Finite Group Databasebeta

← #13169262

Subgroups — #13169262

Order 1728.

1282 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723701C211yesmaximal, characteristic, complemented
2#11723504C211yesmaximal, characteristic, complemented
3#11723482C211yesmaximal, characteristic, complemented
4#11723416C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63868C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723010C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722968C211yesmaximal, characteristic, complemented
12#11722961C211yesmaximal, characteristic, complemented
13#11722952C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10594658—31nomaximal
17#10594638—31nomaximal
18#10594013—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic, complemented
28C2×#6289C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic, complemented
32#88859C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic, complemented
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39#88806C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic, complemented
44C3×#3724C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64104—31no—
55#64103—31no—
56#64084—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#893—31no—
61C3×#876—31no—
62C3×C4×D12—31no—
63#63923—31no—
64#63923—31no—
65#63923—31no—
66#63923—31no—
67#63922—31no—
68#63922—31no—
69#63921—31no—
70D3×(C2×D3)⋊C4—31no—
71D3×(C2×D3)⋊C4—31no—
72#63913—31no—
73#63912—31no—
74#63910—31no—
75#63910—31no—
76#63910—31no—
77#63909—31no—
78#63906—31no—
79#63905—31no—
80#63904—31no—
81C4×#626—31no—
82#63899—31no—
83#63896—31no—
84#63894—31no—
85#63894D311yescharacteristic, complemented
86#63886—31no—
87#63886—31no—
88#63886—61no—
89#63868D311yescharacteristic, complemented
90#63865—31no—
91#63854—31no—
92#63854—31no—
93#63854—31no—
94#63854—61no—
95#63852—31no—
96#63852—31no—
97#63852—31no—
98#63852—31no—
99#63852—61no—
100#63850—31no—
101#63848D311yescharacteristic, complemented
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C2×#1113—22no—
108C2×#1113—41no—
109C2×#1113—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4⋊(C3⋊D3)—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—41no—
122#6295—41no—
123#6293—41no—
124#6292—22no—
125#6292—41no—
126#6292—41no—
127#6292—41no—
128#6289—41no—
129Dic3×C3⋊D3—41no—
130C3×#624—41no—
131C3×#624—41no—
132#5704—91no—
133#5704—91no—
134#5560—91no—
135C22×D32—31no—
136C22×D32—31no—
137C22×D32—31no—
138C2×C4⋊(C3⋊D3)—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×#634—31no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—61no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×#627—31no—
154C2×#627—31no—
155C2×#627—61no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—61no—
169C2×#626—61no—
170C2×#626—61no—
171C2×#626—61no—
172C2×#625—31no—
173C2×#625—31no—
174C2×#624—31no—
175C2×#624—31no—
176C2×#624—61no—
177C2×#624C2×D311yescharacteristic
178C2×#624C2×D311yescharacteristic, complemented
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—61no—
182C32×C4⋊C4—31no—
183C32×C4⋊C4—31no—
184C32×C42—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—61no—
193#3752—61no—
194#3752—61no—
195#3752—121no—
196#3752C2×D311yescharacteristic
197#3752C2×D311yescharacteristic
198#3750—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—61no—
216C3×(C2×D3)⋊C4—61no—
217C3×C4⋊Dic3—21no—
218C3×C4⋊Dic3—31no—
219C3×C4⋊Dic3—31no—
220C3×C4⋊Dic3C2×D311yescharacteristic, complemented
221C3×C4⋊Dic3C2×D311yescharacteristic, complemented
222C3×Dic3⋊C4—21no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4C2×D311yescharacteristic, complemented
228C3×Dic3⋊C4C2×D311yescharacteristic, complemented
