Finite Group Databasebeta

← #13169249

Subgroups — #13169249

Order 1728.

1348 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723683C211yesmaximal, characteristic, complemented
2#11723542C211yesmaximal, characteristic
3#11723498C211yesmaximal, characteristic, complemented
4#11723494C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63862C211yesmaximal, characteristic, complemented
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723005C211yesmaximal, characteristic, complemented
9#11722999C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722933C211yesmaximal, characteristic, complemented
13#11722920C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10594655—31nomaximal
17#10594654—31nomaximal
18#10594165—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic, complemented
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#624C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic, complemented
34C32×Dic3⋊C4C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic
37#88813C2211yescharacteristic, complemented
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64103—31no—
55#64102—31no—
56#64091—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#897—31no—
60C3×#896—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63975—31no—
64#63974—31no—
65#63974—31no—
66#63953—31no—
67#63923—31no—
68#63923—31no—
69#63923—61no—
70#63921—31no—
71#63921—31no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63907—31no—
75#63907—31no—
76#63904—31no—
77C4×#626—31no—
78#63897—31no—
79#63897—31no—
80#63897—31no—
81#63897—61no—
82#63895—31no—
83#63895D311yescharacteristic, complemented
84#63894—31no—
85#63894—31no—
86#63894—31no—
87#63894—61no—
88#63890—31no—
89#63890—31no—
90#63888—31no—
91#63878—31no—
92#63877—31no—
93#63871—31no—
94#63862D311yescharacteristic, complemented
95#63858D311yescharacteristic, complemented
96#63854—31no—
97#63853—31no—
98#63849—31no—
99#63836—31no—
100#63836—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×C33×C4C2311yescharacteristic
110C4⋊(C3⋊(C3⋊D3))—22no—
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
120C2×C32×Dic3C2311yescharacteristic
121#6294—22no—
122#6292—22no—
123#6291—41no—
124#6289—22no—
125#6289—41no—
126#6289—41no—
127C3×#627—41no—
128C3×#624—41no—
129#5705—91no—
130#5705—91no—
131#5637—91no—
132C23×C3⋊D3—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×D32—61no—
136C2×#638—31no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4⋊(C3⋊D3)—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—61no—
142C2×C4⋊(C3⋊D3)—61no—
143C2×C4⋊(C3⋊D3)—61no—
144C2×C4⋊(C3⋊D3)—121no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊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—31no—
156C2×#626—31no—
157C2×#626—61no—
158C2×#626—61no—
159C2×#624—31no—
160C2×#624—31no—
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—31no—
164C2×#624—31no—
165C2×#624—31no—
166C2×#624—61no—
167C2×#624—61no—
168C2×#624—61no—
169C2×#624C2×D311yescharacteristic
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C32×C4⋊C4—31no—
173C32×C4⋊C4—31no—
174C32×C22⋊C4—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752C2×D311yescharacteristic
182#3750C2×D311yescharacteristic, complemented
183C4×C3⋊Dic3C2×D311yescharacteristic, complemented
