Finite Group Databasebeta

← #13171961

Subgroups — #13171961

Order 1728.

1274 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#11723729C211yesmaximal, characteristic
2#11723621C211yesmaximal, characteristic, complemented
3Dic3×#638C211yesmaximal, characteristic, complemented
4#11723591C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723024C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722921C211yesmaximal, characteristic, complemented
13#11722915C211yesmaximal, characteristic, complemented
14#11722905C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595088—31nomaximal
17#10594304—31nomaximal
18#10594299—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic, complemented
24C2×#6293C2211yescharacteristic, complemented
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29#88864C2211yescharacteristic, complemented
30C32×#217C2211yescharacteristic, complemented
31C32×#217C2211yescharacteristic, complemented
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88807C2211yescharacteristic, complemented
36#88806C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38#88803C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic, complemented
43Dic3×C3⋊Dic3C2211yescharacteristic, complemented
44C3×#3724C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54C4×#638—31no—
55#64094—31no—
56#64092—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#886—31no—
60C3×#883—31no—
61C3×#883—31no—
62C3×#67⋊C4—31no—
63#63983—31no—
64#63983—31no—
65#63983—31no—
66#63975D311yescharacteristic, complemented
67Dic3×#67—31no—
68Dic3×#67—31no—
69Dic3×#67—61no—
70#63969—31no—
71#63969—31no—
72#63969—61no—
73#63966D311yescharacteristic, complemented
74#63959—31no—
75#63959—31no—
76#63959—61no—
77#63952D311yescharacteristic, complemented
78#63921—31no—
79#63921—31no—
80D3×(C2×D3)⋊C4—31no—
81D3×(C2×D3)⋊C4—31no—
82D3×(C2×D3)⋊C4—31no—
83D3×(C2×D3)⋊C4—31no—
84#63899—31no—
85#63896—31no—
86#63895—31no—
87#63878—31no—
88#63878—31no—
89#63868—31no—
90#63865—31no—
91#63862—31no—
92#63861—31no—
93#63859—31no—
94#63858—31no—
95#63857—31no—
96#63855—31no—
97#63851—31no—
98#63849—31no—
99#63848—31no—
100#63841—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C2×#1113—22no—
107C2×#1113—22no—
108C2×#1113—41no—
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638—22no—
112C3×#638—22no—
113C3×#638—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124#6293—41no—
125Dic3×C3⋊D3—22no—
126Dic3×C3⋊D3—41no—
127C3×#624—22no—
128C3×#624—41no—
129#5659—91no—
130#5658—91no—
131#5556—91no—
132C22×D32—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×C32×C4—31no—
136C2×#638C2×D311yescharacteristic
137C2×#638C2×D311yescharacteristic
138C2×#638C2×D311yescharacteristic
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×#634—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—61no—
149C2×C3×#67—61no—
150C2×C3×#67—61no—
151C22×C3×Dic3—21no—
152C22×C3×Dic3C2×D311yescharacteristic, complemented
153C22×C3×Dic3C2×D311yescharacteristic, complemented
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#627—61no—
161C2×#624C2×D311yescharacteristic
162C2×#624C2×D311yescharacteristic
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—61no—
168C2×D3×Dic3—61no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—61no—
175#3757—61no—
176#3757—61no—
177#3757—121no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752—31no—
182C4⋊(C3⋊Dic3)—31no—
183#3750—31no—
184#3750—31no—
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—31no—
187C3×#217—21no—
188C3×#217—21no—
189C3×#217C2×D311yescharacteristic, complemented
190C3×#217C2×D311yescharacteristic, complemented
191C3×#217C2×D311yescharacteristic, complemented
192C3×#217C2×D311yescharacteristic, complemented
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213#3724—31no—
214#3724—31no—
215#3724—61no—
216#3724C2×D311yescharacteristic, complemented
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3C2×D311yescharacteristic, complemented
224Dic3⋊Dic3C2×D311yescharacteristic, complemented
225Dic3⋊Dic3C2×D311yescharacteristic, complemented
226Dic3⋊Dic3C2×D311yescharacteristic, complemented
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722C2×D311yescharacteristic
231#3722C2×D311yescharacteristic
232#3722C2×D311yescharacteristic
233#3722C2×D311yescharacteristic
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
