Finite Group Databasebeta

← #13172026

Subgroups — #13172026

Order 1728.

1296 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723716C211yesmaximal, characteristic, complemented
2#11723614C211yesmaximal, characteristic, complemented
3D3×#3757C211yesmaximal, characteristic, complemented
4#11723597C211yesmaximal, characteristic, complemented
5C3×#63976C211yesmaximal, characteristic
6C3×D3×#217C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8#11722989C211yesmaximal, characteristic, complemented
9#11722985C211yesmaximal, characteristic, complemented
10#11722976C211yesmaximal, characteristic, complemented
11#11722969C211yesmaximal, characteristic, complemented
12#11722925C211yesmaximal, characteristic, complemented
13#11722924C211yesmaximal, characteristic, complemented
14#11722916C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595509—31nomaximal
17#10595176—31nomaximal
18#10594092—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C3×#627C2211yescharacteristic, complemented
25C2×C3×#625C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29#88864C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88815C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88813C2211yescharacteristic, complemented
38#88807C2211yescharacteristic, complemented
39#88807C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C2×#3757—31no—
55#64144—31no—
56#64088—31no—
57C3×#953—31no—
58C2×C3×#217—31no—
59C3×#937—31no—
60C3×#936—31no—
61C3×#885—31no—
62C3×D3×C22⋊C4—31no—
63#63982—31no—
64#63976D311yescharacteristic
65#67⋊Dic3—31no—
66#67⋊Dic3—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69#63969—31no—
70#63969—31no—
71#63969—31no—
72#63969—31no—
73#63969—61no—
74D3×#217—31no—
75D3×#217—31no—
76D3×#217—61no—
77D3×#217D311yescharacteristic, complemented
78#63964—31no—
79#63962—31no—
80#63961—31no—
81#63959D311yescharacteristic, complemented
82#63957—31no—
83#63956—31no—
84#63956—31no—
85#63956—31no—
86#63956—31no—
87#63956—31no—
88#63956—61no—
89#63955—31no—
90#63905—31no—
91#63902—31no—
92#63891—31no—
93#63887—31no—
94#63887—31no—
95#63887—31no—
96#63879—31no—
97#63877—31no—
98#63877—31no—
99#63877—31no—
100#63856—31no—
101#63855—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3—22no—
104C22×C32×D3—22no—
105C22×C32×D3—41no—
106C22×C32×D3C2311yescharacteristic
107C22×C32×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
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—41no—
123D3×C3⋊Dic3—41no—
124C3×#627—41no—
125C3×#625—22no—
126C3×#625—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5679—91no—
130#5587—91no—
131#5495—91no—
132C24×C32—31no—
133C23×C3×D3—21no—
134C23×C3×D3C2×D311yescharacteristic
135C23×C3×D3C2×D311yescharacteristic
136C2×C32×D4—31no—
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C2×C3×#67—21no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67C2×D311yescharacteristic
146C2×C3×#67C2×D311yescharacteristic
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×#627C2×D311yescharacteristic, complemented
154C2×#625C2×D311yescharacteristic
155C2×#625C2×D311yescharacteristic
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3C2×D311yescharacteristic
166C2×D3×Dic3C2×D311yescharacteristic
167C32×C22⋊C4—31no—
168#3757—31no—
169#3757—31no—
170#3757—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—61no—
175#3757—61no—
176#3757—61no—
177#3757—121no—
178#3757C2×D311yescharacteristic
179#3757C2×D311yescharacteristic
180#3757C2×D311yescharacteristic
181C4⋊(C3⋊Dic3)—31no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185#3750—31no—
186C4×C3⋊Dic3—31no—
187C3×#217—21no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—61no—
201C3×#217—61no—
202C3×#217—61no—
203C3×#217C2×D311yescharacteristic
204C3×#217C2×D311yescharacteristic
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×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—61no—
221#3724—61no—
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—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
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—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
251(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—44no—
271C2×C32×D3#4112yes—
272C2×C32×D3#4112yes—
273C3⋊(C3⋊Dic3)—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#124—91no—
