Finite Group Databasebeta

← #13168512

Subgroups — #13168512

Order 1728.

1346 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723670C211yesmaximal, characteristic, complemented
2#11723539C211yesmaximal, characteristic, complemented
3#11723472C211yesmaximal, characteristic, complemented
4#11723449C211yesmaximal, characteristic, complemented
5C3×#63896C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723000C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722950C211yesmaximal, characteristic
12Dic3×#626C211yesmaximal, characteristic, complemented
13#11722920C211yesmaximal, characteristic, complemented
14#11722914C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10594655—31nomaximal
17#10594649—31nomaximal
18#10594164—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic, complemented
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic, complemented
33C32×Dic3⋊C4C2211yescharacteristic, complemented
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic, complemented
36#88813C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64106—31no—
55#64102—31no—
56C22⋊C4×C3⋊D3—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#896—31no—
60C3×#894—31no—
61C3×#886—31no—
62C3×#878—31no—
63#63981—31no—
64Dic3×#67—31no—
65C2×#3722—31no—
66#63955—31no—
67#63923—31no—
68#63922—31no—
69#63921—31no—
70#63921—31no—
71#63921—61no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63913—31no—
75#63907—31no—
76#63907—31no—
77C4×#626—31no—
78#63897—31no—
79#63896D311yescharacteristic, complemented
80Dic3×D12—31no—
81#63891—31no—
82#63890—31no—
83#63890D311yescharacteristic, complemented
84#63881—31no—
85#63881—31no—
86#63881—61no—
87#63878—31no—
88#63871—31no—
89#63871—31no—
90#63871—61no—
91#63862—31no—
92#63861—31no—
93#63854—31no—
94#63853—31no—
95#63853—31no—
96#63849—31no—
97#63848—31no—
98#63848D311yescharacteristic, complemented
99#63841—31no—
100#63836—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
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
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C4×C3⋊(C3⋊D3)—41no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×#634—41no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6295—41no—
123#6292—22no—
124#6289—22no—
125Dic3×C3⋊D3—41no—
126C3×#626—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5705—91no—
130#5658—91no—
131#5637—91no—
132C23×C3⋊D3—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×D32—61no—
136C2×C4⋊(C3⋊D3)—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—31no—
142C2×C4×C3⋊D3—61no—
143C2×C4×C3⋊D3—61no—
144C2×C4×C3⋊D3—61no—
145C2×C4×C3⋊D3—121no—
146C2×#634C2×D311yescharacteristic, complemented
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C2×C3×D12—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—61no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—61no—
161C2×#626C2×D311yescharacteristic
162C2×#625—31no—
163C2×#624—31no—
164C2×#624—31no—
165C2×#624—61no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—61no—
169C2×D3×Dic3C2×D311yescharacteristic
170C2×D3×Dic3C2×D311yescharacteristic
171C32×C4⋊C4—31no—
172C32×C4⋊C4—31no—
173C32×C22⋊C4—31no—
174#3757—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752C2×D311yescharacteristic
180#3752C2×D311yescharacteristic, complemented
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—31no—
183C4×C3⋊Dic3—31no—
184C3×#217—31no—
185C3×(C2×D3)⋊C4—21no—
186C3×(C2×D3)⋊C4—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—61no—
198C3×(C2×D3)⋊C4—61no—
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×(C2×D3)⋊C4C2×D311yescharacteristic
201C3×C4⋊Dic3—21no—
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⋊C4C2×D311yescharacteristic, complemented
214C3×Dic3⋊C4C2×D311yescharacteristic, complemented
