Finite Group Databasebeta

← #13170748

Subgroups — #13170748

Order 1728.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88965C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723690C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723486C211yesmaximal, characteristic, complemented
6#11723484C211yesmaximal, characteristic, complemented
7C3×#63893C211yesmaximal, characteristic, complemented
8C3×#63880C211yesmaximal, characteristic, complemented
9C3×#63836C211yesmaximal, characteristic, complemented
10#11722999C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722959C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722932C211yesmaximal, characteristic, complemented
16#10594627—31nomaximal
17#10594066—31nomaximal
18#10593997—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic, complemented
26C2×#6291C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88965—24no—
37D3×#624—24no—
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic, complemented
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic, complemented
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×#3799—31no—
60C2×#3799—31no—
61C2×#3798—31no—
62#64104—31no—
63#64091—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#897—31no—
66C3×#892—31no—
67C3×#67⋊C4—31no—
68C3×#878—31no—
69C3×C4×D12—31no—
70C3×#872—31no—
71#63981—31no—
72#63978—31no—
73#63952—31no—
74#63923—31no—
75#63923—31no—
76#63923—31no—
77#63923—61no—
78#63922—31no—
79#63910—31no—
80#63910—31no—
81#63910—61no—
82#63909—31no—
83#63904—31no—
84C4×#626—31no—
85C4×#626—31no—
86#63897—31no—
87#63895—31no—
88#63894—31no—
89#63894—31no—
90#63894—31no—
91#63894—61no—
92#63893D311yescharacteristic, complemented
93#63891—31no—
94#63890—31no—
95#63890—31no—
96#63890—31no—
97#63888—31no—
98#63886—31no—
99#63880—31no—
100#63880D311yescharacteristic, complemented
101#63871—31no—
102#63854—31no—
103#63836D311yescharacteristic, complemented
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×D3×C3⋊D3—22no—
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×C33×C4C2311yescharacteristic
113C4⋊(C3⋊(C3⋊D3))—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—22no—
124#6294—22no—
125#6292—22no—
126#6292—22no—
127#6292—22no—
128#6291—22no—
129#6289—22no—
130#6289—22no—
131#6289—22no—
132C3×#627—22no—
133C3×#626—22no—
134C3×#624—22no—
135C3×#624D414yescomplemented
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5547—91no—
140#5524—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—61no—
153C2×C4⋊(C3⋊D3)—61no—
154C2×C4⋊(C3⋊D3)—61no—
155C2×C4⋊(C3⋊D3)—121no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C3×#67—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C2×C3×D12—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×Dic6—31no—
170C2×C3×Dic6—31no—
171C2×#627C2×D311yescharacteristic, complemented
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—61no—
183C2×#626—61no—
184C2×#626—61no—
185C2×#626—61no—
186C2×#626C2×D311yescharacteristic
187C2×#625—31no—
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—31no—
193C2×#624—31no—
194C2×#624—31no—
195C2×#624—64no—
196C2×#624—61no—
197C2×#624—61no—
198C2×#624—61no—
199C2×#624C2×D311yescharacteristic
200C2×#624C2×D311yescharacteristic, complemented
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3C2×D311yescharacteristic
204C2×D3×Dic3C2×D311yescharacteristic
205C4×D32—64no—
206C4×D32—64no—
207#3799—64no—
208#3799—64no—
209#3798—64no—
210C32×C4⋊C4—31no—
211C32×C22⋊C4—31no—
212C32×C42—31no—
213#3752—31no—
214#3752—31no—
215#3752—31no—
216#3752—31no—
217#3752C2×D311yescharacteristic
