Finite Group Databasebeta

← #13169270

Subgroups — #13169270

Order 1728.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723700C211yesmaximal, characteristic, complemented
2#11723504C211yesmaximal, characteristic, complemented
3#11723493C211yesmaximal, characteristic, complemented
4#11723417C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63849C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722952C211yesmaximal, characteristic
12#11722937C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic, complemented
14#11722919C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10594654—31nomaximal
17#10594643—31nomaximal
18#10594641—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6289C2211yescharacteristic, complemented
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#624C2211yescharacteristic
29#88859C2211yescharacteristic, complemented
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic, complemented
33C32×C4⋊Dic3C2211yescharacteristic, complemented
34C32×Dic3⋊C4C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×Dic32C2211yescharacteristic, complemented
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64103—31no—
55#64103—31no—
56#64103—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#897—31no—
60C3×#896—31no—
61C3×#892—31no—
62C3×#892—31no—
63#63923—31no—
64#63923—31no—
65#63923—31no—
66#63921—31no—
67#63921—31no—
68D3×(C2×D3)⋊C4—31no—
69D3×(C2×D3)⋊C4—31no—
70D3×(C2×D3)⋊C4—31no—
71D3×(C2×D3)⋊C4—31no—
72#63907—31no—
73#63904—31no—
74C4×#626—31no—
75#63899—31no—
76#63895D311yescharacteristic, complemented
77#63894—31no—
78#63894—31no—
79#63890—31no—
80#63890—31no—
81#63890—61no—
82#63888—31no—
83#63887—31no—
84#63881—31no—
85#63880—31no—
86#63877—31no—
87#63877—31no—
88#63874—31no—
89#63868—31no—
90#63864—31no—
91#63859—31no—
92#63858—31no—
93#63854—31no—
94#63854—31no—
95#63854—61no—
96#63852—31no—
97#63850—31no—
98#63850—31no—
99#63850—61no—
100#63849D311yescharacteristic, complemented
101#63848D311yescharacteristic, complemented
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C2×#1113—22no—
107C2×#1113—22no—
108C2×#1113—41no—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4×C3⋊D3—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6294—41no—
122#6292—22no—
123#6292—22no—
124#6292—41no—
125#6289—41no—
126Dic3×C3⋊D3—22no—
127C3×#627—41no—
128C3×#624—41no—
129#5705—91no—
130#5637—91no—
131#5527—91no—
132C22×D32—31no—
133C22×D32—31no—
134C22×D32—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4⋊(C3⋊D3)—31no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3C2×D311yescharacteristic
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—61no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×#627C2×D311yescharacteristic, complemented
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—61no—
156C2×#626—61no—
157C2×#626—61no—
158C2×#624—31no—
159C2×#624—31no—
160C2×#624—31no—
161C2×#624—61no—
162C2×#624C2×D311yescharacteristic
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—61no—
168C32×C4⋊C4—31no—
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—61no—
179#3752—61no—
180#3752—61no—
181#3752—121no—
182#3752C2×D311yescharacteristic
183#3752C2×D311yescharacteristic
184#3750—31no—
185#3750—31no—
186#3750—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
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—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—61no—
202C3×(C2×D3)⋊C4—61no—
203C3×C4⋊Dic3—21no—
204C3×C4⋊Dic3—21no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3C2×D311yescharacteristic, complemented
208C3×C4⋊Dic3C2×D311yescharacteristic, complemented
209C3×C4⋊Dic3C2×D311yescharacteristic, complemented
