Finite Group Databasebeta

← #13172047

Subgroups — #13172047

Order 1728.

1328 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723720C211yesmaximal, characteristic, complemented
2Dic3×#638C211yesmaximal, characteristic, complemented
3D3×#3757C211yesmaximal, characteristic, complemented
4#11723595C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic
6C3×#63964C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722991C211yesmaximal, characteristic, complemented
12#11722990C211yesmaximal, characteristic, complemented
13#11722976C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722917C211yesmaximal, characteristic, complemented
16#10595509—31nomaximal
17#10594941—31nomaximal
18#10594119—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29#88864C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic, complemented
33#88815C2211yescharacteristic, complemented
34#88814C2211yescharacteristic, complemented
35#88814C2211yescharacteristic, complemented
36#88807C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88807C2211yescharacteristic, complemented
39#88803C2211yescharacteristic, complemented
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic, complemented
43Dic3×C3⋊Dic3C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×#3757—31no—
55C4×#638—31no—
56#64086—31no—
57C3×#953—31no—
58C2×C3×#217—31no—
59C2×C3×(C2×D3)⋊C4—31no—
60C3×#924—31no—
61C3×#882—31no—
62C3×#878—31no—
63#63982—31no—
64#63977D311yescharacteristic
65#67⋊Dic3—31no—
66Dic3×#67—31no—
67Dic3×#67—31no—
68Dic3×#67—61no—
69#63969—31no—
70D3×#217—31no—
71D3×#217—31no—
72D3×#217—61no—
73#63966—31no—
74#63964D311yescharacteristic, complemented
75#63962—31no—
76#63962—31no—
77#63961—31no—
78C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
79#63959—31no—
80#63957—31no—
81#63956—31no—
82#63956—31no—
83#63955—31no—
84#63955—31no—
85#63955—61no—
86#63907—31no—
87#63898—31no—
88#63890—31no—
89#63887—31no—
90#63887—31no—
91#63884—31no—
92#63884—31no—
93#63881—31no—
94#63878—31no—
95#63878—31no—
96#63863—31no—
97#63862—31no—
98#63862—31no—
99#63858—31no—
100#63858—31no—
101#63853—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3—22no—
105C22×C32×D3—22no—
106C22×C32×D3—41no—
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638—22no—
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123Dic3×C3⋊D3—41no—
124D3×C3⋊Dic3—22no—
125D3×C3⋊Dic3—41no—
126C3×#627—41no—
127C3×#626—22no—
128C3×#626—41no—
129#5637—91no—
130#5587—91no—
131#5495—91no—
132C24×C32—31no—
133C23×C3×D3—21no—
134C23×C3×D3C2×D311yescharacteristic
135C23×C3×D3C2×D311yescharacteristic
136C22×C32×C4—31no—
137C2×#638C2×D311yescharacteristic
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3C2×D311yescharacteristic
141C2×C4×C3⋊D3—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—61no—
147C22×C3×Dic3—21no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—61no—
151C22×C3×Dic3C2×D311yescharacteristic
152C22×C3×Dic3C2×D311yescharacteristic
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×#627C2×D311yescharacteristic, complemented
158C2×#626C2×D311yescharacteristic
159C2×#626C2×D311yescharacteristic
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—61no—
167C2×D3×Dic3—61no—
168C2×D3×Dic3—61no—
169C32×C22⋊C4—31no—
170#3757—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—31no—
175#3757—61no—
176#3757—61no—
177#3757—61no—
178#3757—121no—
179#3757C2×D311yescharacteristic
180#3752—31no—
181#3750—31no—
182#3750—31no—
183#3750—31no—
184C4×C3⋊Dic3—31no—
185C4×C3⋊Dic3—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—61no—
197C3×#217C2×D311yescharacteristic
198C3×#217C2×D311yescharacteristic
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211#3724—31no—
212#3724—31no—
213#3724C2×D311yescharacteristic, complemented
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230#3722—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
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—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3C2×D311yescharacteristic
245(C2×D3)⋊Dic3C2×D311yescharacteristic
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32—61no—
258Dic32—61no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—44no—
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—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×C22⋊Q8—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#947—91no—
