Finite Group Databasebeta

← #13168754

Subgroups — #13168754

Order 1728.

1302 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723540C211yesmaximal, characteristic, complemented
3#11723479C211yesmaximal, characteristic, complemented
4#11723453C211yesmaximal, characteristic, complemented
5C3×Dic3×D12C211yesmaximal, characteristic, complemented
6C3×#63885C211yesmaximal, characteristic, complemented
7C3×#63852C211yesmaximal, characteristic, complemented
8#11723005C211yesmaximal, characteristic, complemented
9#11722988C211yesmaximal, characteristic, complemented
10#11722969C211yesmaximal, characteristic, complemented
11#11722958C211yesmaximal, characteristic, complemented
12#11722954C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595221—31nomaximal
17#10594301—31nomaximal
18#10594012—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×#625C2211yescharacteristic, complemented
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3750C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88815C2211yescharacteristic, complemented
39#88814C2211yescharacteristic
40#88814C2211yescharacteristic
41#88813C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64146—31no—
55#64095—31no—
56#64085—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#885—31no—
60C3×#884—31no—
61C3×#875—31no—
62C3×C4×D12—31no—
63#63983—31no—
64#63981—31no—
65#63980—31no—
66#63978—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69#63971—31no—
70#63971—31no—
71#63966—31no—
72#63964—31no—
73C2×#3722—31no—
74#63953—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63922—61no—
79D3×(C2×D3)⋊C4—31no—
80D3×(C2×D3)⋊C4—31no—
81#63907—31no—
82#63907—31no—
83#63906—31no—
84#63905—31no—
85Dic3×D12D311yescharacteristic, complemented
86#63891—31no—
87#63890—31no—
88#63890—31no—
89#63890—61no—
90#63887—31no—
91#63885—31no—
92#63885D311yescharacteristic, complemented
93#63879—31no—
94#63868—31no—
95#63868—31no—
96#63868—61no—
97#63861—31no—
98#63858—31no—
99#63856—31no—
100#63852D311yescharacteristic, complemented
101#63848—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×D12—22no—
121#6291—41no—
122#6291—41no—
123#6290—41no—
124D3×C3⋊Dic3—41no—
125C3×#627—41no—
126C3×#626—41no—
127C3×#625—22no—
128C3×#625—41no—
129C3×D3×Dic3—41no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5678—91no—
133#5617—91no—
134#5560—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×C32×D4—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C22×C3⋊Dic3—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C2×C3×D12—21no—
153C2×C3×D12—31no—
154C2×C3×D12C2×D311yescharacteristic
155C2×C3×D12C2×D311yescharacteristic
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×Dic6—31no—
160C2×C3×Dic6—31no—
161C2×#627C2×D311yescharacteristic, complemented
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—61no—
167C2×#626—61no—
168C2×#626C2×D311yescharacteristic
169C2×#625—31no—
170C2×#625—31no—
171C2×#625—61no—
172C2×#625C2×D311yescharacteristic
173C2×#625C2×D311yescharacteristic, complemented
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—61no—
177C2×D3×Dic3C2×D311yescharacteristic
178C2×D3×Dic3C2×D311yescharacteristic
179C2×D3×Dic3C2×D311yescharacteristic, complemented
180C32×C22⋊C4—31no—
181C32×C42—31no—
182#3757—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—61no—
190#3752—61no—
191#3752—61no—
192#3752—121no—
193#3752C2×D311yescharacteristic
194C4⋊(C3⋊Dic3)—31no—
195C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
196#3750—31no—
197#3750—31no—
198#3750C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×(C2×D3)⋊C4—21no—
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—61no—
213C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
214C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3—61no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—61no—
221C3×C4×Dic3—21no—
222C3×C4×Dic3C2×D311yescharacteristic, complemented
223C3×C4×Dic3C2×D311yescharacteristic, complemented
224#3724—31no—
225#3724—31no—
226#3724—31no—
227#3724—61no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—61no—
245#3722—61no—
246#3722—61no—
247#3722C2×D311yescharacteristic
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—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
259Dic32—31no—
260Dic32—31no—
261Dic32—31no—
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×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3#4112yes—
