Finite Group Databasebeta

← #13169279

Subgroups — #13169279

Order 1728.

1136 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic, complemented
2#11723495C211yesmaximal, characteristic, complemented
3#11723493C211yesmaximal, characteristic, complemented
4#11723417C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×#63848C211yesmaximal, characteristic, complemented
7C3×#63846C211yesmaximal, characteristic, complemented
8#11723021C211yesmaximal, characteristic, complemented
9#11723014C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722983C211yesmaximal, characteristic, complemented
12#11722972C211yesmaximal, characteristic, complemented
13#11722961C211yesmaximal, characteristic
14#11722934C211yesmaximal, characteristic, complemented
15#11722933C211yesmaximal, characteristic, complemented
16#10594542—31nomaximal
17#10594541—31nomaximal
18#10594481—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28#88859C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39#88806C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88803C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64103—31no—
56#64103—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×D3×C4⋊C4—31no—
60C3×D3×C4⋊C4—31no—
61C3×#890—31no—
62C3×#889—31no—
63#63910—31no—
64#63909—31no—
65#63906—31no—
66#63905—31no—
67#63904—31no—
68C4×#626—31no—
69C4×#626—31no—
70#63900D311yescharacteristic, complemented
71#63899—31no—
72#63897—31no—
73#63896—31no—
74#63895—31no—
75#63895—31no—
76#63895—31no—
77#63895—61no—
78#63894—31no—
79#63890—31no—
80#63890—31no—
81#63890—61no—
82#63880—31no—
83#63879—31no—
84#63868—31no—
85#63868—31no—
86#63867—31no—
87#63867—31no—
88#63865—31no—
89#63857—31no—
90#63854—31no—
91#63853—31no—
92#63853—31no—
93#63851—31no—
94#63850—31no—
95#63850—31no—
96#63850—31no—
97#63850—61no—
98#63848—31no—
99#63848D311yescharacteristic, complemented
100#63847—31no—
101#63846D311yescharacteristic, complemented
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊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
111C3×C4×C3⋊D3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6293—41no—
120#6292—22no—
121#6292—41no—
122#6289—41no—
123Dic3×C3⋊D3—41no—
124C3×#624—41no—
125C3×#624—41no—
126#5707—91no—
127#5692—91no—
128#5515—91no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×#634—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—61no—
142C2×#627—31no—
143C2×#627—31no—
144C2×#627—61no—
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×#624—31no—
156C2×#624—61no—
157C2×#624C2×D311yescharacteristic
158C2×#624C2×D311yescharacteristic
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—61no—
162C32×C4⋊C4—31no—
163C32×C4⋊C4—31no—
164C32×C4⋊C4—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—61no—
173#3752—61no—
174#3752—61no—
175#3752—121no—
176#3752C2×D311yescharacteristic
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750C2×D311yescharacteristic
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—61no—
188C3×C4⋊Dic3—21no—
189C3×C4⋊Dic3—21no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3C2×D311yescharacteristic
195C3×C4⋊Dic3C2×D311yescharacteristic
196C3×C4⋊Dic3C2×D311yescharacteristic
197C3×C4⋊Dic3C2×D311yescharacteristic
198C3×Dic3⋊C4—21no—
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—61no—
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#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724C2×D311yescharacteristic
221#3724C2×D311yescharacteristic
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—61no—
243#3722—61no—
244#3722—61no—
245#3722C2×D311yescharacteristic
246#3722C2×D311yescharacteristic
