Finite Group Databasebeta

← #13171978

Subgroups — #13171978

Order 1728.

1276 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723723C211yesmaximal, characteristic, complemented
2#11723634C211yesmaximal, characteristic
3#11723597C211yesmaximal, characteristic, complemented
4#11723596C211yesmaximal, characteristic, complemented
5C3×#63974C211yesmaximal, characteristic, complemented
6C3×#63969C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8#11722998C211yesmaximal, characteristic, complemented
9#11722992C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722970C211yesmaximal, characteristic, complemented
12#11722936C211yesmaximal, characteristic, complemented
13#11722930C211yesmaximal, characteristic, complemented
14#11722922C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595208—31nomaximal
17#10594193—31nomaximal
18#10594092—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29#88864C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64146—31no—
55#64088—31no—
56#64088—31no—
57C3×#936—31no—
58C3×#935—31no—
59C3×#885—31no—
60C3×#883—31no—
61C3×D3×C22⋊C4—31no—
62C3×D3×C22⋊C4—31no—
63#63976—31no—
64#63976—31no—
65#63976—61no—
66#63975—31no—
67#63975—31no—
68#63974—31no—
69#63974D311yescharacteristic, complemented
70#63969D311yescharacteristic, complemented
71D3×#217—31no—
72D3×#217—31no—
73#63959D311yescharacteristic, complemented
74#63956—31no—
75#63956—31no—
76#63956—31no—
77#63956—31no—
78#63956—61no—
79#63956—61no—
80#63952—31no—
81#63952—31no—
82#63905—31no—
83#63905—31no—
84#63902—31no—
85C4×#625—31no—
86#63899—31no—
87#63891—31no—
88#63891—31no—
89#63888—31no—
90#63888—31no—
91#63887—31no—
92#63879—31no—
93#63879—31no—
94#63878—31no—
95#63877—31no—
96#63856—31no—
97#63855—31no—
98#63851—31no—
99#63841—31no—
100#63836—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—41no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6294—22no—
122#6294—41no—
123#6290—22no—
124#6290—22no—
125C3×#627—41no—
126C3×#624—22no—
127C3×#624—41no—
128C3×D3×Dic3—41no—
129#5679—91no—
130#5659—91no—
131#5495—91no—
132C23×C3⋊D3C2×D311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×C32×D4—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×C3×#67—21no—
140C2×C3×#67C2×D311yescharacteristic
141C2×C3×#67C2×D311yescharacteristic
142C22×C3×Dic3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×#627C2×D311yescharacteristic, complemented
151C2×#625—31no—
152C2×#625—31no—
153C2×#625—31no—
154C2×#625—31no—
155C2×#625—61no—
156C2×#625—61no—
157C2×#624—31no—
158C2×#624—31no—
159C2×#624C2×D311yescharacteristic
160C2×#624C2×D311yescharacteristic
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3C2×D311yescharacteristic, complemented
166C32×C22⋊C4—31no—
167C32×C22⋊C4—31no—
168#3757—31no—
169#3757—31no—
170#3757—31no—
171#3757—61no—
172#3757—61no—
173#3757—61no—
174#3757—121no—
175#3757C2×D311yescharacteristic
176#3757C2×D311yescharacteristic
177#3752—31no—
178#3752—31no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)—31no—
181#3750—31no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—31no—
187C3×#217—21no—
188C3×#217—21no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—61no—
197C3×#217—61no—
198C3×#217C2×D311yescharacteristic
199C3×#217C2×D311yescharacteristic
200C3×#217C2×D311yescharacteristic
201C3×#217C2×D311yescharacteristic
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×C4⋊Dic3—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724C2×D311yescharacteristic, complemented
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3C2×D311yescharacteristic, complemented
235#3722—31no—
236#3722—31no—
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
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—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
250(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
251(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
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—44no—
268C2×C3×C3⋊D3#4112yes—
269C2×C3×C3⋊D3#4112yes—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#124—91no—
285C3×#123—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#946—91no—
290#946—91no—
291#937—91no—
292#937—91no—
