Finite Group Databasebeta

← #13168105

Subgroups — #13168105

Order 1728.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723692C211yesmaximal, characteristic, complemented
2#11723531C211yesmaximal, characteristic, complemented
3#11723472C211yesmaximal, characteristic, complemented
4#11723420C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic, complemented
6C3×#63884C211yesmaximal, characteristic, complemented
7C3×#63861C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11723008C211yesmaximal, characteristic, complemented
10#11723006C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722902C211yesmaximal, characteristic, complemented
16#10595185—31nomaximal
17#10594657—31nomaximal
18#10594127—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C32×D12C2211yescharacteristic
22C2×#6296C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3752C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×#3750C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37#88815C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64147—31no—
55#64102—31no—
56#64092—31no—
57C3×#937—31no—
58C3×#935—31no—
59C3×#898—31no—
60C3×#894—31no—
61C3×#882—31no—
62C3×#879—31no—
63#63978—31no—
64#63977—31no—
65#63977—31no—
66Dic3×#67—31no—
67#63971—31no—
68#63971—31no—
69D3×#217—31no—
70D3×#217—31no—
71#63959—31no—
72#63959—31no—
73#63956—31no—
74#63953—31no—
75#63923—31no—
76#63922D311yescharacteristic, complemented
77#63921—31no—
78#63916—31no—
79#63916—31no—
80#63916—61no—
81#63915—31no—
82#63910—31no—
83#63906—31no—
84C4×#626—31no—
85#63899—31no—
86#63895—31no—
87#63893—31no—
88Dic3×D12—31no—
89#63886—31no—
90#63884D311yescharacteristic, complemented
91#63881—31no—
92#63881—31no—
93#63881—61no—
94#63862—31no—
95#63861—31no—
96#63861D311yescharacteristic, complemented
97#63853—31no—
98#63853—31no—
99#63853—61no—
100#63852—31no—
101#63852—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊(C3⋊D3)—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×D12—41no—
122#6296—41no—
123#6294—41no—
124#6292—22no—
125#6291—41no—
126#6291—41no—
127#6291—41no—
128Dic3×C3⋊D3—41no—
129C3×#626—22no—
130C3×#625—41no—
131C3×D3×Dic3—41no—
132#5704—91no—
133#5657—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×C32×D4—31no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—61no—
148C2×C4×C3⋊D3—61no—
149C2×C4×C3⋊D3—61no—
150C2×C4×C3⋊D3—121no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C22×C3×Dic3—31no—
155C2×C3×D12—21no—
156C2×C3×D12—31no—
157C2×C3×D12C2×D311yescharacteristic
158C2×C3×D12C2×D311yescharacteristic
159C2×C3×C4×D3—31no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—61no—
172C2×#626—61no—
173C2×#626—61no—
174C2×#626—61no—
175C2×#626C2×D311yescharacteristic
176C2×#625C2×D311yescharacteristic
177C2×#624—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3C2×D311yescharacteristic, complemented
184C32×C4⋊C4—31no—
185C32×C22⋊C4—31no—
186#3757—31no—
187#3757—31no—
188#3757—31no—
189#3752—31no—
190#3752—31no—
191#3752C2×D311yescharacteristic
192C4⋊(C3⋊Dic3)—31no—
193C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
194#3750C2×D311yescharacteristic, complemented
195C4×C3⋊Dic3—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—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—61no—
212C3×(C2×D3)⋊C4C2×D311yescharacteristic
213C3×(C2×D3)⋊C4C2×D311yescharacteristic
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—61no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—61no—
223C3×Dic3⋊C4C2×D311yescharacteristic, complemented
224C3×Dic3⋊C4C2×D311yescharacteristic, complemented
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227#3724—31no—
228#3724C2×D311yescharacteristic, complemented
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—61no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—61no—
240#3722—61no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258Dic32—31no—
259Dic32—31no—
260Dic32—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#4112yes—
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—21no—
278C3×D32—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×#126—91no—
290C3×#123—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#939—91no—
295#939—91no—
296#938—91no—
297#938—91no—
298#938—181no—
299#937—31no—
300#936—91no—
301#935—31no—
302D4×Dic3—91no—
303#930—91no—
304C4×#67—91no—
305#898—31no—
306#898—91no—
307#897—91no—
308#896—91no—
309#895—91no—
310#895—91no—
311#894—31no—
312#894—91no—
313#893—91no—
