Finite Group Databasebeta

← #13170805

Subgroups — #13170805

Order 1728.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88961C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723683C211yesmaximal, characteristic, complemented
4#11723540C211yesmaximal, characteristic, complemented
5#11723495C211yesmaximal, characteristic, complemented
6#11723461C211yesmaximal, characteristic, complemented
7C3×#63898C211yesmaximal, characteristic, complemented
8C3×#63885C211yesmaximal, characteristic, complemented
9C3×#63854C211yesmaximal, characteristic, complemented
10#11722992C211yesmaximal, characteristic, complemented
11#11722975C211yesmaximal, characteristic, complemented
12#11722964C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722935C211yesmaximal, characteristic, complemented
15#11722924C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10594614—31nomaximal
18#10594267—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6293C2211yescharacteristic, complemented
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic, complemented
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88961—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3750C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×C4⋊Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic
46#88813C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51C3×#3724C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3805—31no—
58C2×#3804—31no—
59C2×C4×D32—31no—
60C2×C4×D32—31no—
61C2×#3795—31no—
62#64146—31no—
63#64105—31no—
64#64090—31no—
65C3×#939—31no—
66C3×D4×Dic3—31no—
67C3×#894—31no—
68C3×#893—31no—
69C3×#884—31no—
70C3×#883—31no—
71#63983—31no—
72#63981—31no—
73#63975—31no—
74#67⋊Dic3—31no—
75Dic3×#67—31no—
76#63964—31no—
77#63958—31no—
78#63958—31no—
79#63952—31no—
80#63922—31no—
81#63922—31no—
82#63922—31no—
83#63922—61no—
84#63912—31no—
85#63905—31no—
86#63905—31no—
87#63904—31no—
88#63898D311yescharacteristic, complemented
89#63896—31no—
90#63895—31no—
91#63895—31no—
92#63895—61no—
93#63885D311yescharacteristic, complemented
94#63881—31no—
95#63880—31no—
96#63880—31no—
97#63880—61no—
98#63879—31no—
99#63878—31no—
100#63877—31no—
101#63854D311yescharacteristic, complemented
102#63851—31no—
103#63836—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×D3×C3⋊D3—22no—
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C32×D12—22no—
123#6294D414yescomplemented
124#6293—22no—
125#6291—22no—
126#6291—22no—
127#6290—22no—
128#6289—22no—
129#6289—22no—
130D3×C3⋊Dic3—22no—
131C3×#626—22no—
132C3×#625—22no—
133C3×#625—22no—
134C3×#624—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5656—91no—
139#5606—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×C32×D4—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C22×C3⋊Dic3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×#634—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C2×C3×D12—21no—
162C2×C3×D12—31no—
163C2×C3×D12C2×D311yescharacteristic
164C2×C3×D12C2×D311yescharacteristic
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×#627—31no—
171C2×#627—31no—
172C2×#627—61no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626—61no—
179C2×#626C2×D311yescharacteristic
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—61no—
183C2×#625C2×D311yescharacteristic
184C2×#625C2×D311yescharacteristic, complemented
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—64no—
191C2×#624—61no—
192C2×#624—61no—
193C2×#624C2×D311yescharacteristic
194#3805—64no—
195#3804—64no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—61no—
201C2×D3×Dic3C2×D311yescharacteristic
202C2×D3×Dic3C2×D311yescharacteristic
203C2×D3×Dic3C2×D311yescharacteristic, complemented
