C2×C32—21no—
920C2×C32—41no—
921C2×C32—41no—
922C2×C32—41no—
923C2×C32—41no—
924C2×C32—42no—
925C2×C32—41no—
926C2×C32—41no—
927C2×C32—81no—
928C2×C32—81no—
929C2×C32—82no—
930C2×C32—121no—
931C2×C32—121no—
932C2×C32#100411yescharacteristic
933C2×C32#100411yescharacteristic
934C2×C32#100411yescharacteristic
935C2×C32#100411yescharacteristic
936C2×C32#100411yescharacteristic
937C2×C32#100411yescharacteristic
938C2×C32#100911yescharacteristic
939C2×C32#100911yescharacteristic
940C2×C32#100911yescharacteristic
941C3⋊D3—41no—
942C3⋊D3—41no—
943C3⋊D3—121no—
944C3⋊D3—122no—
945C3⋊D3—121no—
946C3⋊D3—121no—
947C3⋊D3—241no—
948C3⋊D3—241no—
949C3⋊D3—242no—
950C3×D3—42no—
951C3×D3—41no—
952C3×D3—41no—
953C3×D3—41no—
954C3×D3—41no—
955C3×D3—81no—
956C3×D3—122no—
957C3×D3—121no—
958C3×D3—121no—
959C3×D3—121no—
960C3×D3—121no—
961C3×D3—241no—
962C24—271no—
963C2×D4—31no—
964C2×D4—31no—
965C2×D4—91no—
966C2×D4—91no—
967C2×D4—91no—
968C2×D4—91no—
969C2×D4—91no—
970C2×D4—271no—
971C2×D4—271no—
972C2×D4—271no—
973C2×D4—271no—
974C2×D4—271no—
975C22×C4—91no—
976C22×C4—91no—
977C22×C4—91no—
978C4⋊C4—91no—
979C4⋊C4—91no—
980C4⋊C4—91no—
981C4⋊C4—271no—
982C4⋊C4—271no—
983C4⋊C4—271no—
984C22⋊C4—31no—
985C22⋊C4—91no—
986C22⋊C4—91no—
987C22⋊C4—91no—
988C22⋊C4—91no—
989C22⋊C4—271no—
990C22⋊C4—271no—
991C22⋊C4—271no—
992C22⋊C4—271no—
993C22⋊C4—271no—
994C22⋊C4—271no—
995C22⋊C4—271no—
996C42—271no—
997C22×C3—22no—
998C22×C3—21no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—21no—
1002C22×C3—21no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—41no—
1011C22×C3—41no—
1012C22×C3—41no—
1013C22×C3—41no—
1014C22×C3—41no—
1015C22×C3—41no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—42no—
1019C22×C3—41no—
1020C22×C3—62no—
1021C22×C3—61no—
1022C22×C3—61no—
1023C22×C3—61no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—61no—
1028C22×C3—61no—
1029C22×C3—61no—
1030C22×C3—61no—
1031C22×C3—61no—
1032C22×C3—61no—
1033C22×C3—81no—
1034C22×C3—81no—
1035C22×C3—121no—
1036C22×C3—121no—
1037C22×C3—121no—
1038C22×C3—121no—
1039C22×C3—121no—
1040C22×C3—181no—
1041C22×C3—181no—
1042C22×C3—181no—
1043C22×C3—181no—
1044C22×C3—181no—
1045C22×C3—181no—
1046C22×C3C22×D3211yescharacteristic
1047C22×C3C22×D3211yescharacteristic
1048C22×C3C22×D3211yescharacteristic
1049C2×D3—21no—
1050C2×D3—21no—
1051C2×D3—21no—
1052C2×D3—21no—
1053C2×D3—21no—
1054C2×D3—21no—
1055C2×D3—62no—
1056C2×D3—61no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—61no—
1064C2×D3—61no—
1065C2×D3—61no—
1066C2×D3—61no—
1067C2×D3—61no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C2×D3—121no—
1071C2×D3—121no—
1072C2×D3—121no—
1073C2×D3—182no—
1074C2×D3—181no—
1075C2×D3—181no—
1076C2×D3—181no—
1077C2×D3—181no—
1078C2×D3—181no—
1079C2×D3—181no—
1080C2×D3—181no—
1081C2×D3—181no—
1082C2×D3—181no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—361no—
1087C2×D3—361no—
1088C2×D3—361no—
1089C2×D3—361no—
1090C2×D3—361no—
1091C2×D3—362no—
1092C2×D3—364no—
1093C2×D3—368no—
1094C2×D3—364no—
1095C2×D3—364no—
1096C2×D3—721no—
1097C2×D3—721no—
1098C3×C4—62no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—61no—
1102C3×C4—61no—
1103C3×C4—61no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—121no—
1108C3×C4—121no—
1109C3×C4—121no—
1110C3×C4—181no—
1111C3×C4—181no—
1112C3×C4—181no—
1113C3×C4—181no—
1114Dic3—21no—
1115Dic3—21no—
1116Dic3—21no—
1117Dic3—21no—
1118Dic3—62no—
1119Dic3—61no—
1120Dic3—61no—
1121Dic3—61no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—121no—
1128Dic3—121no—
1129Dic3—121no—
1130Dic3—182no—
1131Dic3—181no—
1132Dic3—181no—
1133Dic3—181no—
1134Dic3—361no—
1135Dic3—361no—
1136Dic3—362no—
1137C32—21no—
1138C32—21no—
1139C32—21no—
1140C32—41no—
1141C32#562011yescharacteristic, complemented
1142C32#562011yescharacteristic, complemented
1143C32#562011yescharacteristic, complemented
1144C23—31no—
