Finite Group Databasebeta

← #13169175

Subgroups — #13169175

Order 1728.

1300 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#11723687C211yesmaximal, characteristic, complemented
2#11723541C211yesmaximal, characteristic, complemented
3#11723416C211yesmaximal, characteristic, complemented
4#11723411C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63859C211yesmaximal, characteristic, complemented
7C3×#63854C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic, complemented
9#11722993C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722961C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722931C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10594639—31nomaximal
17#10594232—31nomaximal
18#10594013—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic, complemented
31C2×C3×#624C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33C3×#3752C2211yescharacteristic, complemented
34C3×#3750C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88814C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64107—31no—
55#64091—31no—
56#64084—31no—
57C3×#894—31no—
58C3×#893—31no—
59C3×#883—31no—
60C3×#879—31no—
61C3×#876—31no—
62C3×C4×D12—31no—
63#63981—31no—
64#63974—31no—
65#63958—31no—
66#63953—31no—
67#63923—31no—
68#63922—31no—
69#63922—31no—
70#63922—31no—
71#63922—61no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63915—31no—
75#63913—31no—
76#63910—31no—
77#63910—31no—
78#63909—31no—
79#63908—31no—
80#63906—31no—
81#63906—31no—
82#63904—31no—
83#63904—31no—
84C4×#625—31no—
85#63897—31no—
86#63896—31no—
87#63895—31no—
88#63894D311yescharacteristic, complemented
89#63893—31no—
90#63886—31no—
91#63885—31no—
92#63859D311yescharacteristic, complemented
93#63854D311yescharacteristic, complemented
94#63852—31no—
95#63852—31no—
96#63852—61no—
97#63850—31no—
98#63850—31no—
99#63848—31no—
100#63848—31no—
101#63848—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊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
115C3×C4⋊(C3⋊D3)—22no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—22no—
122#6295—41no—
123#6294—41no—
124#6293—41no—
125#6292—41no—
126#6292—41no—
127#6290—41no—
128C3×#626—41no—
129C3×#624—41no—
130C3×#624—41no—
131C3×#624—41no—
132#5704—91no—
133#5657—91no—
134#5560—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×#638—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×#634—31no—
144C2×C3×#67—31no—
145C2×C3×D12—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×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×#627—31no—
156C2×#627—31no—
157C2×#627—61no—
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—61no—
167C2×#626—61no—
168C2×#626C2×D311yescharacteristic
169C2×#625—31no—
170C2×#625—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—61no—
174C2×#624—31no—
175C2×#624C2×D311yescharacteristic
176C2×#624C2×D311yescharacteristic, complemented
177C2×#624C2×D311yescharacteristic, complemented
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C32×C4⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C42—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—61no—
192#3752—61no—
193#3752—61no—
194#3752—121no—
195#3752C2×D311yescharacteristic, complemented
196C4⋊(C3⋊Dic3)—31no—
197#3750C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×(C2×D3)⋊C4—21no—
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—61no—
213C3×(C2×D3)⋊C4C2×D311yescharacteristic
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×C4⋊Dic3—21no—
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3C2×D311yescharacteristic, complemented
218C3×C4⋊Dic3C2×D311yescharacteristic, complemented
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—61no—
227C3×C4×Dic3—21no—
228C3×C4×Dic3C2×D311yescharacteristic, complemented
229C3×C4×Dic3C2×D311yescharacteristic, complemented
230#3724C2×D311yescharacteristic, complemented
231#3724C2×D311yescharacteristic, complemented
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3C2×D311yescharacteristic, complemented
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—61no—
244#3722—61no—
245#3722—61no—
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic, complemented
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)⋊Dic3—61no—