204C4×D32—64no—
205C4×D32—64no—
206#3795—64no—
207C32×C4⋊C4—31no—
208C32×C22⋊C4—31no—
209#3757—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—61no—
215#3752—61no—
216#3752—61no—
217#3752—121no—
218#3752C2×D311yescharacteristic
219#3750—31no—
220#3750—31no—
221#3750C2×D311yescharacteristic, complemented
222C4×C3⋊Dic3C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—31no—
226C3×#217—31no—
227C3×(C2×D3)⋊C4—21no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—61no—
235C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
236C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
237C3×C4⋊Dic3—21no—
238C3×C4⋊Dic3C2×D311yescharacteristic, complemented
239C3×C4⋊Dic3C2×D311yescharacteristic, complemented
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—61no—
248#3724—31no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—61no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—61no—
267(C2×D3)⋊Dic3C2×D311yescharacteristic
268(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—31no—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)#4112yescomplemented
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3C2×D412yes—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3#4112yescomplemented
290D3×C3⋊D3—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3C2×D412yes—
297C3×C3⋊Dic3C2×D412yes—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C2×#237—91no—
302C2×#237—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#123—91no—
308C3×#121—91no—
309C3×C4×D4—91no—
310#939—31no—
311#938—91no—
312#937—91no—
313#937—91no—
314#937—91no—
315#937—91no—
316#937—181no—
317D4×Dic3—31no—
318D4×Dic3—91no—
319#929—91no—
320C4×#67—91no—
321C4×#67—91no—
322#924—91no—
323#897—91no—
324#896—91no—
325#896—91no—
326#896—91no—
327#896—181no—
328#894—31no—
329#893—31no—
330#893—91no—
331#892—91no—
332#884—31no—
333#884—91no—
334#884—91no—
335#883—31no—
336#883—91no—
337#883—91no—
338#882—91no—
339#882—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#67⋊C4—181no—
345#878—91no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—31no—
350C23×C32—31no—
351C23×C32—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—62no—
360C22×C3⋊D3—62no—
361C22×C3⋊D3—121no—
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—21no—
365C22×C3×D3—21no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—61no—
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—62no—
376C2×D32—62no—
377C2×D32—62no—
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—122no—
382C2×D32—122no—
383C2×D32—122no—
384C32×D4—62no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—21no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—41no—
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395#638—62no—
396#638—62no—
397#638—62no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—31no—
400C2×C3⋊Dic3—31no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—61no—
404C2×C3⋊Dic3—62no—
405C2×C3⋊Dic3—121no—
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C2×C3⋊Dic3C22×D311yescharacteristic
410C2×C3⋊Dic3C22×D311yescharacteristic
411C4×C3⋊D3—62no—
412C4×C3⋊D3—62no—
413#634—62no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—62no—
417C3×#67—62no—
418C3×#67—62no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—62no—
438C2×C3×Dic3—62no—
439C2×C3×Dic3—62no—
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C3×D12—22no—
447C3×D12—22no—
448C3×D12—42no—
449C3×D12—62no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×C4×D3—62no—
455#627—62no—
456#627—62no—
457#627—122no—
458#626—22no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—64no—
464#626—122no—
465#625—22no—
466#625—22no—
467#625—62no—
