Finite Group Databasebeta

← #13177431

Subgroups — #13177431

Order 1728.

2948 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7#11723627C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9#11723616C211yesmaximal, characteristic, complemented
10C2×#88804C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12#11723525C211yesmaximal, characteristic, complemented
13#11723498C211yesmaximal, characteristic, complemented
14#11723462C211yesmaximal, characteristic, complemented
15#11723442C211yesmaximal, characteristic, complemented
16#10596081—31nomaximal
17#10595163—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic
23D4×C3⋊(C3⋊D3)—24no—
24C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
25C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
26C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic, complemented
29C22×C32×Dic3C2211yescharacteristic, complemented
30C2×#6293C2211yescharacteristic, complemented
31C2×#6291C2211yescharacteristic
32C2×#6291C2211yescharacteristic, complemented
33C2×#6291C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35C2×#6289C2211yescharacteristic, complemented
36#89028—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38C3×#3757C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×D4×C3⋊D3—34no—
58C2×D4×C3⋊D3—64no—
59C2×#3804—34no—
60C32×#121—31no—
61#64148—31no—
62#64146—31no—
63#64146—31no—
64#64144D311yescharacteristic, complemented
65C4×#638—31no—
66C2×#3752—31no—
67#64105—31no—
68#64103—31no—
69#64094—31no—
70#64093—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73C3×#939D314yescomplemented
74C3×#935—34no—
75#63981—34no—
76#63981—34no—
77#63974—34no—
78#63971—34no—
79C2×#3722—34no—
80#63953—34no—
81#63952—34no—
82#63910—34no—
83#63897—34no—
84#63881—34no—
85#63865—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)—22no—
92C22×C3⋊(C3⋊D3)—41no—
93C22×C3⋊(C3⋊D3)—41no—
94C22×C3⋊(C3⋊D3)C2311yescharacteristic
95C22×C3⋊(C3⋊D3)C2311yescharacteristic
96C22×C3⋊(C3⋊D3)C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312D414yescomplemented
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4⋊(C3⋊(C3⋊D3))—22no—
104C4×C3⋊(C3⋊D3)—22no—
105C2×C3×C3⋊Dic3—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C32×#67—22no—
111C32×#67—41no—
112C2×C32×Dic3—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6293—22no—
117#6291—22no—
118#6291—22no—
119#6291—41no—
120#6289—22no—
121#6289—41no—
122D3×C3⋊Dic3—22no—
123#5654—91no—
124#5610—94no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—31no—
127C23×C3⋊D3—34no—
128C23×C3⋊D3—34no—
129C23×C3⋊D3—64no—
130C23×C3⋊D3—64no—
131C2×C32×D4—24no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C2×C32×D4C2×D314yes—
135C2×C32×D4C2×D311yescharacteristic
136C22×C32×C4—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—34no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—64no—
145C2×#638—64no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3C2×D311yescharacteristic, complemented
148#3830—64no—
149D4×C3⋊D3—64no—
150D4×C3⋊D3—616no—
151D4×C3⋊D3—632no—
152C2×C4⋊(C3⋊D3)—31no—
153C2×C4⋊(C3⋊D3)—34no—
154C2×C4⋊(C3⋊D3)—64no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—34no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—64no—
160C2×#634—31no—
161C2×C3×#67C2×D314yescomplemented
162C2×C3×#67C2×D314yescomplemented
163C22×C3×Dic3—34no—
164C22×C3×Dic3C2×D314yescomplemented
165C2×#627—34no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#624—34no—
170C2×#624—34no—
171#3804—616no—
172C2×D3×Dic3—34no—
