Finite Group Databasebeta

← #13167953

Subgroups — #13167953

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723690C211yesmaximal, characteristic, complemented
2#11723472C211yesmaximal, characteristic, complemented
3#11723472C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63848C211yesmaximal, characteristic, complemented
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723021C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11722999C211yesmaximal, characteristic, complemented
11#11722961C211yesmaximal, characteristic
12#11722941C211yesmaximal, characteristic, complemented
13#11722938C211yesmaximal, characteristic, complemented
14#11722921C211yesmaximal, characteristic, complemented
15Dic3×#624C211yesmaximal, characteristic, complemented
16#10594465—31nomaximal
17#10594453—31nomaximal
18#10594442—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88804C2211yescharacteristic
37#88804C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64102—31no—
55#64102—31no—
56#64101—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#897—31no—
60C3×#896—31no—
61C3×#890—31no—
62C3×#889—31no—
63#63910—31no—
64#63909—31no—
65#63907—31no—
66#63906—31no—
67#63902—31no—
68#63897—31no—
69#63895D311yescharacteristic, complemented
70#63891—31no—
71#63890—31no—
72#63890—31no—
73#63890—31no—
74C4×#624—31no—
75#63881—31no—
76#63881—31no—
77#63881—31no—
78#63881—31no—
79#63881—31no—
80#63881—31no—
81#63881—61no—
82#63881—61no—
83#63878—31no—
84#63878—31no—
85C4×D3×Dic3—31no—
86C4×D3×Dic3—31no—
87#63868—31no—
88#63868—31no—
89#63864—31no—
90#63854—31no—
91#63852—31no—
92#63849—31no—
93#63849—31no—
94#63849—31no—
95#63849—61no—
96#63848—31no—
97#63848D311yescharacteristic, complemented
98#63845D311yescharacteristic, complemented
99#63843—31no—
100#63843—31no—
101#63838—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C4×C3⋊(C3⋊D3)—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6294—22no—
120#6292—22no—
121#6292—22no—
122Dic3×C3⋊D3—22no—
123Dic3×C3⋊D3—22no—
124C3×#627—22no—
125C3×#624—22no—
126#5706—91no—
127#5691—91no—
128#5624—91no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—61no—
137C2×C4×C3⋊D3—61no—
138C2×C4×C3⋊D3—61no—
139C2×C4×C3⋊D3—121no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×Dic6—31no—
143C2×C3×Dic6—31no—
144C2×#627C2×D311yescharacteristic
145C2×#626—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—61no—
152C2×#626—61no—
153C2×#625—31no—
154C2×#624—31no—
155C2×#624C2×D311yescharacteristic
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)C2×D311yescharacteristic
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—61no—
189C3×(C2×D3)⋊C4—61no—
190C3×C4⋊Dic3—21no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—61no—
198C3×C4⋊Dic3C2×D311yescharacteristic
199C3×C4⋊Dic3C2×D311yescharacteristic
200C3×Dic3⋊C4—21no—
201C3×Dic3⋊C4—21no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4C2×D311yescharacteristic
209C3×Dic3⋊C4C2×D311yescharacteristic
210C3×Dic3⋊C4C2×D311yescharacteristic
211C3×Dic3⋊C4C2×D311yescharacteristic
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216#3724—31no—
217#3724C2×D311yescharacteristic
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3C2×D311yescharacteristic
