Finite Group Databasebeta

← #13168371

Subgroups — #13168371

Order 1728.

1200 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723679C211yesmaximal, characteristic, complemented
2#11723510C211yesmaximal, characteristic, complemented
3#11723453C211yesmaximal, characteristic, complemented
4#11723419C211yesmaximal, characteristic, complemented
5C3×#63879C211yesmaximal, characteristic, complemented
6C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
7C3×#63859C211yesmaximal, characteristic, complemented
8#11722987C211yesmaximal, characteristic, complemented
9#11722985C211yesmaximal, characteristic, complemented
10#11722975C211yesmaximal, characteristic, complemented
11#11722958C211yesmaximal, characteristic
12#11722942C211yesmaximal, characteristic, complemented
13#11722932C211yesmaximal, characteristic, complemented
14#11722918C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10594839—31nomaximal
17#10594089—31nomaximal
18#10593975—31nomaximal
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×C3×#625C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28#88859C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88815C2211yescharacteristic
38#88807C2211yescharacteristic
39#88806C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C4×#638—31no—
55#64094—31no—
56#64085—31no—
57C3×C4×#67—31no—
58C2×C3×C4×Dic3—31no—
59C3×#67⋊C4—31no—
60C3×#879—31no—
61C3×#876—31no—
62C3×C42×D3—31no—
63#63978—31no—
64#63971—31no—
65#63969—31no—
66#63966—31no—
67#63964—31no—
68#63961—31no—
69#63955—31no—
70#63952—31no—
71C4×#627—31no—
72#63906—31no—
73#63905—31no—
74#63904—31no—
75#63904—31no—
76#63904—61no—
77C4×#626—31no—
78#63896—31no—
79#63890—31no—
80#63880—31no—
81#63879D311yescharacteristic, complemented
82#63877—31no—
83C4×D3×Dic3D311yescharacteristic, complemented
84#63874—31no—
85#63870—31no—
86#63868—31no—
87#63868—31no—
88#63868—61no—
89#63867—31no—
90#63867—31no—
91#63859D311yescharacteristic, complemented
92#63855—31no—
93#63852—31no—
94#63852—31no—
95#63852—61no—
96#63851—31no—
97#63850—31no—
98#63844—31no—
99#63837—31no—
100#63836—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
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
117C32×C4×D3—22no—
118#6293—22no—
119#6291—22no—
120#6291—22no—
121#6289—22no—
122C3×#625—22no—
123C3×D3×Dic3—22no—
124C3×D3×Dic3—22no—
125C3×D3×Dic3—22no—
126#5706—91no—
127#5538—91no—
128#5479—91no—
129C22×C32×C4—31no—
130C2×#638—31no—
131C2×#638—31no—
132C2×C4×C3⋊D3—31no—
133C2×#634—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3C2×D311yescharacteristic
144C2×C3×C4×D3C2×D311yescharacteristic
145C2×#627—31no—
146C2×#627—31no—
147C2×#627—61no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—61no—
153C2×#626—61no—
154C2×#625C2×D311yescharacteristic
155C2×#624—31no—
156C2×#624—31no—
157C2×#624—61no—
158C2×D3×Dic3C2×D311yescharacteristic
159C2×D3×Dic3C2×D311yescharacteristic
160C2×D3×Dic3C2×D311yescharacteristic
161C32×C22⋊C4—31no—
162C32×C42—31no—
163#3757—31no—
164#3757—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—61no—
172#3752—61no—
173#3752—61no—
174#3752—121no—
175#3750—31no—
176#3750—31no—
177#3750C2×D311yescharacteristic
178#3750C2×D311yescharacteristic
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3C2×D311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×(C2×D3)⋊C4—21no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4C2×D311yescharacteristic
189C3×(C2×D3)⋊C4C2×D311yescharacteristic
190C3×C4⋊Dic3—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—61no—
199C3×Dic3⋊C4—61no—
200C3×C4×Dic3—21no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—61no—
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—61no—
219#3724C2×D311yescharacteristic
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—61no—
239#3722—61no—
240#3722—61no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250Dic32—31no—
251Dic32—31no—
252Dic32—61no—
253Dic32C2×D311yescharacteristic
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3#4112yes—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×#126—91no—
279C3×C4×D4—91no—
280C2×C3×C42—91no—