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—31no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
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—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3#4112yes—
271C2×C3×C3⋊D3#4112yes—
272#1113—44no—
273C3⋊(C3⋊Dic3)—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#123—91no—
285C3×#123—91no—
286C3×C4×D4—91no—
287#937—91no—
288#937—91no—
289#937—91no—
290#936—91no—
291#935—91no—
292D4×Dic3—91no—
293#929—31no—
294C4×#67—31no—
295C4×#67—91no—
296C4×#67—91no—
297C4×#67—181no—
298C2×(C2×D3)⋊C4—91no—
299C2×(C2×D3)⋊C4—91no—
300#926—91no—
301#924—91no—
302#898—91no—
303#898—91no—
304#898—91no—
305#897—91no—
306#896—91no—
307#896—91no—
308#896—91no—
309#892—91no—
310#892—91no—
311#892—91no—
312#886—31no—
313#885—91no—
314#885—91no—
315#885—181no—
316#883—31no—
317#883—31no—
318#883—91no—
319#883—91no—
320#883—181no—
321#67⋊C4—31no—
322D3×C22⋊C4—91no—
323D3×C22⋊C4—91no—
324D3×C22⋊C4—91no—
325D3×C22⋊C4—91no—
326#879—91no—
327#879—91no—
328#878—91no—
329#877—91no—
330#876—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D311yescharacteristic
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—61no—
349C22×C3×D3—61no—
350C22×C3×D3—61no—
351C2×D32—62no—
352C2×D32—62no—
353C2×D32—62no—
354C2×D32—62no—
355C2×D32—62no—
356C2×D32—62no—
357C2×D32—121no—
358C2×D32—121no—
359C2×D32—121no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—121no—
367#638—22no—
368#638—22no—
369#638—41no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C4×C3⋊D3—62no—
388C4×C3⋊D3—121no—
389#634—121no—
390C3×#67—62no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C3×#67—64no—
395C3×#67—122no—
396C3×#67—121no—
397C3×#67—121no—
398C3×#67—122no—
399C2×C3×Dic3—21no—
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—41no—
412C2×C3×Dic3—41no—
413C2×C3×Dic3—42no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
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
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C3×C4×D3—62no—
430C3×C4×D3—62no—
431C3×C4×D3—121no—
432C3×C4×D3—121no—
433#627—121no—
434#627—121no—
435#627—122no—
436#624—22no—
437#624—41no—
438D3×Dic3—62no—
439D3×Dic3—62no—
440D3×Dic3—122no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443D3×Dic3—122no—
444#551—271noSylow
445C2×C33—41no—
446C2×C33C2×#4111yescharacteristic
447C2×C33C2×#4111yescharacteristic
448C2×C33H(5,𝔽2)11yescharacteristic
449C3×C3⋊D3—22no—
450C3×C3⋊D3—22no—
451C3×C3⋊D3—41no—
452C23×D3—91no—
453C23×D3—91no—
454C23×D3—91no—
455C2×C3×D4—91no—
456C2×C3×D4—91no—
457C2×C3×D4—91no—
458C22×C3×C4—31no—
459C22×C3×C4—31no—
460C22×C3×C4—61no—
461C22×C3×C4—91no—
462C22×C3×C4—91no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—61no—
470C2×#67—61no—
471C2×#67—61no—
472C22×Dic3—91no—
473C22×Dic3—91no—
474C22×Dic3D3211yescharacteristic, complemented
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×C4×D3—181no—
484C2×C4×D3—181no—
485C2×Dic6—91no—
486C2×Dic6—91no—
487C2×Dic6—91no—
488C2×Dic6—181no—
489C3×C4⋊C4—91no—
490C3×C4⋊C4—91no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—31no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—31no—
497C3×C22⋊C4—31no—
498C3×C22⋊C4—61no—
499C3×C22⋊C4—61no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C42—91no—
505#217—91no—
506#217—91no—
507#217—91no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—181no—
516#217—181no—
517#217—181no—
518#217—361no—
519#217D3211yescharacteristic, complemented
520#217D3211yescharacteristic, complemented
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
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—91no—
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—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—181no—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4—181no—
546(C2×D3)⋊C4—181no—
547C4⋊Dic3—31no—
548C4⋊Dic3—31no—
549C4⋊Dic3—31no—
550C4⋊Dic3—31no—
551C4⋊Dic3—91no—
552C4⋊Dic3—91no—
553C4⋊Dic3—91no—
554C4⋊Dic3—181no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—181no—
568Dic3⋊C4—181no—
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—181no—
578C4×Dic3—181no—
579C22×C32—21no—
580C22×C32—22no—
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—21no—
592C22×C32—41no—
593C22×C32—41no—
594C22×C32—41no—
595C22×C32—42no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—81no—
603C22×C32—81no—