221Dic3⋊Dic3C2×D311yescharacteristic
222Dic3⋊Dic3C2×D311yescharacteristic
223Dic3⋊Dic3C2×D311yescharacteristic
224#3722—31no—
225#3722—31no—
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—61no—
234#3722—61no—
235#3722—61no—
236#3722—61no—
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic
239#3722C2×D311yescharacteristic
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32—61no—
253Dic32—61no—
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
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#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)#4112yes—
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—21no—
277C32×Dic3#4112yes—
278C3×#126—91no—
279C3×#125—91no—
280C3×C22⋊Q8—91no—
281#947—91no—
282Q8×Dic3—91no—
283#930—91no—
284C2×C4×Dic3—91no—
285#898—31no—
286#898—31no—
287#898—91no—
288#898—91no—
289#897—31no—
290#896—31no—
291#895—91no—
292#894—91no—
293#894—91no—
294#894—91no—
295#893—91no—
296#893—91no—
297#893—91no—
298#893—91no—
299#893—91no—
300#893—181no—
301#893—181no—
302#892—91no—
303#892—91no—
304#892—91no—
305#892—91no—
306#892—91no—
307#892—181no—
308#890—31no—
309#889—31no—
310#887—91no—
311#887—91no—
312#886—91no—
313#886—91no—
314#885—91no—
315#884—91no—
316#883—91no—
317#67⋊C4—91no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#67⋊C4—91no—
321#877—91no—
322#876—91no—
323#875—91no—
324C42×D3—91no—
325C42×D3—91no—
326C22×C3⋊D3—31no—
327C22×C3⋊D3—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—61no—
330C22×C3⋊D3—61no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—121no—
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—31no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—61no—
340C22×C3×D3—61no—
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
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—41no—
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353C2×C32×C4C22×D311yescharacteristic
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—121no—
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C4⋊(C3⋊D3)—62no—
366C4⋊(C3⋊D3)—62no—
367C4×C3⋊D3—62no—
368C4×C3⋊D3—62no—
369C4×C3⋊D3—62no—
370C4×C3⋊D3—62no—
371C4×C3⋊D3—62no—
372C4×C3⋊D3—64no—
373C4×C3⋊D3—122no—
374C4×C3⋊D3—122no—
375C4×C3⋊D3—124no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C3×C4×D3—62no—
407C3×C4×D3—62no—
408C3×Dic6—62no—
409C3×Dic6—62no—
410#627—22no—
411#626—62no—
412#626—62no—
413#626—64no—
414#626—64no—
415#626—62no—
416#626—62no—
417#626—62no—
418#626—62no—
419#625—62no—
420#624—22no—
421#624—62no—
422D3×Dic3—62no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425D3×Dic3—62no—
426D3×Dic3—62no—
427D3×Dic3—62no—
428D3×Dic3—122no—
429D3×Dic3—122no—
430#529—271noSylow
431C2×C33C2×#4111yescharacteristic
432C2×C33C2×#4111yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C3⋊(C3⋊D3)—41no—
435C3×C3⋊D3—22no—
436C3×C3⋊D3—41no—
437C2×C3×Q8—91no—
438C22×C3×C4—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C22×Dic3—91no—
444C22×Dic3—91no—
445C22×Dic3—91no—
446C2×D12—91no—
447C2×D12—91no—
448C2×D12—91no—
449C2×D12—91no—
450C2×D12—91no—
451C2×D12—181no—
452C2×D12—181no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—181no—
465C2×C4×D3—181no—
466C2×C4×D3—181no—
