Finite Group Databasebeta

← #13170752

Subgroups — #13170752

Order 1728.

1620 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88965C211yesmaximal, characteristic, complemented
2C2×#88949C211yesmaximal, characteristic, complemented
3#11723701C211yesmaximal, characteristic, complemented
4#11723493C211yesmaximal, characteristic, complemented
5#11723482C211yesmaximal, characteristic, complemented
6#11723471C211yesmaximal, characteristic, complemented
7C3×#63895C211yesmaximal, characteristic, complemented
8C3×#63894C211yesmaximal, characteristic, complemented
9C3×#63836C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722974C211yesmaximal, characteristic, complemented
12#11722961C211yesmaximal, characteristic, complemented
13#11722952C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic, complemented
15#11722933C211yesmaximal, characteristic, complemented
16#10594627—31nomaximal
17#10594623—31nomaximal
18#10593997—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic, complemented
32C2×C3×#624C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C2×C3×#624C2211yescharacteristic, complemented
36#88965—24no—
37#88949—24no—
38#88859C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88807C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×C4×D32—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×#3799—31no—
60C2×#3799—31no—
61C2×#3798—31no—
62#64104—31no—
63#64103—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#897—31no—
66C3×#896—31no—
67C3×#893—31no—
68C3×#892—31no—
69C3×C4×D12—31no—
70C3×#872—31no—
71#63923—31no—
72#63923—31no—
73#63923—31no—
74#63923—31no—
75#63922—31no—
76#63922—31no—
77#63910—31no—
78#63909—31no—
79#63906—31no—
80#63904—31no—
81C4×#626—31no—
82C4×#626—31no—
83#63895D311yescharacteristic, complemented
84#63894—31no—
85#63894D311yescharacteristic, complemented
86#63893—31no—
87#63891—31no—
88#63890—31no—
89#63890—31no—
90#63890—31no—
91#63890—61no—
92#63887—31no—
93#63886—31no—
94#63886—31no—
95#63886—61no—
96#63880—31no—
97#63880—31no—
98#63880—31no—
99#63880—61no—
100#63879—31no—
101#63871—31no—
102#63853—31no—
103#63836D311yescharacteristic, complemented
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C2×#1113—22no—
110C2×#1113—22no—
111C2×#1113—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×C4⋊(C3⋊D3)—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—22no—
124#6295—22no—
125#6292—22no—
126#6292—22no—
127#6292—22no—
128#6292—22no—
129#6289—22no—
130Dic3×C3⋊D3—22no—
131Dic3×C3⋊D3—22no—
132Dic3×C3⋊D3—22no—
133C3×#627—22no—
134C3×#624—22no—
135C3×#624—22no—
136C3×#624—22no—
137C3×#624D414yescomplemented
138#5627—91no—
139#5547—91no—
140#5524—91no—
141C22×D32—31no—
142C22×D32—31no—
143C22×D32—31no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×D12—61no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×Dic6—31no—
165C2×C3×Dic6—31no—
166C2×#627C2×D311yescharacteristic, complemented
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—61no—
180C2×#626—61no—
181C2×#626—61no—
182C2×#626—61no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—61no—
188C2×#624C2×D311yescharacteristic
189C2×#624C2×D311yescharacteristic
190C2×#624C2×D311yescharacteristic
191C2×#624C2×D311yescharacteristic, complemented
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—61no—
199C2×D3×Dic3—61no—
200C2×D3×Dic3—61no—
201C4×D32—64no—
202C4×D32—64no—
203C4×D32—64no—
204#3799—64no—
205#3799—64no—
206#3798—64no—
