Finite Group Databasebeta

← #13171909

Subgroups — #13171909

Order 1728.

1256 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723720C211yesmaximal, characteristic, complemented
2#11723632C211yesmaximal, characteristic
3#11723618C211yesmaximal, characteristic, complemented
4#11723608C211yesmaximal, characteristic, complemented
5C3×#63964C211yesmaximal, characteristic, complemented
6C2×C3×Dic32C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723011C211yesmaximal, characteristic, complemented
11#11723003C211yesmaximal, characteristic, complemented
12Dic3×#627C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic, complemented
14#11722918C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594955—31nomaximal
17#10594839—31nomaximal
18#10594216—31nomaximal
19C2×#6312C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88806C2211yescharacteristic
35Dic3⋊(C3⋊Dic3)C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88803C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×Dic32C2211yescharacteristic
50C3×Dic32C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64139—31no—
55C4×#638—31no—
56#64095—31no—
57C3×C4×#67—31no—
58C3×#924—31no—
59C2×C3×C4×Dic3—31no—
60C2×C3×C4×Dic3—31no—
61C3×#67⋊C4—31no—
62C3×#878—31no—
63#63978—31no—
64#63978—31no—
65#63978—61no—
66#63966—31no—
67#63966—31no—
68#63966—31no—
69#63966—61no—
70#63964D311yescharacteristic, complemented
71#63962—31no—
72#63961—31no—
73C2×Dic32D311yescharacteristic, complemented
74#63952—31no—
75#63952—31no—
76#63952—61no—
77#63952D311yescharacteristic, complemented
78C4×#627—31no—
79#63907—31no—
80#63904—31no—
81C4×#626—31no—
82#63894—31no—
83#63874—31no—
84#63869—31no—
85#63868—31no—
86#63868—31no—
87#63868—31no—
88#63867—31no—
89#63864—31no—
90#63861—31no—
91#63859—31no—
92#63855—31no—
93#63852—31no—
94#63848—31no—
95#63845—31no—
96Dic3×Dic6—31no—
97Dic3×Dic6—31no—
98#63841—31no—
99#63836—31no—
100#63836—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105#6312—22no—
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C3×#638—22no—
108C2×C3×C3⋊Dic3—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3—22no—
115C2×C32×Dic3—22no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6292—22no—
123#6289—22no—
124C3×#627—22no—
125C3×#624—22no—
126#5624—91no—
127#5538—91no—
128#5479—91no—
129C22×C32×C4—31no—
130C22×C32×C4—31no—
131C2×#638—31no—
132C2×#638—31no—
133C2×#638—31no—
134C2×#638—61no—
135C2×#638—61no—
136C2×#638—61no—
137C2×#638—121no—
138C2×#638C2×D311yescharacteristic
139C22×C3⋊Dic3C2×D311yescharacteristic
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4×C3⋊D3—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C22×C3×Dic3—21no—
146C22×C3×Dic3—21no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—61no—
150C22×C3×Dic3C2×D311yescharacteristic
151C22×C3×Dic3C2×D311yescharacteristic
152C22×C3×Dic3C2×D311yescharacteristic
153C22×C3×Dic3C2×D311yescharacteristic
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—31no—
158C2×#627C2×D311yescharacteristic
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—61no—
162C2×#624—31no—
163C2×#624—31no—
164C2×#624—61no—
165C2×#624C2×D311yescharacteristic
166C32×C22⋊C4—31no—
167#3757C2×D311yescharacteristic
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—31no—
176#3750—31no—
177C4×C3⋊Dic3—31no—
178C3×#217—21no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—61no—
182C3×#217C2×D311yescharacteristic
183C3×#217C2×D311yescharacteristic
