Finite Group Databasebeta

← #13178725

Subgroups — #13178725

Order 1728.

1120 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64156C211yesmaximal, characteristic, complemented
2C3×#64155C211yesmaximal, characteristic, complemented
3C3×#64153C211yesmaximal, characteristic, complemented
4#11723694C211yesmaximal, characteristic, complemented
5#11723692C211yesmaximal, characteristic, complemented
6#11723688C211yesmaximal, characteristic, complemented
7#11723687C211yesmaximal, characteristic
8#11723686C211yesmaximal, characteristic, complemented
9#11723684C211yesmaximal, characteristic, complemented
10#11723683C211yesmaximal, characteristic, complemented
11#11723676C211yesmaximal, characteristic, complemented
12#11723675C211yesmaximal, characteristic, complemented
13#11723672C211yesmaximal, characteristic, complemented
14#11723670C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10595391—31nomaximal
17#10595383—31nomaximal
18#10595343—31nomaximal
19C2×C33×Q8C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#634C2211yescharacteristic
23C2×#6296C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42C3×C4×C3⋊Dic3C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64156D311yescharacteristic, complemented
55#64155D311yescharacteristic, complemented
56#64153D311yescharacteristic, complemented
57C3×#947—31no—
58C3×#947—31no—
59C3×#947—61no—
60C3×#946—31no—
61C3×#946—31no—
62C3×#946—61no—
63C3×#944—31no—
64C3×#944—31no—
65C3×#944—61no—
66#63915—31no—
67#63913—31no—
68#63910—31no—
69#63907—31no—
70#63907—31no—
71#63905—31no—
72#63904—31no—
73#63899—31no—
74#63897—31no—
75#63896—31no—
76#63895—31no—
77#63893—31no—
78#63888—31no—
79#63887—31no—
80#63886—31no—
81#63885—31no—
82#63884—31no—
83#63884—31no—
84#63881—31no—
85#63879—31no—
86#63878—31no—
87#63877—31no—
88#63868—31no—
89#63862—31no—
90#63861—31no—
91#63859—31no—
92#63858—31no—
93#63853—31no—
94#63852—31no—
95#63852—31no—
96#63850—31no—
97#63848—31no—
98#63838—31no—
99#63837—31no—
100#63837—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C33×Q8—41no—
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C3×C4⋊(C3⋊D3)—41no—
119C3×C4×C3⋊D3—41no—
120C3×#634—41no—
121#6296—22no—
122#6295—22no—
123#6295—41no—
124#6294—22no—
125#6294—41no—
126#5733—91no—
127#5669—91no—
128#5640—91no—
129C2×C32×Q8—21no—
130C2×C32×Q8—21no—
131C2×C32×Q8—21no—
132C2×C32×Q8—41no—
133C2×C32×Q8C2×D311yescharacteristic
134C2×C32×Q8C2×D311yescharacteristic
135C2×C32×Q8C2×D311yescharacteristic
136C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
137C2×C4×C3⋊D3C2×D311yescharacteristic
138C2×#634C2×D311yescharacteristic
139C2×C3×D12—31no—
140C2×C3×D12—31no—
141C2×C3×D12—61no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—61no—
145C2×C3×Dic6—31no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—61no—
148C2×#627—31no—
149C2×#627—31no—
150C2×#627—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#625—31no—
156C2×#625—31no—
157C2×#624—31no—
158C2×#624—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163#3752C2×D311yescharacteristic
164#3752C2×D311yescharacteristic
165#3752C2×D311yescharacteristic
166#3752C2×D311yescharacteristic
167#3752C2×D311yescharacteristic
168#3752C2×D311yescharacteristic
169C4⋊(C3⋊Dic3)C2×D311yescharacteristic
170#3750C2×D311yescharacteristic
171#3750C2×D311yescharacteristic
172#3750C2×D311yescharacteristic
173#3750C2×D311yescharacteristic
174#3750C2×D311yescharacteristic
175#3750C2×D311yescharacteristic
176C4×C3⋊Dic3C2×D311yescharacteristic
177C4×C3⋊Dic3C2×D311yescharacteristic
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—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—61no—
191C3×(C2×D3)⋊C4—61no—
192C3×(C2×D3)⋊C4—61no—
193C3×(C2×D3)⋊C4—61no—
194C3×(C2×D3)⋊C4—61no—
195C3×(C2×D3)⋊C4—61no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—61no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
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⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×Dic3⋊C4—61no—