468#625—62no—
469#625—122no—
470#624—22no—
471#624—34no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—122no—
477#624—122no—
478D3×Dic3—22no—
479D3×Dic3—22no—
480D3×Dic3—22no—
481D3×Dic3—34no—
482D3×Dic3—34no—
483D3×Dic3—62no—
484D3×Dic3—62no—
485D3×Dic3—122no—
486#525—271noSylow
487C2×C33C22×D411yescharacteristic
488C2×C33C2×#4111yescharacteristic
489C2×C33C2×#4111yescharacteristic
490C3⋊(C3⋊D3)—22no—
491C3×C3⋊D3—22no—
492C32×D3—22no—
493C32×D3—41no—
494C32×D3—41no—
495C23×D3—91no—
496C23×D3—91no—
497C23×D3—91no—
498C23×D3—181no—
499C2×C3×D4—31no—
500C2×C3×D4—31no—
501C2×C3×D4—61no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C2×C3×D4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C22×C3×C4—91no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—181no—
522C2×#67—181no—
523C2×#67—181no—
524C22×Dic3—31no—
525C22×Dic3—31no—
526C22×Dic3—31no—
527C22×Dic3—91no—
528C22×Dic3—91no—
529C22×Dic3—91no—
530C22×Dic3—181no—
531#237—184no—
532#237—184no—
533#235—184no—
534C2×D12—31no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12D3211yescharacteristic
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—31no—
541C2×C4×D3—31no—
542C2×C4×D3—31no—
543C2×C4×D3—91no—
544C2×C4×D3—91no—
545C2×C4×D3—91no—
546C2×C4×D3—91no—
547C2×C4×D3—91no—
548C2×C4×D3—91no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
551C2×C4×D3—91no—
552C2×C4×D3—181no—
553C2×C4×D3—181no—
554C2×C4×D3—184no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×Dic6—91no—
558C2×Dic6—91no—
559C2×Dic6—91no—
560C2×Dic6—181no—
561C3×C4⋊C4—31no—
562C3×C4⋊C4—31no—
563C3×C4⋊C4—61no—
564C3×C4⋊C4—91no—
565C3×C4⋊C4—91no—
566C3×C22⋊C4—31no—
567C3×C22⋊C4—31no—
568C3×C22⋊C4—61no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571C3×C22⋊C4—91no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C42—91no—
575#217—31no—
576#217—31no—
577#217—31no—
578#217—31no—
579#217—91no—
580#217—91no—
581#217—91no—
582#217—181no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—61no—
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—
603(C2×D3)⋊C4—361no—
604(C2×D3)⋊C4D3211yescharacteristic, complemented
605C4⋊Dic3—91no—
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608C4⋊Dic3D3211yescharacteristic, complemented
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—31no—
612Dic3⋊C4—31no—
613Dic3⋊C4—61no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—181no—
621Dic3⋊C4—181no—
622C4×Dic3—31no—
623C4×Dic3—31no—
624C4×Dic3—61no—
625C4×Dic3—91no—
626C4×Dic3—91no—
627C4×Dic3—91no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—32no—
632C22×C32—41no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32C23×D311yescharacteristic
642C22×C32C23×D311yescharacteristic
643C22×C32C23×D311yescharacteristic
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—32no—
647C2×C3⋊D3—32no—
648C2×C3⋊D3—32no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—62no—
651C2×C3⋊D3—62no—
652C2×C3⋊D3—68no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—122no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—121no—
664C2×C3⋊D3—121no—
665C2×C3⋊D3—121no—
666C2×C3⋊D3—241no—
667C2×C3⋊D3—241no—
668C2×C3⋊D3D3×D412yes—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—22no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—21no—
678C2×C3×D3—21no—
679C2×C3×D3—21no—
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—22no—
687C2×C3×D3—32no—
688C2×C3×D3—32no—
689C2×C3×D3—41no—
690C2×C3×D3—41no—
691C2×C3×D3—41no—
692C2×C3×D3—41no—
693C2×C3×D3—41no—
694C2×C3×D3—41no—
695C2×C3×D3—41no—
696C2×C3×D3—62no—
697C2×C3×D3—61no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—121no—
702C2×C3×D3—121no—
703C2×C3×D3#23512yescomplemented
