Finite Group Databasebeta

← #13168108

Subgroups — #13168108

Order 1728.

1298 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#11723688C211yesmaximal, characteristic, complemented
2#11723521C211yesmaximal, characteristic, complemented
3#11723475C211yesmaximal, characteristic, complemented
4#11723471C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic, complemented
6C3×#63860C211yesmaximal, characteristic, complemented
7C3×#63859C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722989C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722964C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722902C211yesmaximal, characteristic, complemented
16#10595184—31nomaximal
17#10594126—31nomaximal
18#10594019—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic, complemented
21C2×C32×D12C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32#88859C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3750C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×C4×Dic3C2211yescharacteristic, complemented
37#88815C2211yescharacteristic, complemented
38#88815C2211yescharacteristic, complemented
39#88814C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, 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×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64148—31no—
55#64094—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×#937—31no—
58C3×#936—31no—
59C3×#882—31no—
60C3×#879—31no—
61C3×#876—31no—
62C3×#875—31no—
63#63977—31no—
64#63977—31no—
65#63975—31no—
66#67⋊Dic3—31no—
67#63971—31no—
68#63969—31no—
69D3×#217—31no—
70D3×#217—31no—
71#63962—31no—
72#63958—31no—
73#63958—31no—
74#63956—31no—
75#63923—31no—
76#63922D311yescharacteristic, complemented
77#63921—31no—
78#63912—31no—
79#63910—31no—
80#63907—31no—
81#63907—31no—
82#63907—61no—
83#63898—31no—
84#63896—31no—
85#63891—31no—
86#63888—31no—
87#63887—31no—
88#63886—31no—
89#63886—31no—
90#63886—31no—
91#63886—61no—
92#63881—31no—
93#63880—31no—
94#63880—31no—
95#63880—61no—
96#63862—31no—
97#63861—31no—
98#63860D311yescharacteristic, complemented
99#63859D311yescharacteristic, complemented
100#63854—31no—
101#63853—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
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×#634—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×D12—41no—
122#6294—41no—
123#6292—22no—
124#6291—41no—
125#6291—41no—
126#6291—41no—
127#6289—41no—
128Dic3×C3⋊D3—41no—
129D3×C3⋊Dic3—41no—
130C3×#626—22no—
131C3×#625—41no—
132#5704—91no—
133#5678—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—
142C22×C3⋊Dic3—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×#634C2×D311yescharacteristic, complemented
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×D12—21no—
151C2×C3×D12—31no—
152C2×C3×D12C2×D311yescharacteristic
153C2×C3×D12C2×D311yescharacteristic
154C2×C3×Dic6—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—61no—
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—61no—
166C2×#626—61no—
167C2×#626—61no—
168C2×#626—61no—
169C2×#626C2×D311yescharacteristic
170C2×#625C2×D311yescharacteristic
171C2×#624—31no—
172C2×#624—31no—
173C2×#624—31no—
174C2×#624—61no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—61no—
182C2×D3×Dic3—61no—
183C32×C22⋊C4—31no—
184C32×C42—31no—
185#3757—31no—
186#3757—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
196C4⋊(C3⋊Dic3)—31no—
197#3750C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—31no—
206C3×(C2×D3)⋊C4—21no—
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—31no—
216C3×(C2×D3)⋊C4—61no—
217C3×(C2×D3)⋊C4C2×D311yescharacteristic
218C3×(C2×D3)⋊C4C2×D311yescharacteristic
219C3×C4⋊Dic3—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—61no—
226C3×C4×Dic3—21no—
227C3×C4×Dic3C2×D311yescharacteristic, complemented
228C3×C4×Dic3C2×D311yescharacteristic, complemented
229#3724—31no—
230#3724—31no—
231#3724C2×D311yescharacteristic, complemented
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3C2×D311yescharacteristic, complemented
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—61no—
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—31no—
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
258(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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#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×#124—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#947—91no—
295#946—91no—
296#939—91no—
297#939—91no—
298#939—91no—
299#939—181no—
300#938—91no—
301#937—31no—
302#936—31no—
303#935—91no—
304D4×Dic3—91no—
305#898—91no—
306#896—91no—
307#895—91no—
308#895—91no—
309#894—91no—
310#893—91no—
311#886—91no—
312#885—91no—
313#885—91no—
314#885—181no—
315#884—91no—
316#884—91no—
317#884—91no—
318#883—91no—
319#883—91no—
320#883—91no—
321#882—31no—
322#882—91no—
323#882—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326D3×C22⋊C4—91no—
327D3×C22⋊C4—91no—
328#879—31no—
329#879—91no—
330#879—91no—
331#878—91no—
332#876—31no—
333#875—31no—
334C4×D12—91no—
335C4×D12—91no—
336C4×D12—181no—
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⋊Dic3—121no—