229C3×C4×Dic3—21no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—31no—
232C3×C4×Dic3C2×D311yescharacteristic, complemented
233C3×C4×Dic3C2×D311yescharacteristic, complemented
234#3724—31no—
235#3724—31no—
236#3724—61no—
237#3724C2×D311yescharacteristic, complemented
238Dic3⋊Dic3C2×D311yescharacteristic, complemented
239Dic3⋊Dic3C2×D311yescharacteristic, complemented
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—61no—
244#3722C2×D311yescharacteristic
245#3722C2×D311yescharacteristic
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic
248#3722C2×D311yescharacteristic
249#3722C2×D311yescharacteristic, complemented
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3—61no—
260(C2×D3)⋊Dic3—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3#4112yes—
278#1113—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#126—91no—
291C3×C4×D4—91no—
292#939—91no—
293#937—91no—
294#930—91no—
295#929—91no—
296C4×#67—91no—
297C2×(C2×D3)⋊C4—91no—
298#898—31no—
299#898—31no—
300#898—31no—
301#896—91no—
302#896—91no—
303#895—91no—
304#895—91no—
305#895—91no—
306#895—91no—
307#895—181no—
308#894—91no—
309#894—91no—
310#894—91no—
311#894—181no—
312#893—31no—
313#893—91no—
314#885—91no—
315#885—91no—
316#885—91no—
317#884—91no—
318#884—91no—
319#884—91no—
320#883—91no—
321#883—91no—
322#882—91no—
323#882—91no—
324#882—91no—
325#882—91no—
326#882—91no—
327D3×C22⋊C4—91no—
328D3×C22⋊C4—91no—
329#878—91no—
330#876—31no—
331#875—91no—
332#875—91no—
333#875—91no—
334#875—181no—
335C4×D12—31no—
336C4×D12—91no—
337C22×C3⋊D3—31no—
338C22×C3⋊D3—31no—
339C22×C3⋊D3—31no—
340C22×C3⋊D3—61no—
341C22×C3⋊D3—61no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—121no—
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—61no—
357C22×C3×D3—61no—
358C22×C3×D3—61no—
359C22×C3×D3—61no—
360C2×D32—62no—
361C2×D32—62no—
362C2×D32—62no—
363C2×D32—121no—
364C2×D32—121no—
365C2×D32—121no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C2×C32×C4—21no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—41no—
379C2×C32×C4C22×D311yescharacteristic
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
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—121no—
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C4⋊(C3⋊D3)—22no—
392C4⋊(C3⋊D3)—62no—
393C4⋊(C3⋊D3)—121no—
394C4⋊(C3⋊D3)—121no—
395C4⋊(C3⋊D3)—121no—
396C4×C3⋊D3—121no—
397C4×C3⋊D3—121no—
398#634—121no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C3×D12—62no—
424C3×D12—62no—
425C3×D12—122no—
426C3×C4×D3—121no—
427C3×C4×D3—121no—
428C3×C4×D3—121no—
429C3×C4×D3—121no—
430#627—121no—
431#627—121no—
432#627—122no—
433#626—62no—
434#626—62no—
435#626—122no—
436#626—121no—
437#626—121no—
438#626—121no—
439#626—121no—
440#626—121no—
441#626—121no—
442#626—122no—
443#626—122no—
444#626—122no—
445#626—121no—
446#626—121no—
447#626—121no—
448#626—121no—
449#625—121no—
450#625—121no—
451#624—41no—
452#624—41no—
453#624—121no—
454#624—121no—
455#624—122no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—122no—
459#538—271noSylow
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3⋊(C3⋊D3)—41no—
464C3×C3⋊D3—22no—
465C3×C3⋊D3—41no—
466C3×C3⋊D3—41no—
467C3×C3⋊D3—41no—
468C23×D3—91no—
469C23×D3—91no—
470C23×D3—91no—
471C2×C3×D4—91no—
472C22×C3×C4—91no—
473C22×C3×C4—91no—
474C2×#67—91no—
475C2×#67—91no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C22×Dic3—91no—
483C2×D12—31no—
484C2×D12—31no—
485C2×D12—61no—
486C2×D12—91no—
487C2×D12—91no—
488C2×D12—91no—
489C2×D12—91no—
490C2×D12—91no—
491C2×D12—91no—
492C2×D12—91no—
493C2×D12—91no—
494C2×D12—91no—
495C2×D12—91no—
496C2×D12—181no—
497C2×D12—181no—
498C2×D12—181no—
499C2×D12—181no—