278D3×C3⋊D3—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×#121—91no—
291C3×C4×D4—91no—
292#947—91no—
293#946—91no—
294#939—31no—
295#939—91no—
296#939—91no—
297#939—91no—
298#937—91no—
299#937—91no—
300#937—91no—
301#937—91no—
302#937—181no—
303D4×Dic3—31no—
304D4×Dic3—91no—
305#930—91no—
306#929—91no—
307C4×#67—91no—
308C2×(C2×D3)⋊C4—91no—
309C2×(C2×D3)⋊C4—91no—
310#924—91no—
311#898—91no—
312#898—91no—
313#898—91no—
314#894—91no—
315#886—91no—
316#886—91no—
317#886—91no—
318#886—181no—
319#885—31no—
320#885—91no—
321#885—91no—
322#884—31no—
323#884—91no—
324#884—91no—
325#883—91no—
326#882—91no—
327#882—91no—
328#67⋊C4—91no—
329D3×C22⋊C4—91no—
330#879—91no—
331#878—91no—
332#876—91no—
333#876—91no—
334#876—181no—
335#875—31no—
336C4×D12—31no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—62no—
347C22×C3⋊D3—121no—
348C22×C3⋊D3—121no—
349C22×C3⋊D3—121no—
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—21no—
353C22×C3×D3—21no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—61no—
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×D32—62no—
364C2×D32—62no—
365C2×D32—122no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C2×D32—121no—
370C2×D32—122no—
371C2×D32—122no—
372C32×D4—62no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—41no—
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383#638—121no—
384#638—121no—
385#638—121no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—31no—
388C2×C3⋊Dic3—31no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C3×#67—62no—
400C3×#67—62no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—121no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—121no—
423C2×C3×Dic3—121no—
424C2×C3×Dic3—121no—
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C3×D12—22no—
432C3×D12—22no—
433C3×D12—42no—
434C3×D12—121no—
435C3×C4×D3—121no—
436C3×C4×D3—121no—
437C3×C4×D3—121no—
438C3×Dic6—121no—
439C3×Dic6—121no—
440#627—41no—
441#626—41no—
442#626—121no—
443#626—121no—
444#626—121no—
445#626—121no—
446#626—122no—
447#626—122no—
448#625—22no—
449#625—41no—
450#625—121no—
451#625—121no—
452#625—122no—
453D3×Dic3—41no—
454D3×Dic3—41no—
455D3×Dic3—41no—
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—41no—
465C32×D3—22no—
466C32×D3—41no—
467C32×D3—41no—
468C23×D3—91no—
469C23×D3—91no—
470C23×D3—91no—
471C23×D3—181no—
472C2×C3×Q8—91no—
473C2×C3×D4—31no—
474C2×C3×D4—31no—
475C2×C3×D4—61no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—181no—
495C2×#67—181no—
496C2×#67—181no—
497C22×Dic3—31no—
498C22×Dic3—31no—
499C22×Dic3—31no—
500C22×Dic3—91no—
501C22×Dic3—91no—
502C22×Dic3—181no—
503C2×D12—31no—
504C2×D12—91no—
505C2×D12—91no—
506C2×D12D3211yescharacteristic
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×C4×D3—31no—
510C2×C4×D3—91no—
511C2×Dic6—31no—
512C2×Dic6—31no—
513C3×C4⋊C4—91no—
514C3×C4⋊C4—91no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—31no—
517C3×C22⋊C4—61no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C42—31no—
525C3×C42—31no—
526C3×C42—61no—
527#217—31no—
528#217—31no—
529#217—31no—
530#217—31no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—181no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—31no—
539(C2×D3)⋊C4—31no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—61no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548(C2×D3)⋊C4—91no—
549(C2×D3)⋊C4—91no—
550(C2×D3)⋊C4—91no—
551(C2×D3)⋊C4—91no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—181no—
563(C2×D3)⋊C4—181no—
564(C2×D3)⋊C4—181no—
565(C2×D3)⋊C4—181no—
566(C2×D3)⋊C4—181no—
567(C2×D3)⋊C4—181no—
568(C2×D3)⋊C4—361no—
569(C2×D3)⋊C4D3211yescharacteristic, complemented
570C4⋊Dic3—31no—
571C4⋊Dic3—31no—
572C4⋊Dic3—61no—
573C4⋊Dic3—91no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577C4⋊Dic3—181no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—61no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—181no—
590Dic3⋊C4—181no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3D3211yescharacteristic, complemented
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—32no—
599C22×C32—41no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32C23×D311yescharacteristic
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—61no—
615C2×C3⋊D3—62no—
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—61no—
624C2×C3⋊D3—121no—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—122no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—124no—