293#937—181no—
294#936—31no—
295#935—31no—
296#929—91no—
297C4×#67—91no—
298C4×#67—91no—
299C4×#67—91no—
300#926—91no—
301#924—91no—
302#896—91no—
303#896—91no—
304#892—91no—
305#892—91no—
306#886—91no—
307#885—31no—
308#883—31no—
309#883—91no—
310#883—91no—
311#883—91no—
312#883—91no—
313#67⋊C4—91no—
314#67⋊C4—91no—
315#67⋊C4—91no—
316D3×C22⋊C4—31no—
317D3×C22⋊C4—31no—
318D3×C22⋊C4—91no—
319D3×C22⋊C4—91no—
320#879—91no—
321#879—91no—
322#879—91no—
323#879—91no—
324#879—91no—
325#879—91no—
326#879—181no—
327#879—181no—
328#878—91no—
329#877—91no—
330#872—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—41no—
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C23×C32C22×D311yescharacteristic
340C22×C3⋊D3—22no—
341C22×C3⋊D3—22no—
342C22×C3⋊D3—41no—
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3—61no—
352C22×C3×D3—62no—
353C22×C3×D3—62no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—122no—
357C22×C3×D3—122no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3—122no—
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C32×D4—121no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369#638—62no—
370#638—62no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—61no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3—121no—
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C3×#67—41no—
390C3×#67—41no—
391C3×#67—42no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—121no—
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C3×C4×D3—62no—
421C3×C4×D3—62no—
422C3×C4×D3—121no—
423C3×C4×D3—121no—
424C3×C4×D3—121no—
425C3×Dic6—121no—
426C3×Dic6—121no—
427#627—41no—
428#625—62no—
429#625—62no—
430#625—62no—
431#625—62no—
432#625—122no—
433#625—122no—
434#624—22no—
435#624—41no—
436#624—62no—
437#624—121no—
438D3×Dic3—41no—
439D3×Dic3—62no—
440D3×Dic3—62no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443#551—271noSylow
444C2×C33—41no—
445C2×C33C2×#4111yescharacteristic
446C2×C33C2×#4111yescharacteristic
447C2×C33H(5,𝔽2)11yescharacteristic
448C3×C3⋊D3—22no—
449C3×C3⋊D3—22no—
450C32×D3—41no—
451C24×C3—91no—
452C23×D3—31no—
453C23×D3—31no—
454C23×D3—61no—
455C2×C3×Q8—91no—
456C2×C3×D4—31no—
457C2×C3×D4—31no—
458C2×C3×D4—61no—
459C22×C3×C4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—181no—
469C2×#67—181no—
470C2×#67D3211yescharacteristic
471C22×Dic3—31no—
472C22×Dic3—91no—
473C22×Dic3—91no—
474C2×C4×D3—31no—
475C2×C4×D3—31no—
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×Dic6—31no—
484C2×Dic6—31no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C22⋊C4—31no—
488C3×C22⋊C4—31no—
489C3×C22⋊C4—31no—
490C3×C22⋊C4—31no—
491C3×C22⋊C4—61no—
492C3×C22⋊C4—61no—
493C3×C22⋊C4—91no—
494C3×C22⋊C4—91no—
495C3×C22⋊C4—91no—
496C3×C22⋊C4—91no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C42—91no—
501#217—31no—
502#217—31no—
503#217—31no—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—61no—
509#217—61no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—181no—
518#217—181no—
519#217—181no—
520#217—361no—
521#217D3211yescharacteristic
522#217D3211yescharacteristic
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—181no—
539(C2×D3)⋊C4—181no—
540C4⋊Dic3—31no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—181no—
548C4⋊Dic3—181no—
549Dic3⋊C4—31no—
550Dic3⋊C4—31no—
551Dic3⋊C4—31no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—181no—
565Dic3⋊C4—181no—
566Dic3⋊C4—181no—
567Dic3⋊C4—181no—
568C4×Dic3—31no—
569C4×Dic3—31no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—181no—
577C4×Dic3—181no—
578C22×C32—21no—
579C22×C32—22no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—41no—
592C22×C32—41no—
593C22×C32—41no—
594C22×C32—42no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—81no—
605C22×C32—81no—
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C22×C32C23×D311yescharacteristic
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—44no—
614C2×C3⋊D3#23512yes—
615C2×C3⋊D3#23712yes—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—32no—
623C2×C3×D3—32no—
624C2×C3×D3—32no—
625C2×C3×D3—32no—
626C2×C3×D3—41no—
627C2×C3×D3—41no—
628C2×C3×D3—41no—
629C2×C3×D3—62no—
630C2×C3×D3—62no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3—124no—
