Finite Group Databasebeta

← #13168418

Subgroups — #13168418

Order 1728.

1194 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723690C211yesmaximal, characteristic, complemented
2#11723528C211yesmaximal, characteristic, complemented
3#11723497C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63880C211yesmaximal, characteristic, complemented
6C3×#63861C211yesmaximal, characteristic, complemented
7C3×#63836C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723016C211yesmaximal, characteristic, complemented
10#11722994C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic
12#11722931C211yesmaximal, characteristic, complemented
13#11722930C211yesmaximal, characteristic, complemented
14#11722913C211yesmaximal, characteristic, complemented
15Dic3×#624C211yesmaximal, characteristic, complemented
16#10594417—31nomaximal
17#10594089—31nomaximal
18#10593910—31nomaximal
19C2×#6308C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6290C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64094—31no—
56C4×#634—31no—
57C3×#898—31no—
58C3×#892—31no—
59C3×#67⋊C4—31no—
60C3×#879—31no—
61C3×C4×D12—31no—
62C3×#872—31no—
63#63971—31no—
64#63969—31no—
65#63955—31no—
66#63952—31no—
67#63913—31no—
68#63913—31no—
69#63913—61no—
70#63912—31no—
71#63904—31no—
72#63904—31no—
73C4×#625—31no—
74C4×#625—31no—
75#63896—31no—
76#63896—31no—
77#63896—61no—
78#63891—31no—
79#63890—31no—
80#63885—31no—
81#63884—31no—
82C4×#624—31no—
83#63880D311yescharacteristic, complemented
84#63879—31no—
85#63877—31no—
86C4×D3×Dic3—31no—
87C4×D3×Dic3—31no—
88#63870—31no—
89#63868—31no—
90#63861D311yescharacteristic, complemented
91#63859—31no—
92#63858—31no—
93#63855—31no—
94#63854—31no—
95#63854—31no—
96#63847—31no—
97#63847—31no—
98#63844—31no—
99#63844—31no—
100#63844—61no—
101#63836D311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108#6308—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6294—22no—
120#6290—22no—
121Dic3×C3⋊D3—22no—
122C3×#626—22no—
123C3×#624—22no—
124C3×#624—22no—
125C3×D3×Dic3—22no—
126#5706—91no—
127#5538—91no—
128#5528—91no—
129C2×#638—31no—
130C2×C4×C3⋊D3—31no—
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—31no—
134C2×#634—61no—
135C2×#634—61no—
136C2×#634—61no—
137C2×#634—121no—
138C2×C3×#67—31no—
139C22×C3×Dic3—31no—
140C2×C3×D12—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#626C2×D311yescharacteristic
149C2×#625—31no—
150C2×#625—31no—
151C2×#625—31no—
152C2×#625—61no—
153C2×#624—31no—
154C2×#624C2×D311yescharacteristic
155C2×#624C2×D311yescharacteristic
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—61no—
161C2×D3×Dic3C2×D311yescharacteristic
162C32×C4⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C42—31no—
165#3757—31no—
166#3752—31no—
167#3752—31no—
168#3752C2×D311yescharacteristic
169#3752C2×D311yescharacteristic
170C4⋊(C3⋊Dic3)C2×D311yescharacteristic
171#3750—31no—
172#3750—31no—
173#3750—31no—
174#3750—31no—
175C4×C3⋊Dic3—31no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—31no—
178C3×#217—31no—
179C3×#217—31no—
180C3×(C2×D3)⋊C4—21no—
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—31no—
189C3×(C2×D3)⋊C4—61no—
190C3×(C2×D3)⋊C4—61no—
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×(C2×D3)⋊C4C2×D311yescharacteristic
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—61no—
198C3×Dic3⋊C4—21no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4C2×D311yescharacteristic
204C3×Dic3⋊C4C2×D311yescharacteristic
205C3×C4×Dic3—21no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3C2×D311yescharacteristic
211C3×C4×Dic3C2×D311yescharacteristic
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724—61no—
222#3724C2×D311yescharacteristic
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230#3722—31no—
231#3722C2×D311yescharacteristic
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—61no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3C2×D311yescharacteristic