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—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)—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—21no—
277C32×Dic3—21no—
278C3×#126—91no—
279C3×#125—91no—
280C2×C3×C4⋊C4—91no—
281#930—91no—
282#929—91no—
283#929—91no—
284C4×#67—91no—
285C4×#67—91no—
286#924—91no—
287#898—31no—
288#898—31no—
289#898—91no—
290#898—91no—
291#897—91no—
292#897—91no—
293#896—91no—
294#896—91no—
295#896—91no—
296#896—91no—
297#896—91no—
298#896—181no—
299#895—91no—
300#894—91no—
301#894—91no—
302#894—91no—
303#894—91no—
304#894—91no—
305#894—91no—
306#894—91no—
307#894—181no—
308#894—181no—
309#893—91no—
310D3×C4⋊C4—31no—
311D3×C4⋊C4—31no—
312#890—31no—
313#889—31no—
314#889—91no—
315#889—91no—
316#886—91no—
317#884—91no—
318#883—91no—
319#883—91no—
320#67⋊C4—91no—
321#878—91no—
322#876—91no—
323C4×D12—91no—
324C4×D12—91no—
325#870—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)—121no—
367C4×C3⋊D3—22no—
368C4×C3⋊D3—121no—
369C4×C3⋊D3—121no—
370#634—121no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
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—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
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
401C3×C4×D3—62no—
402C3×C4×D3—62no—
403C3×C4×D3—122no—
404C3×C4×D3—121no—
405C3×C4×D3—121no—
406C3×C4×D3—121no—
407C3×C4×D3—121no—
408#627—121no—
409#627—121no—
410#627—122no—
411#626—62no—
412#626—62no—
413#626—62no—
414#626—62no—
415#626—122no—
416#626—121no—
417#626—121no—
418#626—122no—
419#625—62no—
420#624—41no—
421#624—41no—
422#624—121no—
423#624—121no—
424#624—122no—
425D3×Dic3—121no—
426D3×Dic3—121no—
427D3×Dic3—122no—
428#539—271noSylow
429C2×C33C2×#4111yescharacteristic
430C2×C33H(5,𝔽2)11yescharacteristic
431C2×C332−1+411yescharacteristic
432C3⋊(C3⋊D3)—41no—
433C3×C3⋊D3—22no—
434C3×C3⋊D3—41no—
435C22×C3×C4—91no—
436C22×C3×C4—91no—
437C22×C3×C4—91no—
438C2×#67—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C22×Dic3—91no—
443C2×D12—91no—
444C2×D12—91no—
445C2×D12—91no—
446C2×D12—91no—
447C2×D12—91no—
448C2×D12—181no—
449C2×D12—181no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—61no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—181no—
463C2×C4×D3—181no—
464C2×Dic6—91no—
465C2×Dic6—91no—
466C2×Dic6—91no—
467C2×Dic6—181no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—61no—
475C3×C4⋊C4—61no—
476C3×C4⋊C4—61no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C22⋊C4—91no—
486C3×C22⋊C4—91no—
487C3×C42—91no—
488C3×C42—91no—
489#217—91no—
490#217—91no—
491#217—91no—
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—61no—
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—
522(C2×D3)⋊C4—181no—
523(C2×D3)⋊C4—181no—
524(C2×D3)⋊C4—361no—
525C4⋊Dic3—31no—
526C4⋊Dic3—31no—
527C4⋊Dic3—31no—
528C4⋊Dic3—31no—
529C4⋊Dic3—91no—
530C4⋊Dic3—91no—
531C4⋊Dic3—91no—
532C4⋊Dic3D3211yescharacteristic
533C4⋊Dic3D3211yescharacteristic
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—31no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—61no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—181no—
555Dic3⋊C4—181no—
556Dic3⋊C4—181no—
557Dic3⋊C4D3211yescharacteristic
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—41no—
566C22×C32C23×D311yescharacteristic
567C22×C32C23×D311yescharacteristic
568C22×C32C23×D311yescharacteristic
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
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#23512yes—
596C2×C3×D3—32no—
597C2×C3×D3—32no—
598C2×C3×D3—62no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—62no—
604C2×C3×D3—61no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