293#946—91no—
294#936—91no—
295#935—91no—
296#935—91no—
297#935—91no—
298D4×Dic3—91no—
299D4×Dic3—91no—
300#929—91no—
301C4×#67—91no—
302C4×#67—91no—
303C4×#67—181no—
304C2×(C2×D3)⋊C4—31no—
305#926—91no—
306#924—31no—
307#898—91no—
308#898—91no—
309#894—91no—
310#894—91no—
311#893—91no—
312#892—91no—
313#886—91no—
314#886—91no—
315#885—91no—
316#883—91no—
317#882—31no—
318#67⋊C4—91no—
319D3×C22⋊C4—91no—
320#879—91no—
321#879—91no—
322#879—91no—
323#879—91no—
324#878—31no—
325#878—91no—
326#878—91no—
327#877—91no—
328#877—91no—
329#877—91no—
330#877—91no—
331#877—181no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—41no—
338C23×C32—62no—
339C23×C32—62no—
340C23×C32—121no—
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C22×C3⋊D3C22×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—31no—
353C22×C3×D3—31no—
354C22×C3×D3—42no—
355C22×C3×D3—41no—
356C22×C3×D3—41no—
357C22×C3×D3—42no—
358C22×C3×D3—61no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—121no—
368#638—22no—
369C2×C3⋊Dic3—22no—
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—62no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3—121no—
385C2×C3⋊Dic3—121no—
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C4×C3⋊D3—121no—
392C3×#67—62no—
393C3×#67—64no—
394C3×#67—62no—
395C3×#67—62no—
396C3×#67—121no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
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—41no—
412C2×C3×Dic3—41no—
413C2×C3×Dic3—42no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—64no—
420C2×C3×Dic3—62no—
421C2×C3×Dic3—62no—
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
429C2×C3×Dic3C22×D311yescharacteristic
430C3×D12—62no—
431C3×D12—121no—
432C3×Dic6—121no—
433C3×Dic6—121no—
434#627—41no—
435#626—22no—
436#626—41no—
437D3×Dic3—62no—
438D3×Dic3—62no—
439D3×Dic3—122no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442D3×Dic3—122no—
443D3×Dic3—121no—
444D3×Dic3—121no—
445D3×Dic3—122no—
446#551—271noSylow
447C2×C33—22no—
448C2×C33C2×#4111yescharacteristic
449C2×C33C2×#4111yescharacteristic
450C2×C33H(5,𝔽2)11yescharacteristic
451C3×C3⋊D3—41no—
452C32×D3—22no—
453C32×D3—41no—
454C24×C3—31no—
455C24×C3—31no—
456C24×C3—61no—
457C23×D3D3211yescharacteristic
458C2×C3×Q8—91no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C2×C3×D4—91no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—61no—
465C22×C3×C4—91no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—61no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—61no—
474C22×Dic3—91no—
475C22×Dic3—91no—
476C22×Dic3—91no—
477C22×Dic3—91no—
478C22×Dic3—91no—
479C22×Dic3—181no—
480C22×Dic3—181no—
481C22×Dic3D3211yescharacteristic
482C2×D12—31no—
483C2×D12—31no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—181no—
489C2×Dic6—31no—
490C2×Dic6—31no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—31no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—61no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
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—91no—
514#217—91no—
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—181no—
524#217—181no—
525#217—181no—
526#217—181no—
527#217—181no—
528#217—361no—
529#217D3211yescharacteristic
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
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—91no—
544(C2×D3)⋊C4—181no—
545C4⋊Dic3—31no—
546C4⋊Dic3—31no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
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—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—181no—
579C4×Dic3—181no—
580C4×Dic3—181no—
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—22no—
591C22×C32—22no—
592C22×C32—22no—
593C22×C32—32no—
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—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—81no—
608C22×C32—81no—
609C22×C32—124no—
610C22×C32#23712yes—
611C22×C32#23712yes—
612C22×C32#23912yes—
613C22×C32C23×D311yescharacteristic
614C22×C32C23×D311yescharacteristic
615C22×C32C23×D311yescharacteristic
616C2×C3⋊D3—21no—
617C2×C3⋊D3—21no—
618C2×C3⋊D3—21no—
619C2×C3×D3—22no—
620C2×C3×D3—22no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—22no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—22no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—44no—