210C3×C4⋊Dic3C2×D311yescharacteristic, complemented
211C3×Dic3⋊C4—21no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4C2×D311yescharacteristic, complemented
215C3×Dic3⋊C4C2×D311yescharacteristic, complemented
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226#3724—61no—
227#3724—61no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic, complemented
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—61no—
240#3722—61no—
241#3722C2×D311yescharacteristic
242#3722C2×D311yescharacteristic
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic
245#3722C2×D311yescharacteristic
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256Dic32C2×D311yescharacteristic, complemented
257Dic32C2×D311yescharacteristic, complemented
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—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3#4112yes—
271C2×C3×C3⋊D3#4112yes—
272#1113—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×C22⋊Q8—91no—
286C3×#117—91no—
287#947—91no—
288#946—91no—
289#929—91no—
290C4×#67—91no—
291C2×(C2×D3)⋊C4—91no—
292C2×(C2×D3)⋊C4—91no—
293#898—31no—
294#898—31no—
295#898—91no—
296#897—31no—
297#896—31no—
298#896—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#894—91no—
303#894—91no—
304#894—91no—
305#894—181no—
306#894—181no—
307#894—181no—
308#893—91no—
309#893—91no—
310#892—31no—
311#892—31no—
312#886—91no—
313#885—91no—
314#883—91no—
315#882—91no—
316#882—91no—
317#882—91no—
318#67⋊C4—91no—
319D3×C22⋊C4—91no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322D3×C22⋊C4—91no—
323#879—91no—
324#878—91no—
325#877—91no—
326#876—91no—
327#875—91no—
328C4×D12—91no—
329C4×D12—91no—
330#872—91no—
331#872—91no—
332C22×C3⋊D3—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—61no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—121no—
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D311yescharacteristic
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—61no—
349C22×C3×D3—61no—
350C22×C3×D3—61no—
351C2×D32—62no—
352C2×D32—62no—
353C2×D32—62no—
354C2×D32—62no—
355C2×D32—62no—
356C2×D32—62no—
357C2×D32—121no—
358C2×D32—121no—
359C2×D32—121no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—41no—
370C2×C32×C4C22×D311yescharacteristic
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
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—121no—
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C4⋊(C3⋊D3)—62no—
384C4⋊(C3⋊D3)—62no—
385C4⋊(C3⋊D3)—121no—
386C4×C3⋊D3—22no—
387C4×C3⋊D3—62no—
388C4×C3⋊D3—121no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
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—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C3×C4×D3—62no—
417C3×C4×D3—62no—
418C3×C4×D3—122no—
419C3×C4×D3—121no—
420C3×C4×D3—121no—
421C3×Dic6—121no—
422C3×Dic6—121no—
423#627—41no—
424#626—62no—
425#626—62no—
426#626—62no—
427#626—62no—
428#626—122no—
429#626—122no—
430#626—121no—
431#626—121no—
432#626—122no—
433#624—41no—
434#624—121no—
435#624—121no—
436#624—122no—
437#624—121no—
438D3×Dic3—62no—
439D3×Dic3—62no—
440D3×Dic3—122no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443#551—271noSylow
444C2×C33C2×#4111yescharacteristic
445C2×C33C2×#4111yescharacteristic
446C2×C33H(5,𝔽2)11yescharacteristic
447C3⋊(C3⋊D3)—41no—
448C3×C3⋊D3—22no—
449C3×C3⋊D3—22no—
450C3×C3⋊D3—41no—
451C23×D3—91no—
452C23×D3—91no—
453C23×D3—91no—
454C2×C3×Q8—91no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C2×#67—91no—
458C2×#67—91no—
459C2×#67—91no—
460C22×Dic3—91no—
461C22×Dic3—91no—
462C2×D12—91no—
463C2×D12—91no—
464C2×D12—91no—
465C2×D12—91no—
466C2×D12—91no—
467C2×D12—91no—
