Finite Group Databasebeta

← #13172296

Subgroups — #13172296

Order 1728.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723727C211yesmaximal, characteristic, complemented
2#11723634C211yesmaximal, characteristic, complemented
3#11723600C211yesmaximal, characteristic, complemented
4#11723591C211yesmaximal, characteristic, complemented
5C3×#63983C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8#11723010C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11723009C211yesmaximal, characteristic, complemented
11#11723007C211yesmaximal, characteristic, complemented
12#11723002C211yesmaximal, characteristic, complemented
13#11723001C211yesmaximal, characteristic, complemented
14#11722947C211yesmaximal, characteristic, complemented
15#11722947C211yesmaximal, characteristic, complemented
16#10595262—31nomaximal
17#10595256—31nomaximal
18#10594309—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic, complemented
20C22×C3×D32C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6293C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33#88864C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic, complemented
36#88814C2211yescharacteristic, complemented
37#88814C2211yescharacteristic, complemented
38#88803C2211yescharacteristic, complemented
39#88803C2211yescharacteristic, complemented
40#88803C2211yescharacteristic, complemented
41#88803C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64146—31no—
55#64145—31no—
56#64094—31no—
57C3×#937—31no—
58C3×#937—31no—
59C3×#937—31no—
60C3×#936—31no—
61C3×#885—31no—
62C3×#882—31no—
63#63983D311yescharacteristic, complemented
64#63981—31no—
65#63981D311yescharacteristic, complemented
66#63977—31no—
67#63977—31no—
68#63977—31no—
69#63976—31no—
70#63976—31no—
71#63976—31no—
72#63976—31no—
73#63976—31no—
74#63976—61no—
75#63959—31no—
76#63959—31no—
77#63959—31no—
78#63959—31no—
79#63959—31no—
80#63959—31no—
81#63959—61no—
82#63959—61no—
83#63959D311yescharacteristic, complemented
84#63953—31no—
85#63953—31no—
86#63922—31no—
87#63922—31no—
88#63915—31no—
89#63915—31no—
90#63915—31no—
91#63913—31no—
92#63913—31no—
93#63913—31no—
94#63907—31no—
95#63907—31no—
96#63907—31no—
97#63863—31no—
98#63860—31no—
99#63852—31no—
100#63852—31no—
101#63852—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—41no—
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×C3×D32—41no—
112C2×C3×D32—41no—
113C2×C3×D32—41no—
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
116C3×#638—41no—
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#6295—41no—
128#6293—41no—
129#6293—41no—
130#6290—41no—
131#6290—41no—
132C3×#627—41no—
133C3×#626—41no—
134C3×#626—41no—
135#5683—91no—
136#5594—91no—
137#5594—91no—
138C23×C3⋊D3C2×D311yescharacteristic, complemented
139C23×C3×D3—31no—
140C23×C3×D3—31no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C23×C3×D3—61no—
144C22×D32C2×D311yescharacteristic, complemented
145C2×C32×D4—31no—
146C2×C32×D4—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638C2×D311yescharacteristic
150C2×#634—31no—
151C2×#634—31no—
152C2×C3×#67—21no—
153C2×C3×#67—21no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—61no—
159C2×C3×#67C2×D311yescharacteristic
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic
163C2×C3×D12—31no—
164C2×C3×D12—31no—
165C2×C3×Dic6—31no—
166C2×C3×Dic6—31no—
167C2×#627—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627—31no—
171C2×#627—61no—
172C2×#627—61no—
173C2×#627C2×D311yescharacteristic, complemented
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626C2×D311yescharacteristic