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×C4×Dic3—31no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—61no—
209#3724C2×D311yescharacteristic
210#3724C2×D311yescharacteristic
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—61no—
237#3722—61no—
238#3722—61no—
239#3722—61no—
240#3722C2×D311yescharacteristic
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—61no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33#4112yes—
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C3⋊(C3⋊Dic3)—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3#4112yes—
277C32×Dic3#4112yes—
278C3×C22⋊Q8—91no—
279C3×C4×D4—91no—
280C2×C3×C42—91no—
281#947—91no—
282Q8×Dic3—91no—
283#939—91no—
284#935—91no—
285#930—91no—
286#930—91no—
287#930—181no—
288#929—91no—
289#929—91no—
290C4×#67—31no—
291C4×#67—91no—
292C4×#67—91no—
293C4×#67—91no—
294C4×#67—181no—
295#926—91no—
296#924—31no—
297C2×C4×Dic3—31no—
298C2×C4×Dic3—31no—
299#898—91no—
300#898—91no—
301#898—91no—
302#893—91no—
303#892—91no—
304#892—91no—
305#890—91no—
306#889—91no—
307#886—91no—
308#886—91no—
309#886—91no—
310#886—181no—
311#885—91no—
312#67⋊C4—31no—
313#67⋊C4—91no—
314#879—91no—
315#878—31no—
316#876—91no—
317#876—91no—
318#875—91no—
319C4×D12—91no—
320#872—91no—
321#872—91no—
322#872—91no—
323#870—91no—
324C4×Dic6—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—41no—
330C23×C32C22×D311yescharacteristic
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—121no—
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—61no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—31no—
348C2×C32×C4—31no—
349C2×C32×C4—31no—
350C2×C32×C4—62no—
351C2×C32×C4—62no—
352#638—22no—
353#638—62no—
354#638—64no—
355#638—62no—
356#638—62no—
357#638—122no—
358#638—122no—
359#638—124no—
360C2×C3⋊Dic3—22no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—61no—
365C2×C3⋊Dic3—61no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—121no—
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C4⋊(C3⋊D3)—62no—
374C4×C3⋊D3—62no—
375C3×#67—62no—
376C3×#67—62no—
377C3×#67—122no—
378C2×C3×Dic3—22no—
379C2×C3×Dic3—22no—
380C2×C3×Dic3—22no—
381C2×C3×Dic3—22no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—21no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—42no—
399C2×C3×Dic3—42no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—62no—
406C2×C3×Dic3—62no—
407C2×C3×Dic3—122no—
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C3×C4×D3—62no—
421C3×C4×D3—62no—
422C3×Dic6—62no—
423C3×Dic6—62no—
424#627—22no—
425#626—62no—
426#626—62no—
427#626—122no—
428#624—22no—
429#624—62no—
430#624—62no—
431#624—122no—
432#529—271noSylow
433C2×C33—22no—
434C2×C33C2×#4111yescharacteristic
435C2×C33C2×#4111yescharacteristic
436C2×C33C2×#4111yescharacteristic
437C3⋊(C3⋊D3)—41no—
438C3×C3⋊D3—41no—
439C2×C3×Q8—91no—
440C2×C3×D4—91no—
441C22×C3×C4—31no—
442C22×C3×C4—31no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—61no—
446C22×C3×C4—61no—
447C22×C3×C4—91no—
448C22×C3×C4—91no—
449C2×#67—31no—
450C2×#67—31no—
451C2×#67—61no—
452C2×#67—91no—
453C2×#67—91no—
454C2×#67—91no—
455C2×#67—91no—
456C2×#67—181no—
457C2×#67—181no—
458C2×#67—181no—
459C2×#67—361no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—61no—
463C22×Dic3D3211yescharacteristic
464C22×Dic3D3211yescharacteristic
465C2×D12—91no—
466C2×D12—91no—
467C2×D12—181no—
468C2×C4×D3—31no—
469C2×C4×D3—31no—
470C2×C4×D3—91no—
471C2×C4×D3—91no—
472C2×C4×D3—91no—
473C2×C4×D3—181no—
474C2×Dic6—31no—