218#3752C2×D311yescharacteristic, complemented
219C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
220C3×#217—31no—
221C3×(C2×D3)⋊C4—21no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—61no—
230C3×(C2×D3)⋊C4—61no—
231C3×(C2×D3)⋊C4C2×D311yescharacteristic
232C3×(C2×D3)⋊C4C2×D311yescharacteristic
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3—31no—
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×C4⋊Dic3—61no—
239C3×Dic3⋊C4—21no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×C4×Dic3—21no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3C2×D311yescharacteristic, complemented
249C3×C4×Dic3C2×D311yescharacteristic, complemented
250#3724—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—61no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269#3722C2×D311yescharacteristic
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273Dic32C2×D311yescharacteristic, complemented
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)—21no—
278C2×C3⋊(C3⋊D3)—21no—
279C2×C3⋊(C3⋊D3)—21no—
280C2×C3⋊(C3⋊D3)#4112yescomplemented
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3C2×D412yes—
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—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3C2×D412yes—
300C32×Dic3C2×D412yes—
301C2×#239—91no—
302C2×#235—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×C4×D4—91no—
309C3×#117—91no—
310#946—91no—
311#939—91no—
312#937—91no—
313#930—91no—
314C4×#67—91no—
315C4×#67—91no—
316#897—31no—
317#897—91no—
318#896—91no—
319#895—91no—
320#895—91no—
321#895—91no—
322#895—181no—
323#894—91no—
324#894—91no—
325#894—91no—
326#893—91no—
327#893—91no—
328#892—31no—
329#886—91no—
330#886—91no—
331#884—91no—
332#883—91no—
333#882—91no—
334#882—91no—
335#882—91no—
336#882—91no—
337#882—91no—
338#882—181no—
339#67⋊C4—31no—
340#67⋊C4—91no—
341#878—31no—
342C4×D12—31no—
343C4×D12—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—181no—
348#872—31no—
349C23×C32—31no—
350C22×C3⋊D3—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—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—61no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—62no—
363C22×C3⋊D3—62no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—121no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3×D3—21no—
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—61no—
375C22×C3×D3—61no—
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—62no—
382C2×D32—62no—
383C2×D32—62no—
384C2×D32—122no—
385C2×D32—122no—
386C2×D32—122no—
387C2×C32×C4—21no—
388C2×C32×C4—21no—
389C2×C32×C4—21no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—31no—
395C2×C32×C4—41no—
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C22×D311yescharacteristic
398C2×C32×C4C22×D311yescharacteristic
399#638—62no—
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C4⋊(C3⋊D3)—62no—
405C4⋊(C3⋊D3)—62no—
406C4⋊(C3⋊D3)—62no—
407C4⋊(C3⋊D3)—64no—
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—62no—
410C4⋊(C3⋊D3)—62no—
411C4⋊(C3⋊D3)—122no—
412C4⋊(C3⋊D3)—122no—
413C4⋊(C3⋊D3)—124no—
414C4×C3⋊D3—62no—
415C4×C3⋊D3—62no—
416C4×C3⋊D3—62no—
417C3×#67—62no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
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—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—62no—
436C2×C3×Dic3—62no—
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C3×D12—62no—
448C3×C4×D3—34no—
449C3×C4×D3—34no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×Dic6—62no—
455C3×Dic6—62no—
456#627—22no—
457#626—22no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—62no—
466#626—62no—
467#626—62no—