467C2×C4×D3—181no—
468C2×C4×D3—181no—
469C2×C4×D3—361no—
470C2×Dic6—31no—
471C2×Dic6—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4—61no—
480C3×C4⋊C4—61no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C22⋊C4—91no—
489C3×C22⋊C4—91no—
490C3×C22⋊C4—91no—
491C3×C22⋊C4—91no—
492C3×C42—91no—
493C3×C42—91no—
494#217—91no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—61no—
506(C2×D3)⋊C4—61no—
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—91no—
518(C2×D3)⋊C4—91no—
519(C2×D3)⋊C4—91no—
520(C2×D3)⋊C4—91no—
521(C2×D3)⋊C4—181no—
522(C2×D3)⋊C4—181no—
523(C2×D3)⋊C4—181no—
524(C2×D3)⋊C4—181no—
525C4⋊Dic3—31no—
526C4⋊Dic3—31no—
527C4⋊Dic3—31no—
528C4⋊Dic3—31no—
529C4⋊Dic3—31no—
530C4⋊Dic3—31no—
531C4⋊Dic3—61no—
532C4⋊Dic3—91no—
533C4⋊Dic3D3211yescharacteristic
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4D3211yescharacteristic
543Dic3⋊C4D3211yescharacteristic
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—91no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—181no—
561C4×Dic3—181no—
562C4×Dic3—181no—
563C4×Dic3—181no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—41no—
568C22×C32C23×D311yescharacteristic
569C22×C32C23×D311yescharacteristic
570C22×C32C23×D311yescharacteristic
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3—61no—
577C2×C3⋊D3—61no—
578C2×C3⋊D3—61no—
579C2×C3⋊D3—62no—
580C2×C3⋊D3—62no—
581C2×C3⋊D3—62no—
582C2×C3⋊D3—61no—
583C2×C3⋊D3—61no—
584C2×C3⋊D3—61no—
585C2×C3⋊D3—61no—
586C2×C3⋊D3—61no—
587C2×C3⋊D3—61no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—121no—
594C2×C3⋊D3—122no—
595C2×C3⋊D3—122no—
596C2×C3⋊D3—122no—
597C2×C3⋊D3#23912yes—
598C2×C3×D3—32no—
599C2×C3×D3—32no—
600C2×C3×D3—62no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—62no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
614C2×C3×D3—121no—
615C2×C3×D3—121no—
616C32×C4—21no—
617C32×C4—22no—
618C32×C4—21no—
619C32×C4—21no—
620C32×C4—32no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—42no—
624C32×C4—61no—
625C32×C4—61no—
626C32×C4—61no—
627C32×C4—61no—
628C32×C4—61no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—32no—
634C3⋊Dic3—32no—
635C3⋊Dic3—32no—
636C3⋊Dic3—62no—
637C3⋊Dic3—62no—
638C3⋊Dic3—62no—
639C3⋊Dic3—122no—
640C3×Dic3—22no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—22no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—41no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3#23712yes—
669C3×Dic3#23912yes—
670#126—91no—
671#126—271no—
672#125—91no—
673#124—271no—
674#123—271no—
675#123—271no—
676C22⋊Q8—91no—
677#121—271no—
678C4×Q8—271no—
679C4×D4—271no—
680C4×D4—271no—
681C4×D4—271no—
682#117—271no—
683#117—271no—
684C2×C42—271no—
685C33#52911yescharacteristic, complemented, Sylow
686C23×C3—91no—
687C23×C3—91no—
688C22×D3—31no—
689C22×D3—31no—
690C22×D3—31no—
691C22×D3—31no—
692C22×D3—61no—
693C22×D3—61no—
694C22×D3—91no—
695C22×D3—91no—
696C22×D3—91no—
697C22×D3—181no—
698C22×D3—181no—
699C22×D3—181no—
700C22×D3—361no—
701C3×Q8—182no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—41no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—91no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—182no—
729C2×C3×C4C2×D3211yescharacteristic