314#893—91no—
315#893—181no—
316#885—91no—
317#885—91no—
318#885—91no—
319#885—91no—
320#884—91no—
321#884—91no—
322#883—91no—
323#883—91no—
324#883—181no—
325#882—31no—
326#882—91no—
327#882—91no—
328#67⋊C4—91no—
329D3×C22⋊C4—91no—
330D3×C22⋊C4—91no—
331#879—31no—
332#879—91no—
333#879—91no—
334#878—91no—
335#875—91no—
336C4×D12—91no—
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—121no—
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—21no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—121no—
357C22×C3×D3—121no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—22no—
367C2×D32—41no—
368C2×D32—41no—
369C32×D4—121no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—41no—
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380#638—121no—
381#638—121no—
382#638—121no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—121no—
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C4⋊(C3⋊D3)—62no—
396C4×C3⋊D3—121no—
397C4×C3⋊D3—121no—
398C4×C3⋊D3—121no—
399C4×C3⋊D3—122no—
400C4×C3⋊D3—121no—
401C4×C3⋊D3—122no—
402C4×C3⋊D3—122no—
403C4×C3⋊D3—124no—
404C3×#67—62no—
405C3×#67—121no—
406C3×#67—121no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
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—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—121no—
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C3×D12—41no—
433C3×D12—41no—
434C3×D12—42no—
435C3×D12—62no—
436C3×C4×D3—121no—
437#627—121no—
438#627—121no—
439#627—121no—
440#626—22no—
441#626—62no—
442#626—62no—
443#626—64no—
444#626—121no—
445#626—121no—
446#626—121no—
447#626—121no—
448#626—121no—
449#626—121no—
450#626—122no—
451#626—122no—
452#626—122no—
453#625—41no—
454#624—121no—
455D3×Dic3—41no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—122no—
459D3×Dic3—121no—
460D3×Dic3—121no—
461#538—271noSylow
462C2×C33C2×#4111yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C2×C33H(5,𝔽2)11yescharacteristic
465C3⋊(C3⋊D3)—41no—
466C3×C3⋊D3—22no—
467C32×D3—41no—
468C32×D3—41no—
469C32×D3—41no—
470C24×C3—91no—
471C23×D3—31no—
472C23×D3—31no—
473C2×C3×D4—31no—
474C2×C3×D4—31no—
475C2×C3×D4—61no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C22×C3×C4—91no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—181no—
490C2×#67—181no—
491C2×#67—181no—
492C22×Dic3—31no—
493C22×Dic3—91no—
494C22×Dic3—91no—
495C2×D12—31no—
496C2×D12—91no—
497C2×D12—91no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—181no—
502C2×D12D3211yescharacteristic
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—91no—
510C2×C4×D3—91no—
511C2×C4×D3—181no—
512C2×C4×D3—181no—
513C2×C4×D3—181no—
514C2×C4×D3—181no—
515C2×C4×D3—361no—
516C2×Dic6—91no—
517C2×Dic6—91no—
518C2×Dic6—91no—
519C3×C4⋊C4—31no—
520C3×C4⋊C4—31no—
521C3×C4⋊C4—61no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C22⋊C4—31no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—61no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C42—91no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—31no—
541#217—31no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—91no—
548#217—91no—
549#217—181no—
550#217—181no—
551#217—181no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—61no—
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)⋊C4D3211yescharacteristic
575C4⋊Dic3—31no—
576C4⋊Dic3—31no—
577C4⋊Dic3—61no—
578C4⋊Dic3—91no—
579C4⋊Dic3—91no—
580C4⋊Dic3—91no—
581C4⋊Dic3—181no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—61no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4D3211yescharacteristic, complemented
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—181no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—41no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—61no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—62no—
619C2×C3⋊D3—62no—
620C2×C3⋊D3—62no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—61no—
626C2×C3⋊D3—61no—
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—122no—
634C2×C3⋊D3—122no—
635C2×C3⋊D3—122no—
636C2×C3⋊D3#23712yes—
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—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—21no—
654C2×C3×D3—21no—
655C2×C3×D3—32no—
656C2×C3×D3—32no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—41no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—62no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673C2×C3×D3—124no—
674C2×C3×D3—124no—
675D32—44no—
676C32×C4—21no—
677C32×C4—22no—
678C32×C4—21no—