244(C2×D3)⋊Dic3C2×D311yescharacteristic
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
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#4112yes—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3⋊(C3⋊Dic3)#4112yes—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×#126—91no—
279C3×C4×D4—91no—
280C3×#117—91no—
281#939—91no—
282#935—91no—
283C4×#67—91no—
284C4×#67—91no—
285C4×#67—91no—
286C4×#67—91no—
287#926—91no—
288C2×C4×Dic3—91no—
289#898—31no—
290#898—91no—
291#896—91no—
292#896—91no—
293#896—181no—
294#894—91no—
295#894—91no—
296#893—91no—
297#892—31no—
298#889—91no—
299#889—91no—
300#889—91no—
301#887—91no—
302#886—91no—
303#885—91no—
304#885—91no—
305#885—91no—
306#885—181no—
307#884—91no—
308#884—91no—
309#883—91no—
310#883—91no—
311#67⋊C4—31no—
312#67⋊C4—91no—
313#879—31no—
314#879—91no—
315#878—91no—
316#877—91no—
317#876—91no—
318C4×D12—31no—
319#872—31no—
320#872—91no—
321C42×D3—91no—
322C42×D3—91no—
323C4×Dic6—91no—
324C4×Dic6—91no—
325C4×Dic6—181no—
326C23×C32—31no—
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—61no—
335C22×C3×D3—61no—
336C22×C3×D3C22×D311yescharacteristic
337C22×C3×D3C22×D311yescharacteristic
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—41no—
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350#638—62no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
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—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C4×C3⋊D3—62no—
370#634—62no—
371#634—62no—
372#634—62no—
373#634—64no—
374#634—122no—
375#634—122no—
376#634—124no—
377C3×#67—62no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—21no—
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—31no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—62no—
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×D12—62no—
407C3×C4×D3—62no—
408C3×C4×D3—62no—
409C3×C4×D3—62no—
410C3×C4×D3—62no—
411C3×C4×D3—62no—
412#626—22no—
413#626—62no—
414#626—62no—
415#625—62no—
416#625—62no—
417#625—62no—
418#625—122no—
419#624—22no—
420#624—22no—
421#624—62no—
422D3×Dic3—22no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425D3×Dic3—62no—
426D3×Dic3—62no—
427D3×Dic3—122no—
428#529—271noSylow
429C2×C33C2×#4111yescharacteristic
430C2×C33C2×#4111yescharacteristic
431C2×C33C2×#4111yescharacteristic
432C3×C3⋊D3—22no—
433C3×C3⋊D3—41no—
434C32×D3—41no—
435C2×C3×D4—91no—
436C22×C3×C4—91no—
437C22×C3×C4—91no—
438C22×C3×C4—91no—
439C2×#67—31no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—181no—
446C22×Dic3—31no—
447C22×Dic3—91no—
448C22×Dic3—91no—
449C2×D12—31no—
450C2×D12—91no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—181no—
461C2×Dic6—91no—
462C2×Dic6—91no—
463C2×Dic6—91no—
464C2×Dic6—181no—
465C2×Dic6—181no—
466C2×Dic6—181no—
467C2×Dic6—361no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—31no—
477C3×C22⋊C4—61no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C42—31no—
484C3×C42—31no—
485C3×C42—61no—
486C3×C42—91no—
487C3×C42—91no—
488#217—31no—
489#217—31no—
490#217—91no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—181no—
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—61no—
505(C2×D3)⋊C4—61no—
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—181no—
514(C2×D3)⋊C4—181no—
515(C2×D3)⋊C4D3211yescharacteristic
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—61no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—181no—
541Dic3⋊C4—181no—
542Dic3⋊C4—181no—
543Dic3⋊C4—181no—
544Dic3⋊C4D3211yescharacteristic
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—31no—
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—181no—
559C4×Dic3—181no—
560C4×Dic3—181no—
561C4×Dic3D3211yescharacteristic
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—41no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32C23×D311yescharacteristic
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3—21no—