604C22×C32C23×D311yescharacteristic
605C22×C32C23×D311yescharacteristic
606C22×C32C23×D311yescharacteristic
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—21no—
614C2×C3⋊D3#23512yes—
615C2×C3⋊D3#23712yes—
616C2×C3×D3—32no—
617C2×C3×D3—32no—
618C2×C3×D3—32no—
619C2×C3×D3—32no—
620C2×C3×D3—62no—
621C2×C3×D3—62no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—121no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643D32—124no—
644D32—124no—
645D32—124no—
646C32×C4—61no—
647C32×C4—61no—
648C32×C4—61no—
649C32×C4—61no—
650C32×C4—61no—
651C32×C4—61no—
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—22no—
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—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—41no—
687C3×Dic3—62no—
688C3×Dic3—62no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—121no—
696#126—271no—
697#126—271no—
698#124—271no—
699#123—91no—
700#123—91no—
701#123—271no—
702C22⋊Q8—271no—
703C22⋊Q8—271no—
704#120—271no—
705C4×D4—91no—
706C4×D4—271no—
707#117—271no—
708#117—271no—
709C2×C22⋊C4—271no—
710C2×C22⋊C4—271no—
711C33#55111yescharacteristic, complemented, Sylow
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—41no—
716C23×C3—91no—
717C23×C3—91no—
718C23×C3—91no—
719C23×C3C2×D3211yescharacteristic
720C23×C3C2×D3211yescharacteristic
721C23×C3C2×D3211yescharacteristic
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—31no—
727C22×D3—31no—
728C22×D3—61no—
729C22×D3—61no—
730C22×D3—61no—
731C22×D3—182no—
732C22×D3—182no—
733C22×D3—182no—
734C22×D3—182no—
735C22×D3—182no—
736C22×D3—182no—
737C22×D3—361no—
738C22×D3—361no—
739C22×D3—361no—
740C3×D4—182no—
741C3×D4—182no—
742C3×D4—361no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
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—61no—
756C2×C3×C4—61no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—61no—
760C2×C3×C4—61no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—121no—
765C2×C3×C4—121no—
766C2×C3×C4—122no—
767C2×C3×C4—182no—
768C2×C3×C4—361no—
769#67—62no—
770#67—62no—
771#67—62no—
772#67—62no—
773#67—64no—
774#67—122no—
775#67—121no—
776#67—121no—
777#67—122no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—41no—
785C2×Dic3—61no—
786C2×Dic3—61no—
787C2×Dic3—61no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—91no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—181no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—181no—
798C2×Dic3—181no—
799C2×Dic3—181no—
800C2×Dic3—182no—
801C2×Dic3—361no—
802C2×Dic3—361no—
803C2×Dic3—361no—
804C2×Dic3C2×D3211yescharacteristic
805C2×Dic3C2×D3211yescharacteristic
806C2×Dic3C2×D3211yescharacteristic
807C2×Dic3C2×D3211yescharacteristic
808C2×Dic3C2×D3211yescharacteristic
809C2×Dic3C2×D3211yescharacteristic
810C4×D3—62no—
811C4×D3—62no—
812C4×D3—121no—
813C4×D3—121no—
814C4×D3—182no—
815C4×D3—182no—
816C4×D3—362no—
817C4×D3—361no—
818C4×D3—361no—
819C4×D3—362no—
820Dic6—361no—
821Dic6—361no—
822Dic6—361no—
823Dic6—362no—
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—21no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—41no—
837C2×C32—42no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—81no—
841C2×C32—81no—
842C2×C32—82no—
843C2×C32C2×#23511yescharacteristic
844C2×C32C2×#23711yescharacteristic
845C2×C32#100411yescharacteristic
846C2×C32#100411yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32#100911yescharacteristic
852C3⋊D3—22no—
853C3⋊D3—22no—
854C3⋊D3—41no—
855C3×D3—62no—
856C3×D3—62no—
857C3×D3—62no—
858C3×D3—62no—
859C3×D3—122no—
860C3×D3—122no—
861C3×D3—121no—
862C3×D3—121no—
863C3×D3—241no—
864C24—271no—
865C2×Q8—271no—
866C2×D4—91no—
867C2×D4—91no—
868C2×D4—91no—
869C22×C4—31no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—271no—
873C22×C4—271no—
874C4⋊C4—91no—
875C4⋊C4—91no—
876C4⋊C4—91no—
877C4⋊C4—91no—
878C4⋊C4—91no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C22⋊C4—31no—
883C22⋊C4—31no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C22⋊C4—271no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C42—91no—
897C42—271no—
898C42—271no—
899C22×C3—22no—
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—21no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—42no—
921C22×C3—41no—
922C22×C3—81no—
923C22×C3—81no—
924C22×C3—92no—
925C22×C3—92no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3—181no—
