Finite Group Databasebeta

← #13168366

Subgroups — #13168366

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#11723683C211yesmaximal, characteristic, complemented
2#11723540C211yesmaximal, characteristic
3#11723446C211yesmaximal, characteristic, complemented
4#11723411C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic, complemented
6C3×#63895C211yesmaximal, characteristic, complemented
7C3×#63884C211yesmaximal, characteristic, complemented
8#11723005C211yesmaximal, characteristic, complemented
9#11722998C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic, complemented
11#11722969C211yesmaximal, characteristic, complemented
12#11722930C211yesmaximal, characteristic, complemented
13#11722914C211yesmaximal, characteristic, complemented
14#11722904C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595118—31nomaximal
17#10594647—31nomaximal
18#10594642—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic, complemented
25C2×C3×#624C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3750C2211yescharacteristic, complemented
32C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
33C32×C4⋊Dic3C2211yescharacteristic, complemented
34C32×Dic3⋊C4C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic
37#88813C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64146—31no—
55#64107—31no—
56#64107—31no—
57C3×#935—31no—
58C3×D4×Dic3—31no—
59C3×#897—31no—
60C3×#896—31no—
61C3×#894—31no—
62C3×#893—31no—
63#63975—31no—
64#63974—31no—
65#63966—31no—
66#63964—31no—
67C2×#3722—31no—
68#63955—31no—
69#63953—31no—
70#63952—31no—
71#63922—31no—
72#63922—31no—
73#63922—61no—
74D3×(C2×D3)⋊C4—31no—
75D3×(C2×D3)⋊C4—31no—
76D3×(C2×D3)⋊C4—31no—
77D3×(C2×D3)⋊C4—31no—
78#63907—31no—
79#63907—31no—
80C4×#625—31no—
81#63898D311yescharacteristic, complemented
82#63895D311yescharacteristic, complemented
83#63891—31no—
84#63891—31no—
85#63890—31no—
86#63887—31no—
87#63884D311yescharacteristic, complemented
88#63879—31no—
89#63878—31no—
90#63878—31no—
91#63877—31no—
92#63868—31no—
93#63868—31no—
94#63868—61no—
95#63856—31no—
96#63850—31no—
97#63848—31no—
98#63848—31no—
99#63848—61no—
100#63841—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×C33×C4C2311yescharacteristic
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×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×D12—22no—
121#6294—22no—
122#6291—41no—
123#6290—22no—
124C3×#627—41no—
125C3×#624—41no—
126C3×D3×Dic3—22no—
127C3×D3×Dic3—41no—
128C3×D3×Dic3—41no—
129#5658—91no—
130#5637—91no—
131#5556—91no—
132C23×C3⋊D3—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×D32—61no—
136C2×C32×D4—31no—
137C2×#638—31no—
138C2×#638—31no—
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C2×C3×D12—21no—
143C2×C3×D12C2×D311yescharacteristic
144C2×C3×D12C2×D311yescharacteristic
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—31no—
152C2×#627C2×D311yescharacteristic, complemented
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—61no—
156C2×#625—31no—
157C2×#625—31no—
158C2×#625—61no—
159C2×#624—31no—
160C2×#624C2×D311yescharacteristic
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3C2×D311yescharacteristic
164C2×D3×Dic3C2×D311yescharacteristic
165C2×D3×Dic3C2×D311yescharacteristic, complemented
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168#3757—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—61no—
177#3752—61no—
178#3752—61no—
179#3752—121no—
180#3752C2×D311yescharacteristic
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—31no—
183#3750—31no—
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3C2×D311yescharacteristic, complemented
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×(C2×D3)⋊C4—31no—