179C2×#626C2×D311yescharacteristic
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—31no—
186C2×#625—61no—
187C2×#625—61no—
188C32×C22⋊C4—31no—
189#3757—31no—
190#3757—31no—
191#3757—31no—
192#3757—31no—
193#3757—31no—
194#3757—61no—
195#3757—61no—
196#3757—61no—
197#3757—121no—
198#3757C2×D311yescharacteristic, complemented
199#3752—31no—
200#3752—31no—
201#3752—31no—
202#3752—31no—
203C4×C3⋊Dic3—31no—
204C4×C3⋊Dic3—31no—
205C3×#217—21no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—31no—
212C3×#217—61no—
213C3×#217C2×D311yescharacteristic, complemented
214C3×#217C2×D311yescharacteristic, complemented
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227#3722—31no—
228#3722—31no—
229#3722C2×D311yescharacteristic, complemented
230#3722C2×D311yescharacteristic, complemented
231#3722C2×D311yescharacteristic, complemented
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
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—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
255(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
256(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258Dic32—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—31no—
262Dic32—61no—
263Dic32—61no—
264Dic32C2×D311yescharacteristic, complemented
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×C3×C3⋊D3—44no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C3×D32—44no—
286C3⋊(C3⋊Dic3)—21no—
287C3⋊(C3⋊Dic3)—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3—21no—
295C3×#124—91no—
296C3×#120—91no—
297C3×#120—91no—
298#953—91no—
299#953—91no—
300#953—91no—
301#953—91no—
302#947—91no—
303#947—91no—
304#937—31no—
305#937—31no—
306#937—31no—
307#937—91no—
308#937—91no—
309#937—91no—
310#937—91no—
311#937—91no—
312#937—181no—
313#936—31no—
314#936—91no—
315#936—91no—
316#936—91no—
317#936—91no—
318#936—91no—
319#936—181no—
320#885—31no—
321#885—91no—
322#885—91no—
323#885—91no—
324#885—91no—
325#885—91no—
326#885—91no—
327#885—91no—
328#885—91no—
329#885—91no—
330#885—91no—
331#885—91no—
332#885—91no—
333#885—91no—
334#885—91no—
335#885—91no—
336#885—181no—
337#882—31no—
338#882—91no—
339#882—91no—
340#882—91no—
341#875—91no—
342#875—91no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—41no—
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C23×C32C22×D311yescharacteristic
352C22×C3⋊D3—41no—
353C22×C3⋊D3—41no—
354C22×C3⋊D3—41no—
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3⋊D3C22×D311yescharacteristic
358C22×C3×D3—21no—
359C22×C3×D3—21no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—61no—
367C22×C3×D3—61no—
368C22×C3×D3—61no—
369C22×C3×D3—121no—
370C22×C3×D3—121no—
371C22×C3×D3—121no—
372C22×C3×D3—121no—
373C22×C3×D3—121no—
374C22×C3×D3—121no—
375C22×C3×D3—121no—
376C22×C3×D3—121no—
377C22×C3×D3—121no—
378C22×C3×D3—121no—
379C22×C3×D3—121no—
380C22×C3×D3—121no—
381C22×C3×D3—122no—
382C22×C3×D3—122no—
383C22×C3×D3—122no—
384C22×C3×D3C22×D311yescharacteristic
385C22×C3×D3C22×D311yescharacteristic
386C22×C3×D3C22×D311yescharacteristic
387C22×C3×D3C22×D311yescharacteristic
388C2×D32—41no—
389C2×D32—41no—
390C2×D32—41no—
391C32×D4—121no—
392C32×D4—121no—
393C2×C32×C4—31no—
394C2×C32×C4—31no—
395C2×C32×C4—31no—
396C2×C32×C4—31no—
397#638—41no—
398#638—121no—
399#638—121no—
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—61no—
407C2×C3⋊Dic3—61no—
408C2×C3⋊Dic3—61no—
409C2×C3⋊Dic3—61no—
410C2×C3⋊Dic3—61no—
411C2×C3⋊Dic3—61no—
412C2×C3⋊Dic3—121no—
413C2×C3⋊Dic3—121no—
414C2×C3⋊Dic3C22×D311yescharacteristic