281#939—91no—
282#935—91no—
283#930—91no—
284#929—91no—
285#929—91no—
286C4×#67—31no—
287C4×#67—91no—
288C4×#67—91no—
289C4×#67—91no—
290C4×#67—181no—
291#926—91no—
292#924—91no—
293C2×C4×Dic3—31no—
294#898—91no—
295#896—91no—
296#894—91no—
297#893—91no—
298#892—91no—
299#889—91no—
300#889—91no—
301#887—91no—
302#886—91no—
303#885—91no—
304#885—91no—
305#885—181no—
306#884—91no—
307#883—91no—
308#67⋊C4—31no—
309#67⋊C4—91no—
310#879—31no—
311#878—91no—
312#877—91no—
313#876—31no—
314#876—91no—
315#876—91no—
316#876—181no—
317#875—91no—
318C4×D12—91no—
319#872—91no—
320#872—91no—
321#872—91no—
322C42×D3—31no—
323#870—91no—
324C4×Dic6—91no—
325C4×Dic6—91no—
326C23×C32—31no—
327C23×C32—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—31no—
330C22×C3⋊D3—31no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—61no—
333C22×C3⋊D3—61no—
334C22×C3⋊D3—121no—
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3C22×D311yescharacteristic
338C22×C3×D3C22×D311yescharacteristic
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
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—41no—
349C2×C32×C4—62no—
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353#638—62no—
354#638—62no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4×C3⋊D3—62no—
369#634—62no—
370C3×#67—62no—
371C3×#67—62no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
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—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—62no—
395C2×C3×Dic3—62no—
396C2×C3×Dic3—62no—
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
405C3×C4×D3—22no—
406C3×C4×D3—22no—
407C3×C4×D3—42no—
408C3×C4×D3—62no—
409C3×C4×D3—62no—
410C3×C4×D3—62no—
411#627—62no—
412#627—62no—
413#627—122no—
414#626—62no—
415#626—62no—
416#626—64no—
417#626—62no—
418#626—62no—
419#626—122no—
420#625—22no—
421#624—62no—
422#624—62no—
423#624—122no—
424D3×Dic3—22no—
425D3×Dic3—22no—
426D3×Dic3—22no—
427#529—271noSylow
428C2×C33C2×#4111yescharacteristic
429C2×C33C2×#4111yescharacteristic
430C2×C33C2×#4111yescharacteristic
431C3⋊(C3⋊D3)—41no—
432C32×D3—22no—
433C32×D3—41no—
434C2×C3×D4—91no—
435C22×C3×C4—31no—
436C22×C3×C4—31no—
437C22×C3×C4—61no—
438C22×C3×C4—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—31no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—91no—
446C2×#67—91no—
447C2×#67—181no—
448C2×#67—181no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C2×D12—91no—
453C2×D12—91no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—181no—
461C2×C4×D3D3211yescharacteristic
462C2×Dic6—91no—
463C2×Dic6—91no—
464C2×Dic6—91no—
465C2×Dic6—181no—
466C3×C4⋊C4—91no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C22⋊C4—31no—
471C3×C22⋊C4—31no—
472C3×C22⋊C4—61no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C42—31no—
477C3×C42—31no—
478C3×C42—61no—
479C3×C42—91no—
480C3×C42—91no—
481C3×C42—91no—
482C3×C42—91no—
483#217—31no—
484#217—31no—
485#217—31no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
490#217—181no—
491#217—181no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—91no—
496(C2×D3)⋊C4—91no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
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—181no—
510(C2×D3)⋊C4—181no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515(C2×D3)⋊C4—361no—
516(C2×D3)⋊C4D3211yescharacteristic
517C4⋊Dic3—31no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—61no—
531Dic3⋊C4—61no—
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—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—181no—
546Dic3⋊C4—181no—
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—31no—
550C4×Dic3—31no—
551C4×Dic3—31no—
552C4×Dic3—31no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—61no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—181no—
560C4×Dic3D3211yescharacteristic
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—32no—
565C22×C32—41no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C2×C3⋊D3—61no—
575C2×C3⋊D3—62no—
576C2×C3⋊D3—61no—
577C2×C3⋊D3—61no—
578C2×C3⋊D3—61no—
579C2×C3⋊D3—61no—
580C2×C3⋊D3—61no—
581C2×C3⋊D3—61no—
582C2×C3⋊D3—61no—