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×(C2×D3)⋊C4—61no—
202C3×C4⋊Dic3—21no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3C2×D311yescharacteristic, complemented
205C3×C4⋊Dic3C2×D311yescharacteristic, complemented
206C3×Dic3⋊C4—21no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4C2×D311yescharacteristic, complemented
212C3×Dic3⋊C4C2×D311yescharacteristic, complemented
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—61no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—61no—
239#3722—61no—
240#3722—61no—
241#3722—61no—
242#3722C2×D311yescharacteristic
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)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
251(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
252(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—61no—
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272D3×C3⋊D3—44no—
273C33×C4—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×#123—91no—
285C3×C22⋊Q8—91no—
286C3×C4×D4—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290#937—91no—
291#937—181no—
292#935—31no—
293D4×Dic3—31no—
294#929—91no—
295C4×#67—91no—
296C4×#67—91no—
297C2×(C2×D3)⋊C4—91no—
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#898—91no—
306#898—91no—
307#898—181no—
308#898—181no—
309#897—31no—
310#896—31no—
311#894—31no—
312#894—91no—
313#893—31no—
314#892—91no—
315#892—91no—
316#886—91no—
317#886—91no—
318#885—91no—
319#885—91no—
320#883—91no—
321#883—91no—
322#882—91no—
323#67⋊C4—91no—
324D3×C22⋊C4—91no—
325D3×C22⋊C4—91no—
326D3×C22⋊C4—91no—
327#878—91no—
328#877—91no—
329#877—91no—
330#876—91no—
331#872—91no—
332C23×C32—31no—
333C23×C32—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—31no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—61no—
340C22×C3⋊D3—62no—
341C22×C3⋊D3—62no—
342C22×C3⋊D3—121no—
343C22×C3⋊D3—121no—
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—21no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—61no—
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C2×D32—62no—
355C2×D32—62no—
356C2×D32—62no—
357C2×D32—62no—
358C2×D32—122no—
359C2×D32—122no—
360C2×D32—121no—
361C2×D32—121no—
362C2×D32—122no—
363C32×D4—62no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—41no—
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375#638—62no—
376#638—121no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—61no—
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×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
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—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3—121no—
410C2×C3×Dic3—121no—
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
419C3×D12—22no—
420C3×D12—22no—
421C3×D12—42no—
422C3×C4×D3—62no—
423C3×C4×D3—121no—
424C3×C4×D3—121no—
425C3×C4×D3—121no—
426C3×C4×D3—121no—
427C3×Dic6—121no—
428C3×Dic6—121no—
429#627—41no—
430#626—121no—
431#626—121no—
432#626—122no—
433#625—62no—
434#625—62no—
435#625—122no—
436#624—41no—
437#624—62no—
438D3×Dic3—22no—
439D3×Dic3—41no—
440D3×Dic3—41no—
441D3×Dic3—62no—
442D3×Dic3—62no—
443#551—271noSylow
444C2×C33C2×#4111yescharacteristic
445C2×C33C2×#4111yescharacteristic
446C2×C33H(5,𝔽2)11yescharacteristic
447C3⋊(C3⋊D3)—41no—
448C3×C3⋊D3—22no—
449C32×D3—22no—
450C32×D3—41no—
451C23×D3—91no—
452C23×D3—91no—
453C23×D3—91no—
454C23×D3—181no—
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—
462C22×C3×C4—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—181no—
469C2×#67—181no—
470C22×Dic3—31no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—91no—
474C2×D12—91no—
475C2×D12D3211yescharacteristic
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×Dic6—31no—
484C2×Dic6—31no—