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217#3724C2×D311yescharacteristic, complemented
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic, complemented
225Dic3⋊Dic3C2×D311yescharacteristic, complemented
226Dic3⋊Dic3C2×D311yescharacteristic, complemented
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—61no—
236#3722—61no—
237#3722—61no—
238#3722C2×D311yescharacteristic
239#3722C2×D311yescharacteristic
240#3722C2×D311yescharacteristic, complemented
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)#4112yes—
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×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—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#123—91no—
286C3×C22⋊Q8—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290D4×Dic3—91no—
291C4×#67—91no—
292C2×(C2×D3)⋊C4—91no—
293C2×(C2×D3)⋊C4—91no—
294#926—91no—
295#898—31no—
296#898—31no—
297#898—91no—
298#898—91no—
299#897—91no—
300#897—91no—
301#897—181no—
302#896—31no—
303#894—31no—
304#894—91no—
305#894—91no—
306#894—91no—
307#893—91no—
308#893—91no—
309#893—181no—
310#892—91no—
311#892—91no—
312#892—91no—
313#886—31no—
314#886—91no—
315#885—91no—
316#885—91no—
317#883—91no—
318#883—91no—
319#882—91no—
320#882—91no—
321#67⋊C4—91no—
322D3×C22⋊C4—91no—
323D3×C22⋊C4—91no—
324D3×C22⋊C4—91no—
325D3×C22⋊C4—91no—
326D3×C22⋊C4—181no—
327#879—91no—
328#878—31no—
329#877—91no—
330C4×D12—91no—
331#872—91no—
332C23×C32—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—62no—
340C22×C3⋊D3—62no—
341C22×C3⋊D3—121no—
342C22×C3⋊D3—121no—
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3—61no—
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C2×D32—62no—
355C2×D32—62no—
356C2×D32—64no—
357C2×D32—62no—
358C2×D32—62no—
359C2×D32—122no—
360C2×D32—121no—
361C2×D32—121no—
362C2×D32—122no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—31no—
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
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C4⋊(C3⋊D3)—62no—
387C4×C3⋊D3—62no—
388C4×C3⋊D3—121no—
389C4×C3⋊D3—121no—
390C4×C3⋊D3—121no—
391C4×C3⋊D3—122no—
392C4×C3⋊D3—121no—
393C4×C3⋊D3—122no—
394C4×C3⋊D3—122no—
395C4×C3⋊D3—124no—
396#634—41no—
397C3×#67—62no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
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—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—62no—
416C2×C3×Dic3—121no—
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
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C3×D12—62no—
428C3×C4×D3—62no—
429C3×C4×D3—121no—
430C3×Dic6—121no—
431C3×Dic6—121no—
432C3×Dic6—122no—
433#626—22no—
434#626—62no—
435#626—62no—
436#626—64no—
437#626—121no—
438#626—121no—
439#625—121no—
440#624—62no—
441#624—62no—
442#624—122no—
443D3×Dic3—22no—
444D3×Dic3—41no—
445D3×Dic3—121no—
446D3×Dic3—121no—
447D3×Dic3—122no—
448#551—271noSylow
449C2×C33C2×#4111yescharacteristic
450C2×C33C2×#4111yescharacteristic
451C2×C33H(5,𝔽2)11yescharacteristic
452C3⋊(C3⋊D3)—22no—
453C3×C3⋊D3—41no—
454C3×C3⋊D3—41no—
455C32×D3—22no—
456C23×D3—91no—
457C23×D3—91no—
458C23×D3—91no—
459C23×D3—181no—
460C2×C3×Q8—91no—
461C2×C3×D4—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C2×#67—31no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—91no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—91no—
471C2×D12—31no—
472C2×D12—91no—
473C2×D12—91no—
474C2×D12—91no—
475C2×D12—181no—
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—181no—
487C2×C4×D3—181no—
488C2×C4×D3—181no—
489C2×C4×D3—181no—
490C2×C4×D3—181no—
491C2×C4×D3—361no—
492C2×Dic6—31no—
493C2×Dic6—31no—
494C2×Dic6—61no—
495C3×C4⋊C4—31no—
496C3×C4⋊C4—31no—
497C3×C4⋊C4—31no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—61no—
500C3×C4⋊C4—61no—