679C32×C4—21no—
680C32×C4—41no—
681C32×C4—41no—
682C32×C4—42no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—61no—
692C3⋊Dic3—62no—
693C3⋊Dic3—61no—
694C3⋊Dic3—61no—
695C3⋊Dic3—121no—
696C3⋊Dic3—121no—
697C3⋊Dic3—122no—
698C3×Dic3—22no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—41no—
706C3×Dic3—41no—
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—61no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722#126—91no—
723#126—271no—
724#124—271no—
725#124—271no—
726#123—91no—
727#123—271no—
728C22⋊Q8—271no—
729#121—271no—
730#121—271no—
731#121—271no—
732#120—91no—
733#120—271no—
734C4×D4—271no—
735C4×D4—271no—
736C2×C22⋊C4—271no—
737C33#53811yescharacteristic, complemented, Sylow
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—31no—
744C23×C3—61no—
745C23×C3—61no—
746C23×C3—61no—
747C23×C3—91no—
748C23×C3—182no—
749C23×C3—361no—
750C23×C3—361no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—61no—
754C22×D3—62no—
755C22×D3—62no—
756C22×D3—91no—
757C22×D3—91no—
758C22×D3—91no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—121no—
763C22×D3—181no—
764C22×D3—181no—
765C22×D3—181no—
766C22×D3—361no—
767C22×D3C2×D3211yescharacteristic
768C22×D3C2×D3211yescharacteristic
769C22×D3C2×D3211yescharacteristic
770C3×D4—121no—
771C3×D4—121no—
772C3×D4—122no—
773C3×D4—182no—
774C3×D4—361no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
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—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—361no—
794C2×C3×C4C2×D3211yescharacteristic
795C2×C3×C4C2×D3211yescharacteristic
796C2×C3×C4C2×D3211yescharacteristic
797#67—62no—
798#67—121no—
799#67—121no—
800#67—182no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—361no—
805#67—361no—
806#67—361no—
807#67—362no—
808#67—362no—
809#67—362no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—91no—
828C2×Dic3—121no—
829C2×Dic3—181no—
830C2×Dic3—181no—
831C2×Dic3—181no—
832C2×Dic3—361no—
833C2×Dic3—361no—
834C2×Dic3—361no—
835C2×Dic3C2×D3211yescharacteristic
836C2×Dic3C2×D3211yescharacteristic
837C2×Dic3C2×D3211yescharacteristic
838D12—41no—
839D12—62no—
840D12—182no—
841D12—182no—
842D12—184no—
843D12—361no—
844D12—361no—
845D12—361no—
846C4×D3—121no—
847C4×D3—361no—
848C4×D3—361no—
849C4×D3—361no—
850C4×D3—361no—
851C4×D3—361no—
852C4×D3—362no—
853C4×D3—361no—
854C4×D3—361no—
855C4×D3—362no—
856C4×D3—362no—
857C4×D3—362no—
858C4×D3—364no—
859Dic6—361no—
860Dic6—361no—
861Dic6—361no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—41no—
872C2×C32—41no—
873C2×C32—41no—
874C2×C32—121no—
875C2×C32—121no—
876C2×C32—121no—
877C2×C32C2×#23711yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32#100411yescharacteristic
881C2×C32D3×#4111yescharacteristic
882C2×C32D3×#4111yescharacteristic
883C2×C32#100911yescharacteristic
884C2×C32#100911yescharacteristic
885C2×C32#100911yescharacteristic
886C3⋊D3—22no—
887C3⋊D3—122no—
888C3⋊D3—122no—
889C3⋊D3—122no—
890C3⋊D3—124no—
891C3⋊D3—121no—
892C3⋊D3—121no—
893C3⋊D3—121no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—41no—
900C3×D3—62no—
901C3×D3—62no—
902C3×D3—81no—
903C3×D3—81no—
904C3×D3—81no—
905C3×D3—122no—
906C24—91no—
907C2×Q8—271no—
908C2×D4—31no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—271no—
912C2×D4—271no—
913C2×D4—271no—
914C2×D4—271no—
915C22×C4—91no—
916C22×C4—271no—
917C22×C4—271no—
918C22×C4—271no—
919C4⋊C4—31no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—271no—
924C4⋊C4—271no—
925C22⋊C4—31no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—91no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C42—91no—
940C42—271no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—41no—
945C22×C3—61no—
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—61no—
963C22×C3—92no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—121no—
971C22×C3—121no—
972C22×C3—121no—
973C22×C3—181no—
974C22×C3—181no—
975C22×C3—364no—
976C22×C3C22×D3211yescharacteristic
977C22×C3C22×D3211yescharacteristic
978C22×C3C22×D3211yescharacteristic
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—21no—
986C2×D3—21no—
987C2×D3—21no—
988C2×D3—32no—
989C2×D3—32no—
990C2×D3—62no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—121no—
996C2×D3—121no—
997C2×D3—124no—
998C2×D3—124no—
999C2×D3—182no—
1000C2×D3—182no—
1001C2×D3—182no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—181no—
1005C2×D3—181no—
1006C2×D3—181no—
1007C2×D3—181no—
1008C2×D3—181no—
1009C2×D3—181no—