730C2×C3×C4C2×D3211yescharacteristic
731C2×C3×C4C2×D3211yescharacteristic
732#67—182no—
733#67—182no—
734#67—182no—
735#67—182no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—91no—
751C2×Dic3—181no—
752C2×Dic3—181no—
753C2×Dic3—181no—
754C2×Dic3—182no—
755C2×Dic3—182no—
756C2×Dic3—182no—
757C2×Dic3—361no—
758C2×Dic3C2×D3211yescharacteristic
759C2×Dic3C2×D3211yescharacteristic
760C2×Dic3C2×D3211yescharacteristic
761C2×Dic3C2×D3211yescharacteristic
762C2×Dic3C2×D3211yescharacteristic
763C2×Dic3C2×D3211yescharacteristic
764D12—182no—
765D12—182no—
766D12—182no—
767D12—182no—
768D12—184no—
769D12—184no—
770D12—182no—
771C4×D3—62no—
772C4×D3—62no—
773C4×D3—182no—
774C4×D3—182no—
775C4×D3—182no—
776C4×D3—182no—
777C4×D3—182no—
778C4×D3—182no—
779C4×D3—182no—
780C4×D3—182no—
781C4×D3—182no—
782C4×D3—184no—
783C4×D3—362no—
784C4×D3—362no—
785C4×D3—362no—
786C4×D3—362no—
787C4×D3—364no—
788Dic6—62no—
789Dic6—62no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—41no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32C2×#23711yescharacteristic
803C2×C32C2×#23911yescharacteristic
804C2×C32C2×#23911yescharacteristic
805C2×C32D3×#4111yescharacteristic
806C2×C32D3×#4111yescharacteristic
807C2×C32D3×#4111yescharacteristic
808C2×C32D3×#4111yescharacteristic
809C2×C32D3×#4111yescharacteristic
810C2×C32D3×#4111yescharacteristic
811C3⋊D3—22no—
812C3⋊D3—41no—
813C3⋊D3—122no—
814C3⋊D3—122no—
815C3⋊D3—122no—
816C3⋊D3—124no—
817C3⋊D3—121no—
818C3⋊D3—121no—
819C3⋊D3—121no—
820C3×D3—62no—
821C3×D3—62no—
822C3×D3—122no—
823C3×D3—122no—
824C3×D3—121no—
825C3×D3—121no—
826C2×Q8—91no—
827C2×D4—271no—
828C2×D4—271no—
829C2×D4—271no—
830C22×C4—91no—
831C22×C4—271no—
832C22×C4—271no—
833C22×C4—271no—
834C22×C4—271no—
835C4⋊C4—31no—
836C4⋊C4—31no—
837C4⋊C4—31no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—91no—
841C4⋊C4—91no—
842C4⋊C4—91no—
843C4⋊C4—91no—
844C4⋊C4—271no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—91no—
857C42—271no—
858C42—271no—
859C42—271no—
860C42—271no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—41no—
865C22×C3—92no—
866C22×C3—181no—
867C22×C3—181no—
868C22×C3—181no—
869C22×C3—181no—
870C22×C3—181no—
871C22×C3C22×D3211yescharacteristic
872C22×C3C22×D3211yescharacteristic
873C22×C3C22×D3211yescharacteristic
874C2×D3—32no—
875C2×D3—32no—
876C2×D3—62no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—62no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3—61no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—182no—
893C2×D3—182no—
894C2×D3—182no—
895C2×D3—181no—
896C2×D3—181no—
897C2×D3—181no—
898C2×D3—181no—
899C2×D3—181no—
900C2×D3—181no—
901C2×D3—181no—
902C2×D3—181no—
903C2×D3—181no—
904C2×D3—361no—
905C2×D3—361no—
906C2×D3—361no—
907C2×D3—361no—
908C2×D3—361no—
909C2×D3—361no—
910C2×D3—362no—
911C2×D3—362no—
912C2×D3—362no—
913C3×C4—22no—
914C3×C4—21no—
915C3×C4—21no—
916C3×C4—21no—
917C3×C4—32no—
918C3×C4—32no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—42no—
922C3×C4—62no—
923C3×C4—62no—
924C3×C4—61no—
925C3×C4—61no—
926C3×C4—61no—
927C3×C4—61no—
928C3×C4—61no—
929C3×C4—61no—
930C3×C4—61no—
931C3×C4—61no—
932C3×C4—61no—
933C3×C4—61no—
934C3×C4—121no—
935C3×C4—121no—
936C3×C4—121no—
937C3×C4—121no—