704C2×C3×D3#23712yescomplemented
705D32—68no—
706D32—68no—
707D32—128no—
708C32×C4—21no—
709C32×C4—21no—
710C32×C4—21no—
711C32×C4—41no—
712C32×C4—41no—
713C32×C4—41no—
714C32×C4—61no—
715C32×C4—61no—
716C32×C4—61no—
717C32×C4—81no—
718C3⋊Dic3—21no—
719C3⋊Dic3—21no—
720C3⋊Dic3—21no—
721C3⋊Dic3—61no—
722C3⋊Dic3—61no—
723C3⋊Dic3—61no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—121no—
727C3⋊Dic3—241no—
728C3⋊Dic3D3×D412yes—
729C3⋊Dic3D3×D412yes—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—32no—
737C3×Dic3—32no—
738C3×Dic3—32no—
739C3×Dic3—32no—
740C3×Dic3—41no—
741C3×Dic3—41no—
742C3×Dic3—41no—
743C3×Dic3—62no—
744C3×Dic3—62no—
745C3×Dic3—62no—
746C3×Dic3—61no—
747C3×Dic3—61no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—121no—
753C3×Dic3—121no—
754C2×#41—271no—
755C23×C4—271no—
756#123—91no—
757#123—271no—
758C22⋊Q8—271no—
759C22⋊Q8—271no—
760#121—91no—
761#121—271no—
762#120—271no—
763#120—271no—
764C4×D4—91no—
765C4×D4—271no—
766C4×D4—271no—
767C4×D4—271no—
768#117—271no—
769C33#52511yescharacteristic, complemented, Sylow
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—31no—
773C23×C3—31no—
774C23×C3—31no—
775C23×C3—31no—
776C23×C3—61no—
777C23×C3—61no—
778C23×C3—61no—
779C23×C3—91no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—91no—
784C22×D3—91no—
785C22×D3—91no—
786C22×D3—181no—
787C22×D3—181no—
788C22×D3—181no—
789C22×D3—182no—
790C22×D3—182no—
791C22×D3—182no—
792C22×D3—182no—
793C22×D3—182no—
794C22×D3—182no—
795C22×D3—182no—
796C22×D3—182no—
797C22×D3—182no—
798C22×D3—361no—
799C22×D3—362no—
800C22×D3—362no—
801C22×D3—362no—
802C22×D3C2×D3211yescharacteristic
803C22×D3C2×D3211yescharacteristic
804C22×D3C2×D3211yescharacteristic
805C3×D4—62no—
806C3×D4—62no—
807C3×D4—122no—
808C3×D4—182no—
809C3×D4—182no—
810C3×D4—182no—
811C2×C3×C4—21no—
812C2×C3×C4—21no—
813C2×C3×C4—21no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—31no—
819C2×C3×C4—31no—
820C2×C3×C4—41no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—91no—
825C2×C3×C4—91no—
826C2×C3×C4—91no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—182no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4—182no—
833C2×C3×C4C2×D3211yescharacteristic
834C2×C3×C4C2×D3211yescharacteristic
835C2×C3×C4C2×D3211yescharacteristic
836#67—62no—
837#67—62no—
838#67—62no—
839#67—62no—
840#67—62no—
841#67—182no—
842#67—182no—
843#67—182no—
844#67—182no—
845#67—184no—
846#67—182no—
847#67—182no—
848#67—182no—
849#67—362no—
850#67—362no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—31no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—61no—
864C2×Dic3—61no—
865C2×Dic3—61no—
866C2×Dic3—62no—
867C2×Dic3—62no—
868C2×Dic3—62no—
869C2×Dic3—94no—
870C2×Dic3—91no—
871C2×Dic3—91no—
872C2×Dic3—91no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—181no—
876C2×Dic3—182no—
877C2×Dic3—182no—
878C2×Dic3—361no—
879C2×Dic3—362no—
880C2×Dic3C2×D3211yescharacteristic
881C2×Dic3C2×D3211yescharacteristic
882C2×Dic3C2×D3211yescharacteristic
883D12—22no—
884D12—62no—
885D12—182no—
886D12—182no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—62no—
890C4×D3—62no—
891C4×D3—62no—
892C4×D3—94no—
893C4×D3—94no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—182no—
901C4×D3—362no—
902C4×D3—362no—
903Dic6—182no—
904Dic6—182no—
905Dic6—182no—
906Dic6—362no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—21no—
912C2×C32—21no—
913C2×C32—21no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—41no—
917C2×C32—41no—
918C2×C32—41no—
919C2×C32—62no—
920C2×C32—121no—
921C2×C32—121no—
922C2×C32C2×#23511yescharacteristic
923C2×C32C2×D3×D411yescharacteristic
924C2×C32C2×D3×D411yescharacteristic
925C2×C32C2×D3×D411yescharacteristic