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×(C2×D3)⋊C4—21no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—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—61no—
198C3×(C2×D3)⋊C4C2×D311yescharacteristic
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×C4⋊Dic3—21no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×C4⋊Dic3C2×D311yescharacteristic, complemented
206C3×C4⋊Dic3C2×D311yescharacteristic, complemented
207C3×Dic3⋊C4—21no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—61no—
215C3×Dic3⋊C4C2×D311yescharacteristic, complemented
216C3×Dic3⋊C4C2×D311yescharacteristic, complemented
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—61no—
222#3724—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3C2×D311yescharacteristic, complemented
226Dic3⋊Dic3C2×D311yescharacteristic, complemented
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
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—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—61no—
243#3722—61no—
244#3722—61no—
245#3722—61no—
246#3722—61no—
247#3722—61no—
248#3722C2×D311yescharacteristic
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32C2×D311yescharacteristic, complemented
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×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3#4112yes—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
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—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#126—91no—
286C3×C22⋊Q8—91no—
287#947—91no—
288#946—91no—
289C4×#67—91no—
290C2×(C2×D3)⋊C4—91no—
291#898—31no—
292#898—31no—
293#897—31no—
294#897—91no—
295#896—31no—
296#896—91no—
297#894—91no—
298#894—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#894—91no—
303#894—181no—
304#893—91no—
305#893—91no—
306#893—91no—
307#893—181no—
308#892—91no—
309#892—91no—
310#892—91no—
311#886—91no—
312#885—91no—
313#885—91no—
314#883—91no—
315#883—91no—
316#882—91no—
317#882—91no—
318#882—91no—
319#882—181no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322D3×C22⋊C4—91no—
323D3×C22⋊C4—91no—
324D3×C22⋊C4—91no—
325#879—31no—
326#879—31no—
327#877—91no—
328C4×D12—91no—
329C4×D12—91no—
330#872—91no—
331#872—91no—
332C23×C32—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—31no—
337C22×C3⋊D3—31no—
338C22×C3⋊D3—31no—
339C22×C3⋊D3—61no—
340C22×C3⋊D3—61no—
341C22×C3⋊D3—61no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—62no—
346C22×C3⋊D3—62no—
347C22×C3⋊D3—121no—
348C22×C3⋊D3—121no—
349C22×C3⋊D3—121no—
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—61no—
355C22×C3×D3C22×D311yescharacteristic
356C22×C3×D3C22×D311yescharacteristic
357C2×D32—62no—
358C2×D32—62no—
359C2×D32—62no—
360C2×D32—62no—
361C2×D32—122no—
362C2×D32—122no—
363C2×D32—121no—
364C2×D32—121no—
365C2×D32—122no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—41no—
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378#638—121no—
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C4⋊(C3⋊D3)—62no—
385C4⋊(C3⋊D3)—62no—
386C4⋊(C3⋊D3)—62no—
387C4⋊(C3⋊D3)—64no—
388C4⋊(C3⋊D3)—62no—
389C4⋊(C3⋊D3)—122no—
390C4⋊(C3⋊D3)—122no—
391C4⋊(C3⋊D3)—124no—
392C4×C3⋊D3—62no—
393C4×C3⋊D3—121no—
394C4×C3⋊D3—121no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