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C4⋊(C3⋊D3)—62no—
397C4×C3⋊D3—121no—
398C4×C3⋊D3—121no—
399#634—41no—
400C3×#67—62no—
401C3×#67—121no—
402C3×#67—121no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—31no—
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—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C3×D12—41no—
428C3×D12—41no—
429C3×D12—42no—
430C3×D12—62no—
431C3×Dic6—121no—
432C3×Dic6—121no—
433C3×Dic6—122no—
434#626—22no—
435#626—62no—
436#626—62no—
437#626—64no—
438#626—121no—
439#626—121no—
440#626—121no—
441#626—121no—
442#626—121no—
443#626—121no—
444#626—122no—
445#626—122no—
446#626—122no—
447#625—41no—
448#624—121no—
449#624—121no—
450#624—122no—
451#624—121no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—122no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459D3×Dic3—122no—
460#538—271noSylow
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3⋊(C3⋊D3)—41no—
465C3×C3⋊D3—22no—
466C32×D3—41no—
467C32×D3—41no—
468C32×D3—41no—
469C24×C3—91no—
470C23×D3—31no—
471C23×D3—31no—
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×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—181no—
489C2×#67—181no—
490C2×#67—181no—
491C22×Dic3—91no—
492C22×Dic3—91no—
493C22×Dic3—91no—
494C22×Dic3—91no—
495C22×Dic3—181no—
496C2×D12—31no—
497C2×D12—91no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—181no—
503C2×D12D3211yescharacteristic
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—91no—
512C2×C4×D3—181no—
513C2×C4×D3—181no—
514C2×Dic6—31no—
515C2×Dic6—31no—
516C2×Dic6—61no—
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×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C42—31no—
532C3×C42—31no—
533C3×C42—61no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—31no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—181no—
547#217—181no—
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—31no—
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—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—361no—
573(C2×D3)⋊C4D3211yescharacteristic
574C4⋊Dic3—31no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577C4⋊Dic3—91no—
578C4⋊Dic3—91no—
579C4⋊Dic3—181no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—61no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—181no—
595C4×Dic3D3211yescharacteristic, complemented
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
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×C32—61no—
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
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—241no—
634C2×C3⋊D3—241no—
635C2×C3⋊D3#23712yes—
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—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—62no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3—124no—
673C2×C3×D3—124no—
674D32—44no—
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—22no—
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—62no—
707C3×Dic3—62no—
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—61no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—91no—
722#126—271no—
723#124—91no—
724#124—271no—
725#123—271no—
726#123—271no—
727C22⋊Q8—271no—
728#121—271no—
729#121—271no—
730#121—271no—
731#120—91no—
732#120—271no—
733C4×D4—271no—
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—
747C23×C3—182no—
748C23×C3—361no—
749C23×C3—361no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—61no—
753C22×D3—62no—
754C22×D3—62no—
755C22×D3—91no—
756C22×D3—91no—
757C22×D3—91no—
758C22×D3—121no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—181no—
763C22×D3—181no—
764C22×D3—181no—
765C22×D3—361no—
766C22×D3C2×D3211yescharacteristic
767C22×D3C2×D3211yescharacteristic
768C22×D3C2×D3211yescharacteristic
769C3×Q8—361no—
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×C4C2×D3211yescharacteristic
794C2×C3×C4C2×D3211yescharacteristic
795C2×C3×C4C2×D3211yescharacteristic
796#67—62no—
797#67—121no—
798#67—121no—
799#67—182no—
800#67—361no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—361no—
805#67—361no—
806#67—362no—
807#67—362no—
808#67—362no—
809C2×Dic3—31no—
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—61no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—91no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—181no—
828C2×Dic3—181no—
829C2×Dic3—181no—
830C2×Dic3—361no—
831C2×Dic3—361no—
832C2×Dic3—361no—
833C2×Dic3—361no—
834C2×Dic3—361no—
835C2×Dic3—362no—
836C2×Dic3C2×D3211yescharacteristic
837C2×Dic3C2×D3211yescharacteristic
838C2×Dic3C2×D3211yescharacteristic
839D12—41no—
840D12—62no—
841D12—182no—
842D12—182no—
843D12—184no—
844D12—361no—
845D12—361no—
846D12—361no—
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—361no—
856C4×D3—362no—
857Dic6—121no—
858Dic6—121no—
859Dic6—122no—
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—21no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—121no—
873C2×C32—121no—
874C2×C32—121no—
875C2×C32C2×#23711yescharacteristic
876C2×C32#100411yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32D3×#4111yescharacteristic
880C2×C32D3×#4111yescharacteristic