173C32×C4⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176#3757C2×D311yescharacteristic, complemented
177#3757C2×D311yescharacteristic, complemented
178#3757C2×D311yescharacteristic, complemented
179#3752—31no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3750—31no—
187#3750C2×D311yescharacteristic, complemented
188#3750C2×D311yescharacteristic, complemented
189C4×C3⋊Dic3—31no—
190C3×#217—34no—
191C3×#217—34no—
192C3×#217—34no—
193C3×#217C2×D314yescomplemented
194C3×(C2×D3)⋊C4C2×D314yescomplemented
195C3×Dic3⋊C4—34no—
196C3×Dic3⋊C4—34no—
197C3×Dic3⋊C4C2×D314yescomplemented
198#3724—34no—
199#3722—34no—
200#3722—34no—
201#3722—34no—
202#3722—34no—
203#3722—34no—
204#3722—34no—
205#3722—34no—
206Dic32—34no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2×D412yes—
213C22×C33C2411yescharacteristic
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3⋊(C3⋊D3)—21no—
221C2×C3⋊(C3⋊D3)—44no—
222C2×C3⋊(C3⋊D3)—44no—
223C2×C3⋊(C3⋊D3)C2×D412yes—
224C2×C3⋊(C3⋊D3)#4112yescomplemented
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)C2×D412yes—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C32×Dic3—21no—
237C2×#237—94no—
238C2×D3×D4—94no—
239C2×D3×D4—91no—
240C2×D3×D4—184no—
241C2×#235—91no—
242C3×#123—91no—
243C3×#121—34no—
244#939—94no—
245#939C3⋊D311yescharacteristic, complemented
246#937—94no—
247#937—94no—
248#935—34no—
249C4×#67—94no—
250C2×(C2×D3)⋊C4—94no—
251C2×(C2×D3)⋊C4—91no—
252#896—94no—
253#896—91no—
254#895—91no—
255#894—94no—
256#894—91no—
257#893—91no—
258#885—94no—
259#885—91no—
260#884—94no—
261#884—91no—
262#882—91no—
263#882—91no—
264#67⋊C4—94no—
265#67⋊C4—91no—
266D3×C22⋊C4—94no—
267D3×C22⋊C4—91no—
268C23×C32—24no—
269C23×C32—24no—
270C23×C32—31no—
271C23×C32C22×D314yes—
272C23×C32C22×D314yes—
273C23×C32C22×D311yescharacteristic
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3—31no—
276C22×C3⋊D3—31no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—64no—
282C22×C3⋊D3—64no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—62no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—68no—
288C22×C3⋊D3—616no—
289C22×C3⋊D3—616no—
290C22×C3⋊D3—68no—
291C22×C3⋊D3—62no—
292C22×C3⋊D3—68no—
293C22×C3⋊D3—68no—
294C22×C3⋊D3—128no—
295C22×C3⋊D3—128no—
296C22×C3⋊D3—121no—
297C22×C3⋊D3—121no—
298C22×C3⋊D3—124no—
299C22×C3⋊D3—124no—
300C22×C3⋊D3—128no—
301C22×C3⋊D3—128no—
302C22×C3×D3C22×D314yes—
303C32×D4—216no—
304C32×D4—28no—
305C32×D4—22no—
306C32×D4—62no—
307C32×D4—121no—
308C2×C32×C4—24no—
309C2×C32×C4—31no—
310C2×C32×C4—31no—
311C2×C32×C4—31no—
312C2×C32×C4—121no—
313C2×C32×C4C22×D314yes—
314C2×C32×C4C22×D311yescharacteristic
315#638—34no—
316#638—316no—
317#638—616no—
318#638—62no—
319#638—62no—
320#638—62no—
321#638—68no—
322#638—616no—
323#638—121no—
324C2×C3⋊Dic3—22no—
325C2×C3⋊Dic3—31no—
326C2×C3⋊Dic3—34no—
327C2×C3⋊Dic3—64no—
328C2×C3⋊Dic3—62no—
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C2×C3⋊Dic3C22×D311yescharacteristic
332C2×C3⋊Dic3C22×D311yescharacteristic
333C4⋊(C3⋊D3)—62no—
334C4⋊(C3⋊D3)—68no—
335C4⋊(C3⋊D3)—616no—
336C4×C3⋊D3—62no—
337C4×C3⋊D3—62no—
338C4×C3⋊D3—68no—
339C4×C3⋊D3—616no—
340C4×C3⋊D3—121no—
341#634—62no—
342C3×#67—28no—
343C3×#67—44no—
344C2×C3×Dic3—34no—
345C2×C3×Dic3—34no—
346C2×C3×Dic3—34no—
347C2×C3×Dic3—34no—
348C2×C3×Dic3—44no—
349C2×C3×Dic3—68no—
350C2×C3×Dic3C22×D314yes—
351C2×C3×Dic3C22×D314yes—
352C2×C3×Dic3C22×D314yes—
353#627—68no—
354#626—68no—
355#626—68no—
356#626—124no—
357#624—68no—
358#624—124no—
359D3×Dic3—68no—
360#546—271noSylow
361C2×C33—22no—
362C2×C33—41no—
363C2×C33C22×D411yescharacteristic