468C2×D12—181no—
469C2×D12—181no—
470C2×D12—181no—
471C2×C4×D3—31no—
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×C4×D3—31no—
475C2×C4×D3—61no—
476C2×C4×D3—91no—
477C2×C4×D3—91no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—181no—
484C2×C4×D3—181no—
485C2×Dic6—31no—
486C2×Dic6—31no—
487C3×C4⋊C4—31no—
488C3×C4⋊C4—31no—
489C3×C4⋊C4—31no—
490C3×C4⋊C4—31no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—61no—
494C3×C4⋊C4—61no—
495C3×C4⋊C4—61no—
496C3×C4⋊C4—91no—
497C3×C4⋊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—
504C3×C22⋊C4—91no—
505C3×C42—91no—
506C3×C42—91no—
507C3×C42—91no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—91no—
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—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—61no—
527(C2×D3)⋊C4—61no—
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—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—181no—
546(C2×D3)⋊C4—181no—
547(C2×D3)⋊C4—181no—
548(C2×D3)⋊C4—181no—
549(C2×D3)⋊C4—181no—
550(C2×D3)⋊C4—181no—
551(C2×D3)⋊C4—181no—
552(C2×D3)⋊C4—361no—
553C4⋊Dic3—31no—
554C4⋊Dic3—31no—
555C4⋊Dic3—91no—
556C4⋊Dic3D3211yescharacteristic, complemented
557C4⋊Dic3D3211yescharacteristic, complemented
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—181no—
569Dic3⋊C4—181no—
570Dic3⋊C4—181no—
571Dic3⋊C4D3211yescharacteristic, complemented
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—41no—
582C22×C32C23×D311yescharacteristic
583C22×C32C23×D311yescharacteristic
584C22×C32C23×D311yescharacteristic
585C2×C3⋊D3—21no—
586C2×C3⋊D3—21no—
587C2×C3⋊D3—21no—
588C2×C3⋊D3—21no—
589C2×C3⋊D3—21no—
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—61no—
593C2×C3⋊D3—62no—
594C2×C3⋊D3—61no—
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—121no—
603C2×C3⋊D3—121no—
604C2×C3⋊D3—122no—
605C2×C3⋊D3—121no—
606C2×C3⋊D3—121no—
607C2×C3⋊D3—121no—
608C2×C3⋊D3—121no—
609C2×C3⋊D3—121no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—241no—
612C2×C3⋊D3—241no—
613C2×C3⋊D3#23512yes—
614C2×C3⋊D3#23912yes—
615C2×C3×D3—32no—
616C2×C3×D3—32no—
617C2×C3×D3—32no—
618C2×C3×D3—32no—
619C2×C3×D3—62no—
620C2×C3×D3—62no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—121no—
636C2×C3×D3—121no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642D32—124no—
643D32—124no—
644D32—124no—
645C32×C4—21no—
646C32×C4—21no—
647C32×C4—21no—
648C32×C4—41no—
649C32×C4—41no—
650C32×C4—41no—
651C32×C4—61no—
652C32×C4—61no—
653C32×C4—61no—
654C32×C4—61no—
655C32×C4—61no—
656C32×C4—61no—
657C32×C4—81no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3⋊Dic3—21no—
661C3⋊Dic3—61no—
662C3⋊Dic3—61no—
663C3⋊Dic3—61no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—241no—
668C3×Dic3—21no—
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—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—41no—
681C3×Dic3—41no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695#126—91no—
696#126—271no—
697#124—271no—
698#123—271no—
699#123—271no—
700#123—271no—
701C22⋊Q8—91no—
702C22⋊Q8—271no—
703#120—271no—
704C4×D4—271no—
705C4×D4—271no—
706#117—91no—
707#117—271no—
708C2×C22⋊C4—271no—
709C2×C22⋊C4—271no—
710C33#55111yescharacteristic, complemented, Sylow
711C23×C3—91no—
712C23×C3—91no—
713C23×C3—91no—
714C22×D3—31no—
715C22×D3—31no—
716C22×D3—31no—
717C22×D3—31no—
718C22×D3—31no—
719C22×D3—31no—
720C22×D3—61no—
721C22×D3—61no—
722C22×D3—61no—
723C22×D3—91no—
724C22×D3—91no—
725C22×D3—91no—
726C22×D3—181no—
727C22×D3—181no—
728C22×D3—181no—
729C22×D3—182no—
730C22×D3—182no—
731C22×D3—182no—
732C22×D3—182no—
733C22×D3—182no—
734C22×D3—182no—
735C22×D3—361no—
736C22×D3—361no—
737C22×D3—361no—
738C22×D3—361no—
