Finite Group Databasebeta

← #13170797

Subgroups — #13170797

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×#89041C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723541C211yesmaximal, characteristic, complemented
4#11723512C211yesmaximal, characteristic, complemented
5#11723489C211yesmaximal, characteristic, complemented
6C3×#63897C211yesmaximal, characteristic, complemented
7C3×#63896C211yesmaximal, characteristic, complemented
8C3×#63881C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722968C211yesmaximal, characteristic, complemented
11#11722960C211yesmaximal, characteristic, complemented
12#11722950C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14#11722936C211yesmaximal, characteristic, complemented
15#11722922C211yesmaximal, characteristic, complemented
16#10594615—31nomaximal
17#10594614—31nomaximal
18#10594066—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×#634C2211yescharacteristic, complemented
23C2×#6295C2211yescharacteristic
24C2×#6295C2211yescharacteristic, complemented
25C2×#6294C2211yescharacteristic
26C2×#6294C2211yescharacteristic, complemented
27#89041—24no—
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37D3×#624—24no—
38#88859C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88804C2211yescharacteristic
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×#3799—31no—
60C2×#3796—31no—
61C2×#3795—31no—
62#64105—31no—
63#64102—31no—
64#64091—31no—
65C3×#896—31no—
66C3×#894—31no—
67C3×#894—31no—
68C3×#893—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63981—31no—
72#63978—31no—
73#63952—31no—
74#63923—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63922—61no—
79#63912—31no—
80#63910—31no—
81#63910—31no—
82#63906—31no—
83#63905—31no—
84#63904—31no—
85#63904—31no—
86#63904—61no—
87#63902—31no—
88#63897D311yescharacteristic, complemented
89#63896D311yescharacteristic, complemented
90#63894—31no—
91#63888—31no—
92#63888—31no—
93#63888—61no—
94#63885—31no—
95#63881—31no—
96#63881D311yescharacteristic, complemented
97#63880—31no—
98#63879—31no—
99#63878—31no—
100#63877—31no—
101#63854—31no—
102#63850—31no—
103#63836—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
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
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—22no—
118C3×C4×C3⋊D3—22no—
119C3×#634—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6295—22no—
126#6295—22no—
127#6294—22no—
128#6294D414yescomplemented
129#6292—22no—
130#6292—22no—
131#6290—22no—
132#6289—22no—
133#6289—22no—
134C3×#626—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5656—91no—
139#5627—91no—
140#5547—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)C2×D311yescharacteristic
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
152C2×#634C2×D311yescharacteristic, complemented
153C2×C3×#67—31no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12—61no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—61no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—61no—
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—61no—
179C2×#626—61no—
180C2×#626C2×D311yescharacteristic
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—61no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—64no—
193C2×#624—61no—
194C2×#624—61no—
195C2×#624C2×D311yescharacteristic
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3C2×D311yescharacteristic
201C2×D3×Dic3C2×D311yescharacteristic
202C4×D32—64no—
203C4×D32—64no—
204#3799—64no—
205#3796—64no—
206#3795—64no—
207C32×C4⋊C4—31no—
208C32×C4⋊C4—31no—
209C32×C22⋊C4—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—31no—
215#3752—31no—
216#3752—61no—
217#3752—61no—