364C2×C33C2×#4111yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C3⋊(C3⋊D3)—22no—
367C3⋊(C3⋊D3)—22no—
368C3⋊(C3⋊D3)—41no—
369C32×D3—41no—
370C23×D3—94no—
371C23×D3—94no—
372C23×D3—91no—
373C23×D3—91no—
374C23×D3—184no—
375C23×D3—184no—
376C2×C3×D4—24no—
377C2×C3×D4—34no—
378C2×C3×D4—34no—
379C2×C3×D4D3214yes—
380C2×C3×D4C2×C3⋊D311yescharacteristic
381C22×C3×C4—34no—
382C22×C3×C4—91no—
383C2×#67—94no—
384C2×#67—94no—
385C2×#67—94no—
386C2×#67—94no—
387C2×#67—91no—
388C2×#67—94no—
389C2×#67—91no—
390C2×#67—184no—
391C2×#67—184no—
392C2×#67C2×C3⋊D311yescharacteristic, complemented
393C2×#67C2×C3⋊D311yescharacteristic, complemented
394C22×Dic3—34no—
395C22×Dic3—94no—
396C22×Dic3C2×C3⋊D311yescharacteristic, complemented
397#237—1816no—
398D3×D4—1816no—
399D3×D4—184no—
400D3×D4—1832no—
401#235—184no—
402C2×D12—91no—
403C2×D12—91no—
404C2×D12—94no—
405C2×D12—91no—
406C2×D12—91no—
407C2×D12—184no—
408C2×C4×D3—94no—
409C2×C4×D3—91no—
410C2×C4×D3—94no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—94no—
414C2×C4×D3—91no—
415C2×C4×D3—184no—
416C2×Dic6—94no—
417C2×Dic6—91no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426#217—34no—
427#217—34no—
428#217—34no—
429#217C2×C3⋊D311yescharacteristic, complemented
430(C2×D3)⋊C4—94no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—94no—
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—94no—
435(C2×D3)⋊C4—94no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—94no—
448Dic3⋊C4—91no—
449Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
450C4×Dic3—94no—
451C4×Dic3—91no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—28no—
455C22×C32—24no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—24no—
460C22×C32—28no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32—61no—
472C22×C32D3×D418yes—
473C22×C32D3×D412yes—
474C22×C32C23×D314yes—
475C22×C32C23×D311yescharacteristic
476C2×C3⋊D3—32no—
477C2×C3⋊D3—32no—
478C2×C3⋊D3—38no—
479C2×C3⋊D3—38no—
480C2×C3⋊D3—68no—
481C2×C3⋊D3—68no—
482C2×C3⋊D3—68no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—64no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—68no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—61no—
493C2×C3⋊D3—61no—
494C2×C3⋊D3—61no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3—124no—
501C2×C3⋊D3—124no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—1216no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—1216no—
507C2×C3⋊D3—1232no—
508C2×C3⋊D3—1232no—
509C2×C3×D3—24no—
510C2×C3×D3—24no—
511C2×C3×D3—24no—
512C32×C4—28no—
513C32×C4—24no—
514C32×C4—21no—
515C32×C4—61no—
516C32×C4—61no—
517C32×C4—61no—
518C3⋊Dic3—21no—
519C3⋊Dic3—21no—
520C3⋊Dic3—21no—
521C3⋊Dic3—21no—
522C3⋊Dic3—32no—
523C3⋊Dic3—38no—
524C3⋊Dic3—68no—
525C3×Dic3—24no—
526C3×Dic3—24no—
527C3×Dic3—24no—
528C3×Dic3—64no—
529C3×Dic3—64no—
530C3×Dic3—64no—
531C3×Dic3—64no—
532C2×#41—271no—
533C22×D4—271no—
534#124—271no—
535#123—91no—
536#123—271no—
537C22⋊Q8—271no—
538#121—31no—
539#121—271no—
540#121—271no—
541#120—271no—
542#120—271no—
543C4×D4—271no—
544C4×D4—271no—
545C2×C22⋊C4—271no—
546C2×C22⋊C4—271no—
547C33#54611yescharacteristic, complemented, Sylow
548C23×C3—24no—
549C23×C3—24no—
550C23×C3—34no—
551C23×C3C2×D3214yes—
552C23×C3C2×D3214yes—
553C23×C3C22×C3⋊D311yescharacteristic
554C23×C3C22×C3⋊D311yescharacteristic
555C22×D3—94no—
556C22×D3—94no—
557C22×D3—91no—
558C22×D3—91no—
559C22×D3—94no—
560C22×D3—91no—
561C22×D3—184no—
562C22×D3—184no—
563C22×D3—184no—
564C22×D3—188no—
565C22×D3—182no—
566C22×D3—182no—
