Finite Group Databasebeta

← #13169182

Subgroups — #13169182

Order 1728.

1332 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723690C211yesmaximal, characteristic, complemented
2#11723539C211yesmaximal, characteristic, complemented
3#11723421C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63861C211yesmaximal, characteristic, complemented
7C3×#63854C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722977C211yesmaximal, characteristic, complemented
11#11722950C211yesmaximal, characteristic
12#11722933C211yesmaximal, characteristic, complemented
13#11722931C211yesmaximal, characteristic, complemented
14#11722922C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10594654—31nomaximal
17#10594653—31nomaximal
18#10594228—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic, complemented
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic, complemented
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic, complemented
34C32×Dic3⋊C4C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64103—31no—
55#64101—31no—
56C22⋊C4×C3⋊D3—31no—
57C3×#898—31no—
58C3×#897—31no—
59C3×#896—31no—
60C3×#894—31no—
61C3×#883—31no—
62C3×#879—31no—
63#63981—31no—
64#63974—31no—
65#63959—31no—
66#63956—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#63907—31no—
75#63904—31no—
76#63904—31no—
77#63904—31no—
78C4×#626—31no—
79C4×#625—31no—
80#63895D311yescharacteristic, complemented
81#63894—31no—
82#63891—31no—
83#63890—31no—
84#63888—31no—
85#63888—31no—
86#63878—31no—
87#63877—31no—
88#63865—31no—
89#63863—31no—
90#63862—31no—
91#63861D311yescharacteristic, complemented
92#63858—31no—
93#63854—31no—
94#63854D311yescharacteristic, complemented
95#63853—31no—
96#63853—31no—
97#63853—61no—
98#63849—31no—
99#63849—31no—
100#63849—61no—
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)—22no—
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#6295—22no—
122#6294—22no—
123#6292—22no—
124#6289—41no—
125C3×#627—41no—
126C3×#626—41no—
127C3×#624—41no—
128C3×#624—41no—
129#5705—91no—
130#5659—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—61no—
142C2×C4×C3⋊D3—61no—
143C2×C4×C3⋊D3—61no—
144C2×C4×C3⋊D3—121no—
145C2×C3×#67—31no—
146C2×C3×D12—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×#627C2×D311yescharacteristic, complemented
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—61no—
159C2×#626C2×D311yescharacteristic
160C2×#625—31no—
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—31no—
164C2×#624—61no—
165C2×#624C2×D311yescharacteristic
166C2×#624C2×D311yescharacteristic, complemented
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C22⋊C4—31no—
172#3757—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752C2×D311yescharacteristic
179#3752C2×D311yescharacteristic, complemented
180C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
181#3750—31no—
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×(C2×D3)⋊C4—21no—
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⋊Dic3—61no—
206C3×C4⋊Dic3C2×D311yescharacteristic, complemented
207C3×C4⋊Dic3C2×D311yescharacteristic, complemented
208C3×Dic3⋊C4—21no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
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—
218#3724—31no—
219#3724C2×D311yescharacteristic, complemented
220#3724C2×D311yescharacteristic, complemented
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—61no—
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—61no—
235#3722—61no—
236#3722—61no—
237#3722C2×D311yescharacteristic
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
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—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
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#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×#123—91no—
286C3×C22⋊Q8—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290#936—91no—
291C4×#67—91no—
292C4×#67—91no—
293C4×#67—91no—
294C2×(C2×D3)⋊C4—91no—
295#898—31no—
296#898—91no—
297#897—31no—
298#896—31no—
299#896—91no—
300#896—91no—
301#894—31no—
302#894—91no—
303#894—91no—
304#894—91no—
305#894—181no—
306#893—91no—