415C2×C3⋊Dic3C22×D311yescharacteristic
416C2×C3⋊Dic3C22×D311yescharacteristic
417#634—121no—
418#634—121no—
419C3×#67—41no—
420C3×#67—41no—
421C3×#67—41no—
422C3×#67—41no—
423C3×#67—42no—
424C3×#67—42no—
425C3×#67—121no—
426C3×#67—121no—
427C3×#67—121no—
428C3×#67—121no—
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—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—61no—
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C3×D12—121no—
452C3×D12—121no—
453C3×Dic6—121no—
454C3×Dic6—121no—
455#627—41no—
456#627—121no—
457#627—121no—
458#627—121no—
459#627—121no—
460#627—122no—
461#627—122no—
462#626—41no—
463#626—41no—
464#626—121no—
465#626—121no—
466#626—121no—
467#626—121no—
468#625—121no—
469#625—121no—
470#625—121no—
471#625—121no—
472#625—121no—
473#625—121no—
474#625—122no—
475#625—122no—
476H(3,𝔽4)—271noSylow
477C2×C33—41no—
478C2×C33H(5,𝔽2)11yescharacteristic
479C2×C33H(5,𝔽2)11yescharacteristic
480C2×C33H(5,𝔽2)11yescharacteristic
481C3×C3⋊D3—41no—
482C3×C3⋊D3—41no—
483C3×C3⋊D3—41no—
484C32×D3—41no—
485C32×D3—41no—
486C24×C3—91no—
487C24×C3—91no—
488C23×D3—31no—
489C23×D3—31no—
490C23×D3—31no—
491C23×D3—31no—
492C23×D3—61no—
493C2×C3×Q8—91no—
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×#67—31no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—61no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—181no—
519C2×#67—181no—
520C2×#67D3211yescharacteristic
521C2×#67D3211yescharacteristic
522C2×D12—31no—
523C2×D12—31no—
524C2×D12—91no—
525C2×D12—91no—
526C2×Dic6—31no—
527C2×Dic6—31no—
528C2×Dic6—91no—
529C2×Dic6—91no—
530C2×Dic6—91no—
531C2×Dic6—91no—
532C2×Dic6—91no—
533C2×Dic6—91no—
534C2×Dic6—181no—
535C2×Dic6—181no—
536C3×C22⋊C4—31no—
537C3×C22⋊C4—31no—
538C3×C22⋊C4—61no—
539C3×C22⋊C4—91no—
540C3×C22⋊C4—91no—
541C3×C22⋊C4—91no—
542C3×C22⋊C4—91no—
543C3×C22⋊C4—91no—
544C3×C22⋊C4—91no—
545C3×C22⋊C4—91no—
546C3×C22⋊C4—91no—
547C3×C42—91no—
548#217—31no—
549#217—31no—
550#217—31no—
551#217—31no—
552#217—31no—
553#217—31no—
554#217—61no—
555#217—91no—
556#217—91no—
557#217—91no—
558#217—91no—
559#217—91no—
560#217—91no—
561#217—91no—
562#217—91no—
563#217—91no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—181no—
569#217—181no—
570#217—181no—
571#217—181no—
572#217—181no—
573#217—361no—
574#217D3211yescharacteristic, complemented
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
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—91no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—181no—
603C4×Dic3—31no—
604C4×Dic3—31no—
605C4×Dic3—91no—
606C4×Dic3—91no—
607C4×Dic3—91no—
608C4×Dic3—91no—
609C4×Dic3—91no—
610C4×Dic3—91no—
611C4×Dic3—181no—
612C4×Dic3—181no—
613C22×C32—21no—
614C22×C32—22no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—41no—
629C22×C32—42no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—81no—
643C22×C32—81no—
644C22×C32C23×D311yescharacteristic
645C22×C32C23×D311yescharacteristic
646C22×C32C23×D311yescharacteristic
647C2×C3⋊D3—21no—
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3⋊D3—44no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—41no—
670C2×C3×D3—41no—
671C2×C3×D3—41no—
672C2×C3×D3—41no—
673C2×C3×D3—41no—
674C2×C3×D3—41no—
675C2×C3×D3—62no—
676C2×C3×D3—62no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—121no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—121no—
702C2×C3×D3—124no—
703C2×C3×D3—124no—
704C2×C3×D3—128no—
705C2×C3×D3—124no—
706C2×C3×D3—124no—
707D32—44no—
708C32×C4—61no—
709C32×C4—61no—
710C32×C4—61no—
711C32×C4—61no—
712C3⋊Dic3—21no—
713C3⋊Dic3—21no—