485C3×C4⋊C4—31no—
486C3×C4⋊C4—31no—
487C3×C4⋊C4—31no—
488C3×C4⋊C4—31no—
489C3×C4⋊C4—61no—
490C3×C4⋊C4—61no—
491C3×C4⋊C4—91no—
492C3×C4⋊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×C22⋊C4—91no—
500C3×C42—91no—
501#217—31no—
502#217—31no—
503#217—31no—
504#217—31no—
505#217—31no—
506#217—91no—
507#217—91no—
508#217—91no—
509#217—181no—
510(C2×D3)⋊C4—31no—
511(C2×D3)⋊C4—31no—
512(C2×D3)⋊C4—31no—
513(C2×D3)⋊C4—31no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—31no—
517(C2×D3)⋊C4—31no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—61no—
520(C2×D3)⋊C4—91no—
521(C2×D3)⋊C4—91no—
522(C2×D3)⋊C4—91no—
523(C2×D3)⋊C4—91no—
524(C2×D3)⋊C4—91no—
525(C2×D3)⋊C4—91no—
526(C2×D3)⋊C4—91no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
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—181no—
539(C2×D3)⋊C4—181no—
540(C2×D3)⋊C4—181no—
541(C2×D3)⋊C4—181no—
542(C2×D3)⋊C4—181no—
543(C2×D3)⋊C4—181no—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4—361no—
546C4⋊Dic3—31no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—181no—
553C4⋊Dic3—181no—
554C4⋊Dic3D3211yescharacteristic, complemented
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—61no—
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⋊C4D3211yescharacteristic, complemented
568C4×Dic3—31no—
569C4×Dic3—31no—
570C4×Dic3—61no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—181no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—32no—
582C22×C32—41no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—61no—
594C2×C3⋊D3—62no—
595C2×C3⋊D3—61no—
596C2×C3⋊D3—61no—
597C2×C3⋊D3—61no—
598C2×C3⋊D3—61no—
599C2×C3⋊D3—61no—
600C2×C3⋊D3—61no—
601C2×C3⋊D3—61no—
602C2×C3⋊D3—61no—
603C2×C3⋊D3—121no—
604C2×C3⋊D3—121no—
605C2×C3⋊D3—122no—
606C2×C3⋊D3—121no—
607C2×C3⋊D3—121no—
608C2×C3⋊D3—121no—
609C2×C3⋊D3—121no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—124no—
613C2×C3⋊D3—241no—
614C2×C3⋊D3—241no—
615C2×C3⋊D3#23912yes—
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—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—22no—
627C2×C3×D3—32no—
628C2×C3×D3—32no—
629C2×C3×D3—41no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—62no—
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#23512yes—
642C2×C3×D3#23712yes—
643D32—124no—
644D32—124no—
645D32—128no—
646C32×C4—21no—
647C32×C4—21no—
648C32×C4—21no—
649C32×C4—41no—
650C32×C4—41no—
651C32×C4—41no—
652C32×C4—61no—
653C32×C4—61no—
654C32×C4—61no—
655C32×C4—61no—
656C32×C4—81no—
657C3⋊Dic3—21no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3⋊Dic3—21no—
661C3⋊Dic3—21no—
662C3⋊Dic3—61no—
663C3⋊Dic3—61no—
664C3⋊Dic3—61no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
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—41no—
678C3×Dic3—41no—
679C3×Dic3—41no—
680C3×Dic3—41no—
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—
696#126—271no—
697#126—271no—
698#124—271no—
699#123—91no—
700#123—271no—
701#123—271no—
702C22⋊Q8—91no—
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—31no—
713C23×C3—31no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—61no—
717C23×C3—61no—
718C23×C3—91no—
719C22×D3—31no—
720C22×D3—31no—
721C22×D3—61no—
722C22×D3—91no—
723C22×D3—91no—
724C22×D3—91no—
725C22×D3—181no—
726C22×D3—181no—
727C22×D3—181no—
728C22×D3—182no—
729C22×D3—182no—
730C22×D3—182no—
731C22×D3—182no—
732C22×D3—182no—
733C22×D3—182no—
734C22×D3—361no—
735C22×D3—362no—
736C22×D3—362no—
737C22×D3—361no—
738C22×D3—361no—
739C22×D3—361no—
740C22×D3—362no—
741C22×D3C2×D3211yescharacteristic
742C22×D3C2×D3211yescharacteristic
743C3×Q8—361no—
744C3×D4—62no—
745C3×D4—62no—
746C3×D4—122no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
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—41no—