215C3×Dic3⋊C4—61no—
216C3×Dic3⋊C4—61no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—61no—
222C3×C4×Dic3—61no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
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—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
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—21no—
266C33×C4—21no—
267C33×C4—21no—
268C33×C4—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3#4112yes—
278C3×C4⋊Q8—91no—
279C3×#124—91no—
280C3×C22⋊Q8—91no—
281#947—31no—
282#947—31no—
283#947—61no—
284#947—91no—
285#946—31no—
286#946—31no—
287#946—61no—
288#946—91no—
289#944—31no—
290#944—31no—
291#944—61no—
292#939—91no—
293#935—91no—
294#929—91no—
295C4×#67—91no—
296#898—91no—
297#898—91no—
298#898—91no—
299#897—91no—
300#896—91no—
301#896—91no—
302#895—91no—
303#894—91no—
304#894—91no—
305#894—91no—
306#893—91no—
307#892—91no—
308#887—91no—
309#887—91no—
310#885—91no—
311#885—91no—
312#885—91no—
313#885—91no—
314#884—91no—
315#883—91no—
316#67⋊C4—91no—
317#879—91no—
318#879—91no—
319#878—91no—
320#878—91no—
321#877—91no—
322#876—91no—
323#875—91no—
324#872—91no—
325C4×Dic6—91no—
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—31no—
335C22×C3×D3—61no—
336C22×C3×D3—61no—
337C22×C3×D3—61no—
338C32×Q8—41no—
339C32×Q8—41no—
340C32×Q8—41no—
341C32×Q8—42no—
342C32×Q8—42no—
343C32×Q8—42no—
344C32×Q8—44no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—21no—
348C2×C32×C4—21no—
349C2×C32×C4—21no—
350C2×C32×C4—21no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—41no—
355C2×C32×C4—41no—
356C2×C32×C4—41no—
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C4⋊(C3⋊D3)—41no—
376C4×C3⋊D3—41no—
377#634—41no—
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—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—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C3×D12—121no—
406C3×D12—121no—
407C3×D12—122no—
408C3×C4×D3—121no—
409C3×C4×D3—121no—
410C3×C4×D3—122no—
411C3×Dic6—121no—
412C3×Dic6—121no—
413C3×Dic6—122no—
414#627—62no—
415#627—62no—
416#627—62no—
417#626—62no—
418#626—62no—
419#626—121no—
420#626—121no—
421#625—62no—
422#625—121no—
423#624—62no—
424#624—121no—
425D3×Dic3—62no—
426D3×Dic3—62no—
427D3×Dic3—121no—
428D3×Dic3—121no—
429#542—271noSylow
430C2×C33C2×#4111yescharacteristic
431C2×C33H(5,𝔽2)11yescharacteristic
432C2×C332−1+411yescharacteristic
433C3×C3⋊D3—41no—
434C3×C3⋊D3—41no—
435C3×C3⋊D3—41no—
436C2×C3×Q8—21no—
437C2×C3×Q8—21no—
438C2×C3×Q8—21no—
439C2×C3×Q8—41no—
440C2×C3×Q8—91no—
441C2×C3×Q8D3211yescharacteristic
442C2×C3×Q8D3211yescharacteristic
443C2×C3×Q8D3211yescharacteristic
444C2×C3×D4—91no—
445C22×C3×C4—91no—
446C2×#67—91no—
447C2×#67—91no—
448C2×#67—91no—
449C2×#67—91no—
450C22×Dic3—91no—
451C22×Dic3—91no—
452C2×D12—31no—
453C2×D12—31no—
454C2×D12—61no—
455C2×D12—91no—
456C2×D12—91no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—61no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×Dic6—31no—
465C2×Dic6—31no—
466C2×Dic6—61no—
467C2×Dic6—91no—
468C2×Dic6—91no—
469C2×Dic6—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C42—91no—
484C3×C42—91no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
490#217—91no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
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—61no—
504(C2×D3)⋊C4—61no—
505(C2×D3)⋊C4—61no—
506(C2×D3)⋊C4—61no—
507(C2×D3)⋊C4—61no—
508(C2×D3)⋊C4—61no—
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—
521C4⋊Dic3—31no—
522C4⋊Dic3—31no—
523C4⋊Dic3—61no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—61no—
540Dic3⋊C4—61no—
541Dic3⋊C4—61no—
542Dic3⋊C4—61no—
543Dic3⋊C4—61no—
544Dic3⋊C4—61no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551C4×Dic3—31no—
552C4×Dic3—31no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—61no—
556C4×Dic3—61no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—41no—
567C22×C32C23×D311yescharacteristic
568C22×C32C23×D311yescharacteristic