500C2×C4×D3—31no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
503C2×C4×D3—31no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—181no—
510C2×C4×D3—181no—
511C2×Dic6—91no—
512C2×Dic6—91no—
513C2×Dic6—91no—
514C2×Dic6—181no—
515C3×C4⋊C4—31no—
516C3×C4⋊C4—31no—
517C3×C4⋊C4—31no—
518C3×C4⋊C4—31no—
519C3×C4⋊C4—61no—
520C3×C4⋊C4—61no—
521C3×C4⋊C4—91no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C42—31no—
533C3×C42—31no—
534C3×C42—61no—
535C3×C42—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—61no—
557(C2×D3)⋊C4—61no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578(C2×D3)⋊C4—181no—
579(C2×D3)⋊C4—361no—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3D3211yescharacteristic, complemented
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—181no—
591Dic3⋊C4D3211yescharacteristic, complemented
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3D3211yescharacteristic, complemented
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—41no—
599C22×C32C23×D311yescharacteristic
600C22×C32C23×D311yescharacteristic
601C22×C32C23×D311yescharacteristic
602C2×C3⋊D3—21no—
603C2×C3⋊D3—21no—
604C2×C3⋊D3—21no—
605C2×C3⋊D3—21no—
606C2×C3⋊D3—21no—
607C2×C3⋊D3—21no—
608C2×C3⋊D3—21no—
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—61no—
614C2×C3⋊D3—62no—
615C2×C3⋊D3—61no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—61no—
620C2×C3⋊D3—61no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—121no—
624C2×C3⋊D3—121no—
625C2×C3⋊D3—122no—
626C2×C3⋊D3—121no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—241no—
633C2×C3⋊D3—241no—
634C2×C3⋊D3#23512yes—
635C2×C3×D3—32no—
636C2×C3×D3—32no—
637C2×C3×D3—62no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—121no—
661C2×C3×D3—121no—
662C2×C3×D3—121no—
663C2×C3×D3—121no—
664C2×C3×D3—121no—
665C2×C3×D3—121no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671D32—124no—
672D32—124no—
673D32—124no—
674C32×C4—21no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—41no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C32×C4—81no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—61no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—121no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—241no—
696C3×Dic3—22no—
697C3×Dic3—22no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—41no—
713C3×Dic3—41no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720#126—91no—
721#126—91no—
722#124—271no—
723#124—271no—
724#123—271no—
725#123—271no—
726C22⋊Q8—271no—
727#121—271no—
728#121—271no—
729#121—271no—
730#120—271no—
731#120—271no—
732C4×D4—91no—
733C4×D4—271no—
734C2×C22⋊C4—271no—
735C33#53811yescharacteristic, complemented, Sylow
736C23×C3—91no—
737C23×C3—91no—
738C23×C3—91no—
739C23×C3—91no—
740C22×D3—31no—
741C22×D3—31no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—61no—
749C22×D3—61no—
750C22×D3—61no—
751C22×D3—61no—
752C22×D3—91no—
753C22×D3—91no—
754C22×D3—91no—
755C22×D3—181no—
756C22×D3—181no—
757C22×D3—181no—
758C22×D3—182no—
759C22×D3—182no—
760C22×D3—182no—
761C22×D3—361no—
762C22×D3—361no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—361no—
768C3×D4—182no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—31no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—41no—
785C2×C3×C4—61no—
786C2×C3×C4—61no—
787C2×C3×C4—61no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—361no—
794C2×C3×C4—361no—
795C2×C3×C4C2×D3211yescharacteristic
796C2×C3×C4C2×D3211yescharacteristic
797C2×C3×C4C2×D3211yescharacteristic
798#67—182no—
799#67—361no—
800#67—361no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—361no—
805#67—361no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—91no—