501C3×C4⋊C4—91no—
502C3×C4⋊C4—91no—
503C3×C4⋊C4—91no—
504C3×C4⋊C4—91no—
505C3×C22⋊C4—31no—
506C3×C22⋊C4—31no—
507C3×C22⋊C4—61no—
508C3×C22⋊C4—91no—
509C3×C22⋊C4—91no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C42—91no—
515#217—31no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—181no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
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—31no—
533(C2×D3)⋊C4—61no—
534(C2×D3)⋊C4—61no—
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—181no—
552(C2×D3)⋊C4—181no—
553(C2×D3)⋊C4—181no—
554(C2×D3)⋊C4—181no—
555(C2×D3)⋊C4D3211yescharacteristic
556C4⋊Dic3—31no—
557C4⋊Dic3—31no—
558C4⋊Dic3—31no—
559C4⋊Dic3—91no—
560C4⋊Dic3—91no—
561C4⋊Dic3—91no—
562C4⋊Dic3—91no—
563C4⋊Dic3—181no—
564C4⋊Dic3—181no—
565C4⋊Dic3D3211yescharacteristic, complemented
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4D3211yescharacteristic, complemented
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—181no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—32no—
587C22×C32—41no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32C23×D311yescharacteristic
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3—21no—
598C2×C3⋊D3—21no—
599C2×C3⋊D3—32no—
600C2×C3⋊D3—32no—
601C2×C3⋊D3—32no—
602C2×C3⋊D3—62no—
603C2×C3⋊D3—62no—
604C2×C3⋊D3—62no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—62no—
608C2×C3⋊D3—62no—
609C2×C3⋊D3—61no—
610C2×C3⋊D3—61no—
611C2×C3⋊D3—61no—
612C2×C3⋊D3—61no—
613C2×C3⋊D3—122no—
614C2×C3⋊D3—121no—
615C2×C3⋊D3—121no—
616C2×C3⋊D3—121no—
617C2×C3⋊D3—121no—
618C2×C3⋊D3—122no—
619C2×C3⋊D3—122no—
620C2×C3⋊D3—124no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—22no—
626C2×C3×D3—41no—
627C2×C3×D3—41no—
628C2×C3×D3—62no—
629C2×C3×D3—62no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3—121no—
645C2×C3×D3—121no—
646C2×C3×D3#23712yes—
647C2×C3×D3#23912yes—
648D32—124no—
649D32—124no—
650D32—128no—
651C32×C4—21no—
652C32×C4—22no—
653C32×C4—21no—
654C32×C4—21no—
655C32×C4—41no—
656C32×C4—41no—
657C32×C4—42no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—61no—
661C32×C4—61no—
662C32×C4—61no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—21no—
667C3⋊Dic3—61no—
668C3⋊Dic3—62no—
669C3⋊Dic3—61no—
670C3⋊Dic3—61no—
671C3⋊Dic3—121no—
672C3⋊Dic3—121no—
673C3⋊Dic3—122no—
674C3×Dic3—22no—
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—41no—
686C3×Dic3—41no—
687C3×Dic3—41no—
688C3×Dic3—41no—
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—
699C3×Dic3—121no—
700C3×Dic3—121no—
701#126—91no—
702#126—271no—
703#124—271no—
704#123—91no—
705#123—271no—
706#123—271no—
707C22⋊Q8—91no—
708C22⋊Q8—271no—
709#120—271no—
710C4×D4—271no—
711C4×D4—271no—
712#117—271no—
713#117—271no—
714C2×C22⋊C4—271no—
715C2×C22⋊C4—271no—
716C33#55111yescharacteristic, complemented, Sylow
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—61no—
720C23×C3—91no—
721C23×C3—91no—
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—61no—
727C22×D3—61no—
728C22×D3—91no—
729C22×D3—91no—
730C22×D3—91no—
731C22×D3—181no—
732C22×D3—181no—
733C22×D3—181no—
734C22×D3—182no—
735C22×D3—182no—
736C22×D3—182no—
737C22×D3—182no—
738C22×D3—182no—
739C22×D3—184no—
740C22×D3—182no—
741C22×D3—361no—
742C22×D3—362no—
743C22×D3—361no—
744C22×D3—361no—
745C22×D3—361no—
746C22×D3—362no—
747C22×D3C2×D3211yescharacteristic
748C3×Q8—361no—
749C3×D4—182no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—31no—
762C2×C3×C4—31no—
763C2×C3×C4—41no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—61no—
768C2×C3×C4—61no—
769C2×C3×C4—91no—
770C2×C3×C4—91no—
771C2×C3×C4—91no—
772C2×C3×C4—91no—
773C2×C3×C4—182no—
774C2×C3×C4—361no—
775C2×C3×C4C2×D3211yescharacteristic
776C2×C3×C4C2×D3211yescharacteristic
777C2×C3×C4C2×D3211yescharacteristic