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
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#4112yes—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278D3×C3⋊D3—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#123—91no—
291C3×C4×D4—91no—
292#939—91no—
293#938—91no—
294#937—91no—
295#937—91no—
296#930—91no—
297#930—91no—
298#929—91no—
299C4×#67—91no—
300C4×#67—91no—
301C2×(C2×D3)⋊C4—91no—
302#898—91no—
303#898—91no—
304#898—91no—
305#898—181no—
306#897—91no—
307#896—91no—
308#895—91no—
309#895—91no—
310#894—31no—
311#894—91no—
312#894—91no—
313#893—31no—
314#893—91no—
315#885—91no—
316#885—91no—
317#885—91no—
318#885—91no—
319#884—91no—
320#884—91no—
321#884—91no—
322#883—31no—
323#882—91no—
324#882—91no—
325#882—91no—
326#882—91no—
327#882—181no—
328D3×C22⋊C4—91no—
329D3×C22⋊C4—91no—
330#879—31no—
331#878—91no—
332#876—31no—
333#875—91no—
334#875—91no—
335#875—181no—
336C4×D12—31no—
337C23×C32—31no—
338C22×C3⋊D3—31no—
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—61no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—62no—
345C22×C3⋊D3—121no—
346C22×C3⋊D3—121no—
347C22×C3⋊D3—121no—
348C22×C3⋊D3C22×D311yescharacteristic
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3—61no—
360C22×C3×D3—61no—
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—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—41no—
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383C2×C32×C4C22×D311yescharacteristic
384#638—121no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—31no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C4⋊(C3⋊D3)—22no—
396C4⋊(C3⋊D3)—121no—
397C4⋊(C3⋊D3)—121no—
398#634—121no—
399C3×#67—121no—
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—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
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
423C2×C3×Dic3C22×D311yescharacteristic
424C3×D12—62no—
425C3×D12—62no—
426C3×D12—122no—
427C3×D12—121no—
428C3×C4×D3—121no—
429C3×C4×D3—121no—
430C3×C4×D3—121no—
431C3×C4×D3—121no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434#627—121no—
435#627—121no—
436#627—122no—
437#626—41no—
438#626—62no—
439#626—62no—
440#626—121no—
441#626—121no—
442#626—121no—
443#626—121no—
444#626—122no—
445#626—122no—
446#626—121no—
447#626—121no—
448#625—62no—
449#625—121no—
450#625—121no—
451#625—121no—
452#625—122no—
453#624—41no—
454#624—41no—
455#624—41no—
456#624—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
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—
467C32×D3—41no—
468C23×D3—91no—
469C23×D3—91no—
470C23×D3—91no—
471C23×D3—181no—
472C2×C3×D4—91no—
473C2×C3×D4—91no—
474C22×C3×C4—91no—
475C22×C3×C4—91no—
476C22×C3×C4—91no—
477C2×#67—31no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—181no—
488C22×Dic3—91no—
489C2×D12—31no—
490C2×D12—31no—
491C2×D12—31no—
492C2×D12—61no—
493C2×D12—91no—
494C2×D12—91no—
495C2×D12—91no—
496C2×D12—91no—
497C2×D12—91no—
498C2×D12—91no—
499C2×D12—181no—
500C2×D12—181no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
503C2×C4×D3—31no—
504C2×C4×D3—31no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×Dic6—91no—
510C2×Dic6—91no—
511C2×Dic6—91no—
512C2×Dic6—181no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—31no—
515C3×C4⋊C4—61no—
516C3×C4⋊C4—91no—
517C3×C4⋊C4—91no—
518C3×C4⋊C4—91no—
519C3×C4⋊C4—91no—
520C3×C22⋊C4—31no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C42—31no—
530C3×C42—31no—
531C3×C42—61no—
532#217—31no—
533#217—31no—
534#217—31no—
535#217—91no—
536#217—91no—
537#217—91no—
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—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—61no—
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—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—181no—
567(C2×D3)⋊C4—181no—
568(C2×D3)⋊C4—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4—361no—
575(C2×D3)⋊C4D3211yescharacteristic
576C4⋊Dic3—31no—
577C4⋊Dic3—91no—
578C4⋊Dic3—91no—
579C4⋊Dic3—181no—
580C4⋊Dic3D3211yescharacteristic, complemented
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—61no—
589Dic3⋊C4—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—181no—