739C3×Q8—361no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—41no—
756C2×C3×C4—61no—
757C2×C3×C4—61no—
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—182no—
766C2×C3×C4—361no—
767C2×C3×C4C2×D3211yescharacteristic
768C2×C3×C4C2×D3211yescharacteristic
769C2×C3×C4C2×D3211yescharacteristic
770#67—182no—
771#67—182no—
772#67—361no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—61no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—91no—
783C2×Dic3—91no—
784C2×Dic3—91no—
785C2×Dic3—181no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—182no—
789C2×Dic3—361no—
790C2×Dic3—361no—
791C2×Dic3C2×D3211yescharacteristic
792C2×Dic3C2×D3211yescharacteristic
793C2×Dic3C2×D3211yescharacteristic
794C2×Dic3C2×D3211yescharacteristic
795C2×Dic3C2×D3211yescharacteristic
796C2×Dic3C2×D3211yescharacteristic
797D12—182no—
798D12—182no—
799D12—182no—
800D12—182no—
801D12—362no—
802D12—362no—
803D12—361no—
804D12—361no—
805D12—362no—
806C4×D3—62no—
807C4×D3—62no—
808C4×D3—122no—
809C4×D3—121no—
810C4×D3—121no—
811C4×D3—182no—
812C4×D3—182no—
813C4×D3—362no—
814C4×D3—361no—
815C4×D3—361no—
816C4×D3—361no—
817C4×D3—361no—
818C4×D3—361no—
819C4×D3—362no—
820Dic6—121no—
821Dic6—121no—
822C2×C32—21no—
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—41no—
832C2×C32—41no—
833C2×C32—41no—
834C2×C32C2×#23511yescharacteristic
835C2×C32#100411yescharacteristic
836C2×C32C2×#23911yescharacteristic
837C2×C32D3×#4111yescharacteristic
838C2×C32D3×#4111yescharacteristic
839C2×C32D3×#4111yescharacteristic
840C2×C32D3×#4111yescharacteristic
841C2×C32#100911yescharacteristic
842C2×C32#100911yescharacteristic
843C3⋊D3—22no—
844C3⋊D3—22no—
845C3⋊D3—41no—
846C3⋊D3—121no—
847C3⋊D3—122no—
848C3⋊D3—121no—
849C3⋊D3—121no—
850C3⋊D3—241no—
851C3⋊D3—241no—
852C3⋊D3—242no—
853C3×D3—62no—
854C3×D3—62no—
855C3×D3—62no—
856C3×D3—62no—
857C3×D3—122no—
858C3×D3—122no—
859C3×D3—121no—
860C3×D3—121no—
861C3×D3—241no—
862C24—271no—
863C2×Q8—91no—
864C2×D4—271no—
865C2×D4—271no—
866C2×D4—271no—
867C22×C4—91no—
868C22×C4—91no—
869C22×C4—271no—
870C22×C4—271no—
871C22×C4—271no—
872C4⋊C4—31no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—91no—
876C4⋊C4—91no—
877C4⋊C4—271no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C22⋊C4—91no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C22⋊C4—271no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C42—91no—
895C42—91no—
896C42—91no—
897C22×C3—21no—
898C22×C3—21no—
899C22×C3—21no—
900C22×C3—41no—
901C22×C3—92no—
902C22×C3—92no—
903C22×C3—181no—
904C22×C3—181no—
905C22×C3—181no—
906C22×C3—181no—
907C22×C3—181no—
908C22×C3—181no—
909C22×C3—181no—
910C22×C3C22×D3211yescharacteristic
911C22×C3C22×D3211yescharacteristic
912C22×C3C22×D3211yescharacteristic
913C2×D3—32no—
914C2×D3—32no—
915C2×D3—32no—
916C2×D3—32no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—61no—
920C2×D3—61no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—121no—
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—721no—
963C2×D3—721no—
964C3×C4—21no—
965C3×C4—21no—
966C3×C4—21no—
967C3×C4—41no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—81no—
983C3×C4—121no—
984C3×C4—121no—
985C3×C4—121no—
986C3×C4—121no—
987C3×C4—121no—
988C3×C4—121no—
989C3×C4—181no—
990C3×C4—181no—
991C3×C4—181no—
992Dic3—21no—
993Dic3—21no—
994Dic3—21no—
995Dic3—21no—
996Dic3—21no—
997Dic3—21no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—121no—
1005Dic3—121no—
1006Dic3—121no—
1007Dic3—181no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—361no—
1011Dic3—361no—
1012Dic3—361no—
1013Dic3—721no—
1014C32—21no—
1015C32—21no—
1016C32—21no—
1017C32—41no—