218#3752—61no—
219#3752—121no—
220#3750—31no—
221#3750—31no—
222C4×C3⋊Dic3—31no—
223C3×#217—31no—
224C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
235C3×(C2×D3)⋊C4C2×D311yescharacteristic
236C3×C4⋊Dic3—31no—
237C3×Dic3⋊C4—21no—
238C3×Dic3⋊C4—21no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4C2×D311yescharacteristic, complemented
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×Dic3⋊C4C2×D311yescharacteristic, complemented
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248#3724—31no—
249#3724—31no—
250#3724—61no—
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—61no—
259#3722C2×D311yescharacteristic
260#3722C2×D311yescharacteristic, complemented
261#3722C2×D311yescharacteristic, complemented
262#3722C2×D311yescharacteristic, complemented
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—61no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic
270Dic32—31no—
271Dic32—31no—
272Dic32—61no—
273Dic32C2×D311yescharacteristic, complemented
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⋊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⋊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⋊Dic3C2×D412yes—
295C3×C3⋊Dic3C2×D412yes—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C2×#239—91no—
302C2×#237—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#123—91no—
308C3×C22⋊Q8—91no—
309C3×C4×D4—91no—
310#946—91no—
311#939—91no—
312#937—91no—
313#937—91no—
314#930—91no—
315#929—91no—
316C4×#67—91no—
317C4×#67—91no—
318#896—31no—
319#896—91no—
320#896—91no—
321#896—181no—
322#895—91no—
323#894—31no—
324#894—31no—
325#894—91no—
326#893—31no—
327#893—91no—
328#893—91no—
329#893—91no—
330#893—181no—
331#892—91no—
332#884—91no—
333#884—91no—
334#884—91no—
335#883—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#882—91no—
340#882—181no—
341#67⋊C4—31no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#67⋊C4—91no—
345#878—31no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—31no—
350C22×C3⋊D3—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—61no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—62no—
357C22×C3⋊D3—62no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—121no—
360C22×C3⋊D3C22×D311yescharacteristic
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—31no—
370C22×C3×D3—61no—
371C22×C3×D3—61no—
372C22×C3×D3—61no—
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—
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—41no—
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395C2×C32×C4C22×D311yescharacteristic
396#638—62no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—31no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C4⋊(C3⋊D3)—22no—
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—62no—
410C4×C3⋊D3—22no—
411C4×C3⋊D3—62no—
412C4×C3⋊D3—62no—
413#634—22no—
414C3×#67—62no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—62no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C3×D12—62no—
442C3×D12—62no—
443C3×D12—62no—
444C3×D12—122no—
445C3×C4×D3—62no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451C3×C4×D3—122no—
452C3×Dic6—62no—
453C3×Dic6—62no—
454C3×Dic6—122no—
455#626—22no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—64no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—122no—
466#625—62no—
467#625—62no—
468#625—62no—
469#625—62no—
470#625—122no—
471#624—22no—
472#624—34no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—122no—
479#624—122no—
480D3×Dic3—22no—
481D3×Dic3—22no—
482D3×Dic3—34no—
483D3×Dic3—34no—
484D3×Dic3—62no—
485D3×Dic3—62no—
486#525—271noSylow
487C2×C33C22×D411yescharacteristic
488C2×C33C2×#4111yescharacteristic
489C2×C33C2×#4111yescharacteristic
