Finite Group Databasebeta

← #13170758

Subgroups — #13170758

Order 1728.

1726 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89015C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723688C211yesmaximal, characteristic, complemented
4#11723472C211yesmaximal, characteristic, complemented
5#11723462C211yesmaximal, characteristic, complemented
6C3×#63922C211yesmaximal, characteristic, complemented
7C3×#63896C211yesmaximal, characteristic, complemented
8C3×#63884C211yesmaximal, characteristic, complemented
9#11722987C211yesmaximal, characteristic, complemented
10#11722966C211yesmaximal, characteristic, complemented
11#11722958C211yesmaximal, characteristic, complemented
12#11722948C211yesmaximal, characteristic, complemented
13#11722929C211yesmaximal, characteristic, complemented
14#11722925C211yesmaximal, characteristic, complemented
15#11722917C211yesmaximal, characteristic, complemented
16#10595160—31nomaximal
17#10594615—31nomaximal
18#10594055—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×#634C2211yescharacteristic, complemented
22C2×C32×D12C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
32#89015—24no—
33C2×C3×#626C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37D32×Dic3—24no—
38C3×#3752C2211yescharacteristic
39C3×#3750C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3830—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59C2×C4×D32—31no—
60C2×#3796—31no—
61C2×#3796—31no—
62C2×#3796—61no—
63#64102—31no—
64#64090—31no—
65C3×#937—31no—
66C3×#935—31no—
67C3×#896—31no—
68C3×#894—31no—
69C3×#882—31no—
70C3×#878—31no—
71#63978—31no—
72#63977—31no—
73#63977—31no—
74#67⋊Dic3—31no—
75#67⋊Dic3—31no—
76#67⋊Dic3—31no—
77#63971—31no—
78#63971—31no—
79#63966—31no—
80#63957—31no—
81#63923—31no—
82#63922D311yescharacteristic, complemented
83#63910—31no—
84#63906—31no—
85#63902—31no—
86#63898—31no—
87#63896—31no—
88#63896D311yescharacteristic, complemented
89#63890—31no—
90#63888—31no—
91#63887—31no—
92#63886—31no—
93#63884D311yescharacteristic, complemented
94#63881—31no—
95#63881—31no—
96#63881—31no—
97#63881—31no—
98#63881—31no—
99#63881—61no—
100#63881—61no—
101#63878—31no—
102#63878—31no—
103#63850—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3×D32—22no—
110C2×C3×D32—22no—
111C2×C3×D32—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊(C3⋊D3)—22no—
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C3×#634—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×D12—22no—
125#6294—22no—
126#6292—22no—
127#6291—22no—
128#6291—22no—
129#6291—22no—
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132D3×C3⋊Dic3—22no—
133D3×C3⋊Dic3D414yescomplemented
134C3×#626—22no—
135C3×#625—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5656—91no—
139#5627—91no—
140#5586—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C22×D32C2×D311yescharacteristic
144C2×C32×D4—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3—31no—
150C22×C3⋊Dic3—31no—
151#3830—64no—
152C2×C4⋊(C3⋊D3)—31no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—31no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—61no—
158C2×C4×C3⋊D3—61no—
159C2×C4×C3⋊D3—61no—
160C2×C4×C3⋊D3—121no—
161C2×#634C2×D311yescharacteristic, complemented
