Finite Group Databasebeta

← #13168103

Subgroups — #13168103

Order 1728.

1312 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723671C211yesmaximal, characteristic, complemented
2C4×#6292C211yesmaximal, characteristic, complemented
3#11723462C211yesmaximal, characteristic, complemented
4#11723420C211yesmaximal, characteristic, complemented
5C3×#63921C211yesmaximal, characteristic, complemented
6C3×#63877C211yesmaximal, characteristic, complemented
7C3×#63859C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11723008C211yesmaximal, characteristic, complemented
10#11722993C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722981C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic
14#11722915C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10594093—31nomaximal
17#10594037—31nomaximal
18#10594017—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×#6296C2211yescharacteristic, complemented
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C3×#3750C2211yescharacteristic, complemented
30C3×#3750C2211yescharacteristic, complemented
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#88804C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64092—31no—
55#64090—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×D3×C22⋊C4—31no—
58C3×D3×C22⋊C4—31no—
59C3×#879—31no—
60C3×#877—31no—
61C3×#876—31no—
62C3×#872—31no—
63#63982—31no—
64#63977—31no—
65#63977—31no—
66D3×#217—31no—
67#63966—31no—
68C2×(C2×D3)⋊Dic3—31no—
69#63956—31no—
70#63953—31no—
71#63923—31no—
72#63921D311yescharacteristic, complemented
73D3×(C2×D3)⋊C4—31no—
74C4×#626—31no—
75C4×#626—31no—
76C4×#626—61no—
77#63897—31no—
78#63893—31no—
79#63893—31no—
80#63890—31no—
81#63881—31no—
82#63881—31no—
83#63881—61no—
84#63877D311yescharacteristic, complemented
85#63865—31no—
86#63862—31no—
87#63861—31no—
88#63859D311yescharacteristic, complemented
89#63855—31no—
90#63853—31no—
91#63853—31no—
92#63853—61no—
93#63852—31no—
94#63852—31no—
95#63851—31no—
96#63851—31no—
97#63850—31no—
98#63850—31no—
99#63850—31no—
100#63841—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3×D32—22no—
107C2×C3×D32—22no—
108C2×C3×D32—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
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4×C3⋊D3—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6296—41no—
123#6292—22no—
124#6291—22no—
125#6291—41no—
126D3×C3⋊Dic3—41no—
127C3×#624—22no—
128C3×D3×Dic3—22no—
129#5705—91no—
130#5527—91no—
131#5495—91no—
132C23×C3×D3—31no—
133C23×C3×D3—31no—
134C22×D32C2×D311yescharacteristic
135C2×#638—31no—
136C2×#638—31no—
137C22×C3⋊Dic3—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×C4×C3⋊D3C2×D311yescharacteristic
147C22×C3×Dic3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—61no—
154C2×#627—31no—
155C2×#627—31no—
156C2×#627—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—61no—
164C2×#626—61no—
165C2×#626—61no—
166C2×#624C2×D311yescharacteristic
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—61no—
170C2×D3×Dic3C2×D311yescharacteristic
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C42—31no—
174#3757—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)—31no—
181#3750C2×D311yescharacteristic, complemented
182#3750C2×D311yescharacteristic, complemented
183C4×C3⋊Dic3—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×(C2×D3)⋊C4—21no—
190C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
197C3×(C2×D3)⋊C4C2×D311yescharacteristic
198C3×(C2×D3)⋊C4C2×D311yescharacteristic