714C3⋊Dic3—21no—
715C3⋊Dic3—61no—
716C3⋊Dic3—61no—
717C3⋊Dic3—61no—
718C3⋊Dic3—61no—
719C3⋊Dic3—61no—
720C3⋊Dic3—61no—
721C3⋊Dic3—121no—
722C3⋊Dic3—121no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—121no—
727C3⋊Dic3—241no—
728C3⋊Dic3—241no—
729C3×Dic3—22no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—41no—
739C3×Dic3—41no—
740C3×Dic3—41no—
741C3×Dic3—62no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—61no—
747C3×Dic3—61no—
748C3×Dic3—121no—
749C3×Dic3—121no—
750#124—91no—
751#124—271no—
752#124—271no—
753#124—271no—
754#124—271no—
755#124—271no—
756#124—271no—
757#124—271no—
758#124—271no—
759#120—91no—
760#120—91no—
761#120—271no—
762#120—271no—
763#120—271no—
764#120—271no—
765C33H(3,𝔽4)11yescharacteristic, complemented, Sylow
766C23×C3—21no—
767C23×C3—21no—
768C23×C3—21no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—31no—
773C23×C3—41no—
774C23×C3—61no—
775C23×C3—61no—
776C23×C3—91no—
777C23×C3—91no—
778C23×C3—91no—
779C23×C3—361no—
780C23×C3—361no—
781C23×C3—361no—
782C23×C3—361no—
783C23×C3—361no—
784C23×C3—361no—
785C23×C3C2×D3211yescharacteristic
786C23×C3C2×D3211yescharacteristic
787C23×C3C2×D3211yescharacteristic
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—31no—
793C22×D3—31no—
794C22×D3—61no—
795C22×D3—61no—
796C22×D3—61no—
797C22×D3—121no—
798C22×D3—121no—
799C22×D3—121no—
800C22×D3—121no—
801C22×D3—121no—
802C22×D3—121no—
803C22×D3—121no—
804C22×D3—121no—
805C22×D3—121no—
806C22×D3—121no—
807C22×D3—121no—
808C22×D3—121no—
809C22×D3—122no—
810C22×D3—122no—
811C22×D3—122no—
812C22×D3C2×D3211yescharacteristic
813C22×D3C2×D3211yescharacteristic
814C3×Q8—361no—
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—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
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—61no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—91no—
837C2×C3×C4—91no—
838C2×C3×C4—91no—
839#67—41no—
840#67—41no—
841#67—121no—
842#67—121no—
843#67—121no—
844#67—121no—
845#67—122no—
846#67—361no—
847#67—361no—
848#67—361no—
849#67—361no—
850#67—361no—
851#67—361no—
852#67—361no—
853#67—361no—
854#67—361no—
855#67—361no—
856#67—362no—
857#67—362no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—61no—
865C2×Dic3—61no—
866C2×Dic3—61no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—91no—
870C2×Dic3—91no—
871C2×Dic3—91no—
872C2×Dic3—91no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—181no—
876C2×Dic3—181no—
877C2×Dic3—181no—
878C2×Dic3—181no—
879C2×Dic3—361no—
880C2×Dic3—361no—
881C2×Dic3C2×D3211yescharacteristic
882C2×Dic3C2×D3211yescharacteristic
883C2×Dic3C2×D3211yescharacteristic
884C2×Dic3C2×D3211yescharacteristic
885D12—121no—
886D12—121no—
887D12—361no—
888D12—361no—
889Dic6—121no—
890Dic6—121no—
891Dic6—361no—
892Dic6—361no—
893Dic6—361no—
894Dic6—361no—
895Dic6—361no—
896Dic6—361no—
897Dic6—362no—
898Dic6—362no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—21no—
908C2×C32—41no—
909C2×C32—41no—
910C2×C32—41no—
911C2×C32—41no—
912C2×C32—42no—
913C2×C32—41no—
914C2×C32—41no—
915C2×C32—81no—
916C2×C32—81no—
917C2×C32—82no—
918C2×C32—121no—
919C2×C32—121no—
920C2×C32#100411yescharacteristic
921C2×C32#100411yescharacteristic
922C2×C32#100411yescharacteristic
923C2×C32#100411yescharacteristic
924C2×C32#100411yescharacteristic
925C2×C32#100411yescharacteristic
926C2×C32#100411yescharacteristic
927C2×C32#100911yescharacteristic
928C2×C32#100911yescharacteristic
929C3⋊D3—41no—
930C3⋊D3—41no—
931C3⋊D3—41no—
932C3×D3—41no—
933C3×D3—41no—
934C3×D3—41no—
935C3×D3—41no—