614C32×C4—21no—
615C32×C4—21no—
616C32×C4—21no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—61no—
621C32×C4—61no—
622C32×C4—61no—
623C32×C4—61no—
624C32×C4—61no—
625C32×C4—61no—
626C32×C4—81no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—61no—
632C3⋊Dic3—61no—
633C3⋊Dic3—61no—
634C3⋊Dic3—121no—
635C3⋊Dic3—121no—
636C3⋊Dic3—121no—
637C3⋊Dic3—241no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
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—41no—
651C3×Dic3—41no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—41no—
656C3×Dic3—62no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668#126—91no—
669#126—271no—
670#125—91no—
671#125—271no—
672#123—271no—
673#123—271no—
674#123—271no—
675#123—271no—
676C22⋊Q8—271no—
677C22⋊Q8—271no—
678C22⋊Q8—271no—
679#121—271no—
680C4×D4—271no—
681C4×D4—271no—
682C2×C4⋊C4—91no—
683C33#53911yescharacteristic, complemented, Sylow
684C23×C3—91no—
685C23×C3—91no—
686C22×D3—31no—
687C22×D3—31no—
688C22×D3—31no—
689C22×D3—31no—
690C22×D3—61no—
691C22×D3—61no—
692C22×D3—91no—
693C22×D3—91no—
694C22×D3—91no—
695C22×D3—181no—
696C22×D3—181no—
697C22×D3—181no—
698C22×D3—361no—
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—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—41no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—91no—
725C2×C3×C4—182no—
726C2×C3×C4—361no—
727C2×C3×C4—361no—
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730C2×C3×C4C2×D3211yescharacteristic
731#67—182no—
732#67—182no—
733#67—182no—
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—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—91no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—181no—
751C2×Dic3—181no—
752C2×Dic3—181no—
753C2×Dic3—361no—
754C2×Dic3—361no—
755C2×Dic3C2×D3211yescharacteristic
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C2×Dic3C2×D3211yescharacteristic
759C2×Dic3C2×D3211yescharacteristic
760C2×Dic3C2×D3211yescharacteristic
761D12—182no—
762D12—182no—
763D12—182no—
764D12—362no—
765D12—361no—
766D12—361no—
767D12—362no—
768C4×D3—62no—
769C4×D3—62no—
770C4×D3—122no—
771C4×D3—121no—
772C4×D3—121no—
773C4×D3—121no—
774C4×D3—121no—
775C4×D3—361no—
776C4×D3—361no—
777C4×D3—361no—
778C4×D3—362no—
779C4×D3—361no—
780C4×D3—361no—
781C4×D3—362no—
782Dic6—361no—
783Dic6—361no—
784Dic6—361no—
785Dic6—362no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—41no—
796C2×C32—41no—
797C2×C32—41no—
798C2×C32C2×#23511yescharacteristic
799C2×C32#100411yescharacteristic
800C2×C32#100711yescharacteristic
801C2×C32#100711yescharacteristic
802C2×C32D3×#4111yescharacteristic
803C2×C32D3×#4111yescharacteristic
804C2×C32#100911yescharacteristic
805C2×C32#100911yescharacteristic
806C2×C32#101011yescharacteristic
807C3⋊D3—22no—
808C3⋊D3—41no—
809C3⋊D3—121no—
810C3⋊D3—122no—
811C3⋊D3—121no—
812C3⋊D3—121no—
813C3⋊D3—241no—
814C3⋊D3—241no—
815C3⋊D3—242no—
816C3×D3—62no—
817C3×D3—62no—
818C3×D3—122no—
819C3×D3—122no—
820C3×D3—121no—
821C3×D3—121no—
822C2×Q8—271no—
823C2×D4—271no—
824C2×D4—271no—
825C2×D4—271no—
826C22×C4—91no—
827C22×C4—91no—
828C22×C4—91no—
829C22×C4—271no—
830C22×C4—271no—
831C4⋊C4—31no—
832C4⋊C4—31no—
833C4⋊C4—31no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—91no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—271no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—91no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—41no—
861C22×C3—92no—
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—32no—
871C2×D3—32no—
872C2×D3—62no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
876C2×D3—61no—
877C2×D3—62no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—182no—