307#893—91no—
308#892—91no—
309#892—91no—
310#892—91no—
311#892—91no—
312#892—181no—
313#886—91no—
314#885—91no—
315#883—31no—
316#883—91no—
317#883—91no—
318#882—91no—
319#882—91no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322D3×C22⋊C4—91no—
323D3×C22⋊C4—91no—
324D3×C22⋊C4—91no—
325D3×C22⋊C4—181no—
326#879—31no—
327#879—91no—
328#879—91no—
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—62no—
357C2×D32—62no—
358C2×D32—64no—
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—62no—
389C4×C3⋊D3—62no—
390C4×C3⋊D3—64no—
391C4×C3⋊D3—122no—
392C4×C3⋊D3—122no—
393C4×C3⋊D3—124no—
394C4×C3⋊D3—121no—
395C3×#67—121no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
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
423C3×D12—121no—
424C3×C4×D3—121no—
425C3×C4×D3—121no—
426C3×C4×D3—121no—
427C3×C4×D3—121no—
428C3×Dic6—121no—
429C3×Dic6—121no—
430#627—41no—
431#626—41no—
432#626—62no—
433#626—62no—
434#626—62no—
435#626—62no—
436#626—122no—
437#625—62no—
438#624—41no—
439#624—41no—
440#624—62no—
441#624—121no—
442#624—121no—
443#624—122no—
444D3×Dic3—62no—
445D3×Dic3—62no—
446#551—271noSylow
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C3⋊(C3⋊D3)—22no—
451C3×C3⋊D3—22no—
452C3×C3⋊D3—41no—
453C32×D3—41no—
454C23×D3—91no—
455C23×D3—91no—
456C23×D3—91no—
457C23×D3—181no—
458C2×C3×Q8—91no—
459C2×C3×D4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C2×#67—31no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C22×Dic3—91no—
467C2×D12—31no—
468C2×D12—91no—
469C2×D12—91no—
470C2×D12—91no—
471C2×D12—181no—
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×C4×D3—31no—
475C2×C4×D3—31no—
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—91no—
484C2×C4×D3—181no—
485C2×C4×D3—181no—
486C2×C4×D3—181no—
487C2×C4×D3—181no—
488C2×C4×D3—361no—
489C2×Dic6—31no—
490C2×Dic6—31no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—61no—
496C3×C4⋊C4—61no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C4⋊C4—91no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—31no—
503C3×C22⋊C4—61no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C22⋊C4—91no—
509C3×C22⋊C4—91no—
510C3×C42—91no—
511#217—31no—
512#217—31no—
513#217—31no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—181no—
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—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—61no—
530(C2×D3)⋊C4—61no—
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—91no—
546(C2×D3)⋊C4—91no—
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)⋊C4D3211yescharacteristic
553C4⋊Dic3—31no—
554C4⋊Dic3—31no—
555C4⋊Dic3—31no—
556C4⋊Dic3—61no—
557C4⋊Dic3—91no—
558C4⋊Dic3—91no—
559C4⋊Dic3D3211yescharacteristic, complemented
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—181no—
570Dic3⋊C4D3211yescharacteristic, complemented
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—181no—
580C4×Dic3—181no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—41no—
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—21no—
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—62no—
605C2×C3⋊D3—62no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—61no—
608C2×C3⋊D3—61no—
609C2×C3⋊D3—61no—
610C2×C3⋊D3—122no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—121no—
615C2×C3⋊D3—122no—
616C2×C3⋊D3—122no—
617C2×C3⋊D3—124no—
618C2×C3⋊D3#23912yes—
619C2×C3×D3—22no—
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—32no—
627C2×C3×D3—32no—
628C2×C3×D3—41no—
629C2×C3×D3—41no—
630C2×C3×D3—62no—
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—121no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3—121no—
645C2×C3×D3—121no—
646D32—124no—
647D32—124no—
648D32—128no—
649C32×C4—21no—
650C32×C4—22no—
651C32×C4—21no—
652C32×C4—21no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—42no—
656C32×C4—61no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—61no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—61no—
666C3⋊Dic3—62no—
667C3⋊Dic3—61no—
668C3⋊Dic3—61no—
669C3⋊Dic3—121no—
670C3⋊Dic3—121no—
671C3⋊Dic3—122no—
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—21no—