569C22×C32C23×D311yescharacteristic
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3—21no—
577C2×C3⋊D3—21no—
578C2×C3⋊D3—21no—
579C2×C3×D3—62no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
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—61no—
589C2×C3×D3—61no—
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—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C2×C3×D3—121no—
603C2×C3×D3—121no—
604C2×C3×D3—121no—
605C2×C3×D3—121no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—22no—
610C32×C4—22no—
611C32×C4—22no—
612C32×C4—21no—
613C32×C4—21no—
614C32×C4—21no—
615C32×C4—21no—
616C32×C4—21no—
617C32×C4—21no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—41no—
624C32×C4—42no—
625C32×C4—42no—
626C32×C4—42no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—21no—
634C3⋊Dic3—21no—
635C3⋊Dic3#23912yes—
636C3×Dic3—32no—
637C3×Dic3—32no—
638C3×Dic3—62no—
639C3×Dic3—62no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
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—121no—
661C3×Dic3—121no—
662C3×Dic3—121no—
663C4⋊Q8—91no—
664#126—271no—
665#126—271no—
666#124—91no—
667#124—271no—
668#124—271no—
669#123—271no—
670#123—271no—
671C22⋊Q8—91no—
672C22⋊Q8—271no—
673C22⋊Q8—271no—
674#121—271no—
675C4×Q8—271no—
676C4×D4—271no—
677#117—271no—
678C33#54211yescharacteristic, complemented, Sylow
679C23×C3—91no—
680C23×C3—91no—
681C23×C3—91no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—31no—
685C22×D3—31no—
686C22×D3—31no—
687C22×D3—31no—
688C22×D3—61no—
689C22×D3—61no—
690C22×D3—61no—
691C3×Q8—41no—
692C3×Q8—41no—
693C3×Q8—41no—
694C3×Q8—42no—
695C3×Q8—42no—
696C3×Q8—42no—
697C3×Q8—44no—
698C3×Q8—361no—
699C3×D4—361no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—21no—
707C2×C3×C4—21no—
708C2×C3×C4—21no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—91no—
717C2×C3×C4—91no—
718C2×C3×C4—91no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—361no—
722C2×C3×C4C2×D3211yescharacteristic
723C2×C3×C4C2×D3211yescharacteristic
724C2×C3×C4C2×D3211yescharacteristic
725C2×C3×C4C2×D3211yescharacteristic
726C2×C3×C4C2×D3211yescharacteristic
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730C2×C3×C4C2×D3211yescharacteristic
731#67—182no—
732#67—182no—
733#67—361no—
734#67—361no—
735C2×Dic3—31no—
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—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—61no—
758C2×Dic3—61no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—182no—
763C2×Dic3—361no—
764D12—121no—
765D12—121no—
766D12—122no—
767D12—182no—
768D12—361no—
769C4×D3—121no—
770C4×D3—121no—
771C4×D3—122no—
772C4×D3—182no—
773C4×D3—182no—
774C4×D3—361no—
775C4×D3—361no—
776Dic6—121no—
777Dic6—121no—
778Dic6—122no—
779Dic6—182no—
780Dic6—182no—
781Dic6—182no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—41no—
792C2×C32—41no—
793C2×C32—41no—
794C2×C32#100411yescharacteristic
795C2×C32#100411yescharacteristic
796C2×C32#100411yescharacteristic
797C2×C32C2×#23911yescharacteristic
798C2×C32#100711yescharacteristic
799C2×C32#100711yescharacteristic
800C2×C32D3×#4111yescharacteristic
801C2×C32D3×#4111yescharacteristic
802C2×C32#101011yescharacteristic
803C3⋊D3—41no—
804C3⋊D3—41no—
805C3⋊D3—41no—
806C3×D3—122no—
807C3×D3—121no—
808C3×D3—121no—
809C3×D3—121no—
810C3×D3—121no—
811C3×D3—121no—
812C3×D3—121no—
813C3×D3—241no—
814C3×D3—241no—
815C2×Q8—91no—
816C2×Q8—271no—
817C2×Q8#111311yescharacteristic
818C2×D4—91no—
819C2×D4—271no—
820C2×D4—271no—
821C22×C4—91no—
822C22×C4—271no—
823C22×C4—271no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—271no—
832C4⋊C4—271no—
833C4⋊C4—271no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—91no—
839C22⋊C4—91no—
840C22⋊C4—271no—
841C22⋊C4—271no—
842C22⋊C4—271no—
843C22⋊C4—271no—
844C22⋊C4—271no—
845C22⋊C4—271no—
846C42—91no—
847C42—91no—
848C42—271no—
849C42—271no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—41no—
854C22×C3—181no—
855C22×C3—181no—