490C3⋊(C3⋊D3)—22no—
491C3×C3⋊D3—22no—
492C3×C3⋊D3—41no—
493C3×C3⋊D3—41no—
494C32×D3—22no—
495C23×D3—91no—
496C23×D3—91no—
497C23×D3—91no—
498C23×D3—181no—
499C2×C3×Q8—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C22×C3×C4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C2×#67—31no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—181no—
517C22×Dic3—31no—
518C22×Dic3—31no—
519C22×Dic3—91no—
520C22×Dic3—91no—
521#239—184no—
522#237—184no—
523#235—184no—
524C2×D12—31no—
525C2×D12—31no—
526C2×D12—31no—
527C2×D12—61no—
528C2×D12—91no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—181no—
535C2×D12—181no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—31no—
541C2×C4×D3—31no—
542C2×C4×D3—61no—
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—91no—
553C2×C4×D3—181no—
554C2×C4×D3—181no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×C4×D3—184no—
558C2×Dic6—31no—
559C2×Dic6—31no—
560C2×Dic6—61no—
561C3×C4⋊C4—31no—
562C3×C4⋊C4—31no—
563C3×C4⋊C4—31no—
564C3×C4⋊C4—31no—
565C3×C4⋊C4—61no—
566C3×C4⋊C4—61no—
567C3×C4⋊C4—91no—
568C3×C4⋊C4—91no—
569C3×C22⋊C4—31no—
570C3×C22⋊C4—31no—
571C3×C22⋊C4—61no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C22⋊C4—91no—
575C3×C22⋊C4—91no—
576C3×C22⋊C4—91no—
577C3×C42—91no—
578#217—31no—
579#217—91no—
580#217—91no—
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—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—91no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—181no—
603(C2×D3)⋊C4—181no—
604(C2×D3)⋊C4—181no—
605(C2×D3)⋊C4—181no—
606(C2×D3)⋊C4—361no—
607(C2×D3)⋊C4D3211yescharacteristic
608C4⋊Dic3—31no—
609C4⋊Dic3—91no—
610Dic3⋊C4—31no—
611Dic3⋊C4—31no—
612Dic3⋊C4—31no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—181no—
619Dic3⋊C4—181no—
620Dic3⋊C4D3211yescharacteristic, complemented
621Dic3⋊C4D3211yescharacteristic, complemented
622C4×Dic3—31no—
623C4×Dic3—31no—
624C4×Dic3—91no—
625C4×Dic3—91no—
626C4×Dic3—91no—
627C4×Dic3—181no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—32no—
632C22×C32—41no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32C23×D311yescharacteristic
636C22×C32C23×D311yescharacteristic
637C22×C32C23×D311yescharacteristic
638C2×C3⋊D3—21no—
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
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—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—32no—
675C2×C3×D3—32no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—62no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—62no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—121no—
702C2×C3×D3—121no—
703C2×C3×D3#23512yescomplemented
704C2×C3×D3#23912yescomplemented
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—61no—
718C32×C4—61no—
719C32×C4—81no—
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—22no—
731C3×Dic3—21no—
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—32no—
742C3×Dic3—32no—
743C3×Dic3—32no—
744C3×Dic3—32no—
745C3×Dic3—41no—
746C3×Dic3—41no—
747C3×Dic3—41no—
748C3×Dic3—41no—
749C3×Dic3—62no—
750C3×Dic3—62no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—121no—
754C2×#41—271no—
755C23×C4—271no—
756#123—91no—
757#123—271no—
758C22⋊Q8—91no—
759C22⋊Q8—271no—
760#121—271no—
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—61no—
773C23×C3—91no—
774C23×C3—91no—
775C23×C3—91no—
776C22×D3—31no—
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—61no—
784C22×D3—61no—
785C22×D3—91no—
786C22×D3—91no—
787C22×D3—91no—
788C22×D3—181no—
789C22×D3—181no—
790C22×D3—181no—
791C22×D3—182no—
792C22×D3—182no—
793C22×D3—182no—
794C22×D3—182no—
795C22×D3—182no—
796C22×D3—182no—
797C22×D3—182no—
798C22×D3—182no—