577C2×C3⋊D3#23512yes—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—32no—
585C2×C3×D3—32no—
586C2×C3×D3—41no—
587C2×C3×D3—41no—
588C2×C3×D3—41no—
589C2×C3×D3—62no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C2×C3×D3—121no—
603C2×C3×D3—121no—
604C2×C3×D3—121no—
605C32×C4—21no—
606C32×C4—22no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—32no—
610C32×C4—41no—
611C32×C4—41no—
612C32×C4—42no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—61no—
616C32×C4—61no—
617C3⋊Dic3—21no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—32no—
622C3⋊Dic3—32no—
623C3⋊Dic3—32no—
624C3⋊Dic3—62no—
625C3⋊Dic3—62no—
626C3⋊Dic3—62no—
627C3⋊Dic3—61no—
628C3⋊Dic3—62no—
629C3⋊Dic3—61no—
630C3⋊Dic3—61no—
631C3⋊Dic3—122no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—122no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—22no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—121no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660C3×Dic3#23512yes—
661C3×Dic3#23712yes—
662#126—91no—
663#126—271no—
664#125—271no—
665#124—271no—
666#123—271no—
667#123—271no—
668C22⋊Q8—271no—
669#121—271no—
670C4×Q8—271no—
671C4×D4—91no—
672C4×D4—271no—
673C4×D4—271no—
674#117—91no—
675#117—271no—
676C2×C42—271no—
677C33#52911yescharacteristic, complemented, Sylow
678C23×C3—31no—
679C23×C3—31no—
680C23×C3—61no—
681C23×C3—91no—
682C23×C3—91no—
683C22×D3—31no—
684C22×D3—31no—
685C22×D3—31no—
686C22×D3—31no—
687C22×D3—61no—
688C22×D3—61no—
689C22×D3C2×D3211yescharacteristic
690C3×D4—182no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—41no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—182no—
715C2×C3×C4—182no—
716C2×C3×C4—182no—
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720#67—62no—
721#67—182no—
722#67—182no—
723#67—182no—
724#67—182no—
725#67—182no—
726#67—362no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—62no—
740C2×Dic3—91no—
741C2×Dic3—91no—
742C2×Dic3—91no—
743C2×Dic3—91no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—181no—
747C2×Dic3—181no—
748C2×Dic3—181no—
749C2×Dic3—181no—
750C2×Dic3—181no—
751C2×Dic3—181no—
752C2×Dic3—182no—
753C2×Dic3—182no—
754C2×Dic3—361no—
755C2×Dic3—361no—
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C2×Dic3C2×D3211yescharacteristic
759C2×Dic3C2×D3211yescharacteristic
760C2×Dic3C2×D3211yescharacteristic
761D12—62no—
762D12—182no—
763C4×D3—62no—
764C4×D3—62no—
765C4×D3—62no—
766C4×D3—62no—
767C4×D3—62no—
768C4×D3—182no—
769C4×D3—182no—
770C4×D3—182no—
771C4×D3—182no—
772C4×D3—362no—
773Dic6—182no—
774Dic6—182no—
775Dic6—182no—
776Dic6—184no—
777Dic6—362no—
778Dic6—362no—
779Dic6—364no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—41no—
790C2×C32—41no—
791C2×C32—41no—
792C2×C32—121no—
793C2×C32C2×#23511yescharacteristic
794C2×C32C2×#23511yescharacteristic
795C2×C32C2×#23711yescharacteristic
796C2×C32D3×#4111yescharacteristic
797C2×C32D3×#4111yescharacteristic
798C2×C32D3×#4111yescharacteristic
799C2×C32D3×#4111yescharacteristic
800C2×C32D3×#4111yescharacteristic
801C2×C32D3×#4111yescharacteristic
802C3⋊D3—22no—
803C3⋊D3—41no—
804C3×D3—41no—
805C3×D3—41no—
806C3×D3—62no—
807C3×D3—62no—
808C3×D3—81no—
809C3×D3—122no—
810C3×D3—121no—
811C3×D3—121no—
812C3×D3—241no—
813C2×Q8—271no—
814C2×D4—91no—
815C2×D4—271no—
816C2×D4—271no—
817C22×C4—91no—
818C22×C4—91no—
819C22×C4—91no—
820C22×C4—271no—
821C22×C4—271no—
822C4⋊C4—31no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—91no—
827C4⋊C4—271no—
828C4⋊C4—271no—
829C4⋊C4—271no—
830C4⋊C4—271no—
831C4⋊C4—271no—
832C22⋊C4—31no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—271no—
839C22⋊C4—271no—
840C22⋊C4—271no—
841C22⋊C4—271no—
842C42—31no—
843C42—91no—
844C42—91no—
845C42—271no—
846C42—271no—
847C42—271no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—41no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—92no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—181no—