759C2×C3×C4—61no—
760C2×C3×C4—61no—
761C2×C3×C4—61no—
762C2×C3×C4—61no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—91no—
768C2×C3×C4—182no—
769C2×C3×C4—361no—
770C2×C3×C4—361no—
771C2×C3×C4—361no—
772C2×C3×C4C2×D3211yescharacteristic
773C2×C3×C4C2×D3211yescharacteristic
774C2×C3×C4C2×D3211yescharacteristic
775#67—182no—
776#67—182no—
777#67—182no—
778#67—362no—
779#67—361no—
780#67—361no—
781#67—362no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—61no—
795C2×Dic3—61no—
796C2×Dic3—61no—
797C2×Dic3—62no—
798C2×Dic3—91no—
799C2×Dic3—91no—
800C2×Dic3—91no—
801C2×Dic3—121no—
802C2×Dic3—121no—
803C2×Dic3—181no—
804C2×Dic3—181no—
805C2×Dic3—181no—
806C2×Dic3—182no—
807C2×Dic3—361no—
808C2×Dic3C2×D3211yescharacteristic
809C2×Dic3C2×D3211yescharacteristic
810C2×Dic3C2×D3211yescharacteristic
811C2×Dic3C2×D3211yescharacteristic
812D12—22no—
813D12—361no—
814C4×D3—62no—
815C4×D3—121no—
816C4×D3—121no—
817C4×D3—121no—
818C4×D3—121no—
819C4×D3—182no—
820C4×D3—182no—
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—62no—
836C2×C32—121no—
837C2×C32C2×#23511yescharacteristic
838C2×C32C2×#23711yescharacteristic
839C2×C32#100411yescharacteristic
840C2×C32#100411yescharacteristic
841C2×C32C2×#23911yescharacteristic
842C2×C32D3×#4111yescharacteristic
843C2×C32D3×#4111yescharacteristic
844C2×C32D3×#4111yescharacteristic
845C2×C32#100911yescharacteristic
846C3⋊D3—22no—
847C3⋊D3—121no—
848C3⋊D3—122no—
849C3⋊D3—121no—
850C3⋊D3—121no—
851C3⋊D3—241no—
852C3⋊D3—241no—
853C3⋊D3—242no—
854C3×D3—22no—
855C3×D3—22no—
856C3×D3—42no—
857C3×D3—41no—
858C3×D3—41no—
859C3×D3—62no—
860C3×D3—62no—
861C3×D3—81no—
862C3×D3—122no—
863C24—271no—
864C2×Q8—91no—
865C2×D4—31no—
866C2×D4—271no—
867C2×D4—271no—
868C22×C4—91no—
869C22×C4—91no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—271no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—91no—
876C4⋊C4—91no—
877C4⋊C4—271no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
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—
895C42—91no—
896C42—271no—
897C42—271no—
898C22×C3—21no—
899C22×C3—21no—
900C22×C3—21no—
901C22×C3—32no—
902C22×C3—32no—
903C22×C3—41no—
904C22×C3—62no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—61no—
910C22×C3—61no—
911C22×C3—61no—
912C22×C3—61no—
913C22×C3—61no—
914C22×C3—61no—
915C22×C3—92no—
916C22×C3—121no—
917C22×C3—121no—
918C22×C3—121no—
919C22×C3—121no—
920C22×C3—121no—
921C22×C3—181no—
922C22×C3—181no—
923C22×C3C22×D3211yescharacteristic
924C22×C3C22×D3211yescharacteristic
925C22×C3C22×D3211yescharacteristic
926C2×D3—21no—
927C2×D3—21no—
928C2×D3—21no—
929C2×D3—21no—
930C2×D3—21no—
931C2×D3—32no—
932C2×D3—32no—
933C2×D3—62no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—182no—
941C2×D3—181no—
942C2×D3—181no—
943C2×D3—181no—
944C2×D3—181no—
945C2×D3—181no—
946C2×D3—181no—
947C2×D3—181no—
948C2×D3—181no—
949C2×D3—181no—
950C2×D3—361no—
951C2×D3—361no—
952C2×D3—361no—
953C2×D3—361no—
954C2×D3—361no—
955C2×D3—361no—
956C2×D3—361no—
957C2×D3—361no—
958C2×D3—362no—
959C2×D3—364no—
960C2×D3—364no—
961C2×D3—364no—
962C2×D3—368no—
963C2×D3—721no—
964C2×D3—721no—
965C2×D3#380412yes—
966C3×C4—21no—
967C3×C4—21no—
968C3×C4—21no—
969C3×C4—41no—
970C3×C4—41no—
971C3×C4—41no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—81no—
981C3×C4—121no—
982C3×C4—121no—
983C3×C4—121no—
984C3×C4—121no—
985C3×C4—181no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989C3×C4—181no—
990Dic3—21no—
991Dic3—21no—
992Dic3—21no—
993Dic3—21no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—121no—
1005Dic3—121no—
1006Dic3—121no—
1007Dic3—121no—
1008Dic3—121no—
1009Dic3—181no—
1010Dic3—181no—
1011Dic3—181no—
1012Dic3—361no—