207C32×C4⋊C4—31no—
208C32×C4⋊C4—31no—
209C32×C42—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—31no—
215#3752—61no—
216#3752—61no—
217#3752—61no—
218#3752—121no—
219#3752C2×D311yescharacteristic
220#3752C2×D311yescharacteristic
221C4⋊(C3⋊Dic3)—31no—
222#3750—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—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—31no—
235C3×(C2×D3)⋊C4—61no—
236C3×(C2×D3)⋊C4—61no—
237C3×C4⋊Dic3—21no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3—31no—
240C3×C4⋊Dic3C2×D311yescharacteristic, complemented
241C3×C4⋊Dic3C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4—21no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4C2×D311yescharacteristic, complemented
246C3×Dic3⋊C4C2×D311yescharacteristic, complemented
247C3×C4×Dic3—21no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250C3×C4×Dic3C2×D311yescharacteristic, complemented
251C3×C4×Dic3C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722C2×D311yescharacteristic
265#3722C2×D311yescharacteristic
266#3722C2×D311yescharacteristic
267#3722C2×D311yescharacteristic, complemented
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—61no—
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—21no—
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⋊D3—21no—
287C2×C3×C3⋊D3C2×D412yes—
288C2×C3×C3⋊D3#4112yescomplemented
289C2×C3×C3⋊D3#4112yescomplemented
290#1113—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C32×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—31no—
319#895—91no—
320#895—91no—
321#895—91no—
322#895—181no—
323#894—91no—
324#894—91no—
325#894—91no—
326#894—181no—
327#893—31no—
328#893—91no—
329#892—31no—
330#886—91no—
331#886—91no—
332#884—91no—
333#883—91no—
334#882—91no—
335#882—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#878—91no—
342C4×D12—31no—
343C4×D12—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—181no—
348#872—31no—
349C22×C3⋊D3—31no—
350C22×C3⋊D3—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—61no—
353C22×C3⋊D3—61no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—121no—
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3⋊D3C22×D311yescharacteristic
358C22×C3⋊D3C22×D311yescharacteristic
359C22×C3⋊D3C22×D311yescharacteristic
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—31no—
367C22×C3×D3—31no—
368C22×C3×D3—61no—
369C22×C3×D3—61no—
370C22×C3×D3—61no—
371C22×C3×D3—61no—
372C2×D32—62no—
373C2×D32—62no—
374C2×D32—62no—
375C2×D32—62no—
376C2×D32—62no—
377C2×D32—62no—
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×C32×C4—21no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—31no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—41no—
391C2×C32×C4C22×D311yescharacteristic
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—121no—
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C4⋊(C3⋊D3)—22no—
404C4⋊(C3⋊D3)—62no—
405C4⋊(C3⋊D3)—62no—
406C4⋊(C3⋊D3)—62no—
407C4⋊(C3⋊D3)—62no—
408C4×C3⋊D3—62no—
409C4×C3⋊D3—62no—
410C4×C3⋊D3—62no—
411C4×C3⋊D3—62no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—21no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C3×D12—62no—
437C3×D12—62no—
438C3×D12—122no—
439C3×C4×D3—34no—
440C3×C4×D3—34no—
441C3×C4×D3—62no—
442C3×C4×D3—62no—
443C3×C4×D3—62no—
444C3×C4×D3—62no—
445C3×C4×D3—62no—
446C3×C4×D3—62no—
447C3×Dic6—62no—
448C3×Dic6—62no—
449#627—22no—
450#626—62no—
451#626—62no—
452#626—62no—
453#626—62no—
454#626—62no—
455#626—62no—