285C3×#120—91no—
286C2×C3×C22⋊C4—91no—
287#953—31no—
288C2×#217—31no—
289C2×#217—91no—
290C2×#217—91no—
291C2×#217—181no—
292#946—91no—
293#946—91no—
294#937—31no—
295#936—31no—
296#935—91no—
297#935—91no—
298#935—91no—
299#935—91no—
300#935—181no—
301D4×Dic3—91no—
302D4×Dic3—91no—
303#929—91no—
304C4×#67—91no—
305#926—91no—
306#924—91no—
307#886—91no—
308#885—31no—
309#883—91no—
310#883—91no—
311#883—91no—
312#67⋊C4—91no—
313#67⋊C4—91no—
314#67⋊C4—91no—
315D3×C22⋊C4—31no—
316D3×C22⋊C4—91no—
317#879—91no—
318#879—91no—
319#879—91no—
320#879—91no—
321#879—91no—
322#879—91no—
323#879—181no—
324#878—91no—
325#878—91no—
326#878—91no—
327#877—91no—
328#877—91no—
329#877—91no—
330#872—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—31no—
338C23×C32—41no—
339C23×C32—62no—
340C23×C32—62no—
341C23×C32—121no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3×D3—24no—
346C22×C3×D3—22no—
347C22×C3×D3—22no—
348C22×C3×D3—22no—
349C22×C3×D3—22no—
350C22×C3×D3—21no—
351C22×C3×D3—21no—
352C22×C3×D3—21no—
353C22×C3×D3—42no—
354C22×C3×D3—41no—
355C22×C3×D3—41no—
356C22×C3×D3—42no—
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C32×D4—121no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—61no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—62no—
380C2×C3⋊Dic3—121no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C3×#67—41no—
391C3×#67—41no—
392C3×#67—42no—
393C3×#67—62no—
394C3×#67—62no—
395C3×#67—62no—
396C3×#67—62no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
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—31no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—62no—
419C2×C3×Dic3—121no—
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C3×C4×D3—62no—
427C3×C4×D3—121no—
428C3×Dic6—121no—
429C3×Dic6—121no—
430#627—41no—
431#625—22no—
432#625—22no—
433D3×Dic3—22no—
434D3×Dic3—41no—
435D3×Dic3—62no—
436D3×Dic3—62no—
437D3×Dic3—122no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442D3×Dic3—122no—
443D3×Dic3—122no—
444#551—271noSylow
445C2×C33—41no—
446C2×C33C2×#4111yescharacteristic
447C2×C33C2×#4111yescharacteristic
448C2×C33H(5,𝔽2)11yescharacteristic
449C32×D3—22no—
450C32×D3—22no—
451C32×D3—41no—
452C24×C3—31no—
453C24×C3—31no—
454C24×C3—61no—
455C23×D3D3211yescharacteristic
456C2×C3×Q8—91no—
457C2×C3×D4—31no—
458C2×C3×D4—31no—
459C2×C3×D4—61no—
460C2×C3×D4—91no—
461C2×C3×D4—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67D3211yescharacteristic
469C22×Dic3—31no—
470C22×Dic3—31no—
471C22×Dic3—91no—
472C22×Dic3—91no—
473C22×Dic3—91no—
474C22×Dic3—91no—
475C22×Dic3—91no—
476C22×Dic3—91no—
477C22×Dic3—181no—
478C22×Dic3—181no—
479C22×Dic3—181no—
480C2×C4×D3—31no—
481C2×C4×D3—31no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×Dic6—31no—
486C2×Dic6—31no—
487C3×C22⋊C4—31no—
488C3×C22⋊C4—31no—
489C3×C22⋊C4—61no—
490C3×C22⋊C4—91no—
491C3×C22⋊C4—91no—
492C3×C22⋊C4—91no—
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×C42—91no—
500#217—31no—
501#217—31no—
502#217—31no—
503#217—31no—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—61no—
513#217—61no—
514#217—61no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—91no—
524#217—181no—
525#217—181no—
526#217—181no—
527#217—181no—
528#217—181no—
529#217—181no—
530#217—361no—
531#217D3211yescharacteristic
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—181no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
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—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—181no—
567Dic3⋊C4—181no—
568Dic3⋊C4—181no—
569Dic3⋊C4—181no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
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—32no—
593C22×C32—32no—
594C22×C32—41no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—42no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
611C22×C32—81no—
612C22×C32—81no—
613C22×C32—124no—
614C22×C32C23×D311yescharacteristic
615C22×C32C23×D311yescharacteristic
616C22×C32C23×D311yescharacteristic
617C2×C3×D3—22no—
618C2×C3×D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—22no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—21no—
633C2×C3×D3—21no—
634C2×C3×D3—22no—
635C2×C3×D3—22no—
636C2×C3×D3—41no—
637C2×C3×D3—41no—
638C2×C3×D3—41no—
639C2×C3×D3—41no—
640C2×C3×D3—44no—
641C2×C3×D3—44no—