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×C4⋊Dic3—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×C4×Dic3—21no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3C2×D311yescharacteristic, complemented
216C3×C4×Dic3C2×D311yescharacteristic, complemented
217#3724—31no—
218#3724C2×D311yescharacteristic, complemented
219#3724C2×D311yescharacteristic, complemented
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—61no—
238#3722—61no—
239#3722—61no—
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—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3C2×D311yescharacteristic
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—61no—
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×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272C3×D32—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#117—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#929—91no—
290#929—91no—
291C4×#67—91no—
292C2×(C2×D3)⋊C4—91no—
293#926—91no—
294#924—91no—
295#898—91no—
296#897—91no—
297#896—91no—
298#896—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#894—91no—
303#893—91no—
304#892—91no—
305#886—91no—
306#885—91no—
307#885—91no—
308#883—91no—
309#883—91no—
310#883—181no—
311#882—91no—
312#882—91no—
313#67⋊C4—91no—
314#67⋊C4—91no—
315#67⋊C4—181no—
316D3×C22⋊C4—31no—
317D3×C22⋊C4—31no—
318D3×C22⋊C4—91no—
319#879—31no—
320#879—91no—
321#879—91no—
322#878—91no—
323#878—91no—
324#877—31no—
325#876—31no—
326#875—91no—
327C4×D12—91no—
328C4×D12—91no—
329C4×D12—181no—
330#872—31no—
331#872—91no—
332C23×C32—31no—
333C23×C32—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—31no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—61no—
340C22×C3⋊D3—121no—
341C22×C3⋊D3C22×D311yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3—62no—
348C22×C3×D3—62no—
349C22×C3×D3—62no—
350C22×C3×D3—62no—
351C22×C3×D3—121no—
352C22×C3×D3—121no—
353C22×C3×D3C22×D311yescharacteristic
354C22×C3×D3C22×D311yescharacteristic
355C22×C3×D3C22×D311yescharacteristic
356C22×C3×D3C22×D311yescharacteristic
357C2×D32—22no—
358C2×D32—22no—
359C2×D32—41no—
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—41no—
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370C2×C32×C4C22×D311yescharacteristic
371#638—62no—
372#638—121no—
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⋊Dic3—121no—
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C4⋊(C3⋊D3)—62no—
387C4×C3⋊D3—41no—
388C4×C3⋊D3—121no—
389C4×C3⋊D3—121no—
390C4×C3⋊D3—121no—
391C4×C3⋊D3—122no—
392C4×C3⋊D3—122no—
393C4×C3⋊D3—122no—
394C4×C3⋊D3—124no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—31no—
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—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—62no—
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×C4×D3—62no—
424C3×C4×D3—62no—
425C3×C4×D3—62no—
426C3×C4×D3—121no—
427C3×C4×D3—121no—
428C3×C4×D3—122no—
429#627—121no—
430#627—121no—
431#627—121no—
432#626—62no—
433#626—62no—
434#626—64no—
435#626—64no—
436#626—62no—
437#626—62no—
438#626—121no—
439#626—121no—
440#626—122no—
441#624—22no—
442D3×Dic3—22no—
443D3×Dic3—121no—
444D3×Dic3—121no—
445D3×Dic3—122no—
446#551—271noSylow
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C3⋊(C3⋊D3)—41no—
451C3×C3⋊D3—22no—
452C32×D3—22no—
453C32×D3—41no—
454C24×C3—91no—
455C23×D3—31no—
456C23×D3—31no—
457C22×C3×C4—91no—
458C22×C3×C4—91no—
459C22×C3×C4—91no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—181no—
466C2×#67—181no—
467C22×Dic3—31no—
468C22×Dic3—91no—
469C22×Dic3—91no—
470C22×Dic3—181no—
471C2×D12—91no—
472C2×D12—91no—
473C2×D12—91no—
474C2×D12—91no—
475C2×D12—181no—