456#626—64no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—122no—
464#626—122no—
465#626—122no—
466#625—62no—
467#625—62no—
468#624—22no—
469#624—22no—
470#624—22no—
471#624—62no—
472#624—62no—
473#624—122no—
474#624D1214yescomplemented
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—122no—
482D3×Dic3—122no—
483D3×Dic3—122no—
484#525—271noSylow
485C2×C33C22×D411yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C2×C33C2×#4111yescharacteristic
488C3⋊(C3⋊D3)—41no—
489C3×C3⋊D3—22no—
490C3×C3⋊D3—22no—
491C3×C3⋊D3—22no—
492C3×C3⋊D3—41no—
493C23×D3—91no—
494C23×D3—91no—
495C23×D3—91no—
496C2×C3×Q8—91no—
497C2×C3×D4—91no—
498C22×C3×C4—91no—
499C22×C3×C4—91no—
500C22×C3×C4—91no—
501C22×C3×C4—91no—
502C2×#67—91no—
503C2×#67—91no—
504C2×#67—91no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C22×Dic3—91no—
511C22×Dic3—91no—
512C22×Dic3—91no—
513#239—184no—
514#235—184no—
515#235—184no—
516C2×D12—31no—
517C2×D12—31no—
518C2×D12—61no—
519C2×D12—91no—
520C2×D12—91no—
521C2×D12—91no—
522C2×D12—91no—
523C2×D12—91no—
524C2×D12—91no—
525C2×D12—91no—
526C2×D12—91no—
527C2×D12—91no—
528C2×D12—91no—
529C2×D12—181no—
530C2×D12—181no—
531C2×D12—181no—
532C2×D12—181no—
533C2×C4×D3—31no—
534C2×C4×D3—31no—
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—31no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
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—181no—
551C2×C4×D3—181no—
552C2×C4×D3—181no—
553C2×C4×D3—181no—
554C2×C4×D3—184no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×Dic6—31no—
558C2×Dic6—31no—
559C3×C4⋊C4—31no—
560C3×C4⋊C4—31no—
561C3×C4⋊C4—31no—
562C3×C4⋊C4—31no—
563C3×C4⋊C4—61no—
564C3×C4⋊C4—61no—
565C3×C4⋊C4—91no—
566C3×C4⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571C3×C22⋊C4—91no—
572C3×C22⋊C4—91no—
573C3×C42—31no—
574C3×C42—31no—
575C3×C42—61no—
576C3×C42—91no—
577#217—91no—
578#217—91no—
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—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—61no—
592(C2×D3)⋊C4—61no—
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—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—181no—
604(C2×D3)⋊C4—181no—
605(C2×D3)⋊C4—181no—
606(C2×D3)⋊C4—181no—
607(C2×D3)⋊C4—181no—
608(C2×D3)⋊C4—361no—
609C4⋊Dic3—31no—
610C4⋊Dic3—31no—
611C4⋊Dic3—91no—
612C4⋊Dic3—91no—
613C4⋊Dic3—91no—
614C4⋊Dic3—181no—
615C4⋊Dic3D3211yescharacteristic, complemented
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—91no—
621Dic3⋊C4—181no—
622Dic3⋊C4D3211yescharacteristic, complemented
623C4×Dic3—31no—
624C4×Dic3—31no—
625C4×Dic3D3211yescharacteristic, complemented
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—41no—
630C22×C32C23×D311yescharacteristic
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—61no—
643C2×C3⋊D3—62no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—61no—
646C2×C3⋊D3—61no—
647C2×C3⋊D3—61no—
648C2×C3⋊D3—61no—
649C2×C3⋊D3—61no—
650C2×C3⋊D3—61no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—122no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—121no—
657C2×C3⋊D3—121no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—121no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—241no—
662C2×C3⋊D3—241no—
663C2×C3⋊D3C2×D1212yes—
664C2×C3⋊D3#23512yescomplemented
665C2×C3⋊D3#23912yescomplemented
666C2×C3×D3—32no—
667C2×C3×D3—32no—
668C2×C3×D3—32no—
669C2×C3×D3—32no—
670C2×C3×D3—32no—
671C2×C3×D3—32no—
672C2×C3×D3—62no—
673C2×C3×D3—62no—