642C2×C3×D3—48no—
643C2×C3×D3#23512yes—
644C2×C3×D3#23712yes—
645C2×C3×D3#23712yes—
646C2×C3×D3#23712yes—
647C32×C4—61no—
648C32×C4—61no—
649C32×C4—61no—
650C3⋊Dic3—21no—
651C3⋊Dic3—21no—
652C3⋊Dic3—21no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—61no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—61no—
662C3⋊Dic3—121no—
663C3⋊Dic3—121no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
668C3⋊Dic3—241no—
669C3⋊Dic3—241no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—41no—
677C3×Dic3—41no—
678C3×Dic3—41no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—121no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697#126—271no—
698#126—271no—
699#124—91no—
700#123—271no—
701#123—271no—
702#123—271no—
703C22⋊Q8—271no—
704C22⋊Q8—271no—
705#120—91no—
706C4×D4—271no—
707C4×D4—271no—
708#117—271no—
709#117—271no—
710C2×C22⋊C4—91no—
711C2×C22⋊C4—271no—
712C33#55111yescharacteristic, complemented, Sylow
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—31no—
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—31no—
721C23×C3—31no—
722C23×C3—41no—
723C23×C3—61no—
724C23×C3—61no—
725C23×C3—61no—
726C23×C3—62no—
727C23×C3—62no—
728C23×C3—62no—
729C23×C3—62no—
730C23×C3—64no—
731C23×C3—122no—
732C23×C3—121no—
733C23×C3—121no—
734C23×C3—122no—
735C23×C3C2×D3211yescharacteristic
736C23×C3C2×D3211yescharacteristic
737C23×C3C2×D3211yescharacteristic
738C22×D3—22no—
739C22×D3—22no—
740C22×D3—41no—
741C22×D3C2×D3211yescharacteristic
742C22×D3C2×D3211yescharacteristic
743C22×D3C2×D3211yescharacteristic
744C3×Q8—361no—
745C3×D4—121no—
746C3×D4—121no—
747C3×D4—122no—
748C3×D4—182no—
749C3×D4—182no—
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—61no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—91no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—182no—
766C2×C3×C4—361no—
767#67—41no—
768#67—62no—
769#67—62no—
770#67—62no—
771#67—62no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—61no—
785C2×Dic3—61no—
786C2×Dic3—61no—
787C2×Dic3—61no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—62no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—91no—
795C2×Dic3—91no—
796C2×Dic3—91no—
797C2×Dic3—121no—
798C2×Dic3—181no—
799C2×Dic3—181no—
800C2×Dic3—181no—
801C2×Dic3—181no—
802C2×Dic3—181no—
803C2×Dic3—181no—
804C2×Dic3—182no—
805C2×Dic3—182no—
806C2×Dic3—361no—
807C2×Dic3—361no—
808C2×Dic3—362no—
809C2×Dic3—361no—
810C2×Dic3—361no—
811C2×Dic3—361no—
812C2×Dic3—361no—
813C2×Dic3—362no—
814C2×Dic3—362no—
815C2×Dic3C2×D3211yescharacteristic
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C4×D3—62no—
819C4×D3—121no—
820C4×D3—182no—
821C4×D3—361no—
822C4×D3—361no—
823Dic6—121no—
824Dic6—121no—
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—21no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—41no—
837C2×C32—41no—
838C2×C32—42no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—62no—
842C2×C32—62no—
843C2×C32—81no—
844C2×C32—81no—
845C2×C32—82no—
846C2×C32—121no—
847C2×C32C2×#23511yescharacteristic
848C2×C32C2×#23711yescharacteristic
849C2×C32C2×#23711yescharacteristic
850C2×C32C2×#23711yescharacteristic
851C2×C32#100411yescharacteristic
852C2×C32#100411yescharacteristic
853C2×C32#100411yescharacteristic
854C2×C32D3×#4111yescharacteristic
855C2×C32D3×#4111yescharacteristic
856C3×D3—24no—
857C3×D3—22no—
858C3×D3—22no—
859C3×D3—22no—
860C3×D3—22no—
861C3×D3—42no—
862C3×D3—42no—
863C3×D3—41no—
864C3×D3—41no—
865C24—31no—
866C2×Q8—91no—
867C2×D4—31no—
868C2×D4—91no—
869C2×D4—91no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—271no—
873C22×C4—271no—
874C22×C4—271no—
875C4⋊C4—271no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C4⋊C4—271no—
883C22⋊C4—31no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C42—91no—
898C42—271no—
899C42—271no—
900C22×C3—22no—
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—21no—
913C22×C3—32no—
914C22×C3—32no—
915C22×C3—32no—
916C22×C3—32no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—41no—
923C22×C3—41no—
924C22×C3—41no—
925C22×C3—42no—
926C22×C3—41no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—62no—
931C22×C3—62no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—81no—
947C22×C3—81no—
948C22×C3—121no—
949C22×C3—121no—
950C22×C3—121no—
951C22×C3—121no—
952C22×C3—124no—
953C22×C3—124no—