813C2×Dic3—91no—
814C2×Dic3—91no—
815C2×Dic3—181no—
816C2×Dic3—181no—
817C2×Dic3—181no—
818C2×Dic3—361no—
819C2×Dic3—361no—
820C2×Dic3C2×D3211yescharacteristic
821C2×Dic3C2×D3211yescharacteristic
822C2×Dic3C2×D3211yescharacteristic
823C2×Dic3C2×D3211yescharacteristic
824C2×Dic3C2×D3211yescharacteristic
825C2×Dic3C2×D3211yescharacteristic
826D12—62no—
827D12—62no—
828D12—122no—
829D12—182no—
830D12—182no—
831D12—362no—
832D12—361no—
833D12—361no—
834D12—361no—
835D12—361no—
836D12—361no—
837D12—361no—
838D12—362no—
839D12—362no—
840D12—362no—
841D12—361no—
842D12—361no—
843C4×D3—121no—
844C4×D3—121no—
845C4×D3—121no—
846C4×D3—121no—
847C4×D3—361no—
848C4×D3—361no—
849C4×D3—361no—
850C4×D3—362no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—362no—
854Dic6—361no—
855Dic6—361no—
856Dic6—361no—
857Dic6—362no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—41no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32C2×#23511yescharacteristic
871C2×C32#100411yescharacteristic
872C2×C32D3×#4111yescharacteristic
873C2×C32D3×#4111yescharacteristic
874C2×C32#100911yescharacteristic
875C2×C32#100911yescharacteristic
876C2×C32#100911yescharacteristic
877C2×C32#100911yescharacteristic
878C2×C32#100911yescharacteristic
879C3⋊D3—22no—
880C3⋊D3—41no—
881C3⋊D3—41no—
882C3⋊D3—41no—
883C3⋊D3—121no—
884C3⋊D3—122no—
885C3⋊D3—121no—
886C3⋊D3—121no—
887C3⋊D3—241no—
888C3⋊D3—241no—
889C3⋊D3—242no—
890C3×D3—62no—
891C3×D3—62no—
892C3×D3—122no—
893C3×D3—121no—
894C3×D3—121no—
895C3×D3—121no—
896C3×D3—121no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—241no—
900C3×D3—241no—
901C3×D3—241no—
902C24—271no—
903C2×Q8—271no—
904C2×D4—91no—
905C2×D4—271no—
906C2×D4—271no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C2×D4—271no—
911C22×C4—91no—
912C22×C4—91no—
913C22×C4—271no—
914C22×C4—271no—
915C4⋊C4—31no—
916C4⋊C4—31no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—271no—
921C22⋊C4—91no—
922C22⋊C4—91no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C42—31no—
936C42—91no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—41no—
941C22×C3—92no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—181no—
948C22×C3—181no—
949C22×C3—181no—
950C22×C3—181no—
951C22×C3—181no—
952C22×C3—181no—
953C22×C3C22×D3211yescharacteristic
954C22×C3C22×D3211yescharacteristic
955C22×C3C22×D3211yescharacteristic
956C2×D3—32no—
957C2×D3—32no—
958C2×D3—62no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—121no—
982C2×D3—121no—
983C2×D3—121no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—182no—
993C2×D3—181no—
994C2×D3—181no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—361no—
1003C2×D3—361no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—362no—
1011C2×D3—364no—
1012C2×D3—364no—
1013C2×D3—364no—
1014C2×D3—721no—
1015C2×D3—721no—
1016C3×C4—21no—
1017C3×C4—21no—
1018C3×C4—21no—
1019C3×C4—41no—
1020C3×C4—41no—
1021C3×C4—41no—
1022C3×C4—62no—
1023C3×C4—62no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—61no—
1033C3×C4—61no—
1034C3×C4—61no—
1035C3×C4—61no—
1036C3×C4—81no—
1037C3×C4—121no—
1038C3×C4—121no—
1039C3×C4—121no—
1040C3×C4—121no—
1041C3×C4—181no—
1042C3×C4—181no—
1043Dic3—21no—
1044Dic3—21no—
1045Dic3—21no—
1046Dic3—21no—
1047Dic3—21no—
1048Dic3—21no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—121no—
1054Dic3—121no—
1055Dic3—181no—
1056Dic3—181no—
1057Dic3—181no—
1058Dic3—361no—
1059Dic3—361no—
1060Dic3—361no—
1061Dic3—721no—
1062C32—21no—
1063C32—21no—
1064C32—21no—
1065C32—41no—
1066C32#556011yescharacteristic, complemented
1067C32#570411yescharacteristic, complemented
1068C32#570411yescharacteristic, complemented
1069C23—91no—
1070C23—91no—