936C3×D3—81no—
937C3×D3—81no—
938C3×D3—122no—
939C3×D3—122no—
940C3×D3—121no—
941C3×D3—121no—
942C3×D3—121no—
943C3×D3—121no—
944C3×D3—121no—
945C3×D3—121no—
946C3×D3—241no—
947C24—91no—
948C24—91no—
949C2×Q8—91no—
950C2×Q8—271no—
951C2×Q8—271no—
952C2×D4—31no—
953C2×D4—31no—
954C2×D4—91no—
955C2×D4—91no—
956C2×D4—91no—
957C2×D4—271no—
958C2×D4—271no—
959C2×D4—271no—
960C2×D4—271no—
961C22⋊C4—31no—
962C22⋊C4—91no—
963C22⋊C4—91no—
964C22⋊C4—91no—
965C22⋊C4—91no—
966C22⋊C4—91no—
967C22⋊C4—91no—
968C22⋊C4—91no—
969C22⋊C4—91no—
970C22⋊C4—271no—
971C22⋊C4—271no—
972C22⋊C4—271no—
973C22⋊C4—271no—
974C22⋊C4—271no—
975C22⋊C4—271no—
976C22⋊C4—271no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C42—91no—
980C42—271no—
981C42—271no—
982C22×C3—22no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—21no—
993C22×C3—21no—
994C22×C3—21no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—42no—
1004C22×C3—41no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—81no—
1018C22×C3—81no—
1019C22×C3—121no—
1020C22×C3—121no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—181no—
1026C22×C3—181no—
1027C22×C3—181no—
1028C22×C3—181no—
1029C22×C3—181no—
1030C22×C3—181no—
1031C22×C3—181no—
1032C22×C3—181no—
1033C22×C3—181no—
1034C22×C3—364no—
1035C22×C3—364no—
1036C22×C3C22×D3211yescharacteristic
1037C22×C3C22×D3211yescharacteristic
1038C22×C3C22×D3211yescharacteristic
1039C2×D3—21no—
1040C2×D3—21no—
1041C2×D3—21no—
1042C2×D3—21no—
1043C2×D3—21no—
1044C2×D3—21no—
1045C2×D3—62no—
1046C2×D3—62no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—61no—
1050C2×D3—61no—
1051C2×D3—61no—
1052C2×D3—61no—
1053C2×D3—61no—
1054C2×D3—61no—
1055C2×D3—61no—
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—121no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C2×D3—121no—
1071C2×D3—121no—
1072C2×D3—124no—
1073C2×D3—124no—
1074C2×D3—128no—
1075C2×D3—124no—
1076C2×D3—124no—
1077C3×C4—62no—
1078C3×C4—61no—
1079C3×C4—61no—
1080C3×C4—61no—
1081C3×C4—61no—
1082C3×C4—61no—
1083C3×C4—61no—
1084C3×C4—61no—
1085C3×C4—61no—
1086C3×C4—121no—
1087C3×C4—121no—
1088C3×C4—121no—
1089C3×C4—181no—
1090C3×C4—181no—
1091C3×C4—181no—
1092Dic3—21no—
1093Dic3—21no—
1094Dic3—21no—
1095Dic3—21no—
1096Dic3—62no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—61no—
1100Dic3—61no—
1101Dic3—61no—
1102Dic3—61no—
1103Dic3—121no—
1104Dic3—121no—
1105Dic3—181no—
1106Dic3—181no—
1107Dic3—181no—
1108Dic3—181no—
1109Dic3—181no—
1110Dic3—181no—
1111Dic3—361no—
1112Dic3—361no—
1113Dic3—361no—
1114Dic3—361no—
1115Dic3—361no—
1116Dic3—361no—
1117Dic3—721no—
1118Dic3—721no—
1119C32—21no—
1120C32—21no—
1121C32—21no—
1122C32—41no—
1123C32#559411yescharacteristic, complemented
1124C32#559411yescharacteristic, complemented
1125C32#568311yescharacteristic, complemented
1126C23—31no—
1127C23—31no—
1128C23—91no—
1129C23—91no—
1130C23—91no—
1131C23—361no—
1132C23—361no—
1133C23—361no—
1134C23—361no—
1135C23—361no—
1136C23—361no—
1137C23D3311yescharacteristic
1138Q8—361no—
1139Q8—1081no—
1140Q8—1081no—
1141D4—121no—
1142D4—121no—
1143D4—361no—
1144D4—361no—
1145D4—361no—
1146D4—1081no—
1147D4—1081no—
1148D4—1081no—
1149D4—1081no—
1150C2×C4—31no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—91no—
1155C2×C4—91no—
1156C2×C4—91no—
1157C2×C4—271no—
1158C2×C4—271no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—21no—
1162C2×C3—21no—
1163C2×C3—21no—
1164C2×C3—21no—
1165C2×C3—21no—
1166C2×C3—21no—
1167C2×C3—21no—
1168C2×C3—42no—
1169C2×C3—41no—
1170C2×C3—41no—
1171C2×C3—41no—
1172C2×C3—41no—
1173C2×C3—41no—