468#626—122no—
469#626—122no—
470#626—122no—
471#626—122no—
472#625—62no—
473#624—22no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—62no—
480#624—62no—
481#624—122no—
482#624—122no—
483#624—122no—
484#624D1214yescomplemented
485D3×Dic3—22no—
486D3×Dic3—22no—
487D3×Dic3—62no—
488D3×Dic3—62no—
489#525—271noSylow
490C2×C33C22×D411yescharacteristic
491C2×C33C2×#4111yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C3⋊(C3⋊D3)—22no—
494C3⋊(C3⋊D3)—41no—
495C3×C3⋊D3—22no—
496C3×C3⋊D3—41no—
497C32×D3—22no—
498C23×D3—91no—
499C23×D3—91no—
500C23×D3—91no—
501C23×D3—181no—
502C2×C3×Q8—91no—
503C2×C3×D4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C2×#67—31no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—181no—
517C22×Dic3—31no—
518C22×Dic3—31no—
519C22×Dic3—91no—
520#239—184no—
521#235—184no—
522#235—184no—
523C2×D12—31no—
524C2×D12—91no—
525C2×D12—91no—
526C2×D12—91no—
527C2×D12—91no—
528C2×D12—91no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—181no—
536C2×D12—181no—
537C2×D12—181no—
538C2×D12—181no—
539C2×D12—181no—
540C2×D12—181no—
541C2×D12—361no—
542C2×C4×D3—31no—
543C2×C4×D3—31no—
544C2×C4×D3—31no—
545C2×C4×D3—31no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3—91no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
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—181no—
560C2×C4×D3—181no—
561C2×C4×D3—181no—
562C2×C4×D3—184no—
563C2×C4×D3—184no—
564C2×C4×D3—184no—
565C2×Dic6—31no—
566C2×Dic6—31no—
567C3×C4⋊C4—31no—
568C3×C4⋊C4—31no—
569C3×C4⋊C4—61no—
570C3×C4⋊C4—91no—
571C3×C4⋊C4—91no—
572C3×C4⋊C4—91no—
573C3×C4⋊C4—91no—
574C3×C22⋊C4—31no—
575C3×C22⋊C4—31no—
576C3×C22⋊C4—61no—
577C3×C22⋊C4—91no—
578C3×C22⋊C4—91no—
579C3×C22⋊C4—91no—
580C3×C22⋊C4—91no—
581C3×C42—31no—
582C3×C42—31no—
583C3×C42—61no—
584C3×C42—91no—
585#217—31no—
586#217—91no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—61no—
595(C2×D3)⋊C4—61no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—91no—
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—91no—
609(C2×D3)⋊C4—91no—
610(C2×D3)⋊C4—181no—
611(C2×D3)⋊C4—181no—
612(C2×D3)⋊C4—181no—
613(C2×D3)⋊C4—181no—
614(C2×D3)⋊C4D3211yescharacteristic
615C4⋊Dic3—31no—
616C4⋊Dic3—31no—
617C4⋊Dic3—31no—
618C4⋊Dic3—31no—
619C4⋊Dic3—31no—
620C4⋊Dic3—61no—
621C4⋊Dic3—91no—
622Dic3⋊C4—31no—
623Dic3⋊C4—31no—
624Dic3⋊C4—31no—
625Dic3⋊C4—91no—
626Dic3⋊C4—91no—
627Dic3⋊C4D3211yescharacteristic, complemented
628C4×Dic3—31no—
629C4×Dic3—31no—
630C4×Dic3D3211yescharacteristic, complemented
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—32no—
635C22×C32—41no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32C23×D311yescharacteristic
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
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—61no—
653C2×C3⋊D3—68no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—62no—
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—61no—
668C2×C3⋊D3—61no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—121no—
671C2×C3⋊D3—121no—
672C2×C3⋊D3—122no—
673C2×C3⋊D3—121no—
674C2×C3⋊D3—121no—
675C2×C3⋊D3—121no—
676C2×C3⋊D3—121no—
677C2×C3⋊D3—121no—
678C2×C3⋊D3—121no—
679C2×C3⋊D3—121no—
680C2×C3⋊D3—121no—
681C2×C3⋊D3—121no—
682C2×C3⋊D3—121no—
683C2×C3⋊D3—121no—
684C2×C3⋊D3—121no—
685C2×C3⋊D3—241no—
686C2×C3⋊D3—241no—
687C2×C3⋊D3—241no—
688C2×C3⋊D3—241no—
689C2×C3⋊D3C2×D1212yes—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—22no—
695C2×C3×D3—32no—
696C2×C3×D3—32no—
697C2×C3×D3—41no—
698C2×C3×D3—41no—
699C2×C3×D3—62no—
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—
715C2×C3×D3#23512yescomplemented