636C2×C3×D3—44no—
637C2×C3×D3—48no—
638C2×C3×D3—62no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—121no—
646C2×C3×D3—121no—
647C2×C3×D3#23512yes—
648C2×C3×D3#23712yes—
649C32×C4—61no—
650C32×C4—61no—
651C32×C4—61no—
652C32×C4—61no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—21no—
657C3⋊Dic3—21no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—61no—
662C3⋊Dic3—61no—
663C3⋊Dic3—61no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
668C3⋊Dic3—121no—
669C3⋊Dic3—121no—
670C3⋊Dic3—241no—
671C3⋊Dic3—241no—
672C3×Dic3—22no—
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—41no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—62no—
685C3×Dic3—62no—
686C3×Dic3—62no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699#126—271no—
700#126—271no—
701#124—271no—
702#123—271no—
703#123—271no—
704#123—271no—
705C22⋊Q8—91no—
706C22⋊Q8—271no—
707#120—91no—
708C4×D4—271no—
709C4×D4—271no—
710#117—271no—
711#117—271no—
712C2×C22⋊C4—91no—
713C2×C22⋊C4—271no—
714C33#55111yescharacteristic, complemented, Sylow
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—21no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—31no—
721C23×C3—31no—
722C23×C3—41no—
723C23×C3—61no—
724C23×C3—61no—
725C23×C3—62no—
726C23×C3—62no—
727C23×C3—64no—
728C23×C3—62no—
729C23×C3—62no—
730C23×C3—91no—
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—31no—
741C22×D3—31no—
742C22×D3—41no—
743C22×D3—61no—
744C22×D3C2×D3211yescharacteristic
745C22×D3C2×D3211yescharacteristic
746C3×Q8—361no—
747C3×D4—182no—
748C3×D4—182no—
749C3×D4—361no—
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—31no—
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—91no—
767C2×C3×C4—121no—
768C2×C3×C4—121no—
769C2×C3×C4—122no—
770C2×C3×C4—182no—
771#67—62no—
772#67—64no—
773#67—62no—
774#67—62no—
775#67—121no—
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—31no—
785C2×Dic3—31no—
786C2×Dic3—41no—
787C2×Dic3—61no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—64no—
793C2×Dic3—62no—
794C2×Dic3—62no—
795C2×Dic3—91no—
796C2×Dic3—91no—
797C2×Dic3—91no—
798C2×Dic3—91no—
799C2×Dic3—91no—
800C2×Dic3—91no—
801C2×Dic3—181no—
802C2×Dic3—181no—
803C2×Dic3—181no—
804C2×Dic3—181no—
805C2×Dic3—181no—
806C2×Dic3—181no—
807C2×Dic3—182no—
808C2×Dic3—182no—
809C2×Dic3—361no—
810C2×Dic3—361no—
811C2×Dic3—362no—
812C2×Dic3—361no—
813C2×Dic3—361no—
814C2×Dic3—361no—
815C2×Dic3—362no—
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C2×Dic3C2×D3211yescharacteristic
819C2×Dic3C2×D3211yescharacteristic
820D12—62no—
821D12—121no—
822C4×D3—182no—
823C4×D3—361no—
824C4×D3—361no—
825C4×D3—361no—
826C4×D3—362no—
827Dic6—121no—
828Dic6—121no—
829C2×C32—22no—
830C2×C32—22no—
831C2×C32—22no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—41no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—42no—
845C2×C32—42no—
846C2×C32—42no—
847C2×C32—62no—
848C2×C32—82no—
849C2×C32—121no—
850C2×C32C2×#23511yescharacteristic
851C2×C32C2×#23711yescharacteristic
852C2×C32C2×#23711yescharacteristic
853C2×C32C2×#23711yescharacteristic
854C2×C32#100411yescharacteristic
855C2×C32#100411yescharacteristic
856C2×C32#100411yescharacteristic
857C2×C32C2×#23911yescharacteristic
858C2×C32D3×#4111yescharacteristic
859C3⋊D3—41no—
860C3×D3—24no—
861C3×D3—22no—
862C3×D3—22no—
863C3×D3—42no—
864C3×D3—41no—
865C3×D3—41no—
866C3×D3—122no—
867C3×D3—121no—
868C3×D3—121no—
869C24—31no—
870C2×Q8—91no—
871C2×D4—91no—
872C2×D4—91no—
873C2×D4—91no—
874C22×C4—31no—
875C22×C4—91no—
876C22×C4—271no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—271no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C22⋊C4—31no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C42—271no—
902C42—271no—
903C42—271no—
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—22no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—32no—
917C22×C3—32no—
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—62no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—61no—
931C22×C3—61no—
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—81no—
941C22×C3—81no—
942C22×C3—121no—
943C22×C3—121no—
944C22×C3—124no—
945C22×C3—124no—
946C22×C3—128no—
947C22×C3—181no—
948C22×C3—181no—
949C22×C3—181no—
950C22×C3#379612yes—
951C22×C3#379612yes—
952C22×C3#380512yes—
953C22×C3C22×D3211yescharacteristic
954C22×C3C22×D3211yescharacteristic