799C22×D3—182no—
800C22×D3—361no—
801C22×D3—362no—
802C22×D3—362no—
803C22×D3—362no—
804C22×D3C2×D3211yescharacteristic
805C3×Q8—182no—
806C3×D4—182no—
807C3×D4—182no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
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—31no—
821C2×C3×C4—41no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—61no—
825C2×C3×C4—61no—
826C2×C3×C4—61no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—91no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4—182no—
833C2×C3×C4—182no—
834C2×C3×C4C2×D3211yescharacteristic
835C2×C3×C4C2×D3211yescharacteristic
836C2×C3×C4C2×D3211yescharacteristic
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—182no—
846#67—182no—
847#67—362no—
848C2×Dic3—31no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—61no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—62no—
858C2×Dic3—62no—
859C2×Dic3—94no—
860C2×Dic3—91no—
861C2×Dic3—91no—
862C2×Dic3—91no—
863C2×Dic3—181no—
864C2×Dic3—181no—
865C2×Dic3—181no—
866C2×Dic3—182no—
867C2×Dic3—361no—
868C2×Dic3C2×D3211yescharacteristic
869C2×Dic3C2×D3211yescharacteristic
870C2×Dic3C2×D3211yescharacteristic
871C2×Dic3C2×D3211yescharacteristic
872C2×Dic3C2×D3211yescharacteristic
873D12—62no—
874D12—62no—
875D12—62no—
876D12—122no—
877D12—182no—
878D12—182no—
879D12—182no—
880D12—182no—
881D12—184no—
882D12—182no—
883D12—182no—
884D12—362no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—62no—
890C4×D3—62no—
891C4×D3—94no—
892C4×D3—94no—
893C4×D3—122no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—182no—
901C4×D3—182no—
902C4×D3—362no—
903C4×D3—362no—
904Dic6—62no—
905Dic6—62no—
906Dic6—122no—
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×C32C2×#23511yescharacteristic
921C2×C32C2×D3×D411yescharacteristic
922C2×C32C2×D3×D411yescharacteristic
923C2×C32C2×D3×D411yescharacteristic
924C2×C32C2×#23911yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C2×C32D3×#4111yescharacteristic
927C2×C32D3×#4111yescharacteristic
928C2×C32D3×#4111yescharacteristic
929C3⋊D3—22no—
930C3⋊D3—41no—
931C3⋊D3—41no—
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—62no—
943C3×D3—62no—
944C3×D3—122no—
945C3×D3—122no—
946C3×D3—121no—
947C3×D3—121no—
948C3×D3—121no—
949C3×D3—121no—
950C3×D3—241no—
951C24—271no—
952#41—544no—
953C2×Q8—91no—
954C2×D4—91no—
955C2×D4—91no—
956C2×D4—271no—
957C2×D4—271no—
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—31no—
972C4⋊C4—91no—
973C4⋊C4—91no—
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—61no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—92no—
1000C22×C3—121no—
1001C22×C3—121no—
1002C22×C3—181no—
1003C22×C3—181no—
1004C22×C3—181no—
1005C22×C3—181no—
1006C22×C3—181no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3C22×D3211yescharacteristic
1011C22×C3C22×D3211yescharacteristic
1012C22×C3C22×D3211yescharacteristic
1013C2×D3—21no—
1014C2×D3—21no—
1015C2×D3—32no—
1016C2×D3—32no—
1017C2×D3—62no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—62no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—92no—
1036C2×D3—92no—
1037C2×D3—92no—
1038C2×D3—121no—
1039C2×D3—121no—
1040C2×D3—121no—
1041C2×D3—121no—
1042C2×D3—121no—
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#379912yescomplemented
1068C3×C4—21no—
1069C3×C4—21no—
1070C3×C4—21no—
1071C3×C4—41no—
1072C3×C4—41no—
1073C3×C4—41no—
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—61no—
1084C3×C4—61no—
1085C3×C4—81no—
1086C3×C4—92no—
1087C3×C4—92no—
1088C3×C4—121no—
1089C3×C4—121no—
1090C3×C4—121no—
1091C3×C4—121no—
1092C3×C4—181no—
1093Dic3—21no—
1094Dic3—21no—
1095Dic3—21no—
1096Dic3—21no—
1097Dic3—21no—
1098Dic3—32no—
1099Dic3—32no—