567C22×D3—182no—
568C22×D3—188no—
569C22×D3—188no—
570C22×D3—1816no—
571C22×D3—1816no—
572C22×D3—188no—
573C22×D3—182no—
574C22×D3—368no—
575C22×D3—368no—
576C22×D3—364no—
577C22×D3—364no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—368no—
581C22×D3—368no—
582C22×D3C22×C3⋊D311yescharacteristic
583C3×D4—216no—
584C3×D4—28no—
585C3×D4—22no—
586C3×D4—68no—
587C3×D4—124no—
588C2×C3×C4—24no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—34no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—124no—
597C2×C3×C4—182no—
598C2×C3×C4C2×D3214yes—
599C2×C3×C4C22×C3⋊D311yescharacteristic
600#67—22no—
601#67—41no—
602#67—916no—
603#67—94no—
604#67—1816no—
605#67—188no—
606#67—188no—
607#67—188no—
608#67—182no—
609#67—1816no—
610#67—364no—
611C2×Dic3—34no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—34no—
615C2×Dic3—41no—
616C2×Dic3—68no—
617C2×Dic3—94no—
618C2×Dic3—91no—
619C2×Dic3—184no—
620C2×Dic3—188no—
621C2×Dic3C22×C3⋊D311yescharacteristic
622C2×Dic3C22×C3⋊D311yescharacteristic
623C2×Dic3C22×C3⋊D311yescharacteristic
624D12—188no—
625D12—182no—
626D12—1816no—
627D12—182no—
628D12—182no—
629D12—361no—
630C4×D3—182no—
631C4×D3—188no—
632C4×D3—188no—
633C4×D3—182no—
634C4×D3—182no—
635C4×D3—1816no—
636C4×D3—361no—
637C4×D3—364no—
638Dic6—182no—
639Dic6—188no—
640C2×C32—22no—
641C2×C32—24no—
642C2×C32—24no—
643C2×C32—24no—
644C2×C32—28no—
645C2×C32—48no—
646C2×C32—48no—
647C2×C32—41no—
648C2×C32—44no—
649C2×C32—121no—
650C2×C32C2×D3×D414yes—
651C2×C32C2×D3×D411yescharacteristic
652C2×C32#100414yes—
653C2×C32D3×#4114yes—
654C2×C32D3×#4111yescharacteristic
655C2×C32#100911yescharacteristic
656C3⋊D3—616no—
657C3⋊D3—62no—
658C3⋊D3—62no—
659C3⋊D3—68no—
660C3⋊D3—68no—
661C3⋊D3—128no—
662C3⋊D3—128no—
663C3⋊D3—121no—
664C3⋊D3—124no—
665C3×D3—44no—
666C24—271no—
667C24—271no—
668#41—544no—
669C2×Q8—271no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—544no—
679C2×D4D3×C3⋊D311yescharacteristic
680C22×C4—31no—
681C22×C4—91no—
682C22×C4—271no—
683C22×C4—271no—
684C22×C4—271no—
685C22×C4—271no—
686C4⋊C4—31no—
687C4⋊C4—91no—
688C4⋊C4—91no—
689C4⋊C4—271no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C42—271no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—28no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—24no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—44no—
717C22×C3—44no—
718C22×C3—44no—
719C22×C3—44no—
720C22×C3—64no—
721C22×C3—64no—
722C22×C3—64no—
723C22×C3#381118yes—
724C22×C3D4×C3⋊D312yes—
725C22×C3C22×D3214yes—
726C22×C3C23×C3⋊D311yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—98no—
731C2×D3—98no—
732C2×D3—92no—
733C2×D3—92no—
734C2×D3—188no—
735C2×D3—188no—
736C2×D3—188no—
737C2×D3—188no—
738C2×D3—184no—
739C2×D3—184no—
740C2×D3—184no—
741C2×D3—184no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—188no—
747C2×D3—184no—
748C2×D3—184no—
749C2×D3—184no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—364no—
754C2×D3—364no—
755C2×D3—364no—
756C2×D3—364no—
757C2×D3—3616no—
758C2×D3—364no—
759C2×D3—3616no—
760C2×D3—364no—
761C2×D3—3632no—
762C2×D3—3632no—
763C3×C4—28no—
764C3×C4—24no—
765C3×C4—21no—
766C3×C4—64no—
767C3×C4—64no—
768C3×C4—64no—
769C3×C4—181no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773Dic3—21no—
774Dic3—21no—
775Dic3—21no—
776Dic3—64no—
777Dic3—64no—
778Dic3—64no—
779Dic3—64no—
780Dic3—98no—
781Dic3—92no—
782Dic3—188no—
783C32—24no—
784C32#561014yescomplemented
785C32#565411yescharacteristic, complemented
786C23—31no—
787C23—271no—
788C23—271no—
789C23—271no—