863C22×C3—181no—
864C22×C3—181no—
865C22×C3—181no—
866C22×C3—181no—
867C22×C3C22×D3211yescharacteristic
868C22×C3C22×D3211yescharacteristic
869C22×C3C22×D3211yescharacteristic
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—32no—
874C2×D3—32no—
875C2×D3—62no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C3×C4—22no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—32no—
896C3×C4—32no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—42no—
900C3×C4—62no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—61no—
909C3×C4—121no—
910C3×C4—121no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—181no—
914C3×C4—181no—
915C3×C4—181no—
916C3×C4—181no—
917Dic3—21no—
918Dic3—21no—
919Dic3—21no—
920Dic3—21no—
921Dic3—61no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—92no—
930Dic3—92no—
931Dic3—92no—
932Dic3—121no—
933Dic3—121no—
934Dic3—121no—
935Dic3—121no—
936Dic3—182no—
937Dic3—182no—
938Dic3—182no—
939Dic3—182no—
940Dic3—181no—
941Dic3—181no—
942Dic3—181no—
943Dic3—362no—
944Dic3—361no—
945Dic3—361no—
946Dic3—362no—
947Dic3#379512yes—
948C32—21no—
949C32—21no—
950C32—21no—
951C32—41no—
952C32#552811yescharacteristic, complemented
953C32#553811yescharacteristic, complemented
954C32#570611yescharacteristic, complemented
955C23—31no—
956C23—91no—
957C23—91no—
958Q8—542no—
959D4—182no—
960D4—542no—
961D4—542no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—31no—
965C2×C4—31no—
966C2×C4—31no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—182no—
972C2×C4—182no—
973C2×C4—182no—
974C2×C4—271no—
975C2×C4—271no—
976C2×C4—542no—
977C2×C4—542no—
978C2×C4D3311yescharacteristic
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—41no—
989C2×C3—41no—
990C2×C3—41no—
991C2×C3—121no—
992C2×C3—121no—
993C2×C3—182no—
994C2×C3—241no—
995C2×C3—361no—
996C2×C3C2×#379511yescharacteristic
997C2×C3D3×#23511yescharacteristic
998C2×C3D3×#23511yescharacteristic
999C2×C3D3×#23511yescharacteristic
1000C2×C3#6430611yescharacteristic
1001C2×C3D3×#23711yescharacteristic
1002C2×C3#6431211yescharacteristic
1003C2×C3#6431211yescharacteristic
1004C2×C3#6431911yescharacteristic
1005D3—41no—
1006D3—62no—
1007D3—62no—
1008D3—122no—
1009D3—121no—
1010D3—121no—
1011D3—241no—
1012C22—61no—
1013C22—61no—
1014C22—61no—
1015C22—92no—
1016C22—181no—
1017C22—181no—
1018C22—181no—
1019C22—181no—
1020C22—181no—
1021C22C2×D3311yescharacteristic
1022C4—21no—
1023C4—32no—
1024C4—61no—
1025C4—61no—
1026C4—61no—
1027C4—61no—
1028C4—181no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C4—272no—
1033C4—541no—
1034C3—21no—
1035C3—21no—
1036C3—21no—
1037C3—41no—
1038C3#1059391011yescharacteristic, complemented
1039C3#1059408911yescharacteristic, complemented
1040C3#1059441711yescharacteristic, complemented
1041C2—121no—
1042C2—182no—
1043C2—361no—
1044C2D3×#379511yescharacteristic
1045C2#1172438911yescharacteristic
1046C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722967C2
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. #11723528C2semidirect
3. #11723497C2semidirect
4. #11723399C2semidirect
5. C3×#63880C2semidirect
6. C3×#63861C2semidirect
7. C3×#63836C2semidirect
8. #11723024C2semidirect
9. #11723016C2semidirect
10. #11722994C2semidirect
12. #11722931C2semidirect
13. #11722930C2semidirect
14. #11722913C2semidirect
15. Dic3×#624C2semidirect
83. #63880D3semidirect
90. #63861D3semidirect
101. #63836D3semidirect
677. C33#529semidirect
952. C32#5528semidirect
953. C32#5538semidirect
954. C32#5706semidirect
1038. C3#10593910semidirect
1039. C3#10594089semidirect
1040. C3#10594417semidirect

Maximal subgroups

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

subgroupindex
#117236902
#117235282
#117234972
#117233992
C3×#638802
C3×#638612
C3×#638362
#117230242
#117230162
#117229942
#117229672
#117229312
#117229302
#117229132
Dic3×#6242
#105944173
#105940893
#105939103