1071C23—91no—
1072C23—91no—
1073C23—271no—
1074C23—542no—
1075C23—1081no—
1076C23—1081no—
1077Q8—1081no—
1078D4—182no—
1079D4—542no—
1080D4—1081no—
1081D4—1081no—
1082D4—1081no—
1083D4—1081no—
1084D4—1081no—
1085C2×C4—31no—
1086C2×C4—31no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—271no—
1094C2×C4—361no—
1095C2×C4—361no—
1096C2×C4—1081no—
1097C2×C4—1081no—
1098C2×C4D3311yescharacteristic
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—41no—
1109C2×C3—41no—
1110C2×C3—41no—
1111C2×C3—182no—
1112C2×C3—361no—
1113C2×C3—361no—
1114C2×C3—361no—
1115C2×C3D3×#23511yescharacteristic
1116C2×C3D3×#23511yescharacteristic
1117C2×C3#6430711yescharacteristic
1118C2×C3#6430811yescharacteristic
1119C2×C3#6430811yescharacteristic
1120C2×C3#6431211yescharacteristic
1121C2×C3#6431411yescharacteristic
1122C2×C3#6432011yescharacteristic
1123C2×C3#6432011yescharacteristic
1124D3—62no—
1125D3—62no—
1126D3—122no—
1127D3—121no—
1128D3—121no—
1129D3—121no—
1130D3—121no—
1131D3—121no—
1132D3—121no—
1133D3—241no—
1134D3—241no—
1135D3—241no—
1136D3—362no—
1137D3—361no—
1138D3—361no—
1139D3—361no—
1140D3—721no—
1141D3—721no—
1142D3—722no—
1143C22—92no—
1144C22—181no—
1145C22—181no—
1146C22—181no—
1147C22—181no—
1148C22—181no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22—181no—
1154C22—181no—
1155C22—541no—
1156C22—541no—
1157C22—541no—
1158C22—1084no—
1159C22C2×D3311yescharacteristic
1160C4—21no—
1161C4—61no—
1162C4—61no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—61no—
1167C4—181no—
1168C4—181no—
1169C4—541no—
1170C3—21no—
1171C3—21no—
1172C3—21no—
1173C3—41no—
1174C3#1059401311yescharacteristic, complemented
1175C3#1059463811yescharacteristic, complemented
1176C3#1059465811yescharacteristic, complemented
1177C2—182no—
1178C2—361no—
1179C2—361no—
1180C2—361no—
1181C2—1081no—
1182C2#1172438511yescharacteristic
1183C2#1172439011yescharacteristic
1184C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723701C2semidirect
2. #11723504C2semidirect
3. #11723482C2semidirect
4. #11723416C2semidirect
5. C3×#63894C2semidirect
6. C3×#63868C2semidirect
7. C3×#63848C2semidirect
8. #11723010C2semidirect
9. #11722995C2semidirect
10. #11722983C2semidirect
11. #11722968C2semidirect
12. #11722961C2semidirect
13. #11722952C2semidirect
14. #11722933C2semidirect
15. #11722905C2semidirect
23. C2×#6293C22semidirect
27. C2×#6292C22semidirect
28. C2×#6289C22semidirect
31. C2×C3×#624C22semidirect
32. #88859C22semidirect
35. C32×C4⋊Dic3C22semidirect
36. C32×Dic3⋊C4C22semidirect
37. C32×C4×Dic3C22semidirect
39. #88806C22semidirect
40. #88804C22semidirect
43. #88803C22semidirect
44. C3×#3724C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
85. #63894D3semidirect
89. #63868D3semidirect
101. #63848D3semidirect
178. C2×#624C2×D3semidirect
220. C3×C4⋊Dic3C2×D3semidirect
221. C3×C4⋊Dic3C2×D3semidirect
227. C3×Dic3⋊C4C2×D3semidirect
228. C3×Dic3⋊C4C2×D3semidirect
232. C3×C4×Dic3C2×D3semidirect
233. C3×C4×Dic3C2×D3semidirect
237. #3724C2×D3semidirect
238. Dic3⋊Dic3C2×D3semidirect
239. Dic3⋊Dic3C2×D3semidirect
249. #3722C2×D3semidirect
261. Dic32C2×D3semidirect
582. C4⋊Dic3D32semidirect
591. Dic3⋊C4D32semidirect
594. C4×Dic3D32semidirect
735. C33#538semidirect
1066. C32#5560semidirect
1067. C32#5704semidirect
1068. C32#5704semidirect
1174. C3#10594013semidirect
1175. C3#10594638semidirect
1176. C3#10594658semidirect

Maximal subgroups

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

subgroupindex
#117237012
#117235042
#117234822
#117234162
C3×#638942
C3×#638682
C3×#638482
#117230102
#117229952
#117229832
#117229682
#117229612
#117229522
#117229332
#117229052
#105946583
#105946383
#105940133