778#67—62no—
779#67—182no—
780#67—361no—
781#67—361no—
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—61no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—62no—
795C2×Dic3—91no—
796C2×Dic3—91no—
797C2×Dic3—91no—
798C2×Dic3—121no—
799C2×Dic3—181no—
800C2×Dic3—181no—
801C2×Dic3—181no—
802C2×Dic3—361no—
803C2×Dic3—361no—
804C2×Dic3C2×D3211yescharacteristic
805C2×Dic3C2×D3211yescharacteristic
806C2×Dic3C2×D3211yescharacteristic
807C2×Dic3C2×D3211yescharacteristic
808C2×Dic3C2×D3211yescharacteristic
809D12—62no—
810D12—182no—
811D12—182no—
812D12—184no—
813D12—361no—
814C4×D3—62no—
815C4×D3—121no—
816C4×D3—182no—
817C4×D3—182no—
818C4×D3—182no—
819C4×D3—362no—
820C4×D3—361no—
821C4×D3—361no—
822C4×D3—361no—
823C4×D3—362no—
824C4×D3—361no—
825C4×D3—361no—
826C4×D3—362no—
827C4×D3—362no—
828C4×D3—362no—
829C4×D3—364no—
830Dic6—121no—
831Dic6—121no—
832Dic6—122no—
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—21no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—41no—
845C2×C32—62no—
846C2×C32C2×#23711yescharacteristic
847C2×C32#100411yescharacteristic
848C2×C32C2×#23911yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32D3×#4111yescharacteristic
852C2×C32D3×#4111yescharacteristic
853C2×C32#100911yescharacteristic
854C2×C32#100911yescharacteristic
855C3⋊D3—41no—
856C3⋊D3—41no—
857C3⋊D3—62no—
858C3⋊D3—64no—
859C3⋊D3—62no—
860C3⋊D3—62no—
861C3⋊D3—122no—
862C3⋊D3—122no—
863C3⋊D3—124no—
864C3×D3—22no—
865C3×D3—22no—
866C3×D3—42no—
867C3×D3—122no—
868C3×D3—122no—
869C3×D3—121no—
870C3×D3—121no—
871C3×D3—121no—
872C3×D3—121no—
873C24—271no—
874C2×Q8—91no—
875C2×D4—91no—
876C2×D4—271no—
877C2×D4—271no—
878C22×C4—91no—
879C22×C4—91no—
880C22×C4—271no—
881C22×C4—271no—
882C22×C4—271no—
883C4⋊C4—31no—
884C4⋊C4—31no—
885C4⋊C4—91no—
886C4⋊C4—91no—
887C4⋊C4—91no—
888C4⋊C4—91no—
889C4⋊C4—271no—
890C4⋊C4—271no—
891C22⋊C4—31no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—91no—
896C22⋊C4—91no—
897C22⋊C4—91no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C22⋊C4—271no—
902C22⋊C4—271no—
903C22⋊C4—271no—
904C22⋊C4—271no—
905C42—91no—
906C42—271no—
907C42—271no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—32no—
912C22×C3—32no—
913C22×C3—41no—
914C22×C3—62no—
915C22×C3—61no—
916C22×C3—61no—
917C22×C3—61no—
918C22×C3—61no—
919C22×C3—121no—
920C22×C3—121no—
921C22×C3—181no—
922C22×C3—181no—
923C22×C3—181no—
924C22×C3—181no—
925C22×C3—181no—
926C22×C3—181no—
927C22×C3C22×D3211yescharacteristic
928C22×C3C22×D3211yescharacteristic
929C22×C3C22×D3211yescharacteristic
930C2×D3—21no—
931C2×D3—21no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—92no—
947C2×D3—92no—
948C2×D3—92no—
949C2×D3—121no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3—121no—
953C2×D3—182no—
954C2×D3—182no—
955C2×D3—182no—
956C2×D3—182no—
957C2×D3—182no—
958C2×D3—181no—
959C2×D3—181no—
960C2×D3—181no—
961C2×D3—181no—
962C2×D3—181no—
963C2×D3—181no—
964C2×D3—362no—
965C2×D3—361no—
966C2×D3—361no—
967C2×D3—361no—
968C2×D3—361no—
969C2×D3—362no—
970C2×D3—362no—
971C2×D3—364no—
972C2×D3—364no—
973C2×D3—364no—
974C2×D3—368no—
975C2×D3#379612yes—
976C3×C4—22no—
977C3×C4—21no—
978C3×C4—21no—
979C3×C4—21no—
980C3×C4—41no—
981C3×C4—41no—
982C3×C4—42no—
983C3×C4—62no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—61no—
990C3×C4—61no—
991C3×C4—61no—
992C3×C4—61no—
993C3×C4—61no—
994C3×C4—121no—
995C3×C4—121no—
996C3×C4—121no—
997C3×C4—121no—
998C3×C4—181no—
999C3×C4—181no—
1000C3×C4—181no—
1001C3×C4—181no—
1002Dic3—21no—
1003Dic3—21no—
1004Dic3—21no—
1005Dic3—21no—
1006Dic3—21no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—121no—
1016Dic3—121no—
1017Dic3—121no—
1018Dic3—121no—
1019Dic3—182no—
1020Dic3—181no—
1021Dic3—181no—
1022Dic3—181no—
1023Dic3—361no—