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C2×C3×D12—21no—
168C2×C3×D12—31no—
169C2×C3×D12C2×D311yescharacteristic
170C2×C3×D12C2×D311yescharacteristic
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×Dic6—31no—
174C2×C3×Dic6—31no—
175C2×C3×Dic6—61no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—61no—
185C2×#626—61no—
186C2×#626—61no—
187C2×#626—61no—
188C2×#626C2×D311yescharacteristic
189C2×#625C2×D311yescharacteristic
190C2×#624—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—64no—
202C2×D3×Dic3—64no—
203C2×D3×Dic3—61no—
204C2×D3×Dic3—61no—
205C2×D3×Dic3—61no—
206C2×D3×Dic3—61no—
207C2×D3×Dic3C2×D311yescharacteristic
208C2×D3×Dic3C2×D311yescharacteristic
209C4×D32—64no—
210#3796—64no—
211#3796—64no—
212#3796—68no—
213C32×C4⋊C4—31no—
214C32×C22⋊C4—31no—
215#3752—31no—
216#3752—31no—
217#3752C2×D311yescharacteristic
218#3750C2×D311yescharacteristic, complemented
219C4×C3⋊Dic3—31no—
220C4×C3⋊Dic3—31no—
221C3×#217—31no—
222C3×#217—31no—
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—31no—
226C3×(C2×D3)⋊C4—21no—
227C3×(C2×D3)⋊C4—31no—
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
236C3×(C2×D3)⋊C4C2×D311yescharacteristic
237C3×C4⋊Dic3—31no—
238C3×Dic3⋊C4—21no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×Dic3⋊C4C2×D311yescharacteristic, complemented
246C3×Dic3⋊C4C2×D311yescharacteristic, complemented
247#3724—31no—
248#3724—31no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—61no—
261#3722—61no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3C2×D311yescharacteristic
265(C2×D3)⋊Dic3C2×D311yescharacteristic
266(C2×D3)⋊Dic3C2×D311yescharacteristic
267(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
268(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
269Dic32—31no—
270Dic32—31no—
271Dic32—31no—
272Dic32—31no—
273Dic32—61no—
274Dic32—61no—
275C22×C33C2411yescharacteristic
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)—21no—
278C2×C3⋊(C3⋊D3)—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3#4112yescomplemented
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×D3C2×D412yes—
290C2×C32×D3#4112yescomplemented
291C3×D32—28no—
292C33×C4—21no—
293C3⋊(C3⋊Dic3)C2×D412yes—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C3×C3⋊Dic3—21no—
298C3×C3⋊Dic3C2×D412yes—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3—21no—
302C23×Dic3—91no—
303C2×#239—91no—
304C2×#237—91no—
305C2×#237—91no—
306C2×#237—181no—
307C22×C4×D3—91no—
308C22×C4×D3—91no—
309C3×#123—91no—
310C3×C22⋊Q8—91no—
311C3×#120—91no—
312#953—91no—
313#946—91no—
314#939—91no—
315#939—91no—
316#937—31no—
317#935—31no—
318D4×Dic3—91no—
319D4×Dic3—91no—
320#930—91no—
321#929—91no—
322#896—31no—
323#896—91no—
324#895—91no—
325#894—31no—
326#894—91no—
327#893—91no—
328#893—91no—
329#893—91no—
330#893—91no—
331#893—181no—
332#892—91no—
333#886—91no—
334#884—91no—
335#884—91no—
336#882—31no—
337#882—91no—
338#882—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#67⋊C4—91no—
345#67⋊C4—181no—
346#878—31no—
347#878—91no—
348#877—91no—
349#877—91no—
350C23×C32—31no—
351C23×C32—31no—
352C23×C32—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—31no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—121no—