1010C2×D3—181no—
1011C2×D3—361no—
1012C2×D3—361no—
1013C2×D3—361no—
1014C2×D3—361no—
1015C2×D3—361no—
1016C2×D3—361no—
1017C2×D3—362no—
1018C2×D3—362no—
1019C2×D3—362no—
1020C3×C4—22no—
1021C3×C4—21no—
1022C3×C4—21no—
1023C3×C4—21no—
1024C3×C4—41no—
1025C3×C4—41no—
1026C3×C4—42no—
1027C3×C4—62no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—61no—
1033C3×C4—61no—
1034C3×C4—121no—
1035C3×C4—121no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039C3×C4—181no—
1040C3×C4—181no—
1041Dic3—21no—
1042Dic3—21no—
1043Dic3—21no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—121no—
1055Dic3—121no—
1056Dic3—121no—
1057Dic3—121no—
1058Dic3—121no—
1059Dic3—182no—
1060Dic3—181no—
1061Dic3—181no—
1062Dic3—181no—
1063Dic3—361no—
1064Dic3—361no—
1065Dic3—362no—
1066C32—21no—
1067C32—21no—
1068C32—21no—
1069C32—41no—
1070C32#559311yescharacteristic, complemented
1071C32#565711yescharacteristic, complemented
1072C32#570411yescharacteristic, complemented
1073C23—31no—
1074C23—31no—
1075C23—31no—
1076C23—91no—
1077C23—182no—
1078C23—271no—
1079C23—361no—
1080C23—361no—
1081Q8—1081no—
1082D4—121no—
1083D4—182no—
1084D4—361no—
1085D4—542no—
1086D4—1081no—
1087D4—1081no—
1088D4—1081no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—271no—
1098C2×C4—361no—
1099C2×C4—1081no—
1100C2×C4—1081no—
1101C2×C4—1081no—
1102C2×C4D3311yescharacteristic
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—41no—
1113C2×C3—41no—
1114C2×C3—41no—
1115C2×C3—121no—
1116C2×C3—121no—
1117C2×C3—121no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—121no—
1121C2×C3—182no—
1122C2×C3—241no—
1123C2×C3—241no—
1124C2×C3—241no—
1125C2×C3#6430611yescharacteristic
1126C2×C3#6430711yescharacteristic
1127C2×C3D3×#23711yescharacteristic
1128C2×C3D3×#23711yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6431411yescharacteristic
1131C2×C3#6431411yescharacteristic
1132C2×C3#6432011yescharacteristic
1133C2×C3#6433011yescharacteristic
1134D3—41no—
1135D3—41no—
1136D3—41no—
1137D3—62no—
1138D3—62no—
1139D3—122no—
1140D3—362no—
1141D3—362no—
1142D3—362no—
1143D3—364no—
1144D3—361no—
1145D3—361no—
1146D3—361no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—61no—
1155C22—61no—
1156C22—92no—
1157C22—181no—
1158C22—181no—
1159C22—364no—
1160C22—541no—
1161C22—541no—
1162C22—541no—
1163C22C2×D3311yescharacteristic
1164C4—21no—
1165C4—61no—
1166C4—61no—
1167C4—61no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C4—181no—
1173C4—541no—
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059412711yescharacteristic, complemented
1179C3#1059465711yescharacteristic, complemented
1180C3#1059518511yescharacteristic, complemented
1181C2—121no—
1182C2—121no—
1183C2—121no—
1184C2—182no—
1185C2—1081no—
1186C2#1172437311yescharacteristic
1187C2#1172438511yescharacteristic
1188C2#1172441911yescharacteristic
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. #11723692C2semidirect
2. #11723531C2semidirect
3. #11723472C2semidirect
4. #11723420C2semidirect
5. C3×#63922C2semidirect
6. C3×#63884C2semidirect
7. C3×#63861C2semidirect
8. #11723022C2semidirect
9. #11723008C2semidirect
10. #11723006C2semidirect
11. #11722966C2semidirect
12. #11722958C2semidirect
13. #11722948C2semidirect
14. Dic3×#626C2semidirect
15. #11722902C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×#6296C22semidirect
27. C2×#6291C22semidirect
31. C2×C3×D3×Dic3C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C3×#3750C22semidirect
36. C32×Dic3⋊C4C22semidirect
37. #88815C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
40. #88804C22semidirect
41. #88804C22semidirect
44. (C2×D3)⋊(C3⋊Dic3)C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
76. #63922D3semidirect
90. #63884D3semidirect
96. #63861D3semidirect
183. C2×D3×Dic3C2×D3semidirect
193. C4⋊(C3⋊Dic3)C2×D3semidirect
194. #3750C2×D3semidirect
223. C3×Dic3⋊C4C2×D3semidirect
224. C3×Dic3⋊C4C2×D3semidirect
228. #3724C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
590. Dic3⋊C4D32semidirect
737. C33#538semidirect
1070. C32#5593semidirect
1071. C32#5657semidirect
1072. C32#5704semidirect
1178. C3#10594127semidirect
1179. C3#10594657semidirect
1180. C3#10595185semidirect

Maximal subgroups

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

subgroupindex
#117236922
#117235312
#117234722
#117234202
C3×#639222
C3×#638842
C3×#638612
#117230222
#117230082
#117230062
#117229662
#117229582
#117229482
Dic3×#6262
#117229022
#105951853
#105946573
#105941273