938C3×C4—181no—
939C3×C4—181no—
940C3×C4—181no—
941C3×C4—181no—
942Dic3—21no—
943Dic3—21no—
944Dic3—21no—
945Dic3—21no—
946Dic3—21no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—61no—
954Dic3—61no—
955Dic3—92no—
956Dic3—92no—
957Dic3—92no—
958Dic3—121no—
959Dic3—121no—
960Dic3—121no—
961Dic3—121no—
962Dic3—182no—
963Dic3—182no—
964Dic3—182no—
965Dic3—362no—
966Dic3#379612yes—
967C32—21no—
968C32—21no—
969C32—21no—
970C32—41no—
971C32#562411yescharacteristic, complemented
972C32#569111yescharacteristic, complemented
973C32#570611yescharacteristic, complemented
974C23—91no—
975C23—91no—
976C23—271no—
977Q8—182no—
978D4—542no—
979D4—542no—
980D4—542no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—91no—
988C2×C4—91no—
989C2×C4—91no—
990C2×C4—91no—
991C2×C4—182no—
992C2×C4—271no—
993C2×C4—542no—
994C2×C4—542no—
995C2×C4—542no—
996C2×C4—542no—
997C2×C4D3311yescharacteristic
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—41no—
1008C2×C3—41no—
1009C2×C3—41no—
1010C2×C3—182no—
1011C2×C3—361no—
1012C2×C3C2×#379611yescharacteristic
1013C2×C3#6430611yescharacteristic
1014C2×C3#6430611yescharacteristic
1015C2×C3D3×#23711yescharacteristic
1016C2×C3#6431211yescharacteristic
1017C2×C3#6431211yescharacteristic
1018C2×C3D3×#23911yescharacteristic
1019C2×C3D3×#23911yescharacteristic
1020C2×C3D3×#23911yescharacteristic
1021D3—62no—
1022D3—62no—
1023D3—122no—
1024D3—122no—
1025D3—121no—
1026D3—121no—
1027D3—362no—
1028D3—362no—
1029D3—362no—
1030D3—364no—
1031D3—361no—
1032D3—361no—
1033D3—361no—
1034C22—92no—
1035C22—181no—
1036C22—181no—
1037C22—181no—
1038C22—181no—
1039C22—181no—
1040C22—541no—
1041C22—541no—
1042C22—541no—
1043C22C2×D3311yescharacteristic
1044C4—21no—
1045C4—32no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—61no—
1050C4—61no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C4—181no—
1055C4—272no—
1056C3—21no—
1057C3—21no—
1058C3—21no—
1059C3—41no—
1060C3#1059444211yescharacteristic, complemented
1061C3#1059445311yescharacteristic, complemented
1062C3#1059446511yescharacteristic, complemented
1063C2—182no—
1064C2—361no—
1065C2—1081no—
1066C2D3×#379611yescharacteristic
1067C2#1172439111yescharacteristic
1068C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722961C2
hypercenterC2×C4D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723690C2semidirect
2. #11723472C2semidirect
3. #11723472C2semidirect
4. #11723413C2semidirect
5. C3×#63895C2semidirect
6. C3×#63848C2semidirect
7. C3×#63845C2semidirect
8. #11723021C2semidirect
9. #11723003C2semidirect
10. #11722999C2semidirect
12. #11722941C2semidirect
13. #11722938C2semidirect
14. #11722921C2semidirect
15. Dic3×#624C2semidirect
69. #63895D3semidirect
97. #63848D3semidirect
98. #63845D3semidirect
685. C33#529semidirect
971. C32#5624semidirect
972. C32#5691semidirect
973. C32#5706semidirect
1060. C3#10594442semidirect
1061. C3#10594453semidirect
1062. C3#10594465semidirect

Maximal subgroups

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

subgroupindex
#117236902
#117234722
#117234132
C3×#638952
C3×#638482
C3×#638452
#117230212
#117230032
#117229992
#117229612
#117229412
#117229382
#117229212
Dic3×#6242
#105944653
#105944533
#105944423