594C4×Dic3D3211yescharacteristic, complemented
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—41no—
599C22×C32—61no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32C23×D311yescharacteristic
603C22×C32C23×D311yescharacteristic
604C22×C32C23×D311yescharacteristic
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—124no—
633C2×C3⋊D3—241no—
634C2×C3⋊D3—241no—
635C2×C3⋊D3#23512yes—
636C2×C3×D3—22no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—32no—
644C2×C3×D3—32no—
645C2×C3×D3—41no—
646C2×C3×D3—41no—
647C2×C3×D3—62no—
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—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
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—
671C2×C3×D3—121no—
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—61no—
685C32×C4—61no—
686C32×C4—81no—
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—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—41no—
709C3×Dic3—41no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—91no—
722#126—271no—
723#124—271no—
724#124—271no—
725#123—91no—
726#123—271no—
727C22⋊Q8—271no—
728#121—271no—
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—61no—
740C23×C3—91no—
741C23×C3—91no—
742C23×C3—91no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—31no—
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—362no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—361no—
768C22×D3—361no—
769C22×D3—362no—
770C22×D3—362no—
771C22×D3C2×D3211yescharacteristic
772C3×D4—182no—
773C3×D4—361no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
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—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—41no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—361no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799C2×C3×C4C2×D3211yescharacteristic
800C2×C3×C4C2×D3211yescharacteristic
801C2×C3×C4C2×D3211yescharacteristic
802#67—121no—
803#67—182no—
804#67—182no—
805#67—361no—
806#67—361no—
807#67—361no—
808#67—361no—
809#67—361no—
810#67—361no—
811#67—361no—
812#67—362no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—61no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—91no—
823C2×Dic3—91no—
824C2×Dic3—91no—
825C2×Dic3—181no—
826C2×Dic3—181no—
827C2×Dic3—181no—
828C2×Dic3—361no—
829C2×Dic3—361no—
830C2×Dic3C2×D3211yescharacteristic
831C2×Dic3C2×D3211yescharacteristic
832C2×Dic3C2×D3211yescharacteristic
833C2×Dic3C2×D3211yescharacteristic
834C2×Dic3C2×D3211yescharacteristic
835D12—62no—
836D12—62no—
837D12—122no—
838D12—121no—
839D12—182no—
840D12—361no—
841D12—361no—
842D12—361no—
843D12—361no—
844D12—362no—
845D12—362no—
846D12—361no—
847C4×D3—121no—
848C4×D3—121no—
849C4×D3—121no—
850C4×D3—121no—
851C4×D3—121no—
852C4×D3—121no—
853C4×D3—361no—
854C4×D3—361no—
855Dic6—361no—
856Dic6—361no—
857Dic6—361no—
858Dic6—362no—
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—121no—
872C2×C32C2×#23511yescharacteristic
873C2×C32#100411yescharacteristic
874C2×C32#100411yescharacteristic
875C2×C32D3×#4111yescharacteristic
876C2×C32D3×#4111yescharacteristic
877C2×C32#100911yescharacteristic
878C2×C32#100911yescharacteristic
879C2×C32#100911yescharacteristic
880C2×C32#100911yescharacteristic
881C3⋊D3—22no—
882C3⋊D3—41no—
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—42no—
892C3×D3—41no—
893C3×D3—41no—
894C3×D3—62no—
895C3×D3—62no—
896C3×D3—122no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—241no—
902C3×D3—241no—
903C24—271no—
904C2×Q8—271no—
905C2×D4—91no—
906C2×D4—91no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—91no—
915C22×C4—271no—
916C4⋊C4—31no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—91no—
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—41no—
942C22×C3—62no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—61no—
949C22×C3—92no—
950C22×C3—121no—
951C22×C3—121no—
952C22×C3—181no—
953C22×C3—181no—
954C22×C3—181no—
955C22×C3—181no—
956C22×C3—181no—
957C22×C3—181no—
958C22×C3—181no—
959C22×C3—181no—
960C22×C3C22×D3211yescharacteristic
961C22×C3C22×D3211yescharacteristic
962C22×C3C22×D3211yescharacteristic
963C2×D3—21no—
964C2×D3—21no—
965C2×D3—21no—
966C2×D3—32no—
967C2×D3—32no—
968C2×D3—62no—