583C2×C3⋊D3—61no—
584C2×C3⋊D3—121no—
585C2×C3⋊D3—121no—
586C2×C3⋊D3—122no—
587C2×C3⋊D3—121no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—241no—
594C2×C3⋊D3—241no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—22no—
606C2×C3×D3—41no—
607C2×C3×D3—41no—
608C2×C3×D3—41no—
609C2×C3×D3—41no—
610C2×C3×D3—41no—
611C2×C3×D3#23512yes—
612C2×C3×D3#23512yes—
613C32×C4—21no—
614C32×C4—21no—
615C32×C4—21no—
616C32×C4—32no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—61no—
621C32×C4—61no—
622C32×C4—61no—
623C32×C4—81no—
624C3⋊Dic3—21no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—61no—
630C3⋊Dic3—61no—
631C3⋊Dic3—61no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—121no—
635C3⋊Dic3—241no—
636C3⋊Dic3#23512yes—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—22no—
644C3×Dic3—32no—
645C3×Dic3—32no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—62no—
650C3×Dic3—62no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—121no—
662C3×Dic3—121no—
663C3×Dic3—121no—
664C3×Dic3—121no—
665C3×Dic3#23512yes—
666C3×Dic3#23712yes—
667#126—91no—
668#126—271no—
669#125—271no—
670#124—271no—
671#123—271no—
672#123—271no—
673C22⋊Q8—271no—
674#121—271no—
675C4×Q8—271no—
676C4×D4—91no—
677C4×D4—271no—
678C4×D4—271no—
679#117—271no—
680#117—271no—
681C2×C42—91no—
682C33#52911yescharacteristic, complemented, Sylow
683C23×C3—31no—
684C23×C3—31no—
685C23×C3—31no—
686C23×C3—31no—
687C23×C3—61no—
688C23×C3—61no—
689C22×D3—91no—
690C22×D3—91no—
691C22×D3—91no—
692C22×D3—181no—
693C22×D3—181no—
694C22×D3—181no—
695C22×D3—361no—
696C22×D3C2×D3211yescharacteristic
697C22×D3C2×D3211yescharacteristic
698C3×D4—182no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—41no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—62no—
716C2×C3×C4—62no—
717C2×C3×C4—91no—
718C2×C3×C4—91no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—122no—
724C2×C3×C4—182no—
725C2×C3×C4—182no—
726C2×C3×C4—182no—
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730#67—62no—
731#67—62no—
732#67—182no—
733#67—182no—
734#67—182no—
735#67—182no—
736#67—184no—
737#67—362no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—91no—
760C2×Dic3—91no—
761C2×Dic3—91no—
762C2×Dic3—181no—
763C2×Dic3—181no—
764C2×Dic3—181no—
765C2×Dic3—361no—
766C2×Dic3C2×D3211yescharacteristic
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770D12—182no—
771D12—182no—
772C4×D3—22no—
773C4×D3—62no—
774C4×D3—62no—
775C4×D3—62no—
776C4×D3—182no—
777C4×D3—182no—
778C4×D3—182no—
779C4×D3—362no—
780Dic6—182no—
781Dic6—182no—
782Dic6—182no—
783Dic6—362no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—41no—
794C2×C32—41no—
795C2×C32—41no—
796C2×C32—62no—
797C2×C32—121no—
798C2×C32C2×#23511yescharacteristic
799C2×C32C2×#23511yescharacteristic
800C2×C32C2×#23511yescharacteristic
801C2×C32C2×#23511yescharacteristic
802C2×C32C2×#23711yescharacteristic
803C2×C32D3×#4111yescharacteristic
804C2×C32D3×#4111yescharacteristic
805C2×C32D3×#4111yescharacteristic
806C2×C32D3×#4111yescharacteristic
807C3⋊D3—121no—
808C3⋊D3—122no—
809C3⋊D3—121no—
810C3⋊D3—121no—
811C3⋊D3—241no—
812C3⋊D3—241no—
813C3⋊D3—242no—
814C3×D3—22no—
815C3×D3—22no—
816C3×D3—42no—
817C3×D3—41no—
818C3×D3—41no—
819C3×D3—81no—
820C2×Q8—271no—
821C2×D4—91no—
822C2×D4—271no—
823C2×D4—271no—
824C22×C4—31no—
825C22×C4—91no—
826C22×C4—91no—
827C22×C4—91no—
828C22×C4—271no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—271no—
834C4⋊C4—271no—
835C4⋊C4—271no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C22⋊C4—31no—
840C22⋊C4—91no—
841C22⋊C4—91no—
842C22⋊C4—91no—
843C22⋊C4—271no—
844C22⋊C4—271no—
845C22⋊C4—271no—
846C22⋊C4—271no—
847C22⋊C4—271no—
848C22⋊C4—271no—
849C42—31no—
850C42—91no—
851C42—91no—
852C42—91no—
853C42—91no—
854C42—271no—
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—32no—
859C22×C3—32no—
860C22×C3—41no—
861C22×C3—62no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—61no—
865C22×C3—61no—
866C22×C3—61no—
867C22×C3—61no—
868C22×C3—61no—
869C22×C3—61no—
870C22×C3—61no—
871C22×C3—61no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3—121no—
876C22×C3—121no—