681C3×Dic3—21no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—41no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699#126—91no—
700#126—271no—
701#124—271no—
702#123—91no—
703#123—271no—
704#123—271no—
705C22⋊Q8—91no—
706C22⋊Q8—271no—
707#120—271no—
708C4×D4—271no—
709C4×D4—271no—
710#117—271no—
711#117—271no—
712C2×C22⋊C4—271no—
713C2×C22⋊C4—271no—
714C33#55111yescharacteristic, complemented, Sylow
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—61no—
718C23×C3—91no—
719C23×C3—91no—
720C22×D3—31no—
721C22×D3—31no—
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3—61no—
726C22×D3—91no—
727C22×D3—91no—
728C22×D3—91no—
729C22×D3—181no—
730C22×D3—181no—
731C22×D3—181no—
732C22×D3—182no—
733C22×D3—182no—
734C22×D3—182no—
735C22×D3—182no—
736C22×D3—182no—
737C22×D3—182no—
738C22×D3—184no—
739C22×D3—361no—
740C22×D3—362no—
741C22×D3—361no—
742C22×D3—361no—
743C22×D3—361no—
744C22×D3—362no—
745C22×D3C2×D3211yescharacteristic
746C3×Q8—361no—
747C3×D4—361no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
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—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—41no—
762C2×C3×C4—61no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—91no—
768C2×C3×C4—91no—
769C2×C3×C4—91no—
770C2×C3×C4—91no—
771C2×C3×C4—361no—
772C2×C3×C4—361no—
773C2×C3×C4C2×D3211yescharacteristic
774C2×C3×C4C2×D3211yescharacteristic
775C2×C3×C4C2×D3211yescharacteristic
776#67—121no—
777#67—182no—
778#67—182no—
779#67—182no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—91no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—181no—
798C2×Dic3—182no—
799C2×Dic3—361no—
800C2×Dic3C2×D3211yescharacteristic
801C2×Dic3C2×D3211yescharacteristic
802C2×Dic3C2×D3211yescharacteristic
803C2×Dic3C2×D3211yescharacteristic
804C2×Dic3C2×D3211yescharacteristic
805D12—121no—
806D12—182no—
807D12—182no—
808D12—182no—
809D12—362no—
810C4×D3—121no—
811C4×D3—121no—
812C4×D3—121no—
813C4×D3—121no—
814C4×D3—182no—
815C4×D3—182no—
816C4×D3—182no—
817C4×D3—182no—
818C4×D3—182no—
819C4×D3—184no—
820C4×D3—362no—
821C4×D3—362no—
822C4×D3—364no—
823C4×D3—361no—
824C4×D3—361no—
825C4×D3—361no—
826C4×D3—362no—
827Dic6—121no—
828Dic6—121no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—121no—
842C2×C32#100411yescharacteristic
843C2×C32#100411yescharacteristic
844C2×C32C2×#23911yescharacteristic
845C2×C32D3×#4111yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32#100911yescharacteristic
851C3⋊D3—22no—
852C3⋊D3—41no—
853C3⋊D3—62no—
854C3⋊D3—64no—
855C3⋊D3—62no—
856C3⋊D3—62no—
857C3⋊D3—122no—
858C3⋊D3—122no—
859C3⋊D3—124no—
860C3×D3—42no—
861C3×D3—41no—
862C3×D3—41no—
863C3×D3—62no—
864C3×D3—62no—
865C3×D3—122no—
866C3×D3—121no—
867C3×D3—121no—
868C3×D3—241no—
869C24—271no—
870C2×Q8—91no—
871C2×D4—91no—
872C2×D4—271no—
873C2×D4—271no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—271no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—31no—
880C4⋊C4—31no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C22⋊C4—31no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C42—91no—
902C42—271no—
903C42—271no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—41no—
908C22×C3—62no—
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—181no—
919C22×C3—181no—
920C22×C3—181no—
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—32no—
930C2×D3—32no—
931C2×D3—62no—
932C2×D3—61no—
933C2×D3—61no—
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—92no—
943C2×D3—92no—
944C2×D3—92no—
945C2×D3—121no—
946C2×D3—121no—
947C2×D3—121no—
948C2×D3—121no—
949C2×D3—121no—
950C2×D3—182no—
951C2×D3—182no—
952C2×D3—182no—
953C2×D3—182no—
954C2×D3—182no—
955C2×D3—181no—
956C2×D3—181no—
957C2×D3—181no—
958C2×D3—181no—
959C2×D3—181no—
960C2×D3—181no—
961C2×D3—362no—
962C2×D3—361no—
963C2×D3—361no—
964C2×D3—361no—
965C2×D3—361no—
966C2×D3—362no—
967C2×D3—362no—
968C2×D3—364no—
969C2×D3—364no—
970C2×D3—364no—
971C2×D3—368no—
972C3×C4—22no—
973C3×C4—21no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—41no—
977C3×C4—41no—
978C3×C4—42no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—61no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—121no—