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—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
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
425C3×C4×D3—121no—
426C3×C4×D3—121no—
427C3×Dic6—121no—
428C3×Dic6—121no—
429#627—41no—
430#626—62no—
431#626—62no—
432#626—122no—
433#626—121no—
434#626—121no—
435#626—122no—
436#624—41no—
437#624—62no—
438#624—62no—
439#624—62no—
440#624—122no—
441#624—121no—
442#624—121no—
443#624—121no—
444#624—121no—
445#624—122no—
446#624—122no—
447D3×Dic3—62no—
448D3×Dic3—62no—
449#551—271noSylow
450C2×C33C2×#4111yescharacteristic
451C2×C33C2×#4111yescharacteristic
452C2×C33H(5,𝔽2)11yescharacteristic
453C3⋊(C3⋊D3)—22no—
454C3⋊(C3⋊D3)—41no—
455C3×C3⋊D3—22no—
456C32×D3—41no—
457C23×D3—91no—
458C23×D3—91no—
459C23×D3—91no—
460C23×D3—181no—
461C2×C3×Q8—91no—
462C22×C3×C4—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—181no—
467C22×Dic3—91no—
468C2×D12—91no—
469C2×D12—91no—
470C2×D12—91no—
471C2×D12—91no—
472C2×D12—91no—
473C2×D12—91no—
474C2×D12—181no—
475C2×D12—181no—
476C2×D12—181no—
477C2×D12—181no—
478C2×D12—361no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—181no—
493C2×C4×D3—181no—
494C2×C4×D3—181no—
495C2×Dic6—31no—
496C2×Dic6—31no—
497C3×C4⋊C4—31no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4—31no—
501C3×C4⋊C4—61no—
502C3×C4⋊C4—61no—
503C3×C4⋊C4—91no—
504C3×C4⋊C4—91no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C4⋊C4—91no—
508C3×C22⋊C4—31no—
509C3×C22⋊C4—31no—
510C3×C22⋊C4—61no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C22⋊C4—91no—
515C3×C22⋊C4—91no—
516C3×C22⋊C4—91no—
517C3×C42—91no—
518C3×C42—91no—
519#217—31no—
520#217—31no—
521#217—31no—
522#217—31no—
523#217—91no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—61no—
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—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548(C2×D3)⋊C4—91no—
549(C2×D3)⋊C4—91no—
550(C2×D3)⋊C4—91no—
551(C2×D3)⋊C4—91no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—181no—
554(C2×D3)⋊C4—181no—
555(C2×D3)⋊C4—181no—
556(C2×D3)⋊C4—181no—
557(C2×D3)⋊C4—181no—
558(C2×D3)⋊C4—181no—
559(C2×D3)⋊C4D3211yescharacteristic
560C4⋊Dic3—31no—
561C4⋊Dic3—31no—
562C4⋊Dic3—31no—
563C4⋊Dic3—31no—
564C4⋊Dic3—91no—
565C4⋊Dic3D3211yescharacteristic, complemented
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—31no—
572Dic3⋊C4—61no—
573Dic3⋊C4—91no—
574Dic3⋊C4—91no—
575Dic3⋊C4D3211yescharacteristic, complemented
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—31no—
579C4×Dic3—31no—
580C4×Dic3—61no—
581C4×Dic3—91no—
582C4×Dic3—91no—
583C4×Dic3—91no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—41no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—32no—
597C2×C3⋊D3—32no—
598C2×C3⋊D3—32no—
599C2×C3⋊D3—62no—
600C2×C3⋊D3—62no—
601C2×C3⋊D3—62no—
602C2×C3⋊D3—61no—
603C2×C3⋊D3—61no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—61no—
608C2×C3⋊D3—61no—
609C2×C3⋊D3—62no—
610C2×C3⋊D3—61no—
611C2×C3⋊D3—61no—
612C2×C3⋊D3—61no—
613C2×C3⋊D3—61no—
614C2×C3⋊D3—61no—
615C2×C3⋊D3—61no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—122no—
619C2×C3⋊D3—121no—
620C2×C3⋊D3—121no—
621C2×C3⋊D3—122no—
622C2×C3⋊D3—121no—
623C2×C3⋊D3—121no—
624C2×C3⋊D3—121no—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—121no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—121no—