933C22×C3C22×D3211yescharacteristic
934C22×C3C22×D3211yescharacteristic
935C22×C3C22×D3211yescharacteristic
936C2×D3—32no—
937C2×D3—32no—
938C2×D3—32no—
939C2×D3—32no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—121no—
957C2×D3—121no—
958C2×D3—121no—
959C2×D3—121no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3—121no—
963C2×D3—364no—
964C2×D3—364no—
965C2×D3—364no—
966C3×C4—62no—
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—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—121no—
980C3×C4—121no—
981C3×C4—121no—
982C3×C4—121no—
983C3×C4—121no—
984C3×C4—181no—
985C3×C4—181no—
986C3×C4—181no—
987Dic3—21no—
988Dic3—21no—
989Dic3—21no—
990Dic3—21no—
991Dic3—21no—
992Dic3—21no—
993Dic3—62no—
994Dic3—62no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
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#555611yescharacteristic, complemented
1021C32#565811yescharacteristic, complemented
1022C32#565911yescharacteristic, complemented
1023C23—91no—
1024C23—91no—
1025C23—91no—
1026C23—542no—
1027C23—542no—
1028C23—1081no—
1029C23D3311yescharacteristic
1030Q8—1081no—
1031D4—182no—
1032D4—182no—
1033D4—361no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—31no—
1039C2×C4—31no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—121no—
1044C2×C4—182no—
1045C2×C4—271no—
1046C2×C4—271no—
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—182no—
1070C2×C3—182no—
1071C2×C3—361no—
1072C2×C3D3×#23511yescharacteristic
1073C2×C3D3×#23511yescharacteristic
1074C2×C3#6430611yescharacteristic
1075C2×C3#6430711yescharacteristic
1076C2×C3D3×#23711yescharacteristic
1077C2×C3D3×#23711yescharacteristic
1078C2×C3#6431211yescharacteristic
1079C2×C3#6431411yescharacteristic
1080C2×C3#6433011yescharacteristic
1081D3—62no—
1082D3—62no—
1083D3—62no—
1084D3—62no—
1085D3—122no—
1086D3—122no—
1087D3—121no—
1088D3—121no—
1089D3—241no—
1090C22—21no—
1091C22—21no—
1092C22—21no—
1093C22—92no—
1094C22—92no—
1095C22—181no—
1096C22—181no—
1097C22—181no—
1098C22—181no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22—1084no—
1103C22C2×D3311yescharacteristic
1104C4—61no—
1105C4—61no—
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—61no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—541no—
1114C4—541no—
1115C3—21no—
1116C3—21no—
1117C3—21no—
1118C3—41no—
1119C3#1059429911yescharacteristic, complemented
1120C3#1059430411yescharacteristic, complemented
1121C3#1059508811yescharacteristic, complemented
1122C2—41no—
1123C2—182no—
1124C2—182no—
1125C2—361no—
1126C2#1172440711yescharacteristic
1127C2#1172441011yescharacteristic
1128C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723729C2
hypercenterC23D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723621C2semidirect
3. Dic3×#638C2semidirect
4. #11723591C2semidirect
5. C3×#63975C2semidirect
6. C3×#63966C2semidirect
7. C3×#63952C2semidirect
8. #11723027C2semidirect
9. #11723024C2semidirect
10. #11722983C2semidirect
11. #11722972C2semidirect
12. #11722921C2semidirect
13. #11722915C2semidirect
14. #11722905C2semidirect
15. #11722905C2semidirect
23. C22×C32×Dic3C22semidirect
24. C2×#6293C22semidirect
29. #88864C22semidirect
30. C32×#217C22semidirect
31. C32×#217C22semidirect
35. #88807C22semidirect
36. #88806C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
42. Dic3×C3⋊Dic3C22semidirect
43. Dic3×C3⋊Dic3C22semidirect
44. C3×#3724C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
66. #63975D3semidirect
73. #63966D3semidirect
77. #63952D3semidirect
152. C22×C3×Dic3C2×D3semidirect
153. C22×C3×Dic3C2×D3semidirect
189. C3×#217C2×D3semidirect
190. C3×#217C2×D3semidirect
191. C3×#217C2×D3semidirect
192. C3×#217C2×D3semidirect
216. #3724C2×D3semidirect
223. Dic3⋊Dic3C2×D3semidirect
224. Dic3⋊Dic3C2×D3semidirect
225. Dic3⋊Dic3C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
474. C22×Dic3D32semidirect
519. #217D32semidirect
520. #217D32semidirect
711. C33#551semidirect
1020. C32#5556semidirect
1021. C32#5658semidirect
1022. C32#5659semidirect
1119. C3#10594299semidirect
1120. C3#10594304semidirect
1121. C3#10595088semidirect

Maximal subgroups

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

subgroupindex
#117237292
#117236212
Dic3×#6382
#117235912
C3×#639752
C3×#639662
C3×#639522
#117230272
#117230242
#117229832
#117229722
#117229212
#117229152
#117229052
#105950883
#105943043
#105942993