716C2×C3×D3#23912yescomplemented
717D32—68no—
718D32—68no—
719D32—128no—
720C32×C4—21no—
721C32×C4—22no—
722C32×C4—21no—
723C32×C4—21no—
724C32×C4—32no—
725C32×C4—32no—
726C32×C4—41no—
727C32×C4—41no—
728C32×C4—42no—
729C32×C4—61no—
730C32×C4—61no—
731C32×C4—61no—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
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—22no—
743C3×Dic3—22no—
744C3×Dic3—41no—
745C3×Dic3—41no—
746C3×Dic3—41no—
747C3×Dic3—61no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—121no—
756C3×Dic3—121no—
757C3×Dic3—121no—
758C3×Dic3—121no—
759C3×Dic3C2×D1212yes—
760C3×Dic3C2×D1212yes—
761C3×Dic3D3×D412yes—
762C3×Dic3D3×D412yes—
763C2×#41—271no—
764C23×C4—271no—
765#123—271no—
766#123—271no—
767C22⋊Q8—91no—
768C22⋊Q8—271no—
769#121—271no—
770#121—271no—
771#120—271no—
772#120—271no—
773C4×D4—91no—
774C4×D4—271no—
775C4×D4—271no—
776C4×D4—271no—
777#117—91no—
778C33#52511yescharacteristic, complemented, Sylow
779C23×C3—31no—
780C23×C3—31no—
781C23×C3—61no—
782C23×C3—91no—
783C23×C3—91no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—31no—
787C22×D3—31no—
788C22×D3—61no—
789C22×D3—61no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—91no—
793C22×D3—91no—
794C22×D3—91no—
795C22×D3—91no—
796C22×D3—181no—
797C22×D3—181no—
798C22×D3—181no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—181no—
802C22×D3—182no—
803C22×D3—182no—
804C22×D3—182no—
805C22×D3—182no—
806C22×D3—182no—
807C22×D3—182no—
808C22×D3—182no—
809C22×D3—182no—
810C22×D3—182no—
811C22×D3—361no—
812C22×D3—361no—
813C22×D3—362no—
814C22×D3—362no—
815C22×D3—362no—
816C22×D3C2×D3211yescharacteristic
817C3×Q8—182no—
818C3×D4—182no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—31no—
823C2×C3×C4—31no—
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—41no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—94no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—91no—
842C2×C3×C4—91no—
843C2×C3×C4—182no—
844C2×C3×C4—182no—
845C2×C3×C4—182no—
846C2×C3×C4C2×D3211yescharacteristic
847C2×C3×C4C2×D3211yescharacteristic
848C2×C3×C4C2×D3211yescharacteristic
849#67—62no—
850#67—182no—
851#67—182no—
852#67—182no—
853#67—182no—
854#67—182no—
855#67—182no—
856#67—182no—
857#67—362no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—61no—
867C2×Dic3—61no—
868C2×Dic3—61no—
869C2×Dic3—61no—
870C2×Dic3—62no—
871C2×Dic3—62no—
872C2×Dic3—182no—
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876C2×Dic3C2×D3211yescharacteristic
877C2×Dic3C2×D3211yescharacteristic
878D12—62no—
879D12—182no—
880D12—182no—
881D12—182no—
882D12—184no—
883D12—182no—
884D12—182no—
885D12—182no—
886D12—182no—
887D12—182no—
888D12—182no—
889D12—182no—
890D12—182no—
891D12—362no—
892D12—362no—
893D12—364no—
894D12—362no—
895D12—362no—
896D12—362no—
897C4×D3—34no—
898C4×D3—34no—
899C4×D3—62no—
900C4×D3—62no—
901C4×D3—62no—
902C4×D3—62no—
903C4×D3—182no—
904C4×D3—182no—
905C4×D3—182no—
906C4×D3—182no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—182no—
910C4×D3—182no—
911C4×D3—182no—
912C4×D3—182no—
913C4×D3—182no—
914C4×D3—362no—
915C4×D3—362no—
916C4×D3—362no—
917Dic6—62no—
918Dic6—62no—
919C2×C32—21no—
920C2×C32—21no—
921C2×C32—21no—
922C2×C32—21no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—41no—
931C2×C32—62no—
932C2×C32C22×D1211yescharacteristic
933C2×C32C2×#23511yescharacteristic
934C2×C32C2×D3×D411yescharacteristic
935C2×C32C2×D3×D411yescharacteristic
936C2×C32C2×#23911yescharacteristic
937C2×C32D3×#4111yescharacteristic
938C2×C32D3×#4111yescharacteristic
939C2×C32D3×#4111yescharacteristic
940C2×C32D3×#4111yescharacteristic