360C22×C3⋊D3C22×D311yescharacteristic
361C22×C3×D3—21no—
362C22×C3×D3—21no—
363C22×C3×D3—21no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—61no—
367C22×C3×D3—62no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3—62no—
371C22×C3×D3—62no—
372C22×C3×D3—62no—
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C22×C3×D3C22×D311yescharacteristic
379C2×D32—22no—
380C2×D32—22no—
381C2×D32—22no—
382C32×D4—62no—
383C2×C32×C4—21no—
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—41no—
390C2×C32×C4C22×D311yescharacteristic
391C2×C32×C4C22×D311yescharacteristic
392C2×C32×C4C22×D311yescharacteristic
393#638—62no—
394#638—62no—
395#638—62no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—34no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—62no—
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—
413C4×C3⋊D3—62no—
414C4×C3⋊D3—62no—
415C4×C3⋊D3—62no—
416C4×C3⋊D3—64no—
417C4×C3⋊D3—122no—
418C4×C3⋊D3—122no—
419C4×C3⋊D3—124no—
420#634—22no—
421C3×#67—62no—
422C3×#67—62no—
423C3×#67—62no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C3×D12—24no—
451C3×D12—22no—
452C3×D12—22no—
453C3×D12—62no—
454C3×C4×D3—62no—
455C3×C4×D3—62no—
456C3×Dic6—62no—
457C3×Dic6—62no—
458C3×Dic6—64no—
459#626—22no—
460#626—62no—
461#626—62no—
462#626—64no—
463#626—62no—
464#626—62no—
465#626—64no—
466#626—64no—
467#626—64no—
468#626—62no—
469#626—62no—
470#626—62no—
471#626—62no—
472#625—22no—
473#624—62no—
474D3×Dic3—22no—
475D3×Dic3—22no—
476D3×Dic3—34no—
477D3×Dic3—34no—
478D3×Dic3—64no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484D3×Dic3—62no—
485D3×Dic3—62no—
486D3×Dic3—64no—
487D3×Dic3—62no—
488D3×Dic3—122no—
489D3×Dic3—122no—
490#525—271noSylow
491C2×C33C22×D411yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C2×C33C2×#4111yescharacteristic
494C3⋊(C3⋊D3)—41no—
495C3×C3⋊D3—22no—
496C32×D3—22no—
497C32×D3—22no—
498C32×D3—41no—
499C24×C3—91no—
500C23×D3—31no—
501C23×D3—31no—
502C2×C3×Q8—91no—
503C2×C3×D4—31no—
504C2×C3×D4—31no—
505C2×C3×D4—61no—
506C2×C3×D4—91no—
507C2×C3×D4—91no—
508C22×C3×C4—91no—
509C22×C3×C4—91no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—181no—
521C2×#67—181no—
522C2×#67—181no—
523C22×Dic3—31no—
524C22×Dic3—31no—
525C22×Dic3—91no—
526C22×Dic3—91no—
527C22×Dic3—91no—
528C22×Dic3—91no—
529C22×Dic3—91no—
530C22×Dic3—91no—
531C22×Dic3—91no—
532C22×Dic3—91no—
533C22×Dic3—181no—
534C22×Dic3—181no—
535C22×Dic3—181no—
536C22×Dic3—184no—
537#239—184no—
538#237—184no—
539#237—184no—
540#237—188no—
541C2×D12—31no—
542C2×D12—91no—
543C2×D12—91no—
544C2×D12—91no—
545C2×D12—91no—
546C2×D12—91no—
547C2×D12—181no—
548C2×D12D3211yescharacteristic
549C2×C4×D3—31no—
550C2×C4×D3—31no—
551C2×C4×D3—91no—
552C2×C4×D3—91no—
553C2×C4×D3—91no—
554C2×C4×D3—91no—
555C2×C4×D3—91no—
556C2×C4×D3—91no—
557C2×C4×D3—91no—
558C2×C4×D3—91no—
559C2×C4×D3—91no—
560C2×C4×D3—91no—
561C2×C4×D3—181no—
562C2×C4×D3—181no—
563C2×C4×D3—181no—
564C2×C4×D3—181no—
565C2×C4×D3—184no—
566C2×C4×D3—184no—
567C2×C4×D3—361no—
568C2×Dic6—31no—
569C2×Dic6—31no—
570C2×Dic6—61no—
571C3×C4⋊C4—31no—
572C3×C4⋊C4—31no—
573C3×C4⋊C4—61no—
574C3×C4⋊C4—91no—
575C3×C4⋊C4—91no—
576C3×C4⋊C4—91no—
577C3×C22⋊C4—31no—
578C3×C22⋊C4—31no—