475C2×Dic6—31no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C22⋊C4—31no—
481C3×C22⋊C4—31no—
482C3×C22⋊C4—61no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C42—91no—
486C3×C42—91no—
487C3×C42—91no—
488C3×C42—91no—
489C3×C42—91no—
490#217—31no—
491#217—31no—
492#217—61no—
493#217—91no—
494#217—91no—
495#217—91no—
496#217D3211yescharacteristic
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515(C2×D3)⋊C4—91no—
516(C2×D3)⋊C4—91no—
517(C2×D3)⋊C4—181no—
518(C2×D3)⋊C4—181no—
519(C2×D3)⋊C4—181no—
520(C2×D3)⋊C4—181no—
521(C2×D3)⋊C4—181no—
522C4⋊Dic3—31no—
523C4⋊Dic3—31no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—91no—
528C4⋊Dic3—91no—
529C4⋊Dic3—91no—
530C4⋊Dic3—91no—
531C4⋊Dic3—91no—
532C4⋊Dic3—181no—
533C4⋊Dic3—181no—
534C4⋊Dic3—181no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—181no—
552C4×Dic3—31no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—31no—
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C4×Dic3—181no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—22no—
576C22×C32—22no—
577C22×C32—22no—
578C22×C32—41no—
579C22×C32—42no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—81no—
587C22×C32—81no—
588C22×C32#23512yes—
589C22×C32#23512yes—
590C22×C32#23912yes—
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3—61no—
598C2×C3⋊D3—62no—
599C2×C3⋊D3—61no—
600C2×C3⋊D3—61no—
601C2×C3⋊D3—61no—
602C2×C3⋊D3—61no—
603C2×C3⋊D3—61no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—121no—
608C2×C3⋊D3—121no—
609C2×C3⋊D3—122no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—121no—
615C2×C3⋊D3—121no—
616C2×C3⋊D3—241no—
617C2×C3⋊D3—241no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C2×C3×D3—121no—
627C32×C4—32no—
628C32×C4—32no—
629C32×C4—61no—
630C32×C4—61no—
631C32×C4—61no—
632C32×C4—61no—
633C3⋊Dic3—21no—
634C3⋊Dic3—21no—
635C3⋊Dic3—21no—
636C3⋊Dic3—21no—
637C3⋊Dic3—21no—
638C3⋊Dic3—61no—
639C3⋊Dic3—62no—
640C3⋊Dic3—61no—
641C3⋊Dic3—61no—
642C3⋊Dic3—121no—
643C3⋊Dic3—121no—
644C3⋊Dic3—122no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—21no—
652C3×Dic3—21no—
653C3×Dic3—22no—
654C3×Dic3—22no—
655C3×Dic3—41no—
656C3×Dic3—41no—
657C3×Dic3—41no—
658C3×Dic3—41no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—61no—
668C3×Dic3—61no—
669C3×Dic3—121no—
670C3×Dic3—121no—
671C3×Dic3—121no—
672C3×Dic3—121no—
673C3×Dic3—121no—
674C3×Dic3#23512yes—
675C3×Dic3#23512yes—
676C3×Dic3#23712yes—
677C3×Dic3#23712yes—
678#126—271no—
679#126—271no—
680#125—271no—
681#124—271no—
682#123—271no—
683#123—271no—
684C22⋊Q8—91no—
685#121—271no—
686C4×Q8—271no—
687C4×D4—91no—
688C4×D4—271no—
689C4×D4—271no—
690#117—271no—
691#117—271no—
692C2×C42—91no—
693C33#52911yescharacteristic, complemented, Sylow
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—41no—
698C23×C3—91no—
699C23×C3C2×D3211yescharacteristic
700C23×C3C2×D3211yescharacteristic
701C23×C3C2×D3211yescharacteristic
702C22×D3—31no—
703C22×D3—31no—
704C22×D3—61no—
705C22×D3—91no—
706C22×D3—91no—
707C22×D3—91no—
708C22×D3—181no—
709C22×D3—181no—
710C22×D3—181no—
711C22×D3—361no—
712C3×Q8—182no—
713C3×D4—182no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—31no—
718C2×C3×C4—31no—
719C2×C3×C4—31no—
720C2×C3×C4—31no—
721C2×C3×C4—31no—
722C2×C3×C4—31no—
723C2×C3×C4—31no—
724C2×C3×C4—31no—
725C2×C3×C4—31no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—61no—
730C2×C3×C4—61no—
731C2×C3×C4—61no—
732C2×C3×C4—62no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4—91no—
737C2×C3×C4—91no—