674C2×C3×D3—62no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
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—121no—
694C2×C3×D3—121no—
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—
702D32—68no—
703D32—68no—
704D32—68no—
705C32×C4—21no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—32no—
709C32×C4—32no—
710C32×C4—41no—
711C32×C4—41no—
712C32×C4—41no—
713C32×C4—61no—
714C32×C4—61no—
715C32×C4—61no—
716C32×C4—61no—
717C32×C4—81no—
718C3⋊Dic3—21no—
719C3⋊Dic3—21no—
720C3⋊Dic3—61no—
721C3⋊Dic3—61no—
722C3⋊Dic3—61no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—241no—
727C3×Dic3—22no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—22no—
737C3×Dic3—22no—
738C3×Dic3—41no—
739C3×Dic3—41no—
740C3×Dic3—41no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—121no—
746C3×Dic3—121no—
747C3×Dic3C2×D1212yes—
748C3×Dic3C2×D1212yes—
749C3×Dic3D3×D412yes—
750C3×Dic3D3×D412yes—
751C2×#41—271no—
752C23×C4—271no—
753#123—271no—
754#123—271no—
755C22⋊Q8—91no—
756C22⋊Q8—271no—
757#121—271no—
758#121—271no—
759#120—271no—
760#120—271no—
761C4×D4—91no—
762C4×D4—271no—
763C4×D4—271no—
764C4×D4—271no—
765#117—91no—
766C33#52511yescharacteristic, complemented, Sylow
767C23×C3—91no—
768C23×C3—91no—
769C23×C3—91no—
770C23×C3—91no—
771C22×D3—31no—
772C22×D3—31no—
773C22×D3—31no—
774C22×D3—31no—
775C22×D3—31no—
776C22×D3—31no—
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—61no—
780C22×D3—61no—
781C22×D3—61no—
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—
799C3×Q8—182no—
800C3×D4—182no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—31no—
805C2×C3×C4—31no—
806C2×C3×C4—31no—
807C2×C3×C4—31no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—31no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—41no—
817C2×C3×C4—61no—
818C2×C3×C4—61no—
819C2×C3×C4—61no—
820C2×C3×C4—61no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—94no—
824C2×C3×C4—91no—
825C2×C3×C4—91no—
826C2×C3×C4—182no—
827C2×C3×C4—182no—
828C2×C3×C4—182no—
829C2×C3×C4C2×D3211yescharacteristic
830C2×C3×C4C2×D3211yescharacteristic
831C2×C3×C4C2×D3211yescharacteristic
832#67—182no—
833#67—182no—
834#67—182no—
835#67—182no—
836#67—182no—
837#67—182no—
838#67—182no—
839#67—182no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—91no—
847C2×Dic3—91no—
848C2×Dic3—91no—
849C2×Dic3—181no—
850C2×Dic3—181no—
851C2×Dic3—181no—
852C2×Dic3—182no—
853C2×Dic3—182no—
854C2×Dic3—182no—
855C2×Dic3—361no—
856C2×Dic3C2×D3211yescharacteristic
857C2×Dic3C2×D3211yescharacteristic
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860C2×Dic3C2×D3211yescharacteristic
861C2×Dic3C2×D3211yescharacteristic
862D12—62no—
863D12—62no—
864D12—122no—
865D12—182no—
866D12—182no—
867D12—182no—
868D12—182no—
869D12—182no—
870D12—182no—
871D12—182no—
872D12—182no—
873D12—184no—
874D12—182no—
875D12—182no—
876D12—362no—
877D12—362no—
878D12—362no—
879C4×D3—34no—
880C4×D3—34no—
881C4×D3—62no—
882C4×D3—62no—
883C4×D3—62no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—182no—
888C4×D3—182no—
889C4×D3—182no—
890C4×D3—182no—
891C4×D3—182no—
892C4×D3—182no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—362no—
897C4×D3—362no—
898C4×D3—362no—
899C4×D3—362no—
900Dic6—62no—
901Dic6—62no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—41no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32C22×D1211yescharacteristic
915C2×C32C2×#23511yescharacteristic
916C2×C32C2×D3×D411yescharacteristic