579C3×C22⋊C4—61no—
580C3×C22⋊C4—91no—
581C3×C22⋊C4—91no—
582C3×C22⋊C4—91no—
583C3×C22⋊C4—91no—
584C3×C22⋊C4—91no—
585C3×C22⋊C4—91no—
586#217—31no—
587#217—31no—
588#217—31no—
589#217—31no—
590#217—31no—
591#217—91no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—31no—
596(C2×D3)⋊C4—31no—
597(C2×D3)⋊C4—31no—
598(C2×D3)⋊C4—31no—
599(C2×D3)⋊C4—61no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—91no—
607(C2×D3)⋊C4—91no—
608(C2×D3)⋊C4—181no—
609(C2×D3)⋊C4—181no—
610(C2×D3)⋊C4D3211yescharacteristic
611C4⋊Dic3—31no—
612C4⋊Dic3—91no—
613C4⋊Dic3—91no—
614Dic3⋊C4—31no—
615Dic3⋊C4—31no—
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—31no—
619Dic3⋊C4—61no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623Dic3⋊C4—91no—
624Dic3⋊C4D3211yescharacteristic, complemented
625C4×Dic3—91no—
626C4×Dic3—91no—
627C4×Dic3—91no—
628C4×Dic3—91no—
629C4×Dic3—91no—
630C4×Dic3—91no—
631C4×Dic3—181no—
632C4×Dic3—181no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—32no—
637C22×C32—32no—
638C22×C32—41no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—61no—
645C22×C32—61no—
646C22×C32C23×D311yescharacteristic
647C22×C32C23×D311yescharacteristic
648C22×C32C23×D311yescharacteristic
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—62no—
655C2×C3⋊D3—62no—
656C2×C3⋊D3—62no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—61no—
661C2×C3⋊D3—61no—
662C2×C3⋊D3—61no—
663C2×C3⋊D3—121no—
664C2×C3⋊D3—121no—
665C2×C3⋊D3—121no—
666C2×C3⋊D3—121no—
667C2×C3⋊D3—121no—
668C2×C3⋊D3—121no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—122no—
671C2×C3⋊D3—122no—
672C2×C3⋊D3#23712yescomplemented
673C2×C3×D3—21no—
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—22no—
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—22no—
689C2×C3×D3—22no—
690C2×C3×D3—32no—
691C2×C3×D3—32no—
692C2×C3×D3—41no—
693C2×C3×D3—41no—
694C2×C3×D3—41no—
695C2×C3×D3—41no—
696C2×C3×D3—41no—
697C2×C3×D3—41no—
698C2×C3×D3—62no—
699C2×C3×D3—68no—
700C2×C3×D3—68no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—121no—
706C2×C3×D3—121no—
707C2×C3×D3D3×D412yes—
708C2×C3×D3D3×D412yes—
709C2×C3×D3#23712yescomplemented
710C2×C3×D3#23912yescomplemented
711D32—28no—
712C32×C4—21no—
713C32×C4—22no—
714C32×C4—21no—
715C32×C4—21no—
716C32×C4—41no—
717C32×C4—41no—
718C32×C4—42no—
719C32×C4—61no—
720C32×C4—61no—
721C32×C4—61no—
722C3⋊Dic3—21no—
723C3⋊Dic3—21no—
724C3⋊Dic3—21no—
725C3⋊Dic3—21no—
726C3⋊Dic3—32no—
727C3⋊Dic3—32no—
728C3⋊Dic3—32no—
729C3⋊Dic3—62no—
730C3⋊Dic3—62no—
731C3⋊Dic3—62no—
732C3⋊Dic3—122no—
733C3⋊Dic3D3×D412yes—
734C3×Dic3—22no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—32no—
742C3×Dic3—32no—
743C3×Dic3—41no—
744C3×Dic3—41no—
745C3×Dic3—62no—
746C3×Dic3—62no—
747C3×Dic3—62no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—121no—
757C3×Dic3—121no—
758C2×#41—271no—
759C23×C4—271no—
760#123—91no—
761#123—271no—
762C22⋊Q8—91no—
763C22⋊Q8—271no—
764#121—271no—
765#121—271no—
766#120—91no—
767#120—271no—
768C4×D4—271no—
769C4×D4—271no—
770C4×D4—271no—
771C4×D4—271no—
772#117—271no—
773C33#52511yescharacteristic, complemented, Sylow
774C23×C3—31no—
775C23×C3—31no—
776C23×C3—31no—
777C23×C3—31no—
778C23×C3—31no—
779C23×C3—31no—