644C2×C3×D3—124no—
645C2×C3×D3—128no—
646C32×C4—61no—
647C32×C4—61no—
648C32×C4—61no—
649C32×C4—61no—
650C32×C4—61no—
651C3⋊Dic3—21no—
652C3⋊Dic3—21no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—61no—
656C3⋊Dic3—61no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—121no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—241no—
668C3⋊Dic3—241no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—41no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696#126—271no—
697#126—271no—
698#124—91no—
699#123—91no—
700#123—271no—
701#123—271no—
702C22⋊Q8—271no—
703C22⋊Q8—271no—
704#120—271no—
705C4×D4—271no—
706C4×D4—271no—
707#117—271no—
708#117—271no—
709C2×C22⋊C4—91no—
710C2×C22⋊C4—271no—
711C33#55111yescharacteristic, complemented, Sylow
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—41no—
718C23×C3—61no—
719C23×C3—91no—
720C23×C3—91no—
721C23×C3—182no—
722C23×C3—182no—
723C23×C3—361no—
724C23×C3C2×D3211yescharacteristic
725C23×C3C2×D3211yescharacteristic
726C23×C3C2×D3211yescharacteristic
727C22×D3—31no—
728C22×D3—31no—
729C22×D3—31no—
730C22×D3—31no—
731C22×D3—61no—
732C22×D3—61no—
733C22×D3—62no—
734C22×D3—62no—
735C22×D3—62no—
736C22×D3—62no—
737C22×D3—122no—
738C22×D3—122no—
739C22×D3—121no—
740C22×D3—121no—
741C22×D3—122no—
742C22×D3C2×D3211yescharacteristic
743C3×Q8—361no—
744C3×D4—121no—
745C3×D4—121no—
746C3×D4—122no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—61no—
760C2×C3×C4—61no—
761C2×C3×C4—61no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—182no—
767C2×C3×C4—361no—
768C2×C3×C4—361no—
769#67—41no—
770#67—182no—
771#67—182no—
772#67—182no—
773#67—182no—
774#67—182no—
775#67—182no—
776#67—362no—
777#67—362no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—61no—
787C2×Dic3—61no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—91no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—91no—
795C2×Dic3—91no—
796C2×Dic3—121no—
797C2×Dic3—181no—
798C2×Dic3—181no—
799C2×Dic3—181no—
800C2×Dic3—181no—
801C2×Dic3—181no—
802C2×Dic3—181no—
803C2×Dic3—182no—
804C2×Dic3—361no—
805C2×Dic3—361no—
806C2×Dic3—361no—
807C2×Dic3C2×D3211yescharacteristic
808C2×Dic3C2×D3211yescharacteristic
809C2×Dic3C2×D3211yescharacteristic
810C2×Dic3C2×D3211yescharacteristic
811C2×Dic3C2×D3211yescharacteristic
812C4×D3—62no—
813C4×D3—62no—
814C4×D3—121no—
815C4×D3—121no—
816C4×D3—121no—
817C4×D3—182no—
818C4×D3—182no—
819C4×D3—361no—
820C4×D3—361no—
821Dic6—121no—
822Dic6—121no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—41no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—42no—
837C2×C32—41no—
838C2×C32—41no—
839C2×C32—81no—
840C2×C32—81no—
841C2×C32—82no—
842C2×C32—121no—
843C2×C32C2×#23511yescharacteristic
844C2×C32C2×#23711yescharacteristic
845C2×C32#100411yescharacteristic
846C2×C32#100411yescharacteristic
847C2×C32#100411yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32D3×#4111yescharacteristic
852C3⋊D3—22no—
853C3⋊D3—22no—
854C3×D3—41no—
855C3×D3—41no—
856C3×D3—62no—
857C3×D3—62no—
858C3×D3—62no—
859C3×D3—62no—
860C3×D3—81no—
861C3×D3—122no—
862C3×D3—122no—
863C24—91no—
864C2×Q8—91no—
865C2×D4—31no—
866C2×D4—271no—
867C2×D4—271no—
868C22×C4—91no—
869C22×C4—91no—
870C22×C4—91no—
871C22×C4—271no—
872C22×C4—271no—
873C4⋊C4—91no—
874C4⋊C4—91no—
875C4⋊C4—271no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C22⋊C4—31no—
882C22⋊C4—31no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—271no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C42—91no—
896C42—271no—
897C42—271no—
898C22×C3—22no—
899C22×C3—21no—
900C22×C3—21no—
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—41no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—42no—
920C22×C3—41no—
921C22×C3—61no—
922C22×C3—61no—
923C22×C3—61no—
924C22×C3—61no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—81no—
928C22×C3—81no—
929C22×C3—92no—
930C22×C3—92no—
931C22×C3—121no—
932C22×C3—121no—
933C22×C3—121no—
934C22×C3—181no—
935C22×C3—181no—
936C22×C3—181no—
937C22×C3—181no—
938C22×C3—364no—
939C22×C3C22×D3211yescharacteristic
940C22×C3C22×D3211yescharacteristic
941C22×C3C22×D3211yescharacteristic
942C2×D3—21no—
943C2×D3—21no—
944C2×D3—21no—