889C2×D3—181no—
890C2×D3—181no—
891C2×D3—181no—
892C2×D3—181no—
893C2×D3—181no—
894C2×D3—181no—
895C2×D3—181no—
896C2×D3—181no—
897C2×D3—181no—
898C2×D3—361no—
899C2×D3—361no—
900C2×D3—361no—
901C2×D3—361no—
902C2×D3—361no—
903C2×D3—361no—
904C2×D3—361no—
905C2×D3—361no—
906C2×D3—362no—
907C2×D3—721no—
908C2×D3—721no—
909C3×C4—21no—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—61no—
926C3×C4—61no—
927C3×C4—81no—
928C3×C4—121no—
929C3×C4—121no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—121no—
933C3×C4—121no—
934C3×C4—181no—
935C3×C4—181no—
936C3×C4—181no—
937C3×C4—181no—
938Dic3—21no—
939Dic3—21no—
940Dic3—21no—
941Dic3—21no—
942Dic3—21no—
943Dic3—21no—
944Dic3—62no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—121no—
954Dic3—121no—
955Dic3—121no—
956Dic3—181no—
957Dic3—181no—
958Dic3—181no—
959Dic3—361no—
960Dic3—361no—
961Dic3—361no—
962Dic3—721no—
963C32—21no—
964C32—21no—
965C32—21no—
966C32—41no—
967C32#551511yescharacteristic, complemented
968C32#569211yescharacteristic, complemented
969C32#570711yescharacteristic, complemented
970C23—91no—
971C23—91no—
972C23—271no—
973Q8—1081no—
974D4—542no—
975D4—542no—
976D4—1081no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—182no—
988C2×C4—271no—
989C2×C4—361no—
990C2×C4—361no—
991C2×C4—1081no—
992C2×C4—1081no—
993C2×C4D3311yescharacteristic
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—182no—
1007C2×C3—361no—
1008C2×C3#6429711yescharacteristic
1009C2×C3D3×#23511yescharacteristic
1010C2×C3D3×#23511yescharacteristic
1011C2×C3#6431211yescharacteristic
1012C2×C3#6431411yescharacteristic
1013C2×C3#6431411yescharacteristic
1014C2×C3#6431511yescharacteristic
1015C2×C3#6431611yescharacteristic
1016C2×C3#6432011yescharacteristic
1017D3—62no—
1018D3—62no—
1019D3—122no—
1020D3—122no—
1021D3—121no—
1022D3—121no—
1023D3—362no—
1024D3—361no—
1025D3—361no—
1026D3—361no—
1027D3—721no—
1028D3—721no—
1029D3—722no—
1030C22—92no—
1031C22—181no—
1032C22—181no—
1033C22—181no—
1034C22—181no—
1035C22—181no—
1036C22—541no—
1037C22—541no—
1038C22—541no—
1039C22C2×D3311yescharacteristic
1040C4—21no—
1041C4—61no—
1042C4—61no—
1043C4—61no—
1044C4—61no—
1045C4—61no—
1046C4—61no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C4—181no—
1051C4—541no—
1052C3—21no—
1053C3—21no—
1054C3—21no—
1055C3—41no—
1056C3#1059448111yescharacteristic, complemented
1057C3#1059454111yescharacteristic, complemented
1058C3#1059454211yescharacteristic, complemented
1059C2—182no—
1060C2—361no—
1061C2—1081no—
1062C2#1172438611yescharacteristic
1063C2#1172439711yescharacteristic
1064C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722961C2
hypercenterC2×C4D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723694C2semidirect
2. #11723495C2semidirect
3. #11723493C2semidirect
4. #11723417C2semidirect
5. C3×#63900C2semidirect
6. C3×#63848C2semidirect
7. C3×#63846C2semidirect
8. #11723021C2semidirect
9. #11723014C2semidirect
10. #11723000C2semidirect
11. #11722983C2semidirect
12. #11722972C2semidirect
14. #11722934C2semidirect
15. #11722933C2semidirect
70. #63900D3semidirect
99. #63848D3semidirect
101. #63846D3semidirect
683. C33#539semidirect
967. C32#5515semidirect
968. C32#5692semidirect
969. C32#5707semidirect
1056. C3#10594481semidirect
1057. C3#10594541semidirect
1058. C3#10594542semidirect

Maximal subgroups

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

subgroupindex
#117236942
#117234952
#117234932
#117234172
C3×#639002
C3×#638482
C3×#638462
#117230212
#117230142
#117230002
#117229832
#117229722
#117229612
#117229342
#117229332
#105945423
#105945413
#105944813