941C3⋊D3—22no—
942C3⋊D3—41no—
943C3⋊D3—62no—
944C3⋊D3—62no—
945C3⋊D3—62no—
946C3⋊D3—122no—
947C3⋊D3—122no—
948C3⋊D3—122no—
949C3⋊D3—121no—
950C3⋊D3—122no—
951C3⋊D3—121no—
952C3⋊D3—121no—
953C3⋊D3—242no—
954C3⋊D3—241no—
955C3⋊D3—241no—
956C3⋊D3—242no—
957C3×D3—22no—
958C3×D3—22no—
959C3×D3—42no—
960C3×D3—62no—
961C3×D3—62no—
962C3×D3—122no—
963C3×D3—121no—
964C3×D3—121no—
965C3×D3—241no—
966C24—271no—
967#41—544no—
968C2×Q8—91no—
969C2×D4—91no—
970C2×D4—271no—
971C2×D4—271no—
972C2×D4—271no—
973C2×D4—271no—
974C2×D4—271no—
975C2×D4—271no—
976C22×C4—91no—
977C22×C4—91no—
978C22×C4—91no—
979C22×C4—91no—
980C22×C4—271no—
981C22×C4—271no—
982C22×C4—271no—
983C22×C4—271no—
984C22×C4—544no—
985C4⋊C4—31no—
986C4⋊C4—91no—
987C4⋊C4—91no—
988C4⋊C4—91no—
989C4⋊C4—91no—
990C4⋊C4—271no—
991C22⋊C4—31no—
992C22⋊C4—91no—
993C22⋊C4—91no—
994C22⋊C4—91no—
995C22⋊C4—91no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22⋊C4—271no—
1000C22⋊C4—271no—
1001C42—31no—
1002C42—91no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—32no—
1007C22×C3—32no—
1008C22×C3—41no—
1009C22×C3—62no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—92no—
1015C22×C3—121no—
1016C22×C3—121no—
1017C22×C3—181no—
1018C22×C3—181no—
1019C22×C3—181no—
1020C22×C3—181no—
1021C22×C3—181no—
1022C22×C3C22×D3211yescharacteristic
1023C22×C3C22×D3211yescharacteristic
1024C22×C3C22×D3211yescharacteristic
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—32no—
1028C2×D3—32no—
1029C2×D3—62no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
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—121no—
1046C2×D3—121no—
1047C2×D3—121no—
1048C2×D3—182no—
1049C2×D3—182no—
1050C2×D3—182no—
1051C2×D3—188no—
1052C2×D3—188no—
1053C2×D3—188no—
1054C2×D3—181no—
1055C2×D3—181no—
1056C2×D3—181no—
1057C2×D3—181no—
1058C2×D3—181no—
1059C2×D3—181no—
1060C2×D3—182no—
1061C2×D3—181no—
1062C2×D3—181no—
1063C2×D3—181no—
1064C2×D3—181no—
1065C2×D3—181no—
1066C2×D3—181no—
1067C2×D3—181no—
1068C2×D3—181no—
1069C2×D3—181no—
1070C2×D3—362no—
1071C2×D3—368no—
1072C2×D3—361no—
1073C2×D3—361no—
1074C2×D3—361no—
1075C2×D3—361no—
1076C2×D3—361no—
1077C2×D3—361no—
1078C2×D3—361no—
1079C2×D3—361no—
1080C2×D3—361no—
1081C2×D3—361no—
1082C2×D3—361no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—362no—
1087C2×D3—721no—
1088C2×D3—721no—
1089C2×D3—721no—
1090C2×D3—721no—
1091C2×D3#379912yescomplemented
1092C3×C4—22no—
1093C3×C4—21no—
1094C3×C4—21no—
1095C3×C4—21no—
1096C3×C4—32no—
1097C3×C4—32no—
1098C3×C4—32no—
1099C3×C4—32no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—42no—
1103C3×C4—62no—
1104C3×C4—62no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—61no—
1108C3×C4—61no—
1109C3×C4—61no—
1110C3×C4—61no—
1111C3×C4—121no—
1112C3×C4—121no—
1113C3×C4—121no—
1114C3×C4—181no—
1115C3×C4—181no—
1116C3×C4—181no—
1117C3×C4—181no—
1118Dic3—21no—
1119Dic3—21no—
1120Dic3—21no—
1121Dic3—61no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—61no—
1128Dic3—61no—
1129Dic3—121no—
1130Dic3—121no—
1131Dic3—121no—
1132Dic3—121no—
1133Dic3D3×D1212yes—
1134Dic3D3×D1212yes—
1135C32—21no—
1136C32—21no—
1137C32—21no—
1138C32—41no—
1139C32#552411yescharacteristic, complemented
1140C32#554711yescharacteristic, complemented
1141C32#562711yescharacteristic, complemented
1142C23—31no—
1143C23—91no—
1144C23—91no—
1145C23—271no—
1146C23—271no—
1147C23—542no—
1148C23—542no—
1149C23—542no—
1150Q8—182no—
1151D4—182no—
1152D4—542no—
1153D4—542no—
1154D4—542no—
1155D4—542no—
1156D4—542no—
1157D4—542no—
1158C2×C4—31no—
1159C2×C4—31no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—31no—
1163C2×C4—94no—