1013Dic3—361no—
1014Dic3—361no—
1015Dic3—721no—
1016C32—21no—
1017C32—21no—
1018C32—21no—
1019C32—41no—
1020C32#555611yescharacteristic, complemented
1021C32#563711yescharacteristic, complemented
1022C32#565811yescharacteristic, complemented
1023C23—31no—
1024C23—31no—
1025C23—91no—
1026C23—271no—
1027C23—542no—
1028C23—542no—
1029C23—1081no—
1030Q8—361no—
1031D4—62no—
1032D4—542no—
1033D4—1081no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—182no—
1044C2×C4—271no—
1045C2×C4—361no—
1046C2×C4—361no—
1047C2×C4—361no—
1048C2×C4—542no—
1049C2×C4D3311yescharacteristic
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—41no—
1060C2×C3—41no—
1061C2×C3—41no—
1062C2×C3—62no—
1063C2×C3—62no—
1064C2×C3—122no—
1065C2×C3—121no—
1066C2×C3—121no—
1067C2×C3—182no—
1068C2×C3—241no—
1069C2×C3D3×#23511yescharacteristic
1070C2×C3#6430711yescharacteristic
1071C2×C3D3×#23711yescharacteristic
1072C2×C3#6431211yescharacteristic
1073C2×C3#6431311yescharacteristic
1074C2×C3#6431411yescharacteristic
1075C2×C3D3×#23911yescharacteristic
1076C2×C3D3×#23911yescharacteristic
1077C2×C3C2×#380411yescharacteristic
1078D3—22no—
1079D3—41no—
1080D3—62no—
1081D3—62no—
1082D3—122no—
1083D3—362no—
1084D3—361no—
1085D3—361no—
1086D3—361no—
1087D3—721no—
1088D3—721no—
1089D3—722no—
1090C22—32no—
1091C22—61no—
1092C22—61no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—92no—
1097C22—181no—
1098C22—181no—
1099C22—541no—
1100C22—541no—
1101C22—541no—
1102C22—1084no—
1103C22C2×D3311yescharacteristic
1104C4—21no—
1105C4—61no—
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—181no—
1114C4—541no—
1115C3—21no—
1116C3—21no—
1117C3—21no—
1118C3—41no—
1119C3#1059464211yescharacteristic, complemented
1120C3#1059464711yescharacteristic, complemented
1121C3#1059511811yescharacteristic, complemented
1122C2—62no—
1123C2—121no—
1124C2—182no—
1125C2—1081no—
1126C2#1172437711yescharacteristic
1127C2#1172438111yescharacteristic
1128C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723540C2
hypercenterC2×C4D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723683C2semidirect
3. #11723446C2semidirect
4. #11723411C2semidirect
5. C3×#63898C2semidirect
6. C3×#63895C2semidirect
7. C3×#63884C2semidirect
8. #11723005C2semidirect
9. #11722998C2semidirect
10. #11722987C2semidirect
11. #11722969C2semidirect
12. #11722930C2semidirect
13. #11722914C2semidirect
14. #11722904C2semidirect
15. D3×#3722C2semidirect
24. C2×C3×#627C22semidirect
28. C2×C3×D3×Dic3C22semidirect
31. C3×#3750C22semidirect
32. C3×C4×C3⋊Dic3C22semidirect
33. C32×C4⋊Dic3C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. #88815C22semidirect
37. #88813C22semidirect
38. #88806C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
81. #63898D3semidirect
82. #63895D3semidirect
87. #63884D3semidirect
152. C2×#627C2×D3semidirect
165. C2×D3×Dic3C2×D3semidirect
184. #3750C2×D3semidirect
186. C4×C3⋊Dic3C2×D3semidirect
204. C3×C4⋊Dic3C2×D3semidirect
205. C3×C4⋊Dic3C2×D3semidirect
211. C3×Dic3⋊C4C2×D3semidirect
212. C3×Dic3⋊C4C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
250. (C2×D3)⋊Dic3C2×D3semidirect
251. (C2×D3)⋊Dic3C2×D3semidirect
252. (C2×D3)⋊Dic3C2×D3semidirect
554. C4⋊Dic3D32semidirect
567. Dic3⋊C4D32semidirect
711. C33#551semidirect
1020. C32#5556semidirect
1021. C32#5637semidirect
1022. C32#5658semidirect
1119. C3#10594642semidirect
1120. C3#10594647semidirect
1121. C3#10595118semidirect

Maximal subgroups

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

subgroupindex
#117236832
#117235402
#117234462
#117234112
C3×#638982
C3×#638952
C3×#638842
#117230052
#117229982
#117229872
#117229692
#117229302
#117229142
#117229042
D3×#37222
#105951183
#105946473
#105946423