780C23×C3—61no—
781C23×C3—61no—
782C23×C3—61no—
783C23×C3—91no—
784C23×C3—182no—
785C23×C3—182no—
786C23×C3—182no—
787C22×D3—31no—
788C22×D3—31no—
789C22×D3—61no—
790C22×D3—62no—
791C22×D3—62no—
792C22×D3—62no—
793C22×D3—62no—
794C22×D3—62no—
795C22×D3—62no—
796C22×D3—91no—
797C22×D3—91no—
798C22×D3—91no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—181no—
802C22×D3—361no—
803C22×D3C2×D3211yescharacteristic
804C22×D3C2×D3211yescharacteristic
805C22×D3C2×D3211yescharacteristic
806C3×Q8—182no—
807C3×D4—62no—
808C3×D4—62no—
809C3×D4—64no—
810C3×D4—182no—
811C3×D4—182no—
812C2×C3×C4—21no—
813C2×C3×C4—21no—
814C2×C3×C4—21no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—31no—
819C2×C3×C4—31no—
820C2×C3×C4—31no—
821C2×C3×C4—41no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—61no—
825C2×C3×C4—91no—
826C2×C3×C4—91no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—91no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4C2×D3211yescharacteristic
833C2×C3×C4C2×D3211yescharacteristic
834C2×C3×C4C2×D3211yescharacteristic
835#67—62no—
836#67—62no—
837#67—62no—
838#67—182no—
839#67—182no—
840#67—182no—
841#67—182no—
842#67—182no—
843#67—182no—
844#67—182no—
845#67—184no—
846#67—184no—
847#67—184no—
848C2×Dic3—31no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—61no—
859C2×Dic3—61no—
860C2×Dic3—61no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—62no—
864C2×Dic3—62no—
865C2×Dic3—94no—
866C2×Dic3—94no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—91no—
870C2×Dic3—184no—
871C2×Dic3—181no—
872C2×Dic3—181no—
873C2×Dic3—181no—
874C2×Dic3—182no—
875C2×Dic3—182no—
876C2×Dic3—182no—
877C2×Dic3—182no—
878C2×Dic3—182no—
879C2×Dic3—182no—
880C2×Dic3—184no—
881C2×Dic3—361no—
882C2×Dic3—362no—
883C2×Dic3C2×D3211yescharacteristic
884C2×Dic3C2×D3211yescharacteristic
885C2×Dic3C2×D3211yescharacteristic
886D12—22no—
887D12—62no—
888D12—182no—
889D12—182no—
890D12—184no—
891D12—182no—
892D12—182no—
893D12—182no—
894C4×D3—62no—
895C4×D3—62no—
896C4×D3—94no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—182no—
901C4×D3—182no—
902C4×D3—182no—
903C4×D3—182no—
904C4×D3—182no—
905C4×D3—182no—
906C4×D3—184no—
907C4×D3—362no—
908C4×D3—362no—
909C4×D3—362no—
910C4×D3—364no—
911Dic6—62no—
912Dic6—62no—
913Dic6—64no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—21no—
917C2×C32—21no—
918C2×C32—21no—
919C2×C32—21no—
920C2×C32—21no—
921C2×C32—21no—
922C2×C32—21no—
923C2×C32—41no—
924C2×C32—41no—
925C2×C32—41no—
926C2×C32—62no—
927C2×C32—62no—
928C2×C32—121no—
929C2×C32C2×D3×D411yescharacteristic
930C2×C32C2×D3×D411yescharacteristic
931C2×C32C2×D3×D411yescharacteristic
932C2×C32C2×#23711yescharacteristic
933C2×C32C2×#23711yescharacteristic
934C2×C32C2×#23911yescharacteristic
935C2×C32D3×#4111yescharacteristic
936C2×C32D3×#4111yescharacteristic
937C2×C32D3×#4111yescharacteristic
938C3⋊D3—22no—
939C3⋊D3—122no—
940C3⋊D3—122no—
941C3⋊D3—122no—
942C3⋊D3—124no—
943C3⋊D3—121no—
944C3⋊D3—121no—
945C3⋊D3—121no—
946C3×D3—22no—
947C3×D3—22no—
948C3×D3—22no—
949C3×D3—22no—
950C3×D3—42no—
951C3×D3—42no—
952C3×D3—42no—
953C3×D3—41no—
954C3×D3—41no—
955C3×D3—62no—
956C3×D3—62no—
957C3×D3—122no—
958C24—91no—
959#41—544no—
960C2×Q8—91no—