738C2×C3×C4—91no—
739C2×C3×C4—91no—
740C2×C3×C4—91no—
741C2×C3×C4—122no—
742C2×C3×C4—122no—
743C2×C3×C4—182no—
744C2×C3×C4—182no—
745#67—62no—
746#67—62no—
747#67—122no—
748#67—184no—
749#67—182no—
750#67—182no—
751#67—182no—
752#67—182no—
753#67—362no—
754#67—362no—
755#67—364no—
756C2×Dic3—22no—
757C2×Dic3—22no—
758C2×Dic3—31no—
759C2×Dic3—31no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—61no—
769C2×Dic3—61no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—62no—
774C2×Dic3—62no—
775C2×Dic3—91no—
776C2×Dic3—91no—
777C2×Dic3—91no—
778C2×Dic3—122no—
779C2×Dic3—181no—
780C2×Dic3—181no—
781C2×Dic3—181no—
782C2×Dic3—361no—
783C2×Dic3C2×D3211yescharacteristic
784C2×Dic3C2×D3211yescharacteristic
785C2×Dic3C2×D3211yescharacteristic
786C2×Dic3C2×D3211yescharacteristic
787C2×Dic3C2×D3211yescharacteristic
788C2×Dic3C2×D3211yescharacteristic
789D12—182no—
790D12—182no—
791D12—362no—
792C4×D3—62no—
793C4×D3—62no—
794C4×D3—182no—
795C4×D3—182no—
796C4×D3—182no—
797C4×D3—362no—
798Dic6—62no—
799Dic6—62no—
800C2×C32—22no—
801C2×C32—22no—
802C2×C32—22no—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—21no—
808C2×C32—21no—
809C2×C32—21no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—41no—
813C2×C32—41no—
814C2×C32—41no—
815C2×C32—42no—
816C2×C32—42no—
817C2×C32—42no—
818C2×C32—82no—
819C2×C32C2×#23511yescharacteristic
820C2×C32C2×#23511yescharacteristic
821C2×C32C2×#23511yescharacteristic
822C2×C32C2×#23511yescharacteristic
823C2×C32C2×#23711yescharacteristic
824C2×C32C2×#23711yescharacteristic
825C2×C32C2×#23911yescharacteristic
826C2×C32D3×#4111yescharacteristic
827C2×C32D3×#4111yescharacteristic
828C3⋊D3—41no—
829C3⋊D3—121no—
830C3⋊D3—122no—
831C3⋊D3—121no—
832C3⋊D3—121no—
833C3⋊D3—241no—
834C3⋊D3—241no—
835C3⋊D3—242no—
836C3×D3—121no—
837C3×D3—121no—
838C3×D3—241no—
839C2×Q8—91no—
840C2×D4—91no—
841C2×D4—271no—
842C2×D4—271no—
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—91no—
846C22×C4—91no—
847C22×C4—271no—
848C4⋊C4—91no—
849C4⋊C4—91no—
850C4⋊C4—91no—
851C4⋊C4—91no—
852C4⋊C4—271no—
853C4⋊C4—271no—
854C4⋊C4—271no—
855C4⋊C4—271no—
856C4⋊C4—271no—
857C4⋊C4—271no—
858C22⋊C4—31no—
859C22⋊C4—91no—
860C22⋊C4—91no—
861C22⋊C4—271no—
862C22⋊C4—271no—
863C22⋊C4—271no—
864C22⋊C4—271no—
865C22⋊C4—271no—
866C22⋊C4—271no—
867C22⋊C4—271no—
868C42—91no—
869C42—91no—
870C42—91no—
871C42—91no—
872C42—91no—
873C42—271no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—21no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—41no—
887C22×C3—41no—
888C22×C3—41no—
889C22×C3—41no—
890C22×C3—41no—
891C22×C3—41no—
892C22×C3—41no—
893C22×C3—42no—
894C22×C3—81no—
895C22×C3—81no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3#379812yes—
900C22×C3#379912yes—
901C22×C3#379912yes—
902C22×C3C22×D3211yescharacteristic
903C22×C3C22×D3211yescharacteristic
904C22×C3C22×D3211yescharacteristic
905C2×D3—61no—
906C2×D3—61no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—121no—
914C2×D3—182no—
915C2×D3—181no—
916C2×D3—181no—
917C2×D3—181no—
918C2×D3—181no—
919C2×D3—181no—
920C2×D3—181no—
921C2×D3—181no—
922C2×D3—181no—
923C2×D3—181no—
924C2×D3—361no—
925C2×D3—361no—
926C2×D3—361no—
927C2×D3—361no—
928C2×D3—361no—
929C2×D3—361no—
930C2×D3—361no—
931C2×D3—361no—
932C2×D3—362no—
933C2×D3—721no—
934C2×D3—721no—
935C3×C4—32no—
936C3×C4—32no—
937C3×C4—32no—
938C3×C4—32no—
939C3×C4—62no—
940C3×C4—62no—
941C3×C4—61no—
942C3×C4—61no—
943C3×C4—61no—
944C3×C4—61no—
945C3×C4—61no—
946C3×C4—61no—