856C22×C3—181no—
857C22×C3—181no—
858C22×C3—181no—
859C22×C3—181no—
860C22×C3—181no—
861C22×C3—181no—
862C22×C3—181no—
863C22×C3C22×D3211yescharacteristic
864C22×C3C22×D3211yescharacteristic
865C22×C3C22×D3211yescharacteristic
866C2×D3—62no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
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—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—22no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—21no—
900C3×C4—21no—
901C3×C4—21no—
902C3×C4—21no—
903C3×C4—21no—
904C3×C4—21no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—41no—
909C3×C4—41no—
910C3×C4—41no—
911C3×C4—42no—
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—92no—
915C3×C4—181no—
916C3×C4—181no—
917C3×C4—181no—
918C3×C4—181no—
919C3×C4—181no—
920C3×C4—181no—
921C3×C4—181no—
922C3×C4—181no—
923Dic3—32no—
924Dic3—32no—
925Dic3—62no—
926Dic3—62no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—61no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—121no—
944Dic3—121no—
945Dic3—121no—
946Dic3—121no—
947Dic3—121no—
948Dic3—121no—
949Dic3—121no—
950C32—21no—
951C32—21no—
952C32—21no—
953C32—41no—
954C32#564011yescharacteristic, complemented
955C32#566911yescharacteristic, complemented
956C32#573311yescharacteristic, complemented
957C23—91no—
958C23—91no—
959C23—91no—
960Q8—41no—
961Q8—361no—
962Q8—542no—
963D4—361no—
964D4—542no—
965D4—1081no—
966C2×C4—91no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—91no—
972C2×C4—91no—
973C2×C4—91no—
974C2×C4—91no—
975C2×C4—361no—
976C2×C4—542no—
977C2×C4—1081no—
978C2×C4C2×#111311yescharacteristic
979C2×C4C2×#111311yescharacteristic
980C2×C4C2×#111311yescharacteristic
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—41no—
991C2×C3—41no—
992C2×C3—41no—
993C2×C3—361no—
994C2×C3—361no—
995C2×C3—361no—
996C2×C3#6431511yescharacteristic
997C2×C3#6431511yescharacteristic
998C2×C3#6431611yescharacteristic
999C2×C3D3×#23911yescharacteristic
1000C2×C3D3×#23911yescharacteristic
1001C2×C3#6431911yescharacteristic
1002C2×C3#6433011yescharacteristic
1003C2×C3#6433011yescharacteristic
1004C2×C3#6433011yescharacteristic
1005D3—122no—
1006D3—121no—
1007D3—121no—
1008D3—121no—
1009D3—121no—
1010D3—121no—
1011D3—121no—
1012D3—241no—
1013D3—241no—
1014C22—181no—
1015C22—181no—
1016C22—181no—
1017C22—181no—
1018C22—181no—
1019C22—181no—
1020C22—181no—
1021C22—181no—
1022C22—181no—
1023C22C22×#111311yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—21no—
1027C4—92no—
1028C4—181no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C4—181no—
1033C4—181no—
1034C4—181no—
1035C4—181no—
1036C3—21no—
1037C3—21no—
1038C3—21no—
1039C3—41no—
1040C3#1059534311yescharacteristic, complemented
1041C3#1059538311yescharacteristic, complemented
1042C3#1059539111yescharacteristic, complemented
1043C2—361no—
1044C2—361no—
1045C2—361no—
1046C2#1172462411yescharacteristic
1047C2#1172462611yescharacteristic
1048C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radical#11723687C2
hypercenterC2×Q8#1113
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#64156C2semidirect
2. C3×#64155C2semidirect
3. C3×#64153C2semidirect
4. #11723694C2semidirect
5. #11723692C2semidirect
6. #11723688C2semidirect
8. #11723686C2semidirect
9. #11723684C2semidirect
10. #11723683C2semidirect
11. #11723676C2semidirect
12. #11723675C2semidirect
13. #11723672C2semidirect
14. #11723670C2semidirect
15. #11723665C2semidirect
54. #64156D3semidirect
55. #64155D3semidirect
56. #64153D3semidirect
678. C33#542semidirect
954. C32#5640semidirect
955. C32#5669semidirect
956. C32#5733semidirect
1040. C3#10595343semidirect
1041. C3#10595383semidirect
1042. C3#10595391semidirect

Maximal subgroups

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

subgroupindex
C3×#641562
C3×#641552
C3×#641532
#117236942
#117236922
#117236882
#117236872
#117236862
#117236842
#117236832
#117236762
#117236752
#117236722
#117236702
#117236652
#105953913
#105953833
#105953433