1024Dic3—361no—
1025Dic3—362no—
1026C32—21no—
1027C32—21no—
1028C32—21no—
1029C32—41no—
1030C32#563711yescharacteristic, complemented
1031C32#565811yescharacteristic, complemented
1032C32#570511yescharacteristic, complemented
1033C23—31no—
1034C23—91no—
1035C23—91no—
1036C23—271no—
1037C23—542no—
1038C23—542no—
1039C23—1081no—
1040Q8—361no—
1041D4—182no—
1042D4—542no—
1043D4—1081no—
1044C2×C4—31no—
1045C2×C4—31no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—31no—
1049C2×C4—91no—
1050C2×C4—91no—
1051C2×C4—91no—
1052C2×C4—91no—
1053C2×C4—182no—
1054C2×C4—271no—
1055C2×C4—361no—
1056C2×C4—542no—
1057C2×C4—1081no—
1058C2×C4—1081no—
1059C2×C4D3311yescharacteristic
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—21no—
1069C2×C3—41no—
1070C2×C3—41no—
1071C2×C3—41no—
1072C2×C3—62no—
1073C2×C3—62no—
1074C2×C3—122no—
1075C2×C3—361no—
1076C2×C3—361no—
1077C2×C3C2×#379611yescharacteristic
1078C2×C3#6430611yescharacteristic
1079C2×C3#6430811yescharacteristic
1080C2×C3D3×#23711yescharacteristic
1081C2×C3#6431211yescharacteristic
1082C2×C3#6431411yescharacteristic
1083C2×C3#6431411yescharacteristic
1084C2×C3D3×#23911yescharacteristic
1085C2×C3#6431911yescharacteristic
1086D3—22no—
1087D3—122no—
1088D3—122no—
1089D3—121no—
1090D3—121no—
1091D3—121no—
1092D3—121no—
1093D3—184no—
1094D3—182no—
1095D3—182no—
1096D3—182no—
1097D3—362no—
1098D3—362no—
1099D3—364no—
1100C22—32no—
1101C22—61no—
1102C22—61no—
1103C22—181no—
1104C22—181no—
1105C22—181no—
1106C22—181no—
1107C22—181no—
1108C22—181no—
1109C22—272no—
1110C22—541no—
1111C22—541no—
1112C22—1084no—
1113C22C2×D3311yescharacteristic
1114C4—21no—
1115C4—61no—
1116C4—61no—
1117C4—61no—
1118C4—61no—
1119C4—61no—
1120C4—181no—
1121C4—181no—
1122C4—181no—
1123C4—181no—
1124C4—541no—
1125C3—21no—
1126C3—21no—
1127C3—21no—
1128C3—41no—
1129C3#1059416411yescharacteristic, complemented
1130C3#1059464911yescharacteristic, complemented
1131C3#1059465511yescharacteristic, complemented
1132C2—62no—
1133C2—361no—
1134C2—361no—
1135C2—542no—
1136C2D3×#379611yescharacteristic
1137C2#1172437611yescharacteristic
1138C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722950C2
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. #11723670C2semidirect
2. #11723539C2semidirect
3. #11723472C2semidirect
4. #11723449C2semidirect
5. C3×#63896C2semidirect
6. C3×#63890C2semidirect
7. C3×#63848C2semidirect
8. #11723027C2semidirect
9. #11723000C2semidirect
10. #11722997C2semidirect
12. Dic3×#626C2semidirect
13. #11722920C2semidirect
14. #11722914C2semidirect
15. D3×#3722C2semidirect
21. C2×C3×#634C22semidirect
25. C2×Dic3×C3⋊D3C22semidirect
30. C3×#3752C22semidirect
32. C32×C4⋊Dic3C22semidirect
33. C32×Dic3⋊C4C22semidirect
35. #88814C22semidirect
36. #88813C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
79. #63896D3semidirect
83. #63890D3semidirect
98. #63848D3semidirect
146. C2×#634C2×D3semidirect
180. #3752C2×D3semidirect
205. C3×C4⋊Dic3C2×D3semidirect
206. C3×C4⋊Dic3C2×D3semidirect
213. C3×Dic3⋊C4C2×D3semidirect
214. C3×Dic3⋊C4C2×D3semidirect
217. #3724C2×D3semidirect
224. Dic3⋊Dic3C2×D3semidirect
225. Dic3⋊Dic3C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
240. #3722C2×D3semidirect
258. Dic32C2×D3semidirect
565. C4⋊Dic3D32semidirect
573. Dic3⋊C4D32semidirect
716. C33#551semidirect
1030. C32#5637semidirect
1031. C32#5658semidirect
1032. C32#5705semidirect
1129. C3#10594164semidirect
1130. C3#10594649semidirect
1131. C3#10594655semidirect

Maximal subgroups

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

subgroupindex
#117236702
#117235392
#117234722
#117234492
C3×#638962
C3×#638902
C3×#638482
#117230272
#117230002
#117229972
#117229502
Dic3×#6262
#117229202
#117229142
D3×#37222
#105946553
#105946493
#105941643