1174C2×C3—41no—
1175C2×C3—81no—
1176C2×C3—81no—
1177C2×C3—82no—
1178C2×C3—121no—
1179C2×C3—121no—
1180C2×C3—121no—
1181C2×C3—121no—
1182C2×C3—241no—
1183C2×C3—241no—
1184C2×C3—361no—
1185C2×C3—361no—
1186C2×C3—361no—
1187C2×C3#6430711yescharacteristic
1188C2×C3#6431311yescharacteristic
1189C2×C3#6431311yescharacteristic
1190C2×C3#6431311yescharacteristic
1191C2×C3#6431411yescharacteristic
1192C2×C3#6431411yescharacteristic
1193C2×C3#6431411yescharacteristic
1194C2×C3#6433011yescharacteristic
1195C2×C3#6433011yescharacteristic
1196D3—41no—
1197D3—41no—
1198D3—122no—
1199D3—122no—
1200D3—121no—
1201D3—121no—
1202D3—121no—
1203D3—121no—
1204D3—121no—
1205D3—121no—
1206D3—241no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—61no—
1211C22—61no—
1212C22—61no—
1213C22—61no—
1214C22—61no—
1215C22—61no—
1216C22—181no—
1217C22—181no—
1218C22—181no—
1219C22—181no—
1220C22—181no—
1221C22—181no—
1222C22—181no—
1223C22—181no—
1224C22—181no—
1225C22—364no—
1226C22—364no—
1227C22C2×D3311yescharacteristic
1228C4—61no—
1229C4—61no—
1230C4—61no—
1231C4—61no—
1232C4—181no—
1233C4—181no—
1234C4—181no—
1235C4—541no—
1236C4—541no—
1237C3—21no—
1238C3—21no—
1239C3—21no—
1240C3—41no—
1241C3#1059430911yescharacteristic, complemented
1242C3#1059525611yescharacteristic, complemented
1243C3#1059526211yescharacteristic, complemented
1244C2—41no—
1245C2—121no—
1246C2—121no—
1247C2—361no—
1248C2—361no—
1249C2—361no—
1250C2#1172441511yescharacteristic
1251C2#1172441611yescharacteristic
1252C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33H(3,𝔽4)
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723727C2semidirect
2. #11723634C2semidirect
3. #11723600C2semidirect
4. #11723591C2semidirect
5. C3×#63983C2semidirect
6. C3×#63981C2semidirect
7. C3×#63959C2semidirect
8. #11723010C2semidirect
9. #11723009C2semidirect
10. #11723009C2semidirect
11. #11723007C2semidirect
12. #11723002C2semidirect
13. #11723001C2semidirect
14. #11722947C2semidirect
15. #11722947C2semidirect
19. C23×C3×C3⋊D3C22semidirect
20. C22×C3×D32C22semidirect
26. C2×#6293C22semidirect
27. C2×#6293C22semidirect
30. C2×C3×#627C22semidirect
33. #88864C22semidirect
34. C3×#3757C22semidirect
35. C32×#217C22semidirect
36. #88814C22semidirect
37. #88814C22semidirect
38. #88803C22semidirect
39. #88803C22semidirect
40. #88803C22semidirect
41. #88803C22semidirect
42. (C2×D3)⋊(C3⋊Dic3)C22semidirect
43. (C2×D3)⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3722C22semidirect
47. C3×#3722C22semidirect
48. C3×#3722C22semidirect
49. C3×(C2×D3)⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
63. #63983D3semidirect
65. #63981D3semidirect
83. #63959D3semidirect
138. C23×C3⋊D3C2×D3semidirect
144. C22×D32C2×D3semidirect
173. C2×#627C2×D3semidirect
198. #3757C2×D3semidirect
213. C3×#217C2×D3semidirect
214. C3×#217C2×D3semidirect
229. #3722C2×D3semidirect
230. #3722C2×D3semidirect
231. #3722C2×D3semidirect
254. (C2×D3)⋊Dic3C2×D3semidirect
255. (C2×D3)⋊Dic3C2×D3semidirect
256. (C2×D3)⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
264. Dic32C2×D3semidirect
574. #217D32semidirect
765. C33H(3,𝔽4)semidirect
1123. C32#5594semidirect
1124. C32#5594semidirect
1125. C32#5683semidirect
1241. C3#10594309semidirect
1242. C3#10595256semidirect
1243. C3#10595262semidirect

Maximal subgroups

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

subgroupindex
#117237272
#117236342
#117236002
#117235912
C3×#639832
C3×#639812
C3×#639592
#117230102
#117230092
#117230072
#117230022
#117230012
#117229472
#105952623
#105952563
#105943093