1145C23—31no—
1146C23—91no—
1147C23—91no—
1148C23—271no—
1149C23—1081no—
1150C23—1081no—
1151C23—1081no—
1152C23D3311yescharacteristic
1153D4—121no—
1154D4—121no—
1155D4—361no—
1156D4—361no—
1157D4—361no—
1158D4—361no—
1159D4—361no—
1160D4—1081no—
1161D4—1081no—
1162D4—1081no—
1163D4—1081no—
1164D4—1081no—
1165C2×C4—31no—
1166C2×C4—31no—
1167C2×C4—31no—
1168C2×C4—31no—
1169C2×C4—91no—
1170C2×C4—91no—
1171C2×C4—91no—
1172C2×C4—91no—
1173C2×C4—271no—
1174C2×C4—361no—
1175C2×C4—361no—
1176C2×C4—361no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—21no—
1186C2×C3—42no—
1187C2×C3—41no—
1188C2×C3—41no—
1189C2×C3—41no—
1190C2×C3—41no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—81no—
1194C2×C3—81no—
1195C2×C3—82no—
1196C2×C3—122no—
1197C2×C3—121no—
1198C2×C3—121no—
1199C2×C3—121no—
1200C2×C3—121no—
1201C2×C3—241no—
1202C2×C3—361no—
1203C2×C3—361no—
1204C2×C3#6430811yescharacteristic
1205C2×C3#6431311yescharacteristic
1206C2×C3#6431311yescharacteristic
1207C2×C3#6431411yescharacteristic
1208C2×C3#6431411yescharacteristic
1209C2×C3#6431411yescharacteristic
1210C2×C3#6431411yescharacteristic
1211C2×C3#6433011yescharacteristic
1212C2×C3#6433011yescharacteristic
1213D3—41no—
1214D3—41no—
1215D3—122no—
1216D3—121no—
1217D3—121no—
1218D3—121no—
1219D3—121no—
1220D3—241no—
1221D3—362no—
1222D3—361no—
1223D3—361no—
1224D3—361no—
1225D3—721no—
1226D3—721no—
1227D3—722no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—61no—
1232C22—61no—
1233C22—61no—
1234C22—61no—
1235C22—61no—
1236C22—61no—
1237C22—181no—
1238C22—181no—
1239C22—181no—
1240C22—181no—
1241C22—181no—
1242C22—181no—
1243C22—541no—
1244C22—541no—
1245C22—541no—
1246C22—1084no—
1247C22C2×D3311yescharacteristic
1248C4—61no—
1249C4—61no—
1250C4—61no—
1251C4—61no—
1252C4—181no—
1253C4—181no—
1254C4—181no—
1255C4—181no—
1256C4—541no—
1257C3—21no—
1258C3—21no—
1259C3—21no—
1260C3—41no—
1261C3#1059431011yescharacteristic, complemented
1262C3#1059526411yescharacteristic, complemented
1263C3#1059531211yescharacteristic, complemented
1264C2—41no—
1265C2—121no—
1266C2—121no—
1267C2—361no—
1268C2—361no—
1269C2—1081no—
1270C2#1172441411yescharacteristic
1271C2#1172441611yescharacteristic
1272C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723717C2semidirect
2. #11723643C2semidirect
3. #11723633C2semidirect
4. #11723608C2semidirect
5. C3×#63980C2semidirect
6. C3×#63971C2semidirect
7. C3×#63958C2semidirect
8. #11723027C2semidirect
9. #11723022C2semidirect
10. #11722993C2semidirect
11. #11722987C2semidirect
12. #11722957C2semidirect
13. #11722956C2semidirect
14. #11722950C2semidirect
15. #11722949C2semidirect
22. C2×C3×#638C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
29. C2×#6290C22semidirect
33. C2×C3×#624C22semidirect
34. C2×C3×D3×Dic3C22semidirect
35. C32×#217C22semidirect
36. #88815C22semidirect
38. #88814C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×#3724C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
70. #63980D3semidirect
77. #63971D3semidirect
84. #63958D3semidirect
154. C2×#638C2×D3semidirect
155. C22×C3⋊Dic3C2×D3semidirect
171. C2×C3×#67C2×D3semidirect
172. C2×C3×#67C2×D3semidirect
197. C2×#624C2×D3semidirect
198. C2×D3×Dic3C2×D3semidirect
212. C3×#217C2×D3semidirect
213. C3×#217C2×D3semidirect
226. #3724C2×D3semidirect
227. #3724C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
261. (C2×D3)⋊Dic3C2×D3semidirect
536. C2×#67D32semidirect
570. #217D32semidirect
772. C33#560semidirect
1141. C32#5620semidirect
1142. C32#5620semidirect
1143. C32#5620semidirect
1261. C3#10594310semidirect
1262. C3#10595264semidirect
1263. C3#10595312semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236432
#117236332
#117236082
C3×#639802
C3×#639712
C3×#639582
#117230272
#117230222
#117229932
#117229872
#117229572
#117229562
#117229502
#117229492
#105953123
#105952643
#105943103