790C23—542no—
791C23—542no—
792C23—542no—
793C23—542no—
794C23—1081no—
795C23—1081no—
796C23C2×D3×C3⋊D311yescharacteristic
797C23C2×D3×C3⋊D311yescharacteristic
798Q8—542no—
799D4—22no—
800D4—62no—
801D4—121no—
802D4—274no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—121no—
816C2×C4—182no—
817C2×C4—271no—
818C2×C4—542no—
819C2×C4—542no—
820C2×C4—542no—
821C2×C4—1081no—
822C2×C4C2×D3×C3⋊D311yescharacteristic
823C2×C3—28no—
824C2×C3—22no—
825C2×C3—24no—
826C2×C3—24no—
827C2×C3—24no—
828C2×C3—48no—
829C2×C3—48no—
830C2×C3—44no—
831C2×C3—41no—
832C2×C3—124no—
833C2×C3#6431214yes—
834C2×C3#6431414yes—
835C2×C3C2×#381114yes—
836C2×C3C2×D4×C3⋊D311yescharacteristic
837C2×C3#6436111yescharacteristic
838C2×C3#41×C3⋊D311yescharacteristic
839D3—41no—
840D3—1816no—
841D3—188no—
842D3—188no—
843D3—182no—
844D3—182no—
845D3—368no—
846D3—368no—
847D3—364no—
848D3—361no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—272no—
858C22—272no—
859C22—541no—
860C22—541no—
861C22—541no—
862C22—541no—
863C22—541no—
864C22—541no—
865C22—541no—
866C22—1084no—
867C22—1084no—
868C22#8903912yes—
869C22C22×D3×C3⋊D311yescharacteristic
870C4—21no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—181no—
875C4—181no—
876C4—181no—
877C4—181no—
878C4—272no—
879C3—24no—
880C3#1059516314yescomplemented
881C3#1059608111yescharacteristic, complemented
882C2—22no—
883C2—41no—
884C2—121no—
885C2—542no—
886C2—542no—
887C2—1081no—
888C2#1172458611yescharacteristic
889C2#1172458811yescharacteristic
890C2C2×#8903911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×#89028C2semidirect
3. C3×#64144C2semidirect
4. C32×#939C2semidirect
5. #11723638C2semidirect
6. #11723638C2semidirect
7. #11723627C2semidirect
8. #11723618C2semidirect
9. #11723616C2semidirect
10. C2×#88804C2semidirect
11. #11723592C2semidirect
12. #11723525C2semidirect
13. #11723498C2semidirect
14. #11723462C2semidirect
15. #11723442C2semidirect
26. C22×C3×C3⋊Dic3C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×#67C22semidirect
29. C22×C32×Dic3C22semidirect
30. C2×#6293C22semidirect
32. C2×#6291C22semidirect
33. C2×#6291C22semidirect
34. C2×#6289C22semidirect
35. C2×#6289C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. C3×#3757C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
41. C3×#3750C22semidirect
42. C3×#3750C22semidirect
43. C32×#217C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. #88806C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88804C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
64. #64144D3semidirect
73. C3×#939D3semidirect
101. #6312D4semidirect
147. C22×C3⋊Dic3C2×D3semidirect
161. C2×C3×#67C2×D3semidirect
162. C2×C3×#67C2×D3semidirect
164. C22×C3×Dic3C2×D3semidirect
176. #3757C2×D3semidirect
177. #3757C2×D3semidirect
178. #3757C2×D3semidirect
187. #3750C2×D3semidirect
188. #3750C2×D3semidirect
193. C3×#217C2×D3semidirect
194. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×Dic3⋊C4C2×D3semidirect
224. C2×C3⋊(C3⋊D3)#41semidirect
245. #939C3⋊D3semidirect
392. C2×#67C2×C3⋊D3semidirect
393. C2×#67C2×C3⋊D3semidirect
396. C22×Dic3C2×C3⋊D3semidirect
429. #217C2×C3⋊D3semidirect
444. (C2×D3)⋊C4C2×C3⋊D3semidirect
449. Dic3⋊C4C2×C3⋊D3semidirect
547. C33#546semidirect
784. C32#5610semidirect
785. C32#5654semidirect
880. C3#10595163semidirect
881. C3#10596081semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×#890282
C3×#641442
C32×#9392
#117236382
#117236272
#117236182
#117236162
C2×#888042
#117235922
#117235252
#117234982
#117234622
#117234422
#105960813
#105951633