1018C32#552711yescharacteristic, complemented
1019C32#563711yescharacteristic, complemented
1020C32#570511yescharacteristic, complemented
1021C23—91no—
1022C23—91no—
1023C23—91no—
1024C23—271no—
1025C23—542no—
1026C23—542no—
1027C23—1081no—
1028Q8—361no—
1029D4—542no—
1030D4—542no—
1031D4—1081no—
1032C2×C4—31no—
1033C2×C4—31no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—182no—
1042C2×C4—271no—
1043C2×C4—361no—
1044C2×C4—542no—
1045C2×C4—1081no—
1046C2×C4—1081no—
1047C2×C4D3311yescharacteristic
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—41no—
1058C2×C3—41no—
1059C2×C3—41no—
1060C2×C3—182no—
1061C2×C3—182no—
1062C2×C3—361no—
1063C2×C3D3×#23511yescharacteristic
1064C2×C3D3×#23511yescharacteristic
1065C2×C3#6430711yescharacteristic
1066C2×C3#6431211yescharacteristic
1067C2×C3#6431211yescharacteristic
1068C2×C3#6431411yescharacteristic
1069C2×C3D3×#23911yescharacteristic
1070C2×C3D3×#23911yescharacteristic
1071C2×C3#6432011yescharacteristic
1072D3—62no—
1073D3—62no—
1074D3—62no—
1075D3—62no—
1076D3—122no—
1077D3—122no—
1078D3—121no—
1079D3—121no—
1080D3—241no—
1081D3—362no—
1082D3—361no—
1083D3—361no—
1084D3—361no—
1085D3—721no—
1086D3—721no—
1087D3—722no—
1088C22—92no—
1089C22—92no—
1090C22—181no—
1091C22—181no—
1092C22—181no—
1093C22—181no—
1094C22—181no—
1095C22—181no—
1096C22—181no—
1097C22—541no—
1098C22—541no—
1099C22—541no—
1100C22—1084no—
1101C22C2×D3311yescharacteristic
1102C4—21no—
1103C4—61no—
1104C4—61no—
1105C4—61no—
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—541no—
1113C3—21no—
1114C3—21no—
1115C3—21no—
1116C3—41no—
1117C3#1059464111yescharacteristic, complemented
1118C3#1059464311yescharacteristic, complemented
1119C3#1059465411yescharacteristic, complemented
1120C2—182no—
1121C2—182no—
1122C2—361no—
1123C2—1081no—
1124C2#1172437711yescharacteristic
1125C2#1172438511yescharacteristic
1126C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722952C2
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. #11723700C2semidirect
2. #11723504C2semidirect
3. #11723493C2semidirect
4. #11723417C2semidirect
5. C3×#63895C2semidirect
6. C3×#63849C2semidirect
7. C3×#63848C2semidirect
8. #11723024C2semidirect
9. #11723003C2semidirect
10. #11722979C2semidirect
12. #11722937C2semidirect
13. #11722933C2semidirect
14. #11722919C2semidirect
15. #11722905C2semidirect
25. C2×#6289C22semidirect
27. C2×C3×#627C22semidirect
29. #88859C22semidirect
32. C32×C4⋊Dic3C22semidirect
33. C32×C4⋊Dic3C22semidirect
34. C32×Dic3⋊C4C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. #88806C22semidirect
40. #88804C22semidirect
41. #88804C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic32C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
76. #63895D3semidirect
100. #63849D3semidirect
101. #63848D3semidirect
148. C2×#627C2×D3semidirect
207. C3×C4⋊Dic3C2×D3semidirect
208. C3×C4⋊Dic3C2×D3semidirect
209. C3×C4⋊Dic3C2×D3semidirect
210. C3×C4⋊Dic3C2×D3semidirect
214. C3×Dic3⋊C4C2×D3semidirect
215. C3×Dic3⋊C4C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
256. Dic32C2×D3semidirect
257. Dic32C2×D3semidirect
258. Dic32C2×D3semidirect
556. C4⋊Dic3D32semidirect
557. C4⋊Dic3D32semidirect
571. Dic3⋊C4D32semidirect
710. C33#551semidirect
1018. C32#5527semidirect
1019. C32#5637semidirect
1020. C32#5705semidirect
1117. C3#10594641semidirect
1118. C3#10594643semidirect
1119. C3#10594654semidirect

Maximal subgroups

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

subgroupindex
#117237002
#117235042
#117234932
#117234172
C3×#638952
C3×#638492
C3×#638482
#117230242
#117230032
#117229792
#117229522
#117229372
#117229332
#117229192
#117229052
#105946543
#105946433
#105946413