1100Dic3—32no—
1101Dic3—32no—
1102Dic3—62no—
1103Dic3—62no—
1104Dic3—61no—
1105Dic3—61no—
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#562711yescharacteristic, complemented
1120C32#565611yescharacteristic, complemented
1121C23—31no—
1122C23—91no—
1123C23—91no—
1124C23—91no—
1125C23—271no—
1126C23—542no—
1127C23—542no—
1128C23—542no—
1129Q8—182no—
1130D4—182no—
1131D4—182no—
1132D4—542no—
1133D4—542no—
1134D4—542no—
1135D4—542no—
1136D4—542no—
1137C2×C4—31no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—31no—
1141C2×C4—31no—
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—182no—
1171C2×C3—361no—
1172C2×C3—361no—
1173C2×C3C2×#379911yescharacteristic
1174C2×C3D3×#23511yescharacteristic
1175C2×C3#6430611yescharacteristic
1176C2×C3D32×D411yescharacteristic
1177C2×C3D32×D411yescharacteristic
1178C2×C3D32×D411yescharacteristic
1179C2×C3#6431211yescharacteristic
1180C2×C3D3×#23911yescharacteristic
1181C2×C3#6431911yescharacteristic
1182D3—22no—
1183D3—62no—
1184D3—62no—
1185D3—122no—
1186D3—122no—
1187D3—121no—
1188D3—121no—
1189D3—121no—
1190D3—121no—
1191D3—182no—
1192D3—182no—
1193D3—182no—
1194D3—241no—
1195D3—362no—
1196D3—362no—
1197D3—362no—
1198D3—722no—
1199C22—32no—
1200C22—61no—
1201C22—61no—
1202C22—92no—
1203C22—181no—
1204C22—181no—
1205C22—181no—
1206C22—181no—
1207C22—181no—
1208C22—181no—
1209C22—181no—
1210C22—181no—
1211C22—272no—
1212C22—548no—
1213C22—541no—
1214C22—541no—
1215C22C2×D3311yescharacteristic
1216C4—21no—
1217C4—61no—
1218C4—61no—
1219C4—61no—
1220C4—61no—
1221C4—61no—
1222C4—92no—
1223C4—92no—
1224C4—181no—
1225C4—541no—
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059406611yescharacteristic, complemented
1231C3#1059461411yescharacteristic, complemented
1232C3#1059461511yescharacteristic, complemented
1233C2—62no—
1234C2—182no—
1235C2—361no—
1236C2—361no—
1237C2—542no—
1238C2#1172437611yescharacteristic
1239C2D3×#379911yescharacteristic
1240C2#1172444011yescharacteristic
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×#89041C2semidirect
2. C2×D3×#624C2semidirect
3. #11723541C2semidirect
4. #11723512C2semidirect
5. #11723489C2semidirect
6. C3×#63897C2semidirect
7. C3×#63896C2semidirect
8. C3×#63881C2semidirect
9. #11722995C2semidirect
10. #11722968C2semidirect
11. #11722960C2semidirect
12. #11722950C2semidirect
13. #11722937C2semidirect
14. #11722936C2semidirect
15. #11722922C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C3×#634C22semidirect
24. C2×#6295C22semidirect
26. C2×#6294C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
46. #88803C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
88. #63897D3semidirect
89. #63896D3semidirect
96. #63881D3semidirect
128. #6294D4semidirect
151. C2×C4×C3⋊D3C2×D3semidirect
152. C2×#634C2×D3semidirect
242. C3×Dic3⋊C4C2×D3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
245. C3×Dic3⋊C4C2×D3semidirect
251. #3724C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
260. #3722C2×D3semidirect
261. #3722C2×D3semidirect
262. #3722C2×D3semidirect
273. Dic32C2×D3semidirect
277. C2×C3⋊(C3⋊D3)#41semidirect
289. C2×C32×D3#41semidirect
620. Dic3⋊C4D32semidirect
621. Dic3⋊C4D32semidirect
703. C2×C3×D3#235semidirect
704. C2×C3×D3#239semidirect
769. C33#525semidirect
1067. C2×D3#3799semidirect
1118. C32#5547semidirect
1119. C32#5627semidirect
1120. C32#5656semidirect
1230. C3#10594066semidirect
1231. C3#10594614semidirect
1232. C3#10594615semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
C2×D3×#6242
#117235412
#117235122
#117234892
C3×#638972
C3×#638962
C3×#638812
#117229952
#117229682
#117229602
#117229502
#117229372
#117229362
#117229222
#105946153
#105946143
#105940663