961C2×D4—31no—
962C2×D4—91no—
963C2×D4—91no—
964C2×D4—271no—
965C2×D4—271no—
966C2×D4—271no—
967C2×D4—271no—
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—544no—
977C4⋊C4—31no—
978C4⋊C4—91no—
979C4⋊C4—91no—
980C4⋊C4—91no—
981C4⋊C4—271no—
982C4⋊C4—271no—
983C22⋊C4—31no—
984C22⋊C4—91no—
985C22⋊C4—91no—
986C22⋊C4—91no—
987C22⋊C4—91no—
988C22⋊C4—91no—
989C22⋊C4—91no—
990C22⋊C4—271no—
991C22⋊C4—271no—
992C22⋊C4—271no—
993C42—271no—
994C42—271no—
995C22×C3—21no—
996C22×C3—21no—
997C22×C3—21no—
998C22×C3—32no—
999C22×C3—32no—
1000C22×C3—32no—
1001C22×C3—32no—
1002C22×C3—41no—
1003C22×C3—62no—
1004C22×C3—62no—
1005C22×C3—62no—
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—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—92no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—121no—
1027C22×C3—188no—
1028C22×C3—181no—
1029C22×C3—181no—
1030C22×C3C22×D3211yescharacteristic
1031C22×C3C22×D3211yescharacteristic
1032C22×C3C22×D3211yescharacteristic
1033C2×D3—21no—
1034C2×D3—21no—
1035C2×D3—21no—
1036C2×D3—21no—
1037C2×D3—21no—
1038C2×D3—21no—
1039C2×D3—21no—
1040C2×D3—32no—
1041C2×D3—32no—
1042C2×D3—62no—
1043C2×D3—68no—
1044C2×D3—68no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—121no—
1050C2×D3—121no—
1051C2×D3—182no—
1052C2×D3—182no—
1053C2×D3—182no—
1054C2×D3—181no—
1055C2×D3—181no—
1056C2×D3—181no—
1057C2×D3—181no—
1058C2×D3—181no—
1059C2×D3—181no—
1060C2×D3—181no—
1061C2×D3—181no—
1062C2×D3—181no—
1063C2×D3—361no—
1064C2×D3—361no—
1065C2×D3—361no—
1066C2×D3—361no—
1067C2×D3—361no—
1068C2×D3—361no—
1069C2×D3—362no—
1070C2×D3—362no—
1071C2×D3—362no—
1072C2×D3#379612yescomplemented
1073C2×D3#381112yes—
1074C3×C4—22no—
1075C3×C4—21no—
1076C3×C4—21no—
1077C3×C4—21no—
1078C3×C4—41no—
1079C3×C4—41no—
1080C3×C4—42no—
1081C3×C4—62no—
1082C3×C4—61no—
1083C3×C4—61no—
1084C3×C4—61no—
1085C3×C4—61no—
1086C3×C4—61no—
1087C3×C4—61no—
1088C3×C4—92no—
1089C3×C4—121no—
1090C3×C4—121no—
1091C3×C4—181no—
1092C3×C4—181no—
1093C3×C4—181no—
1094C3×C4—181no—
1095Dic3—21no—
1096Dic3—21no—
1097Dic3—21no—
1098Dic3—32no—
1099Dic3—32no—
1100Dic3—62no—
1101Dic3—62no—
1102Dic3—62no—
1103Dic3—61no—
1104Dic3—61no—
1105Dic3—61no—
1106Dic3—61no—
1107Dic3—61no—
1108Dic3—61no—
1109Dic3—61no—
1110Dic3—61no—
1111Dic3—92no—
1112Dic3—92no—
1113Dic3—92no—
1114Dic3—121no—
1115Dic3—121no—
1116Dic3—182no—
1117Dic3—182no—
1118Dic3—182no—
1119Dic3—362no—
1120C32—21no—
1121C32—21no—
1122C32—21no—
1123C32—41no—
1124C32#558611yescharacteristic, complemented
1125C32#562711yescharacteristic, complemented
1126C32#565611yescharacteristic, complemented
1127C23—31no—
1128C23—31no—
1129C23—31no—
1130C23—91no—
1131C23—182no—
1132C23—182no—
1133C23—182no—
1134C23—271no—
1135Q8—182no—
1136D4—62no—
1137D4—182no—
1138D4—182no—
1139D4—542no—
1140D4—542no—
1141D4—542no—
1142D4—542no—
1143C2×C4—31no—
1144C2×C4—31no—
1145C2×C4—31no—
1146C2×C4—91no—
1147C2×C4—91no—
1148C2×C4—91no—
1149C2×C4—91no—
1150C2×C4—91no—
1151C2×C4—182no—
1152C2×C4—182no—
1153C2×C4—274no—
1154C2×C4—271no—
1155C2×C4—542no—
1156C2×C4—542no—
1157C2×C4—542no—
1158C2×C4—542no—
1159C2×C4—542no—
1160C2×C4D3311yescharacteristic
1161C2×C3—21no—
1162C2×C3—21no—
1163C2×C3—21no—
1164C2×C3—21no—