926C2×C32C2×#23711yescharacteristic
927C2×C32D3×#4111yescharacteristic
928C2×C32D3×#4111yescharacteristic
929C2×C32D3×#4111yescharacteristic
930C2×C32D3×#4111yescharacteristic
931C3⋊D3—22no—
932C3⋊D3—62no—
933C3⋊D3—62no—
934C3⋊D3—62no—
935C3⋊D3—122no—
936C3⋊D3—122no—
937C3⋊D3—122no—
938C3⋊D3—242no—
939C3×D3—22no—
940C3×D3—22no—
941C3×D3—42no—
942C3×D3—42no—
943C3×D3—41no—
944C3×D3—41no—
945C3×D3—41no—
946C3×D3—41no—
947C3×D3—62no—
948C3×D3—62no—
949C3×D3—81no—
950C3×D3—122no—
951C24—271no—
952#41—544no—
953C2×Q8—271no—
954C2×D4—31no—
955C2×D4—91no—
956C2×D4—91no—
957C2×D4—91no—
958C2×D4—271no—
959C2×D4—271no—
960C2×D4—271no—
961C22×C4—91no—
962C22×C4—91no—
963C22×C4—91no—
964C22×C4—91no—
965C22×C4—271no—
966C22×C4—271no—
967C22×C4—271no—
968C22×C4—271no—
969C22×C4—544no—
970C4⋊C4—31no—
971C4⋊C4—91no—
972C4⋊C4—91no—
973C4⋊C4—271no—
974C4⋊C4—271no—
975C4⋊C4—271no—
976C22⋊C4—31no—
977C22⋊C4—91no—
978C22⋊C4—91no—
979C22⋊C4—91no—
980C22⋊C4—91no—
981C22⋊C4—91no—
982C22⋊C4—271no—
983C22⋊C4—271no—
984C22⋊C4—271no—
985C22⋊C4—271no—
986C42—91no—
987C42—271no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—32no—
992C22×C3—32no—
993C22×C3—41no—
994C22×C3—62no—
995C22×C3—62no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—61no—
1000C22×C3—61no—
1001C22×C3—61no—
1002C22×C3—61no—
1003C22×C3—61no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—92no—
1013C22×C3—121no—
1014C22×C3—121no—
1015C22×C3—121no—
1016C22×C3—121no—
1017C22×C3—121no—
1018C22×C3—121no—
1019C22×C3—121no—
1020C22×C3—181no—
1021C22×C3—181no—
1022C22×C3C22×D3211yescharacteristic
1023C22×C3C22×D3211yescharacteristic
1024C22×C3C22×D3211yescharacteristic
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—21no—
1028C2×D3—21no—
1029C2×D3—21no—
1030C2×D3—21no—
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—32no—
1034C2×D3—32no—
1035C2×D3—62no—
1036C2×D3—61no—
1037C2×D3—61no—
1038C2×D3—61no—
1039C2×D3—61no—
1040C2×D3—92no—
1041C2×D3—92no—
1042C2×D3—92no—
1043C2×D3—121no—
1044C2×D3—121no—
1045C2×D3—182no—
1046C2×D3—182no—
1047C2×D3—182no—
1048C2×D3—188no—
1049C2×D3—188no—
1050C2×D3—188no—
1051C2×D3—181no—
1052C2×D3—181no—
1053C2×D3—181no—
1054C2×D3—181no—
1055C2×D3—181no—
1056C2×D3—181no—
1057C2×D3—362no—
1058C2×D3—368no—
1059C2×D3—361no—
1060C2×D3—361no—
1061C2×D3—361no—
1062C2×D3—361no—
1063C2×D3—361no—
1064C2×D3—361no—
1065C2×D3—721no—
1066C2×D3—721no—
1067C2×D3#380412yescomplemented
1068C3×C4—21no—
1069C3×C4—21no—
1070C3×C4—21no—
1071C3×C4—41no—
1072C3×C4—41no—
1073C3×C4—41no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—61no—
1078C3×C4—61no—
1079C3×C4—61no—
1080C3×C4—81no—
1081C3×C4—92no—
1082C3×C4—92no—
1083C3×C4—121no—
1084C3×C4—121no—
1085C3×C4—121no—
1086C3×C4—181no—
1087C3×C4—181no—
1088C3×C4—181no—
1089Dic3—21no—
1090Dic3—21no—
1091Dic3—21no—
1092Dic3—32no—
1093Dic3—32no—
1094Dic3—32no—
1095Dic3—32no—
1096Dic3—62no—
1097Dic3—62no—
1098Dic3—62no—
1099Dic3—61no—
1100Dic3—61no—
1101Dic3—61no—
1102Dic3—61no—
1103Dic3—61no—
1104Dic3—61no—
1105Dic3—121no—
1106Dic3—121no—
1107Dic3—181no—
1108Dic3—181no—
1109Dic3—181no—
1110Dic3—361no—
1111Dic3—361no—
1112Dic3—361no—
1113Dic3—721no—
1114C32—21no—
1115C32—21no—
1116C32—21no—
1117C32—41no—
1118C32#554711yescharacteristic, complemented
1119C32#560611yescharacteristic, complemented
1120C32#565611yescharacteristic, complemented
1121C23—31no—
1122C23—31no—
1123C23—31no—
1124C23—91no—
1125C23—271no—
1126C23—542no—
1127C23—542no—
1128C23—542no—
1129Q8—542no—
1130D4—62no—
1131D4—182no—
1132D4—182no—
1133D4—182no—
1134D4—542no—
1135D4—542no—
1136D4—542no—
1137C2×C4—31no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—91no—
1141C2×C4—91no—
1142C2×C4—91no—