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—61no—
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—361no—
490C2×Dic6—91no—
491C2×Dic6—91no—
492C2×Dic6—91no—
493C3×C4⋊C4—91no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C22⋊C4—31no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—61no—
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×C42—31no—
510C3×C42—31no—
511C3×C42—61no—
512C3×C42—91no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—31no—
517#217—31no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—181no—
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—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)⋊C4D3211yescharacteristic
550(C2×D3)⋊C4D3211yescharacteristic
551C4⋊Dic3—31no—
552C4⋊Dic3—91no—
553C4⋊Dic3—91no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—181no—
558C4⋊Dic3—181no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—61no—
569Dic3⋊C4—61no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—181no—
580C4×Dic3D3211yescharacteristic, complemented
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—32no—
585C22×C32—41no—
586C22×C32—61no—
587C22×C32—61no—
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—61no—
597C2×C3⋊D3—61no—
598C2×C3⋊D3—61no—
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—121no—
609C2×C3⋊D3—121no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—122no—
615C2×C3⋊D3—122no—
616C2×C3⋊D3—122no—
617C2×C3⋊D3#23712yes—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—22no—
629C2×C3×D3—32no—
630C2×C3×D3—32no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—62no—
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—124no—
644C2×C3×D3—124no—
645C2×C3×D3#23512yes—
646C2×C3×D3#23512yes—
647D32—44no—
648C32×C4—21no—
649C32×C4—22no—
650C32×C4—21no—
651C32×C4—21no—
652C32×C4—41no—
653C32×C4—41no—
654C32×C4—42no—
655C32×C4—61no—
656C32×C4—61no—
657C32×C4—61no—
658C32×C4—61no—
659C3⋊Dic3—21no—
660C3⋊Dic3—21no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—61no—
665C3⋊Dic3—62no—
666C3⋊Dic3—61no—
667C3⋊Dic3—61no—
668C3⋊Dic3—121no—
669C3⋊Dic3—121no—
670C3⋊Dic3—122no—
671C3×Dic3—22no—
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—62no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698#126—91no—
699#126—271no—
700#124—271no—
701#123—271no—
702#123—271no—
703#123—271no—
704C22⋊Q8—271no—
705C22⋊Q8—271no—
706#120—271no—
707C4×D4—271no—
708C4×D4—271no—
709#117—91no—
710#117—271no—
711C2×C22⋊C4—91no—
712C2×C22⋊C4—271no—
713C33#55111yescharacteristic, complemented, Sylow
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—31no—
718C23×C3—61no—
719C23×C3—61no—
720C23×C3—91no—
721C23×C3—182no—
722C23×C3—182no—
723C23×C3—361no—
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—61no—
727C22×D3—62no—
728C22×D3—62no—
729C22×D3—62no—
730C22×D3—62no—
731C22×D3—91no—
732C22×D3—91no—
733C22×D3—91no—
734C22×D3—121no—
735C22×D3—121no—
736C22×D3—181no—
737C22×D3—181no—
738C22×D3—181no—
739C22×D3—361no—
740C22×D3C2×D3211yescharacteristic
741C22×D3C2×D3211yescharacteristic
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
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—41no—
754C2×C3×C4—61no—
755C2×C3×C4—61no—
756C2×C3×C4—61no—
757C2×C3×C4—61no—
758C2×C3×C4—91no—
759C2×C3×C4—91no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—182no—
764C2×C3×C4—182no—
765C2×C3×C4—361no—
766C2×C3×C4C2×D3211yescharacteristic
767C2×C3×C4C2×D3211yescharacteristic
768C2×C3×C4C2×D3211yescharacteristic
769#67—182no—
770#67—182no—
771#67—182no—
772#67—184no—
773#67—361no—
774#67—361no—