955C22×C3C22×D3211yescharacteristic
956C2×D3—21no—
957C2×D3—21no—
958C2×D3—21no—
959C2×D3—21no—
960C2×D3—21no—
961C2×D3—44no—
962C2×D3—62no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—121no—
970C2×D3—121no—
971C2×D3#380412yes—
972C3×C4—62no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—121no—
982C3×C4—121no—
983C3×C4—121no—
984C3×C4—181no—
985C3×C4—181no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989Dic3—21no—
990Dic3—21no—
991Dic3—21no—
992Dic3—21no—
993Dic3—62no—
994Dic3—62no—
995Dic3—62no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—121no—
1007Dic3—121no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—181no—
1011Dic3—181no—
1012Dic3—181no—
1013Dic3—181no—
1014Dic3—361no—
1015Dic3—361no—
1016Dic3—361no—
1017Dic3—361no—
1018Dic3—361no—
1019Dic3—361no—
1020Dic3—721no—
1021Dic3—721no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#549511yescharacteristic, complemented
1027C32#558711yescharacteristic, complemented
1028C32#563711yescharacteristic, complemented
1029C23—31no—
1030C23—31no—
1031C23—62no—
1032C23—62no—
1033C23—91no—
1034C23—121no—
1035C23D3311yescharacteristic
1036Q8—361no—
1037D4—182no—
1038D4—182no—
1039D4—361no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—31no—
1044C2×C4—91no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—121no—
1050C2×C4—182no—
1051C2×C4—271no—
1052C2×C4—271no—
1053C2×C4—542no—
1054C2×C4—1081no—
1055C2×C4—1081no—
1056C2×C3—22no—
1057C2×C3—22no—
1058C2×C3—22no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—42no—
1069C2×C3—42no—
1070C2×C3—42no—
1071C2×C3—41no—
1072C2×C3—41no—
1073C2×C3—41no—
1074C2×C3—64no—
1075C2×C3—62no—
1076C2×C3—62no—
1077C2×C3—82no—
1078C2×C3—122no—
1079C2×C3—121no—
1080C2×C3—121no—
1081C2×C3—361no—
1082C2×C3C2×#379611yescharacteristic
1083C2×C3C2×#379611yescharacteristic
1084C2×C3D3×#23511yescharacteristic
1085C2×C3D3×#23711yescharacteristic
1086C2×C3#6431311yescharacteristic
1087C2×C3C2×#380411yescharacteristic
1088C2×C3C2×#380511yescharacteristic
1089C2×C3#6433011yescharacteristic
1090C2×C3#6433011yescharacteristic
1091D3—22no—
1092D3—41no—
1093D3—122no—
1094D3—121no—
1095D3—121no—
1096C22—21no—
1097C22—21no—
1098C22—32no—
1099C22—61no—
1100C22—61no—
1101C22—61no—
1102C22—61no—
1103C22—61no—
1104C22—124no—
1105C22—181no—
1106C22—181no—
1107C22—181no—
1108C22#8896412yes—
1109C22C2×D3311yescharacteristic
1110C4—61no—
1111C4—61no—
1112C4—61no—
1113C4—61no—
1114C4—181no—
1115C4—181no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—541no—
1120C4—541no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059411911yescharacteristic, complemented
1126C3#1059494111yescharacteristic, complemented
1127C3#1059550911yescharacteristic, complemented
1128C2—22no—
1129C2—62no—
1130C2—121no—
1131C2—361no—
1132C2D3×#380411yescharacteristic
1133C2#1172441411yescharacteristic
1134C2C2×#8896411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63977C2
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. #11723720C2semidirect
2. Dic3×#638C2semidirect
3. D3×#3757C2semidirect
4. #11723595C2semidirect
6. C3×#63964C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11723019C2semidirect
9. #11723019C2semidirect
10. #11723001C2semidirect
11. #11722991C2semidirect
12. #11722990C2semidirect
13. #11722976C2semidirect
14. #11722929C2semidirect
15. #11722917C2semidirect
23. C2×Dic3×C3⋊D3C22semidirect
26. C2×C3×#627C22semidirect
32. #88815C22semidirect
33. #88815C22semidirect
34. #88814C22semidirect
35. #88814C22semidirect
36. #88807C22semidirect
37. #88807C22semidirect
38. #88807C22semidirect
39. #88803C22semidirect
42. Dic3×C3⋊Dic3C22semidirect
43. Dic3×C3⋊Dic3C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
74. #63964D3semidirect
78. C2×(C2×D3)⋊Dic3D3semidirect
157. C2×#627C2×D3semidirect
213. #3724C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
714. C33#551semidirect
1026. C32#5495semidirect
1027. C32#5587semidirect
1028. C32#5637semidirect
1125. C3#10594119semidirect
1126. C3#10594941semidirect
1127. C3#10595509semidirect

Maximal subgroups

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

subgroupindex
#117237202
Dic3×#6382
D3×#37572
#117235952
C3×#639772
C3×#639642
C2×C3×(C2×D3)⋊Dic32
#117230192
#117230012
#117229912
#117229902
#117229762
#117229292
#117229172
#105955093
#105949413
#105941193