634C2×C3⋊D3—241no—
635C2×C3⋊D3—241no—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—22no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—21no—
653C2×C3×D3—22no—
654C2×C3×D3—41no—
655C2×C3×D3—41no—
656C2×C3×D3—41no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—62no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3#23512yes—
671C2×C3×D3#23712yes—
672D32—124no—
673D32—124no—
674D32—128no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—41no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—81no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—61no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—241no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—41no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—121no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—271no—
722#126—271no—
723#124—91no—
724#124—271no—
725#123—271no—
726#123—271no—
727C22⋊Q8—271no—
728#121—91no—
729#121—271no—
730#121—271no—
731#120—271no—
732#120—271no—
733C4×D4—91no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—61no—
744C23×C3—61no—
745C23×C3—61no—
746C23×C3—91no—
747C22×D3—31no—
748C22×D3—31no—
749C22×D3—61no—
750C22×D3—91no—
751C22×D3—91no—
752C22×D3—91no—
753C22×D3—181no—
754C22×D3—181no—
755C22×D3—181no—
756C22×D3—182no—
757C22×D3—182no—
758C22×D3—182no—
759C22×D3—361no—
760C22×D3—362no—
761C22×D3—361no—
762C22×D3—361no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—362no—
768C22×D3—362no—
769C22×D3C2×D3211yescharacteristic
770C22×D3C2×D3211yescharacteristic
771C22×D3C2×D3211yescharacteristic
772C3×Q8—361no—
773C3×D4—62no—
774C3×D4—62no—
775C3×D4—122no—
776C3×D4—182no—
777C3×D4—361no—
778C3×D4—361no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—21no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—41no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—91no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799C2×C3×C4—361no—
800C2×C3×C4C2×D3211yescharacteristic
801C2×C3×C4C2×D3211yescharacteristic
802C2×C3×C4C2×D3211yescharacteristic
803#67—62no—
804#67—62no—
805#67—121no—
806#67—121no—
807#67—121no—
808#67—361no—
809#67—361no—
810#67—361no—
811#67—361no—
812#67—362no—
813#67—362no—
814#67—361no—
815#67—361no—
816#67—361no—
817#67—362no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—61no—
829C2×Dic3—61no—
830C2×Dic3—61no—
831C2×Dic3—61no—
832C2×Dic3—61no—
833C2×Dic3—91no—
834C2×Dic3—91no—
835C2×Dic3—91no—
836C2×Dic3—121no—
837C2×Dic3—121no—
838C2×Dic3—121no—
839C2×Dic3—181no—
840C2×Dic3—181no—
841C2×Dic3—181no—
842C2×Dic3—361no—
843C2×Dic3—361no—
844C2×Dic3—361no—
845C2×Dic3—362no—
846C2×Dic3C2×D3211yescharacteristic
847C2×Dic3C2×D3211yescharacteristic
848C2×Dic3C2×D3211yescharacteristic
849D12—22no—
850D12—121no—
851D12—361no—
852D12—361no—
853C4×D3—121no—
854C4×D3—121no—
855C4×D3—121no—
856C4×D3—361no—
857Dic6—121no—
858Dic6—121no—
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—21no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—62no—
872C2×C32—121no—
873C2×C32—121no—
874C2×C32C2×#23511yescharacteristic
875C2×C32C2×#23711yescharacteristic
876C2×C32#100411yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32D3×#4111yescharacteristic
880C2×C32#100911yescharacteristic
881C2×C32#100911yescharacteristic
882C2×C32#100911yescharacteristic
883C3⋊D3—41no—
884C3⋊D3—121no—
885C3⋊D3—122no—
886C3⋊D3—121no—
887C3⋊D3—121no—
888C3⋊D3—241no—
889C3⋊D3—241no—
890C3⋊D3—242no—
891C3×D3—22no—
892C3×D3—22no—
893C3×D3—42no—
894C3×D3—42no—
895C3×D3—41no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—81no—
900C3×D3—122no—
901C3×D3—121no—
902C3×D3—121no—
903C24—271no—
904C2×Q8—91no—
905C2×D4—31no—
906C2×D4—91no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—91no—
915C22×C4—271no—
916C4⋊C4—91no—
917C4⋊C4—91no—
918C4⋊C4—271no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C22⋊C4—31no—
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—
935C22⋊C4—271no—
936C42—31no—
937C42—271no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—32no—
942C22×C3—32no—
943C22×C3—41no—
944C22×C3—62no—
945C22×C3—62no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—61no—
951C22×C3—61no—
952C22×C3—61no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—61no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—121no—
963C22×C3—121no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—181no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3C22×D3211yescharacteristic