1165C2×C3—21no—
1166C2×C3—21no—
1167C2×C3—21no—
1168C2×C3—21no—
1169C2×C3—21no—
1170C2×C3—41no—
1171C2×C3—41no—
1172C2×C3—41no—
1173C2×C3—62no—
1174C2×C3—62no—
1175C2×C3—62no—
1176C2×C3—62no—
1177C2×C3—122no—
1178C2×C3—122no—
1179C2×C3—122no—
1180C2×C3—121no—
1181C2×C3—121no—
1182C2×C3—182no—
1183C2×C3C2×#379611yescharacteristic
1184C2×C3#6430611yescharacteristic
1185C2×C3D32×D411yescharacteristic
1186C2×C3D32×D411yescharacteristic
1187C2×C3D3×#23711yescharacteristic
1188C2×C3D3×#23711yescharacteristic
1189C2×C3D3×#23711yescharacteristic
1190C2×C3D3×#23911yescharacteristic
1191C2×C3C2×#381111yescharacteristic
1192D3—22no—
1193D3—22no—
1194D3—41no—
1195D3—62no—
1196D3—62no—
1197D3—122no—
1198D3—362no—
1199D3—362no—
1200D3—362no—
1201D3—364no—
1202D3—361no—
1203D3—361no—
1204D3—361no—
1205C22—32no—
1206C22—32no—
1207C22—61no—
1208C22—61no—
1209C22—61no—
1210C22—61no—
1211C22—61no—
1212C22—61no—
1213C22—61no—
1214C22—92no—
1215C22—188no—
1216C22—181no—
1217C22—181no—
1218C22—541no—
1219C22—541no—
1220C22—541no—
1221C22C2×D3311yescharacteristic
1222C4—21no—
1223C4—61no—
1224C4—61no—
1225C4—61no—
1226C4—92no—
1227C4—181no—
1228C4—181no—
1229C4—181no—
1230C4—181no—
1231C4—272no—
1232C3—21no—
1233C3—21no—
1234C3—21no—
1235C3—41no—
1236C3#1059405511yescharacteristic, complemented
1237C3#1059461511yescharacteristic, complemented
1238C3#1059516011yescharacteristic, complemented
1239C2—62no—
1240C2—62no—
1241C2—121no—
1242C2—182no—
1243C2—1081no—
1244C2D3×#379611yescharacteristic
1245C2#1172437311yescharacteristic
1246C2D3×#381111yescharacteristic
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×#89015C2semidirect
2. C2×D32×Dic3C2semidirect
3. #11723688C2semidirect
4. #11723472C2semidirect
5. #11723462C2semidirect
6. C3×#63922C2semidirect
7. C3×#63896C2semidirect
8. C3×#63884C2semidirect
9. #11722987C2semidirect
10. #11722966C2semidirect
11. #11722958C2semidirect
12. #11722948C2semidirect
13. #11722929C2semidirect
14. #11722925C2semidirect
15. #11722917C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
21. C2×C3×#634C22semidirect
27. C2×#6291C22semidirect
31. C2×D3×C3⋊Dic3C22semidirect
39. C3×#3750C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
82. #63922D3semidirect
88. #63896D3semidirect
93. #63884D3semidirect
133. D3×C3⋊Dic3D4semidirect
161. C2×#634C2×D3semidirect
218. #3750C2×D3semidirect
245. C3×Dic3⋊C4C2×D3semidirect
246. C3×Dic3⋊C4C2×D3semidirect
249. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
267. (C2×D3)⋊Dic3C2×D3semidirect
268. (C2×D3)⋊Dic3C2×D3semidirect
281. C2×C3×C3⋊D3#41semidirect
290. C2×C32×D3#41semidirect
624. Dic3⋊C4D32semidirect
672. C2×C3⋊D3#237semidirect
709. C2×C3×D3#237semidirect
710. C2×C3×D3#239semidirect
773. C33#525semidirect
1072. C2×D3#3796semidirect
1124. C32#5586semidirect
1125. C32#5627semidirect
1126. C32#5656semidirect
1236. C3#10594055semidirect
1237. C3#10594615semidirect
1238. C3#10595160semidirect

Maximal subgroups

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

subgroupindex
C2×#890152
C2×D32×Dic32
#117236882
#117234722
#117234622
C3×#639222
C3×#638962
C3×#638842
#117229872
#117229662
#117229582
#117229482
#117229292
#117229252
#117229172
#105951603
#105946153
#105940553