1143C2×C4—91no—
1144C2×C4—91no—
1145C2×C4—182no—
1146C2×C4—182no—
1147C2×C4—182no—
1148C2×C4—182no—
1149C2×C4—274no—
1150C2×C4—271no—
1151C2×C4—542no—
1152C2×C4—542no—
1153C2×C4—542no—
1154C2×C4D3311yescharacteristic
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—21no—
1162C2×C3—21no—
1163C2×C3—21no—
1164C2×C3—41no—
1165C2×C3—41no—
1166C2×C3—41no—
1167C2×C3—62no—
1168C2×C3—62no—
1169C2×C3—122no—
1170C2×C3—122no—
1171C2×C3—121no—
1172C2×C3—121no—
1173C2×C3—121no—
1174C2×C3—121no—
1175C2×C3—182no—
1176C2×C3—241no—
1177C2×C3D3×#23511yescharacteristic
1178C2×C3#6430611yescharacteristic
1179C2×C3D32×D411yescharacteristic
1180C2×C3D32×D411yescharacteristic
1181C2×C3D32×D411yescharacteristic
1182C2×C3D3×#23711yescharacteristic
1183C2×C3#6431211yescharacteristic
1184C2×C3#6431911yescharacteristic
1185C2×C3C2×#380411yescharacteristic
1186D3—22no—
1187D3—41no—
1188D3—41no—
1189D3—62no—
1190D3—62no—
1191D3—122no—
1192D3—182no—
1193D3—182no—
1194D3—182no—
1195D3—362no—
1196D3—362no—
1197D3—362no—
1198D3—722no—
1199C22—32no—
1200C22—61no—
1201C22—61no—
1202C22—61no—
1203C22—61no—
1204C22—61no—
1205C22—61no—
1206C22—61no—
1207C22—61no—
1208C22—92no—
1209C22—181no—
1210C22—181no—
1211C22—272no—
1212C22—548no—
1213C22—541no—
1214C22—541no—
1215C22C2×D3311yescharacteristic
1216C4—21no—
1217C4—61no—
1218C4—61no—
1219C4—61no—
1220C4—92no—
1221C4—92no—
1222C4—181no—
1223C4—181no—
1224C4—181no—
1225C4—541no—
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059426711yescharacteristic, complemented
1231C3#1059461411yescharacteristic, complemented
1232C3#1059513811yescharacteristic, complemented
1233C2—62no—
1234C2—121no—
1235C2—121no—
1236C2—182no—
1237C2—542no—
1238C2#1172437611yescharacteristic
1239C2#1172440311yescharacteristic
1240C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88961C2semidirect
2. C2×D3×#624C2semidirect
3. #11723683C2semidirect
4. #11723540C2semidirect
5. #11723495C2semidirect
6. #11723461C2semidirect
7. C3×#63898C2semidirect
8. C3×#63885C2semidirect
9. C3×#63854C2semidirect
10. #11722992C2semidirect
11. #11722975C2semidirect
12. #11722964C2semidirect
13. #11722949C2semidirect
14. #11722935C2semidirect
15. #11722924C2semidirect
22. C2×#6293C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
31. C2×C3×#625C22semidirect
35. C2×C3×D3×Dic3C22semidirect
40. C3×#3750C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×C4⋊Dic3C22semidirect
44. #88815C22semidirect
46. #88813C22semidirect
47. #88807C22semidirect
48. #88807C22semidirect
51. C3×#3724C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
88. #63898D3semidirect
93. #63885D3semidirect
101. #63854D3semidirect
123. #6294D4semidirect
184. C2×#625C2×D3semidirect
203. C2×D3×Dic3C2×D3semidirect
221. #3750C2×D3semidirect
222. C4×C3⋊Dic3C2×D3semidirect
235. C3×(C2×D3)⋊C4C2×D3semidirect
236. C3×(C2×D3)⋊C4C2×D3semidirect
238. C3×C4⋊Dic3C2×D3semidirect
239. C3×C4⋊Dic3C2×D3semidirect
249. #3724C2×D3semidirect
268. (C2×D3)⋊Dic3C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
277. C2×C3⋊(C3⋊D3)#41semidirect
289. C2×C32×D3#41semidirect
604. (C2×D3)⋊C4D32semidirect
608. C4⋊Dic3D32semidirect
703. C2×C3×D3#235semidirect
704. C2×C3×D3#237semidirect
769. C33#525semidirect
1067. C2×D3#3804semidirect
1118. C32#5547semidirect
1119. C32#5606semidirect
1120. C32#5656semidirect
1230. C3#10594267semidirect
1231. C3#10594614semidirect
1232. C3#10595138semidirect

Maximal subgroups

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

subgroupindex
C2×#889612
C2×D3×#6242
#117236832
#117235402
#117234952
#117234612
C3×#638982
C3×#638852
C3×#638542
#117229922
#117229752
#117229642
#117229492
#117229352
#117229242
#105951383
#105946143
#105942673