973C22×C3C22×D3211yescharacteristic
974C22×C3C22×D3211yescharacteristic
975C2×D3—21no—
976C2×D3—21no—
977C2×D3—21no—
978C2×D3—21no—
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—62no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
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—368no—
1015C2×D3—721no—
1016C2×D3—721no—
1017C2×D3#380412yes—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—41no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—81no—
1031C3×C4—121no—
1032C3×C4—121no—
1033C3×C4—121no—
1034C3×C4—181no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—121no—
1053Dic3—121no—
1054Dic3—121no—
1055Dic3—121no—
1056Dic3—121no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—721no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#556011yescharacteristic, complemented
1069C32#561711yescharacteristic, complemented
1070C32#567811yescharacteristic, complemented
1071C23—31no—
1072C23—31no—
1073C23—31no—
1074C23—91no—
1075C23—271no—
1076C23—542no—
1077C23—1081no—
1078C23—1081no—
1079Q8—361no—
1080D4—62no—
1081D4—182no—
1082D4—361no—
1083D4—361no—
1084D4—1081no—
1085D4—1081no—
1086D4—1081no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—271no—
1096C2×C4—361no—
1097C2×C4—361no—
1098C2×C4—361no—
1099C2×C4—1081no—
1100C2×C4D3311yescharacteristic
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—41no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—62no—
1114C2×C3—62no—
1115C2×C3—122no—
1116C2×C3—122no—
1117C2×C3—121no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—121no—
1121C2×C3—241no—
1122C2×C3—361no—
1123C2×C3D3×#23511yescharacteristic
1124C2×C3#6430711yescharacteristic
1125C2×C3#6430711yescharacteristic
1126C2×C3#6430811yescharacteristic
1127C2×C3D3×#23711yescharacteristic
1128C2×C3#6431311yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6431411yescharacteristic
1131C2×C3C2×#380411yescharacteristic
1132D3—22no—
1133D3—41no—
1134D3—41no—
1135D3—122no—
1136D3—121no—
1137D3—121no—
1138D3—362no—
1139D3—361no—
1140D3—361no—
1141D3—361no—
1142D3—721no—
1143D3—721no—
1144D3—722no—
1145C22—32no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—541no—
1158C22—541no—
1159C22—541no—
1160C22—1084no—
1161C22C2×D3311yescharacteristic
1162C4—21no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—541no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059401211yescharacteristic, complemented
1177C3#1059430111yescharacteristic, complemented
1178C3#1059522111yescharacteristic, complemented
1179C2—62no—
1180C2—121no—
1181C2—121no—
1182C2—361no—
1183C2—1081no—
1184C2#1172438111yescharacteristic
1185C2#1172438411yescharacteristic
1186C2D3×#380411yescharacteristic
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. #11723675C2semidirect
2. #11723540C2semidirect
3. #11723479C2semidirect
4. #11723453C2semidirect
5. C3×Dic3×D12C2semidirect
6. C3×#63885C2semidirect
7. C3×#63852C2semidirect
8. #11723005C2semidirect
9. #11722988C2semidirect
10. #11722969C2semidirect
11. #11722958C2semidirect
12. #11722954C2semidirect
13. #11722949C2semidirect
14. #11722924C2semidirect
15. D3×#3722C2semidirect
24. C2×D3×C3⋊Dic3C22semidirect
25. C2×C3×#627C22semidirect
28. C2×C3×#625C22semidirect
31. C2×C3×D3×Dic3C22semidirect
34. C3×C4⋊(C3⋊Dic3)C22semidirect
35. C3×#3750C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. C32×C4×Dic3C22semidirect
38. #88815C22semidirect
41. #88813C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
85. Dic3×D12D3semidirect
92. #63885D3semidirect
100. #63852D3semidirect
161. C2×#627C2×D3semidirect
173. C2×#625C2×D3semidirect
179. C2×D3×Dic3C2×D3semidirect
195. C4⋊(C3⋊Dic3)C2×D3semidirect
198. #3750C2×D3semidirect
213. C3×(C2×D3)⋊C4C2×D3semidirect
214. C3×(C2×D3)⋊C4C2×D3semidirect
222. C3×C4×Dic3C2×D3semidirect
223. C3×C4×Dic3C2×D3semidirect
256. (C2×D3)⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
569. (C2×D3)⋊C4D32semidirect
594. C4×Dic3D32semidirect
736. C33#538semidirect
1068. C32#5560semidirect
1069. C32#5617semidirect
1070. C32#5678semidirect
1176. C3#10594012semidirect
1177. C3#10594301semidirect
1178. C3#10595221semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117235402
#117234792
#117234532
C3×Dic3×D122
C3×#638852
C3×#638522
#117230052
#117229882
#117229692
#117229582
#117229542
#117229492
#117229242
D3×#37222
#105952213
#105943013
#105940123