945C2×D3—32no—
946C2×D3—32no—
947C2×D3—32no—
948C2×D3—32no—
949C2×D3—62no—
950C2×D3—62no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—121no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3—121no—
963C2×D3—124no—
964C2×D3—124no—
965C2×D3—128no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—121no—
977C3×C4—121no—
978C3×C4—121no—
979C3×C4—121no—
980C3×C4—121no—
981C3×C4—181no—
982C3×C4—181no—
983C3×C4—181no—
984C3×C4—181no—
985Dic3—21no—
986Dic3—21no—
987Dic3—21no—
988Dic3—21no—
989Dic3—21no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—121no—
999Dic3—121no—
1000Dic3—121no—
1001Dic3—121no—
1002Dic3—181no—
1003Dic3—181no—
1004Dic3—181no—
1005Dic3—181no—
1006Dic3—181no—
1007Dic3—181no—
1008Dic3—361no—
1009Dic3—361no—
1010Dic3—361no—
1011Dic3—361no—
1012Dic3—361no—
1013Dic3—361no—
1014Dic3—721no—
1015Dic3—721no—
1016C32—21no—
1017C32—21no—
1018C32—21no—
1019C32—41no—
1020C32#549511yescharacteristic, complemented
1021C32#565911yescharacteristic, complemented
1022C32#567911yescharacteristic, complemented
1023C23—31no—
1024C23—91no—
1025C23—91no—
1026C23—182no—
1027C23—182no—
1028C23—361no—
1029C23D3311yescharacteristic
1030Q8—361no—
1031D4—121no—
1032D4—542no—
1033D4—542no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—31no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—182no—
1044C2×C4—271no—
1045C2×C4—271no—
1046C2×C4—361no—
1047C2×C4—361no—
1048C2×C4—542no—
1049C2×C4—1081no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—42no—
1060C2×C3—41no—
1061C2×C3—41no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—81no—
1067C2×C3—81no—
1068C2×C3—82no—
1069C2×C3—121no—
1070C2×C3—121no—
1071C2×C3—182no—
1072C2×C3—182no—
1073C2×C3—241no—
1074C2×C3D3×#23511yescharacteristic
1075C2×C3D3×#23511yescharacteristic
1076C2×C3D3×#23711yescharacteristic
1077C2×C3D3×#23711yescharacteristic
1078C2×C3#6431211yescharacteristic
1079C2×C3#6431211yescharacteristic
1080C2×C3#6431311yescharacteristic
1081C2×C3#6431311yescharacteristic
1082C2×C3#6433011yescharacteristic
1083D3—41no—
1084D3—62no—
1085D3—62no—
1086D3—62no—
1087D3—62no—
1088D3—122no—
1089D3—122no—
1090C22—21no—
1091C22—21no—
1092C22—21no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—92no—
1097C22—92no—
1098C22—181no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22—364no—
1103C22C2×D3311yescharacteristic
1104C4—61no—
1105C4—61no—
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—541no—
1114C4—541no—
1115C3—21no—
1116C3—21no—
1117C3—21no—
1118C3—41no—
1119C3#1059409211yescharacteristic, complemented
1120C3#1059419311yescharacteristic, complemented
1121C3#1059520811yescharacteristic, complemented
1122C2—41no—
1123C2—121no—
1124C2—182no—
1125C2—182no—
1126C2#1172440811yescharacteristic
1127C2#1172441011yescharacteristic
1128C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723634C2
hypercenterC23D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723723C2semidirect
3. #11723597C2semidirect
4. #11723596C2semidirect
5. C3×#63974C2semidirect
6. C3×#63969C2semidirect
7. C3×#63959C2semidirect
8. #11722998C2semidirect
9. #11722992C2semidirect
10. #11722979C2semidirect
11. #11722970C2semidirect
12. #11722936C2semidirect
13. #11722930C2semidirect
14. #11722922C2semidirect
15. #11722915C2semidirect
25. C2×C3×#627C22semidirect
28. C2×C3×D3×Dic3C22semidirect
36. #88807C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
69. #63974D3semidirect
70. #63969D3semidirect
73. #63959D3semidirect
150. C2×#627C2×D3semidirect
165. C2×D3×Dic3C2×D3semidirect
221. #3724C2×D3semidirect
234. Dic3⋊Dic3C2×D3semidirect
249. (C2×D3)⋊Dic3C2×D3semidirect
250. (C2×D3)⋊Dic3C2×D3semidirect
251. (C2×D3)⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
711. C33#551semidirect
1020. C32#5495semidirect
1021. C32#5659semidirect
1022. C32#5679semidirect
1119. C3#10594092semidirect
1120. C3#10594193semidirect
1121. C3#10595208semidirect

Maximal subgroups

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

subgroupindex
#117237232
#117236342
#117235972
#117235962
C3×#639742
C3×#639692
C3×#639592
#117229982
#117229922
#117229792
#117229702
#117229362
#117229302
#117229222
#117229152
#105952083
#105941933
#105940923