917C2×C32C2×D3×D411yescharacteristic
918C2×C32C2×#23911yescharacteristic
919C2×C32D3×#4111yescharacteristic
920C2×C32D3×#4111yescharacteristic
921C2×C32D3×#4111yescharacteristic
922C2×C32D3×#4111yescharacteristic
923C3⋊D3—22no—
924C3⋊D3—22no—
925C3⋊D3—22no—
926C3⋊D3—41no—
927C3⋊D3—121no—
928C3⋊D3—122no—
929C3⋊D3—121no—
930C3⋊D3—121no—
931C3⋊D3—241no—
932C3⋊D3—241no—
933C3⋊D3—242no—
934C3×D3—62no—
935C3×D3—62no—
936C3×D3—62no—
937C3×D3—62no—
938C3×D3—62no—
939C3×D3—62no—
940C3×D3—122no—
941C3×D3—122no—
942C3×D3—122no—
943C3×D3—121no—
944C3×D3—121no—
945C3×D3—241no—
946C24—271no—
947#41—544no—
948C2×Q8—91no—
949C2×D4—91no—
950C2×D4—271no—
951C2×D4—271no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4—91no—
960C22×C4—271no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—544no—
965C4⋊C4—31no—
966C4⋊C4—31no—
967C4⋊C4—91no—
968C4⋊C4—91no—
969C4⋊C4—271no—
970C4⋊C4—271no—
971C22⋊C4—91no—
972C22⋊C4—91no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C42—31no—
982C42—91no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—41no—
987C22×C3—92no—
988C22×C3—92no—
989C22×C3—92no—
990C22×C3—181no—
991C22×C3—181no—
992C22×C3—181no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3—181no—
998C22×C3—181no—
999C22×C3C22×D3211yescharacteristic
1000C22×C3C22×D3211yescharacteristic
1001C22×C3C22×D3211yescharacteristic
1002C2×D3—32no—
1003C2×D3—32no—
1004C2×D3—32no—
1005C2×D3—32no—
1006C2×D3—32no—
1007C2×D3—32no—
1008C2×D3—62no—
1009C2×D3—62no—
1010C2×D3—62no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—121no—
1030C2×D3—121no—
1031C2×D3—121no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C2×D3—121no—
1038C2×D3—188no—
1039C2×D3—188no—
1040C2×D3—188no—
1041C2×D3—182no—
1042C2×D3—181no—
1043C2×D3—181no—
1044C2×D3—181no—
1045C2×D3—181no—
1046C2×D3—181no—
1047C2×D3—181no—
1048C2×D3—181no—
1049C2×D3—181no—
1050C2×D3—181no—
1051C2×D3—361no—
1052C2×D3—361no—
1053C2×D3—361no—
1054C2×D3—361no—
1055C2×D3—361no—
1056C2×D3—361no—
1057C2×D3—361no—
1058C2×D3—361no—
1059C2×D3—362no—
1060C2×D3—721no—
1061C2×D3—721no—
1062C3×C4—21no—
1063C3×C4—21no—
1064C3×C4—21no—
1065C3×C4—32no—
1066C3×C4—32no—
1067C3×C4—32no—
1068C3×C4—32no—
1069C3×C4—41no—
1070C3×C4—41no—
1071C3×C4—41no—
1072C3×C4—62no—
1073C3×C4—62no—
1074C3×C4—62no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—61no—
1078C3×C4—61no—
1079C3×C4—61no—
1080C3×C4—61no—
1081C3×C4—61no—
1082C3×C4—61no—
1083C3×C4—81no—
1084C3×C4—121no—
1085C3×C4—121no—
1086C3×C4—121no—
1087C3×C4—181no—
1088C3×C4—181no—
1089Dic3—21no—
1090Dic3—21no—
1091Dic3—21no—
1092Dic3—21no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—121no—
1098Dic3—121no—
1099Dic3—181no—
1100Dic3—181no—
1101Dic3—181no—
1102Dic3—361no—
1103Dic3—361no—
1104Dic3—361no—
1105Dic3—721no—
1106Dic3D3×D1212yes—
1107Dic3D3×D1212yes—
1108C32—21no—
1109C32—21no—
1110C32—21no—
1111C32—41no—
1112C32#552411yescharacteristic, complemented
1113C32#554711yescharacteristic, complemented
1114C32#562711yescharacteristic, complemented
1115C23—91no—
1116C23—91no—
1117C23—91no—
1118C23—91no—
1119C23—271no—
1120C23—542no—
1121C23—542no—
1122C23—542no—
1123Q8—182no—
1124D4—182no—
1125D4—542no—
1126D4—542no—
1127D4—542no—
1128D4—542no—
1129D4—542no—
1130D4—542no—
1131C2×C4—31no—
1132C2×C4—31no—
1133C2×C4—31no—
1134C2×C4—31no—
1135C2×C4—31no—
1136C2×C4—31no—
1137C2×C4—94no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—182no—
1141C2×C4—182no—
1142C2×C4—182no—
1143C2×C4—271no—