990C3×C4—121no—
991C3×C4—121no—
992C3×C4—121no—
993C3×C4—121no—
994C3×C4—181no—
995C3×C4—181no—
996C3×C4—181no—
997C3×C4—181no—
998Dic3—21no—
999Dic3—21no—
1000Dic3—21no—
1001Dic3—21no—
1002Dic3—21no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—121no—
1012Dic3—121no—
1013Dic3—121no—
1014Dic3—121no—
1015Dic3—182no—
1016Dic3—181no—
1017Dic3—181no—
1018Dic3—181no—
1019Dic3—361no—
1020Dic3—361no—
1021Dic3—362no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#563711yescharacteristic, complemented
1027C32#565911yescharacteristic, complemented
1028C32#570511yescharacteristic, complemented
1029C23—31no—
1030C23—91no—
1031C23—91no—
1032C23—271no—
1033C23—542no—
1034C23—542no—
1035C23—1081no—
1036Q8—361no—
1037D4—361no—
1038D4—542no—
1039D4—542no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—31no—
1044C2×C4—31no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—271no—
1050C2×C4—361no—
1051C2×C4—361no—
1052C2×C4—542no—
1053C2×C4—542no—
1054C2×C4—1081no—
1055C2×C4D3311yescharacteristic
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—41no—
1068C2×C3—122no—
1069C2×C3—121no—
1070C2×C3—121no—
1071C2×C3—182no—
1072C2×C3—361no—
1073C2×C3#6430611yescharacteristic
1074C2×C3#6430611yescharacteristic
1075C2×C3#6430711yescharacteristic
1076C2×C3#6431211yescharacteristic
1077C2×C3#6431211yescharacteristic
1078C2×C3#6431311yescharacteristic
1079C2×C3#6431411yescharacteristic
1080C2×C3D3×#23911yescharacteristic
1081C2×C3D3×#23911yescharacteristic
1082D3—41no—
1083D3—62no—
1084D3—62no—
1085D3—122no—
1086D3—121no—
1087D3—121no—
1088D3—184no—
1089D3—182no—
1090D3—182no—
1091D3—182no—
1092D3—241no—
1093D3—362no—
1094D3—362no—
1095D3—364no—
1096C22—61no—
1097C22—61no—
1098C22—61no—
1099C22—92no—
1100C22—181no—
1101C22—181no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22—272no—
1106C22—541no—
1107C22—541no—
1108C22—1084no—
1109C22C2×D3311yescharacteristic
1110C4—21no—
1111C4—61no—
1112C4—61no—
1113C4—61no—
1114C4—61no—
1115C4—61no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—181no—
1120C4—541no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059422811yescharacteristic, complemented
1126C3#1059465311yescharacteristic, complemented
1127C3#1059465411yescharacteristic, complemented
1128C2—121no—
1129C2—182no—
1130C2—361no—
1131C2—542no—
1132C2#1172438111yescharacteristic
1133C2#1172439111yescharacteristic
1134C2#1172441111yescharacteristic
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. #11723690C2semidirect
2. #11723539C2semidirect
3. #11723421C2semidirect
4. #11723413C2semidirect
5. C3×#63895C2semidirect
6. C3×#63861C2semidirect
7. C3×#63854C2semidirect
8. #11723019C2semidirect
9. #11723001C2semidirect
10. #11722977C2semidirect
12. #11722933C2semidirect
13. #11722931C2semidirect
14. #11722922C2semidirect
15. #11722904C2semidirect
25. C2×C3×#627C22semidirect
28. C2×C3×#624C22semidirect
30. C3×#3752C22semidirect
31. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C32×C4⋊Dic3C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. #88815C22semidirect
36. #88814C22semidirect
37. #88807C22semidirect
42. #88803C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
80. #63895D3semidirect
91. #63861D3semidirect
94. #63854D3semidirect
153. C2×#627C2×D3semidirect
166. C2×#624C2×D3semidirect
179. #3752C2×D3semidirect
180. C4⋊(C3⋊Dic3)C2×D3semidirect
206. C3×C4⋊Dic3C2×D3semidirect
207. C3×C4⋊Dic3C2×D3semidirect
214. C3×Dic3⋊C4C2×D3semidirect
215. C3×Dic3⋊C4C2×D3semidirect
219. #3724C2×D3semidirect
220. #3724C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
559. C4⋊Dic3D32semidirect
570. Dic3⋊C4D32semidirect
714. C33#551semidirect
1026. C32#5637semidirect
1027. C32#5659semidirect
1028. C32#5705semidirect
1125. C3#10594228semidirect
1126. C3#10594653semidirect
1127. C3#10594654semidirect

Maximal subgroups

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

subgroupindex
#117236902
#117235392
#117234212
#117234132
C3×#638952
C3×#638612
C3×#638542
#117230192
#117230012
#117229772
#117229502
#117229332
#117229312
#117229222
#117229042
#105946543
#105946533
#105942283