634C2×C3⋊D3—124no—
635C2×C3⋊D3—241no—
636C2×C3⋊D3—241no—
637C2×C3⋊D3—241no—
638C2×C3⋊D3—241no—
639C2×C3⋊D3#23912yes—
640C2×C3×D3—22no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—32no—
648C2×C3×D3—32no—
649C2×C3×D3—41no—
650C2×C3×D3—41no—
651C2×C3×D3—62no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658D32—124no—
659D32—124no—
660D32—128no—
661C32×C4—21no—
662C32×C4—22no—
663C32×C4—21no—
664C32×C4—21no—
665C32×C4—41no—
666C32×C4—41no—
667C32×C4—42no—
668C32×C4—61no—
669C32×C4—61no—
670C32×C4—61no—
671C32×C4—61no—
672C32×C4—61no—
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—21no—
683C3×Dic3—21no—
684C3×Dic3—21no—
685C3×Dic3—21no—
686C3×Dic3—21no—
687C3×Dic3—21no—
688C3×Dic3—41no—
689C3×Dic3—41no—
690C3×Dic3—41no—
691C3×Dic3—41no—
692C3×Dic3—41no—
693C3×Dic3—62no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—121no—
705C3×Dic3—121no—
706C3×Dic3—121no—
707C3×Dic3—121no—
708#126—91no—
709#126—91no—
710#124—271no—
711#123—271no—
712#123—271no—
713#123—271no—
714C22⋊Q8—91no—
715C22⋊Q8—271no—
716#120—271no—
717C4×D4—271no—
718C4×D4—271no—
719#117—271no—
720#117—271no—
721C2×C22⋊C4—271no—
722C2×C22⋊C4—271no—
723C33#55111yescharacteristic, complemented, Sylow
724C23×C3—31no—
725C23×C3—31no—
726C23×C3—61no—
727C23×C3—91no—
728C22×D3—31no—
729C22×D3—31no—
730C22×D3—61no—
731C22×D3—91no—
732C22×D3—91no—
733C22×D3—91no—
734C22×D3—91no—
735C22×D3—91no—
736C22×D3—91no—
737C22×D3—181no—
738C22×D3—181no—
739C22×D3—181no—
740C22×D3—181no—
741C22×D3—181no—
742C22×D3—181no—
743C22×D3—182no—
744C22×D3—182no—
745C22×D3—182no—
746C22×D3—182no—
747C22×D3—182no—
748C22×D3—182no—
749C22×D3—361no—
750C22×D3—361no—
751C22×D3—362no—
752C22×D3—362no—
753C22×D3—361no—
754C22×D3—361no—
755C22×D3—361no—
756C22×D3—362no—
757C22×D3C2×D3211yescharacteristic
758C3×Q8—361no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—31no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—41no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—91no—
782C2×C3×C4—91no—
783C2×C3×C4—361no—
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787#67—182no—
788#67—361no—
789#67—361no—
790#67—362no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—182no—
807C2×Dic3C2×D3211yescharacteristic
808C2×Dic3C2×D3211yescharacteristic
809C2×Dic3C2×D3211yescharacteristic
810C2×Dic3C2×D3211yescharacteristic
811C2×Dic3C2×D3211yescharacteristic
812D12—182no—
813D12—182no—
814D12—182no—
815D12—184no—
816D12—182no—
817D12—182no—
818D12—362no—
819D12—362no—
820D12—364no—
821D12—362no—
822D12—361no—
823C4×D3—121no—
824C4×D3—121no—
825C4×D3—182no—
826C4×D3—182no—
827C4×D3—182no—
828C4×D3—182no—
829C4×D3—182no—
830C4×D3—362no—
831C4×D3—361no—
832C4×D3—361no—
833C4×D3—361no—
834C4×D3—361no—
835C4×D3—361no—
836C4×D3—361no—
837C4×D3—362no—
838C4×D3—362no—
839Dic6—121no—
840Dic6—121no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—41no—
851C2×C32—41no—
852C2×C32—41no—
853C2×C32—121no—
854C2×C32#100411yescharacteristic
855C2×C32C2×#23911yescharacteristic
856C2×C32D3×#4111yescharacteristic
857C2×C32D3×#4111yescharacteristic
858C2×C32D3×#4111yescharacteristic
859C2×C32D3×#4111yescharacteristic
860C2×C32D3×#4111yescharacteristic
861C2×C32#100911yescharacteristic
862C2×C32#100911yescharacteristic