1144C2×C4—542no—
1145C2×C4—542no—
1146C2×C4—542no—
1147C2×C4—542no—
1148C2×C4D3311yescharacteristic
1149C2×C3—21no—
1150C2×C3—21no—
1151C2×C3—21no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—41no—
1159C2×C3—41no—
1160C2×C3—41no—
1161C2×C3—182no—
1162C2×C3—182no—
1163C2×C3—182no—
1164C2×C3—361no—
1165C2×C3C2×D3×D1211yescharacteristic
1166C2×C3C2×D3×D1211yescharacteristic
1167C2×C3D3×#23511yescharacteristic
1168C2×C3D3×#23511yescharacteristic
1169C2×C3#6430611yescharacteristic
1170C2×C3D32×D411yescharacteristic
1171C2×C3#6431211yescharacteristic
1172C2×C3D3×#23911yescharacteristic
1173C2×C3D3×#23911yescharacteristic
1174D3—62no—
1175D3—62no—
1176D3—62no—
1177D3—62no—
1178D3—62no—
1179D3—62no—
1180D3—122no—
1181D3—122no—
1182D3—122no—
1183D3—121no—
1184D3—121no—
1185D3—241no—
1186D3—362no—
1187D3—361no—
1188D3—361no—
1189D3—361no—
1190D3—721no—
1191D3—721no—
1192D3—722no—
1193C22—92no—
1194C22—92no—
1195C22—92no—
1196C22—181no—
1197C22—181no—
1198C22—181no—
1199C22—181no—
1200C22—181no—
1201C22—181no—
1202C22—181no—
1203C22—181no—
1204C22—181no—
1205C22—548no—
1206C22—541no—
1207C22—541no—
1208C22—541no—
1209C22C2×D3311yescharacteristic
1210C4—21no—
1211C4—32no—
1212C4—32no—
1213C4—61no—
1214C4—61no—
1215C4—61no—
1216C4—61no—
1217C4—181no—
1218C4—181no—
1219C4—541no—
1220C3—21no—
1221C3—21no—
1222C3—21no—
1223C3—41no—
1224C3#1059399711yescharacteristic, complemented
1225C3#1059462311yescharacteristic, complemented
1226C3#1059462711yescharacteristic, complemented
1227C2—182no—
1228C2—182no—
1229C2—182no—
1230C2—361no—
1231C2—1081no—
1232C2#1172439111yescharacteristic
1233C2D32×D1211yescharacteristic
1234C2#1172441011yescharacteristic
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×#88949C2semidirect
3. #11723701C2semidirect
4. #11723493C2semidirect
5. #11723482C2semidirect
6. #11723471C2semidirect
7. C3×#63895C2semidirect
8. C3×#63894C2semidirect
9. C3×#63836C2semidirect
10. #11722997C2semidirect
11. #11722974C2semidirect
12. #11722961C2semidirect
13. #11722952C2semidirect
14. #11722934C2semidirect
15. #11722933C2semidirect
26. C2×#6292C22semidirect
27. C2×#6289C22semidirect
31. C2×C3×#627C22semidirect
35. C2×C3×#624C22semidirect
38. #88859C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
45. #88807C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
48. #88803C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
83. #63895D3semidirect
85. #63894D3semidirect
103. #63836D3semidirect
137. C3×#624D4semidirect
166. C2×#627C2×D3semidirect
191. C2×#624C2×D3semidirect
240. C3×C4⋊Dic3C2×D3semidirect
241. C3×C4⋊Dic3C2×D3semidirect
245. C3×Dic3⋊C4C2×D3semidirect
246. C3×Dic3⋊C4C2×D3semidirect
250. C3×C4×Dic3C2×D3semidirect
251. C3×C4×Dic3C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
267. #3722C2×D3semidirect
273. Dic32C2×D3semidirect
288. C2×C3×C3⋊D3#41semidirect
289. C2×C3×C3⋊D3#41semidirect
474. #624D12semidirect
615. C4⋊Dic3D32semidirect
622. Dic3⋊C4D32semidirect
625. C4×Dic3D32semidirect
664. C2×C3⋊D3#235semidirect
665. C2×C3⋊D3#239semidirect
766. C33#525semidirect
1112. C32#5524semidirect
1113. C32#5547semidirect
1114. C32#5627semidirect
1224. C3#10593997semidirect
1225. C3#10594623semidirect
1226. 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×#889492
#117237012
#117234932
#117234822
#117234712
C3×#638952
C3×#638942
C3×#638362
#117229972
#117229742
#117229612
#117229522
#117229342
#117229332
#105946273
#105946233
#105939973