954C22×C3—128no—
955C22×C3C22×D3211yescharacteristic
956C22×C3C22×D3211yescharacteristic
957C22×C3C22×D3211yescharacteristic
958C2×D3—21no—
959C2×D3—21no—
960C2×D3—21no—
961C2×D3—21no—
962C2×D3—21no—
963C2×D3—21no—
964C2×D3—21no—
965C2×D3—44no—
966C2×D3#380412yes—
967C2×D3#380512yes—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—121no—
975C3×C4—121no—
976C3×C4—121no—
977C3×C4—181no—
978C3×C4—181no—
979C3×C4—181no—
980C3×C4—181no—
981C3×C4—181no—
982C3×C4—181no—
983Dic3—21no—
984Dic3—21no—
985Dic3—21no—
986Dic3—61no—
987Dic3—61no—
988Dic3—61no—
989Dic3—61no—
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—121no—
1003Dic3—121no—
1004Dic3—181no—
1005Dic3—181no—
1006Dic3—181no—
1007Dic3—181no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—361no—
1011Dic3—361no—
1012Dic3—361no—
1013Dic3—361no—
1014Dic3—361no—
1015Dic3—361no—
1016Dic3—721no—
1017Dic3—721no—
1018C32—21no—
1019C32—21no—
1020C32—21no—
1021C32—41no—
1022C32#549511yescharacteristic, complemented
1023C32#558711yescharacteristic, complemented
1024C32#567911yescharacteristic, complemented
1025C23—31no—
1026C23—31no—
1027C23—31no—
1028C23—62no—
1029C23—62no—
1030C23—121no—
1031C23D3311yescharacteristic
1032Q8—361no—
1033D4—121no—
1034D4—182no—
1035D4—182no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—31no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—91no—
1045C2×C4—182no—
1046C2×C4—271no—
1047C2×C4—271no—
1048C2×C4—361no—
1049C2×C4—542no—
1050C2×C4—1081no—
1051C2×C4—1081no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—42no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—41no—
1068C2×C3—64no—
1069C2×C3—62no—
1070C2×C3—62no—
1071C2×C3—62no—
1072C2×C3—62no—
1073C2×C3—81no—
1074C2×C3—81no—
1075C2×C3—82no—
1076C2×C3—122no—
1077C2×C3—122no—
1078C2×C3—121no—
1079C2×C3—121no—
1080C2×C3D3×#23511yescharacteristic
1081C2×C3D3×#23711yescharacteristic
1082C2×C3D3×#23711yescharacteristic
1083C2×C3D3×#23711yescharacteristic
1084C2×C3#6431311yescharacteristic
1085C2×C3C2×#380411yescharacteristic
1086C2×C3C2×#380511yescharacteristic
1087C2×C3#6433011yescharacteristic
1088C2×C3#6433011yescharacteristic
1089D3—22no—
1090D3—22no—
1091D3—41no—
1092C22—21no—
1093C22—21no—
1094C22—21no—
1095C22—32no—
1096C22—32no—
1097C22—61no—
1098C22—61no—
1099C22—61no—
1100C22—61no—
1101C22—61no—
1102C22—61no—
1103C22—61no—
1104C22—124no—
1105C22C2×D3311yescharacteristic
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—181no—
1114C4—181no—
1115C4—541no—
1116C4—541no—
1117C3—21no—
1118C3—21no—
1119C3—21no—
1120C3—41no—
1121C3#1059409211yescharacteristic, complemented
1122C3#1059517611yescharacteristic, complemented
1123C3#1059550911yescharacteristic, complemented
1124C2—41no—
1125C2—62no—
1126C2—62no—
1127C2—121no—
1128C2D3×#380411yescharacteristic
1129C2D3×#380511yescharacteristic
1130C2#1172441411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63976C2
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. #11723716C2semidirect
2. #11723614C2semidirect
3. D3×#3757C2semidirect
4. #11723597C2semidirect
6. C3×D3×#217C2semidirect
7. C3×#63959C2semidirect
8. #11722989C2semidirect
9. #11722985C2semidirect
10. #11722976C2semidirect
11. #11722969C2semidirect
12. #11722925C2semidirect
13. #11722924C2semidirect
14. #11722916C2semidirect
15. #11722913C2semidirect
23. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#627C22semidirect
34. #88815C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
37. #88813C22semidirect
38. #88807C22semidirect
39. #88807C22semidirect
40. #88806C22semidirect
41. #88806C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
45. (C2×D3)⋊(C3⋊Dic3)C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
77. D3×#217D3semidirect
81. #63959D3semidirect
153. C2×#627C2×D3semidirect
250. (C2×D3)⋊Dic3C2×D3semidirect
251. (C2×D3)⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
712. C33#551semidirect
1022. C32#5495semidirect
1023. C32#5587semidirect
1024. C32#5679semidirect
1121. C3#10594092semidirect
1122. C3#10595176semidirect
1123. C3#10595509semidirect

Maximal subgroups

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

subgroupindex
#117237162
#117236142
D3×#37572
#117235972
C3×#639762
C3×D3×#2172
C3×#639592
#117229892
#117229852
#117229762
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