863C3⋊D3—22no—
864C3⋊D3—62no—
865C3⋊D3—62no—
866C3⋊D3—62no—
867C3⋊D3—122no—
868C3⋊D3—122no—
869C3⋊D3—122no—
870C3⋊D3—121no—
871C3⋊D3—122no—
872C3⋊D3—121no—
873C3⋊D3—121no—
874C3⋊D3—242no—
875C3⋊D3—241no—
876C3⋊D3—241no—
877C3⋊D3—242no—
878C3×D3—42no—
879C3×D3—41no—
880C3×D3—41no—
881C3×D3—62no—
882C3×D3—62no—
883C3×D3—122no—
884C24—271no—
885C2×Q8—91no—
886C2×D4—271no—
887C2×D4—271no—
888C2×D4—271no—
889C22×C4—91no—
890C22×C4—271no—
891C22×C4—271no—
892C22×C4—271no—
893C22×C4—271no—
894C4⋊C4—31no—
895C4⋊C4—31no—
896C4⋊C4—91no—
897C4⋊C4—91no—
898C4⋊C4—91no—
899C4⋊C4—91no—
900C4⋊C4—91no—
901C4⋊C4—271no—
902C22⋊C4—31no—
903C22⋊C4—91no—
904C22⋊C4—91no—
905C22⋊C4—91no—
906C22⋊C4—91no—
907C22⋊C4—91no—
908C22⋊C4—91no—
909C22⋊C4—271no—
910C22⋊C4—271no—
911C22⋊C4—271no—
912C22⋊C4—271no—
913C22⋊C4—271no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C42—91no—
917C42—91no—
918C42—271no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—41no—
923C22×C3—62no—
924C22×C3—61no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—92no—
931C22×C3—121no—
932C22×C3—121no—
933C22×C3—181no—
934C22×C3—181no—
935C22×C3C22×D3211yescharacteristic
936C22×C3C22×D3211yescharacteristic
937C22×C3C22×D3211yescharacteristic
938C2×D3—21no—
939C2×D3—21no—
940C2×D3—21no—
941C2×D3—32no—
942C2×D3—32no—
943C2×D3—62no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—92no—
949C2×D3—92no—
950C2×D3—92no—
951C2×D3—121no—
952C2×D3—121no—
953C2×D3—182no—
954C2×D3—182no—
955C2×D3—182no—
956C2×D3—181no—
957C2×D3—181no—
958C2×D3—181no—
959C2×D3—181no—
960C2×D3—181no—
961C2×D3—181no—
962C2×D3—182no—
963C2×D3—181no—
964C2×D3—181no—
965C2×D3—181no—
966C2×D3—181no—
967C2×D3—181no—
968C2×D3—181no—
969C2×D3—181no—
970C2×D3—181no—
971C2×D3—181no—
972C2×D3—362no—
973C2×D3—361no—
974C2×D3—361no—
975C2×D3—361no—
976C2×D3—361no—
977C2×D3—361no—
978C2×D3—361no—
979C2×D3—361no—
980C2×D3—361no—
981C2×D3—361no—
982C2×D3—361no—
983C2×D3—361no—
984C2×D3—361no—
985C2×D3—361no—
986C2×D3—361no—
987C2×D3—362no—
988C2×D3—364no—
989C2×D3—364no—
990C2×D3—364no—
991C2×D3—368no—
992C2×D3—721no—
993C2×D3—721no—
994C2×D3—721no—
995C2×D3—721no—
996C3×C4—22no—
997C3×C4—21no—
998C3×C4—21no—
999C3×C4—21no—
1000C3×C4—41no—
1001C3×C4—41no—
1002C3×C4—42no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—61no—
1011C3×C4—61no—
1012C3×C4—61no—
1013C3×C4—121no—
1014C3×C4—121no—
1015C3×C4—121no—
1016C3×C4—121no—
1017C3×C4—121no—
1018C3×C4—181no—
1019C3×C4—181no—
1020C3×C4—181no—
1021C3×C4—181no—
1022C3×C4—181no—
1023Dic3—21no—
1024Dic3—21no—
1025Dic3—21no—
1026Dic3—21no—
1027Dic3—21no—
1028Dic3—62no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—61no—
1035Dic3—61no—
1036Dic3—61no—
1037Dic3—61no—
1038Dic3—61no—
1039Dic3—121no—
1040Dic3—121no—
1041Dic3—121no—
1042Dic3—121no—
1043C32—21no—
1044C32—21no—
1045C32—21no—
1046C32—41no—
1047C32#563711yescharacteristic, complemented
1048C32#570511yescharacteristic, complemented
1049C32#570511yescharacteristic, complemented
1050C23—31no—
1051C23—91no—
1052C23—271no—
1053C23—271no—
1054C23—542no—
1055C23—542no—
1056C23—1081no—
1057Q8—361no—
1058D4—542no—
1059D4—542no—
1060D4—1081no—
1061C2×C4—31no—
1062C2×C4—31no—
1063C2×C4—31no—
1064C2×C4—31no—
1065C2×C4—31no—
1066C2×C4—91no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—91no—