1164C2×C4—91no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—91no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—182no—
1171C2×C4—542no—
1172C2×C4—542no—
1173C2×C4—542no—
1174C2×C4—542no—
1175C2×C4D3311yescharacteristic
1176C2×C3—21no—
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—41no—
1186C2×C3—41no—
1187C2×C3—41no—
1188C2×C3—62no—
1189C2×C3—62no—
1190C2×C3—122no—
1191C2×C3—182no—
1192C2×C3—361no—
1193C2×C3C2×#379911yescharacteristic
1194C2×C3C2×D3×D1211yescharacteristic
1195C2×C3C2×D3×D1211yescharacteristic
1196C2×C3D3×#23511yescharacteristic
1197C2×C3#6430611yescharacteristic
1198C2×C3D32×D411yescharacteristic
1199C2×C3#6431211yescharacteristic
1200C2×C3#6431211yescharacteristic
1201C2×C3D3×#23911yescharacteristic
1202D3—22no—
1203D3—62no—
1204D3—62no—
1205D3—122no—
1206D3—121no—
1207D3—121no—
1208D3—182no—
1209D3—182no—
1210D3—182no—
1211D3—241no—
1212D3—362no—
1213D3—362no—
1214D3—362no—
1215D3—362no—
1216D3—361no—
1217D3—361no—
1218D3—361no—
1219D3—722no—
1220D3—721no—
1221D3—721no—
1222D3—722no—
1223C22—32no—
1224C22—61no—
1225C22—61no—
1226C22—92no—
1227C22—181no—
1228C22—181no—
1229C22—181no—
1230C22—181no—
1231C22—181no—
1232C22—272no—
1233C22—548no—
1234C22—541no—
1235C22—541no—
1236C22—541no—
1237C22—541no—
1238C22—541no—
1239C22C2×D3311yescharacteristic
1240C4—21no—
1241C4—32no—
1242C4—32no—
1243C4—61no—
1244C4—61no—
1245C4—61no—
1246C4—181no—
1247C4—181no—
1248C4—181no—
1249C4—181no—
1250C3—21no—
1251C3—21no—
1252C3—21no—
1253C3—41no—
1254C3#1059399711yescharacteristic, complemented
1255C3#1059406611yescharacteristic, complemented
1256C3#1059462711yescharacteristic, complemented
1257C2—62no—
1258C2—182no—
1259C2—361no—
1260C2—542no—
1261C2—1081no—
1262C2D3×#379911yescharacteristic
1263C2D32×D1211yescharacteristic
1264C2#1172441111yescharacteristic
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×#88965C2semidirect
2. C2×D3×#624C2semidirect
3. #11723690C2semidirect
4. #11723542C2semidirect
5. #11723486C2semidirect
6. #11723484C2semidirect
7. C3×#63893C2semidirect
8. C3×#63880C2semidirect
9. C3×#63836C2semidirect
10. #11722999C2semidirect
11. #11722973C2semidirect
12. #11722959C2semidirect
13. #11722950C2semidirect
14. #11722933C2semidirect
15. #11722932C2semidirect
25. C2×#6292C22semidirect
29. C2×#6289C22semidirect
30. C2×C3×#627C22semidirect
33. C2×C3×#624C22semidirect
39. C3×#3752C22semidirect
40. C3×C4⋊(C3⋊Dic3)C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88815C22semidirect
45. #88814C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
92. #63893D3semidirect
100. #63880D3semidirect
103. #63836D3semidirect
135. C3×#624D4semidirect
171. C2×#627C2×D3semidirect
200. C2×#624C2×D3semidirect
218. #3752C2×D3semidirect
219. C4⋊(C3⋊Dic3)C2×D3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
248. C3×C4×Dic3C2×D3semidirect
249. C3×C4×Dic3C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
280. C2×C3⋊(C3⋊D3)#41semidirect
289. C2×C32×D3#41semidirect
484. #624D12semidirect
627. Dic3⋊C4D32semidirect
630. C4×Dic3D32semidirect
715. C2×C3×D3#235semidirect
716. C2×C3×D3#239semidirect
778. C33#525semidirect
1091. C2×D3#3799semidirect
1139. C32#5524semidirect
1140. C32#5547semidirect
1141. C32#5627semidirect
1254. C3#10593997semidirect
1255. C3#10594066semidirect
1256. C3#10594627semidirect

Maximal subgroups

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

subgroupindex
C2×#889652
C2×D3×#6242
#117236902
#117235422
#117234862
#117234842
C3×#638932
C3×#638802
C3×#638362
#117229992
#117229732
#117229592
#117229502
#117229332
#117229322
#105946273
#105940663
#105939973