775#67—362no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—61no—
787C2×Dic3—61no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—61no—
791C2×Dic3—62no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—91no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—181no—
798C2×Dic3—361no—
799C2×Dic3—361no—
800C2×Dic3—361no—
801C2×Dic3—362no—
802C2×Dic3C2×D3211yescharacteristic
803C2×Dic3C2×D3211yescharacteristic
804C2×Dic3C2×D3211yescharacteristic
805C2×Dic3C2×D3211yescharacteristic
806D12—182no—
807D12—182no—
808D12—184no—
809D12—182no—
810D12—361no—
811C4×D3—62no—
812C4×D3—62no—
813C4×D3—62no—
814C4×D3—121no—
815C4×D3—121no—
816C4×D3—122no—
817C4×D3—361no—
818C4×D3—361no—
819C4×D3—361no—
820C4×D3—362no—
821C4×D3—361no—
822C4×D3—362no—
823C4×D3—362no—
824C4×D3—364no—
825Dic6—361no—
826Dic6—361no—
827Dic6—361no—
828C2×C32—21no—
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—41no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—62no—
841C2×C32—121no—
842C2×C32C2×#23511yescharacteristic
843C2×C32C2×#23511yescharacteristic
844C2×C32C2×#23711yescharacteristic
845C2×C32#100411yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32#100911yescharacteristic
850C2×C32#100911yescharacteristic
851C3⋊D3—22no—
852C3⋊D3—122no—
853C3⋊D3—122no—
854C3⋊D3—122no—
855C3⋊D3—124no—
856C3⋊D3—121no—
857C3⋊D3—121no—
858C3⋊D3—121no—
859C3×D3—22no—
860C3×D3—22no—
861C3×D3—42no—
862C3×D3—41no—
863C3×D3—41no—
864C3×D3—62no—
865C3×D3—62no—
866C3×D3—81no—
867C3×D3—122no—
868C24—91no—
869C2×Q8—271no—
870C2×D4—271no—
871C2×D4—271no—
872C2×D4—271no—
873C22×C4—91no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—271no—
877C22×C4—271no—
878C4⋊C4—91no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C22⋊C4—31no—
887C22⋊C4—31no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C42—31no—
901C42—91no—
902C42—271no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—32no—
907C22×C3—32no—
908C22×C3—41no—
909C22×C3—62no—
910C22×C3—61no—
911C22×C3—61no—
912C22×C3—61no—
913C22×C3—61no—
914C22×C3—61no—
915C22×C3—61no—
916C22×C3—61no—
917C22×C3—61no—
918C22×C3—61no—
919C22×C3—61no—
920C22×C3—92no—
921C22×C3—121no—
922C22×C3—121no—
923C22×C3—121no—
924C22×C3—121no—
925C22×C3—121no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—364no—
929C22×C3C22×D3211yescharacteristic
930C22×C3C22×D3211yescharacteristic
931C22×C3C22×D3211yescharacteristic
932C2×D3—21no—
933C2×D3—21no—
934C2×D3—21no—
935C2×D3—21no—
936C2×D3—21no—
937C2×D3—32no—
938C2×D3—32no—
939C2×D3—62no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—121no—
945C2×D3—121no—
946C2×D3—124no—
947C2×D3—124no—
948C2×D3—182no—
949C2×D3—182no—
950C2×D3—182no—
951C2×D3—181no—
952C2×D3—181no—
953C2×D3—181no—
954C2×D3—181no—
955C2×D3—181no—
956C2×D3—181no—
957C2×D3—181no—
958C2×D3—181no—
959C2×D3—181no—
960C2×D3—361no—
961C2×D3—361no—
962C2×D3—361no—
963C2×D3—361no—
964C2×D3—361no—
965C2×D3—361no—
966C2×D3—362no—
967C2×D3—362no—
968C2×D3—362no—
969C2×D3#379812yes—
970C3×C4—22no—
971C3×C4—21no—
972C3×C4—21no—
973C3×C4—21no—
974C3×C4—41no—
975C3×C4—41no—
976C3×C4—42no—
977C3×C4—62no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—61no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—121no—
987C3×C4—121no—
988C3×C4—121no—
989C3×C4—181no—
990C3×C4—181no—
991C3×C4—181no—
992C3×C4—181no—
993C3×C4—181no—
994Dic3—21no—
995Dic3—21no—
996Dic3—21no—
997Dic3—21no—
998Dic3—62no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—121no—
1010Dic3—121no—
1011Dic3—121no—
1012Dic3—121no—
1013Dic3—182no—
1014Dic3—181no—
1015Dic3—181no—
1016Dic3—181no—
1017Dic3—361no—