881C2×C32#100911yescharacteristic
882C2×C32#100911yescharacteristic
883C2×C32#100911yescharacteristic
884C3⋊D3—22no—
885C3⋊D3—121no—
886C3⋊D3—122no—
887C3⋊D3—121no—
888C3⋊D3—121no—
889C3⋊D3—241no—
890C3⋊D3—241no—
891C3⋊D3—242no—
892C3×D3—42no—
893C3×D3—41no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—62no—
900C3×D3—62no—
901C3×D3—81no—
902C3×D3—81no—
903C3×D3—122no—
904C24—91no—
905C2×Q8—91no—
906C2×D4—31no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C2×D4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C22×C4—271no—
916C22×C4—271no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—31no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C42—31no—
938C42—271no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—41no—
943C22×C3—62no—
944C22×C3—61no—
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—92no—
963C22×C3—121no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—121no—
971C22×C3—181no—
972C22×C3—181no—
973C22×C3—364no—
974C22×C3C22×D3211yescharacteristic
975C22×C3C22×D3211yescharacteristic
976C22×C3C22×D3211yescharacteristic
977C2×D3—21no—
978C2×D3—21no—
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—21no—
986C2×D3—32no—
987C2×D3—32no—
988C2×D3—62no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—121no—
994C2×D3—121no—
995C2×D3—124no—
996C2×D3—124no—
997C2×D3—182no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—181no—
1005C2×D3—181no—
1006C2×D3—181no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—361no—
1011C2×D3—361no—
1012C2×D3—361no—
1013C2×D3—361no—
1014C2×D3—361no—
1015C2×D3—362no—
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—62no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—81no—
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—62no—
1043Dic3—62no—
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—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—721no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#559311yescharacteristic, complemented
1069C32#567811yescharacteristic, complemented
1070C32#570411yescharacteristic, complemented
1071C23—31no—
1072C23—31no—
1073C23—31no—
1074C23—91no—
1075C23—182no—
1076C23—271no—
1077C23—361no—
1078C23—361no—
1079Q8—361no—
1080D4—121no—
1081D4—182no—
1082D4—361no—
1083D4—542no—
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—1081no—
1097C2×C4—1081no—
1098C2×C4—1081no—
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—121no—
1117C2×C3—121no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—182no—
1121C2×C3—241no—
1122C2×C3—241no—
1123C2×C3#6430611yescharacteristic
1124C2×C3#6430711yescharacteristic
1125C2×C3#6430711yescharacteristic
1126C2×C3#6430811yescharacteristic
1127C2×C3D3×#23711yescharacteristic
1128C2×C3D3×#23711yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6431411yescharacteristic
1131C2×C3#6433011yescharacteristic
1132D3—41no—
1133D3—41no—
1134D3—41no—
1135D3—62no—
1136D3—62no—
1137D3—122no—
1138D3—362no—
1139D3—361no—
1140D3—361no—
1141D3—361no—
1142D3—721no—
1143D3—721no—
1144D3—722no—
1145C22—61no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—92no—
1155C22—181no—
1156C22—181no—
1157C22—364no—
1158C22—541no—
1159C22—541no—
1160C22—541no—
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#1059401911yescharacteristic, complemented
1177C3#1059412611yescharacteristic, complemented
1178C3#1059518411yescharacteristic, complemented
1179C2—121no—
1180C2—121no—
1181C2—121no—
1182C2—182no—
1183C2—1081no—
1184C2#1172437311yescharacteristic
1185C2#1172438411yescharacteristic
1186C2#1172441811yescharacteristic
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. #11723688C2semidirect
2. #11723521C2semidirect
3. #11723475C2semidirect
4. #11723471C2semidirect
5. C3×#63922C2semidirect
6. C3×#63860C2semidirect
7. C3×#63859C2semidirect
8. #11723022C2semidirect
9. #11722996C2semidirect
10. #11722989C2semidirect
11. #11722966C2semidirect
12. #11722964C2semidirect
13. #11722948C2semidirect
14. #11722929C2semidirect
15. #11722902C2semidirect
20. C2×C3×#634C22semidirect
26. C2×#6291C22semidirect
27. C2×#6289C22semidirect
29. C2×D3×C3⋊Dic3C22semidirect
32. #88859C22semidirect
34. C3×#3750C22semidirect
36. C32×C4×Dic3C22semidirect
37. #88815C22semidirect
38. #88815C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. #88804C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
76. #63922D3semidirect
98. #63860D3semidirect
99. #63859D3semidirect
146. C2×#634C2×D3semidirect
197. #3750C2×D3semidirect
227. C3×C4×Dic3C2×D3semidirect
228. C3×C4×Dic3C2×D3semidirect
231. #3724C2×D3semidirect
239. Dic3⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
595. C4×Dic3D32semidirect
736. C33#538semidirect
1068. C32#5593semidirect
1069. C32#5678semidirect
1070. C32#5704semidirect
1176. C3#10594019semidirect
1177. C3#10594126semidirect
1178. C3#10595184semidirect

Maximal subgroups

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

subgroupindex
#117236882
#117235212
#117234752
#117234712
C3×#639222
C3×#638602
C3×#638592
#117230222
#117229962
#117229892
#117229662
#117229642
#117229482
#117229292
#117229022
#105951843
#105941263
#105940193