1070C2×C4—91no—
1071C2×C4—361no—
1072C2×C4—542no—
1073C2×C4—542no—
1074C2×C4—1081no—
1075C2×C4—1081no—
1076C2×C4D3311yescharacteristic
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—41no—
1087C2×C3—41no—
1088C2×C3—41no—
1089C2×C3—122no—
1090C2×C3—121no—
1091C2×C3—121no—
1092C2×C3—182no—
1093C2×C3#6430611yescharacteristic
1094C2×C3#6430711yescharacteristic
1095C2×C3#6430811yescharacteristic
1096C2×C3#6431211yescharacteristic
1097C2×C3#6431211yescharacteristic
1098C2×C3#6431211yescharacteristic
1099C2×C3#6431411yescharacteristic
1100C2×C3D3×#23911yescharacteristic
1101C2×C3D3×#23911yescharacteristic
1102D3—41no—
1103D3—62no—
1104D3—62no—
1105D3—122no—
1106D3—182no—
1107D3—182no—
1108D3—182no—
1109D3—362no—
1110D3—362no—
1111D3—362no—
1112D3—362no—
1113D3—361no—
1114D3—361no—
1115D3—361no—
1116D3—722no—
1117D3—721no—
1118D3—721no—
1119D3—722no—
1120C22—61no—
1121C22—61no—
1122C22—61no—
1123C22—92no—
1124C22—181no—
1125C22—181no—
1126C22—272no—
1127C22—541no—
1128C22—541no—
1129C22—541no—
1130C22—541no—
1131C22—541no—
1132C22—1084no—
1133C22C2×D3311yescharacteristic
1134C4—21no—
1135C4—61no—
1136C4—61no—
1137C4—61no—
1138C4—61no—
1139C4—61no—
1140C4—181no—
1141C4—181no—
1142C4—181no—
1143C4—181no—
1144C4—181no—
1145C3—21no—
1146C3—21no—
1147C3—21no—
1148C3—41no—
1149C3#1059416511yescharacteristic, complemented
1150C3#1059465411yescharacteristic, complemented
1151C3#1059465511yescharacteristic, complemented
1152C2—121no—
1153C2—182no—
1154C2—542no—
1155C2—1081no—
1156C2#1172437711yescharacteristic
1157C2#1172438411yescharacteristic
1158C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723542C2
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. #11723498C2semidirect
4. #11723494C2semidirect
5. C3×#63895C2semidirect
6. C3×#63862C2semidirect
7. C3×#63858C2semidirect
8. #11723005C2semidirect
9. #11722999C2semidirect
10. #11722996C2semidirect
11. #11722973C2semidirect
12. #11722933C2semidirect
13. #11722920C2semidirect
14. #11722906C2semidirect
15. #11722904C2semidirect
26. C2×#6289C22semidirect
27. C2×C3×#627C22semidirect
30. C3×#3750C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
33. C32×C4⋊Dic3C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. #88815C22semidirect
37. #88813C22semidirect
41. #88804C22semidirect
42. #88804C22semidirect
43. #88804C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
83. #63895D3semidirect
94. #63862D3semidirect
95. #63858D3semidirect
152. C2×#627C2×D3semidirect
182. #3750C2×D3semidirect
183. C4×C3⋊Dic3C2×D3semidirect
205. C3×C4⋊Dic3C2×D3semidirect
206. C3×C4⋊Dic3C2×D3semidirect
215. C3×Dic3⋊C4C2×D3semidirect
216. C3×Dic3⋊C4C2×D3semidirect
225. Dic3⋊Dic3C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
565. C4⋊Dic3D32semidirect
575. Dic3⋊C4D32semidirect
723. C33#551semidirect
1047. C32#5637semidirect
1048. C32#5705semidirect
1049. C32#5705semidirect
1149. C3#10594165semidirect
1150. C3#10594654semidirect
1151. C3#10594655semidirect

Maximal subgroups

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

subgroupindex
#117236832
#117235422
#117234982
#117234942
C3×#638952
C3×#638622
C3×#638582
#117230052
#117229992
#117229962
#117229732
#117229332
#117229202
#117229062
#117229042
#105946553
#105946543
#105941653