1018Dic3—361no—
1019Dic3—362no—
1020C32—21no—
1021C32—21no—
1022C32—21no—
1023C32—41no—
1024C32#549511yescharacteristic, complemented
1025C32#552711yescharacteristic, complemented
1026C32#570511yescharacteristic, complemented
1027C23—31no—
1028C23—31no—
1029C23—91no—
1030C23—182no—
1031C23—182no—
1032C23—271no—
1033C23—361no—
1034Q8—1081no—
1035D4—542no—
1036D4—542no—
1037D4—1081no—
1038C2×C4—31no—
1039C2×C4—31no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—91no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—182no—
1048C2×C4—182no—
1049C2×C4—271no—
1050C2×C4—361no—
1051C2×C4—1081no—
1052C2×C4—1081no—
1053C2×C4D3311yescharacteristic
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—62no—
1067C2×C3—62no—
1068C2×C3—122no—
1069C2×C3—121no—
1070C2×C3—121no—
1071C2×C3—182no—
1072C2×C3—241no—
1073C2×C3C2×#379811yescharacteristic
1074C2×C3D3×#23511yescharacteristic
1075C2×C3D3×#23511yescharacteristic
1076C2×C3#6430611yescharacteristic
1077C2×C3#6430811yescharacteristic
1078C2×C3D3×#23711yescharacteristic
1079C2×C3D3×#23711yescharacteristic
1080C2×C3#6431411yescharacteristic
1081C2×C3#6431411yescharacteristic
1082D3—22no—
1083D3—41no—
1084D3—62no—
1085D3—62no—
1086D3—122no—
1087D3—362no—
1088D3—362no—
1089D3—362no—
1090D3—364no—
1091D3—361no—
1092D3—361no—
1093D3—361no—
1094C22—32no—
1095C22—61no—
1096C22—61no—
1097C22—61no—
1098C22—61no—
1099C22—61no—
1100C22—92no—
1101C22—181no—
1102C22—181no—
1103C22—364no—
1104C22—541no—
1105C22—541no—
1106C22—541no—
1107C22C2×D3311yescharacteristic
1108C4—21no—
1109C4—61no—
1110C4—61no—
1111C4—61no—
1112C4—61no—
1113C4—181no—
1114C4—181no—
1115C4—181no—
1116C4—181no—
1117C4—181no—
1118C4—541no—
1119C3—21no—
1120C3—21no—
1121C3—21no—
1122C3—41no—
1123C3#1059401711yescharacteristic, complemented
1124C3#1059403711yescharacteristic, complemented
1125C3#1059409311yescharacteristic, complemented
1126C2—62no—
1127C2—121no—
1128C2—182no—
1129C2—1081no—
1130C2#1172437311yescharacteristic
1131C2D3×#379811yescharacteristic
1132C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722948C2
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. #11723671C2semidirect
2. C4×#6292C2semidirect
3. #11723462C2semidirect
4. #11723420C2semidirect
5. C3×#63921C2semidirect
6. C3×#63877C2semidirect
7. C3×#63859C2semidirect
8. #11723022C2semidirect
9. #11723008C2semidirect
10. #11722993C2semidirect
11. #11722987C2semidirect
12. #11722981C2semidirect
14. #11722915C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×#6296C22semidirect
29. C3×#3750C22semidirect
30. C3×#3750C22semidirect
33. C32×C4×Dic3C22semidirect
34. #88815C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
39. #88804C22semidirect
40. #88804C22semidirect
41. #88804C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
72. #63921D3semidirect
84. #63877D3semidirect
88. #63859D3semidirect
181. #3750C2×D3semidirect
182. #3750C2×D3semidirect
215. C3×C4×Dic3C2×D3semidirect
216. C3×C4×Dic3C2×D3semidirect
218. #3724C2×D3semidirect
219. #3724C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
580. C4×Dic3D32semidirect
713. C33#551semidirect
1024. C32#5495semidirect
1025. C32#5527semidirect
1026. C32#5705semidirect
1123. C3#10594017semidirect
1124. C3#10594037semidirect
1125. C3#10594093semidirect

Maximal subgroups

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

subgroupindex
#117236712
C4×#62922
#117234622
#117234202
C3×#639212
C3×#638772
C3×#638592
#117230222
#117230082
#117229932
#117229872
#117229812
#117229482
#117229152
D3×(C2×D3)⋊Dic32
#105940933
#105940373
#105940173