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—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—121no—
993C2×D3—182no—
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—181no—
1003C2×D3—361no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—361no—
1011C2×D3—362no—
1012C2×D3—364no—
1013C2×D3—364no—
1014C2×D3—364no—
1015C2×D3—368no—
1016C2×D3—721no—
1017C2×D3—721no—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—41no—
1024C3×C4—62no—
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—81no—
1036C3×C4—121no—
1037C3×C4—121no—
1038C3×C4—121no—
1039C3×C4—121no—
1040C3×C4—181no—
1041C3×C4—181no—
1042C3×C4—181no—
1043Dic3—21no—
1044Dic3—21no—
1045Dic3—21no—
1046Dic3—21no—
1047Dic3—21no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
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#565711yescharacteristic, complemented
1070C32#570411yescharacteristic, complemented
1071C23—31no—
1072C23—91no—
1073C23—91no—
1074C23—91no—
1075C23—271no—
1076C23—542no—
1077C23—1081no—
1078C23—1081no—
1079Q8—1081no—
1080D4—182no—
1081D4—361no—
1082D4—542no—
1083D4—1081no—
1084D4—1081no—
1085D4—1081no—
1086D4—1081no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
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—122no—
1114C2×C3—121no—
1115C2×C3—121no—
1116C2×C3—182no—
1117C2×C3—361no—
1118C2×C3—361no—
1119C2×C3D3×#23511yescharacteristic
1120C2×C3D3×#23511yescharacteristic
1121C2×C3#6430711yescharacteristic
1122C2×C3#6430811yescharacteristic
1123C2×C3#6430811yescharacteristic
1124C2×C3#6431211yescharacteristic
1125C2×C3#6431311yescharacteristic
1126C2×C3#6431411yescharacteristic
1127C2×C3#6432011yescharacteristic
1128D3—41no—
1129D3—62no—
1130D3—62no—
1131D3—122no—
1132D3—121no—
1133D3—121no—
1134D3—121no—
1135D3—121no—
1136D3—241no—
1137D3—241no—
1138D3—362no—
1139D3—361no—
1140D3—361no—
1141D3—361no—
1142D3—721no—
1143D3—721no—
1144D3—722no—
1145C22—61no—
1146C22—61no—
1147C22—61no—
1148C22—92no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22—181no—
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—61no—
1167C4—61no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—541no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059401311yescharacteristic, complemented
1177C3#1059423211yescharacteristic, complemented
1178C3#1059463911yescharacteristic, complemented
1179C2—121no—
1180C2—182no—
1181C2—361no—
1182C2—361no—
1183C2—1081no—
1184C2#1172438111yescharacteristic
1185C2#1172439011yescharacteristic
1186C2#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. #11723687C2semidirect
2. #11723541C2semidirect
3. #11723416C2semidirect
4. #11723411C2semidirect
5. C3×#63894C2semidirect
6. C3×#63859C2semidirect
7. C3×#63854C2semidirect
8. #11723009C2semidirect
9. #11722993C2semidirect
10. #11722984C2semidirect
11. #11722961C2semidirect
12. #11722957C2semidirect
13. #11722950C2semidirect
14. #11722931C2semidirect
15. #11722904C2semidirect
22. C2×#6295C22semidirect
24. C2×#6293C22semidirect
30. C2×C3×#624C22semidirect
31. C2×C3×#624C22semidirect
33. C3×#3752C22semidirect
34. C3×#3750C22semidirect
36. C32×C4⋊Dic3C22semidirect
37. C32×C4×Dic3C22semidirect
38. #88814C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88803C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
88. #63894D3semidirect
92. #63859D3semidirect
93. #63854D3semidirect
176. C2×#624C2×D3semidirect
177. C2×#624C2×D3semidirect
195. #3752C2×D3semidirect
197. #3750C2×D3semidirect
217. C3×C4⋊Dic3C2×D3semidirect
218. C3×C4⋊Dic3C2×D3semidirect
228. C3×C4×Dic3C2×D3semidirect
229. C3×C4×Dic3C2×D3semidirect
230. #3724C2×D3semidirect
231. #3724C2×D3semidirect
235. Dic3⋊Dic3C2×D3semidirect
247. #3722C2×D3semidirect
580. C4⋊Dic3D32semidirect
594. C4×Dic3D32semidirect
736. C33#538semidirect
1068. C32#5560semidirect
1069. C32#5657semidirect
1070. C32#5704semidirect
1176. C3#10594013semidirect
1177. C3#10594232semidirect
1178. C3#10594639semidirect

Maximal subgroups

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

subgroupindex
#117236872
#117235412
#117234162
#117234112
C3×#638942
C3×#638592
C3×#638542
#117230092
#117229932
#117229842
#117229612
#117229572
#117229502
#117229312
#117229042
#105946393
#105942323
#105940133