947C3×C4—61no—
948C3×C4—61no—
949C3×C4—121no—
950C3×C4—121no—
951C3×C4—121no—
952C3×C4—121no—
953C3×C4—181no—
954C3×C4—181no—
955C3×C4—181no—
956C3×C4—181no—
957C3×C4—181no—
958Dic3—21no—
959Dic3—21no—
960Dic3—21no—
961Dic3—21no—
962Dic3—61no—
963Dic3—61no—
964Dic3—61no—
965Dic3—61no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—121no—
973Dic3—121no—
974Dic3—121no—
975Dic3—121no—
976Dic3—121no—
977Dic3—182no—
978Dic3—181no—
979Dic3—181no—
980Dic3—181no—
981Dic3—361no—
982Dic3—361no—
983Dic3—362no—
984Dic3#380412yes—
985Dic3#380412yes—
986C32—21no—
987C32—21no—
988C32—21no—
989C32—41no—
990C32#547911yescharacteristic, complemented
991C32#553811yescharacteristic, complemented
992C32#562411yescharacteristic, complemented
993C23—91no—
994C23—271no—
995C23D3311yescharacteristic
996Q8—182no—
997D4—182no—
998D4—542no—
999D4—542no—
1000C2×C4—31no—
1001C2×C4—31no—
1002C2×C4—31no—
1003C2×C4—31no—
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—91no—
1009C2×C4—91no—
1010C2×C4—91no—
1011C2×C4—91no—
1012C2×C4—91no—
1013C2×C4—182no—
1014C2×C4—182no—
1015C2×C4—271no—
1016C2×C4—542no—
1017C2×C3—22no—
1018C2×C3—22no—
1019C2×C3—22no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—42no—
1030C2×C3—42no—
1031C2×C3—42no—
1032C2×C3—41no—
1033C2×C3—41no—
1034C2×C3—41no—
1035C2×C3—82no—
1036C2×C3—361no—
1037C2×C3C2×#379811yescharacteristic
1038C2×C3C2×#379911yescharacteristic
1039C2×C3C2×#379911yescharacteristic
1040C2×C3D3×#23511yescharacteristic
1041C2×C3D3×#23511yescharacteristic
1042C2×C3D3×#23711yescharacteristic
1043C2×C3D3×#23711yescharacteristic
1044C2×C3C2×#380411yescharacteristic
1045C2×C3C2×#380411yescharacteristic
1046D3—121no—
1047D3—121no—
1048D3—241no—
1049D3—362no—
1050D3—361no—
1051D3—361no—
1052D3—361no—
1053D3—721no—
1054D3—721no—
1055D3—722no—
1056C22—21no—
1057C22—21no—
1058C22—181no—
1059C22—181no—
1060C22—181no—
1061C22—541no—
1062C22—541no—
1063C22—541no—
1064C22#8896512yes—
1065C22C2×D3311yescharacteristic
1066C4—32no—
1067C4—32no—
1068C4—61no—
1069C4—61no—
1070C4—61no—
1071C4—61no—
1072C4—181no—
1073C4—181no—
1074C4—181no—
1075C4—181no—
1076C4—181no—
1077C4—541no—
1078C3—21no—
1079C3—21no—
1080C3—21no—
1081C3—41no—
1082C3#1059421611yescharacteristic, complemented
1083C3#1059483911yescharacteristic, complemented
1084C3#1059495511yescharacteristic, complemented
1085C2—22no—
1086C2—361no—
1087C2—1081no—
1088C2D3×#380411yescharacteristic
1089C2D3×#380411yescharacteristic
1090C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723632C2
hypercenterC23D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723720C2semidirect
3. #11723618C2semidirect
4. #11723608C2semidirect
5. C3×#63964C2semidirect
6. C2×C3×Dic32C2semidirect
7. C3×#63952C2semidirect
8. #11723023C2semidirect
9. #11723021C2semidirect
10. #11723011C2semidirect
11. #11723003C2semidirect
12. Dic3×#627C2semidirect
13. #11722933C2semidirect
14. #11722918C2semidirect
15. #11722915C2semidirect
70. #63964D3semidirect
73. C2×Dic32D3semidirect
77. #63952D3semidirect
693. C33#529semidirect
990. C32#5479semidirect
991. C32#5538semidirect
992. C32#5624semidirect
1082. C3#10594216semidirect
1083. C3#10594839semidirect
1084. C3#10594955semidirect

Maximal subgroups

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

subgroupindex
#117237202
#117236322
#117236182
#117236082
C3×#639642
C2×C3×Dic322
C3×#639522
#117230232
#117230212
#117230112
#117230032
Dic3×#6272
#117229332
#117229182
#117229152
#105949553
#105948393
#105942163