877C22×C3C22×D3211yescharacteristic
878C22×C3C22×D3211yescharacteristic
879C22×C3C22×D3211yescharacteristic
880C2×D3—21no—
881C2×D3—21no—
882C2×D3—21no—
883C2×D3—21no—
884C2×D3—21no—
885C2×D3—182no—
886C2×D3—181no—
887C2×D3—181no—
888C2×D3—181no—
889C2×D3—181no—
890C2×D3—181no—
891C2×D3—181no—
892C2×D3—181no—
893C2×D3—181no—
894C2×D3—181no—
895C2×D3—361no—
896C2×D3—361no—
897C2×D3—361no—
898C2×D3—361no—
899C2×D3—361no—
900C2×D3—361no—
901C2×D3—361no—
902C2×D3—361no—
903C2×D3—362no—
904C2×D3—721no—
905C2×D3—721no—
906C2×D3#379812yes—
907C3×C4—21no—
908C3×C4—21no—
909C3×C4—21no—
910C3×C4—32no—
911C3×C4—32no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—62no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—81no—
923C3×C4—92no—
924C3×C4—121no—
925C3×C4—121no—
926C3×C4—121no—
927C3×C4—181no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931C3×C4—181no—
932Dic3—21no—
933Dic3—21no—
934Dic3—21no—
935Dic3—32no—
936Dic3—32no—
937Dic3—62no—
938Dic3—62no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—121no—
950Dic3—121no—
951Dic3—121no—
952Dic3—121no—
953Dic3—181no—
954Dic3—181no—
955Dic3—181no—
956Dic3—361no—
957Dic3—361no—
958Dic3—361no—
959Dic3—721no—
960Dic3#380412yes—
961C32—21no—
962C32—21no—
963C32—21no—
964C32—41no—
965C32#547911yescharacteristic, complemented
966C32#553811yescharacteristic, complemented
967C32#570611yescharacteristic, complemented
968C23—31no—
969C23—31no—
970C23—271no—
971Q8—542no—
972D4—182no—
973D4—542no—
974D4—542no—
975C2×C4—31no—
976C2×C4—31no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—62no—
980C2×C4—91no—
981C2×C4—91no—
982C2×C4—91no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—182no—
987C2×C4—182no—
988C2×C4—182no—
989C2×C4—271no—
990C2×C4—542no—
991C2×C4D3311yescharacteristic
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—41no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—62no—
1005C2×C3—62no—
1006C2×C3—122no—
1007C2×C3—121no—
1008C2×C3—121no—
1009C2×C3—241no—
1010C2×C3C2×#379811yescharacteristic
1011C2×C3D3×#23511yescharacteristic
1012C2×C3D3×#23511yescharacteristic
1013C2×C3D3×#23511yescharacteristic
1014C2×C3D3×#23511yescharacteristic
1015C2×C3D3×#23511yescharacteristic
1016C2×C3D3×#23711yescharacteristic
1017C2×C3#6431211yescharacteristic
1018C2×C3C2×#380411yescharacteristic
1019D3—22no—
1020D3—41no—
1021D3—362no—
1022D3—361no—
1023D3—361no—
1024D3—361no—
1025D3—721no—
1026D3—721no—
1027D3—722no—
1028C22—32no—
1029C22—61no—
1030C22—61no—
1031C22—61no—
1032C22—61no—
1033C22—61no—
1034C22—541no—
1035C22—541no—
1036C22—541no—
1037C22C2×D3311yescharacteristic
1038C4—21no—
1039C4—32no—
1040C4—61no—
1041C4—61no—
1042C4—61no—
1043C4—92no—
1044C4—181no—
1045C4—181no—
1046C4—181no—
1047C4—181no—
1048C4—181no—
1049C4—541no—
1050C3—21no—
1051C3—21no—
1052C3—21no—
1053C3—41no—
1054C3#1059397511yescharacteristic, complemented
1055C3#1059408911yescharacteristic, complemented
1056C3#1059483911yescharacteristic, complemented
1057C2—62no—
1058C2—121no—
1059C2—1081no—
1060C2D3×#379811yescharacteristic
1061C2#1172438811yescharacteristic
1062C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722958C2
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. #11723679C2semidirect
2. #11723510C2semidirect
3. #11723453C2semidirect
4. #11723419C2semidirect
5. C3×#63879C2semidirect
6. C3×C4×D3×Dic3C2semidirect
7. C3×#63859C2semidirect
8. #11722987C2semidirect
9. #11722985C2semidirect
10. #11722975C2semidirect
12. #11722942C2semidirect
13. #11722932C2semidirect
14. #11722918C2semidirect
15. #11722913C2semidirect
81. #63879D3semidirect
83. C4×D3×Dic3D3semidirect
91. #63859D3semidirect
682. C33#529semidirect
965. C32#5479semidirect
966. C32#5538semidirect
967. C32#5706semidirect
1054. C3#10593975semidirect
1055. C3#10594089semidirect
1056. C3#10594839semidirect

Maximal subgroups

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

subgroupindex
#117236792
#117235102
#117234532
#117234192
C3×#638792
C3×C4×D3×Dic32
C3×#638592
#117229872
#117229852
#117229752
#117229582
#117229422
#117229322
#117229182
#117229132
#105948393
#105940893
#105939753