Finite Group Databasebeta

← #13177505

Subgroups — #13177505

Order 1728.

2944 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3C2×D3×#638C211yesmaximal, characteristic, complemented
4C22×#6290C211yesmaximal, characteristic, complemented
5#11723980C211yesmaximal, characteristic, complemented
6C32×#937C211yesmaximal, characteristic, complemented
7#11723636C211yesmaximal, characteristic, complemented
8#11723634C211yesmaximal, characteristic, complemented
9#11723633C211yesmaximal, characteristic, complemented
10#11723626C211yesmaximal, characteristic, complemented
11#11723615C211yesmaximal, characteristic, complemented
12#11723541C211yesmaximal, characteristic, complemented
13#11723520C211yesmaximal, characteristic, complemented
14#11723519C211yesmaximal, characteristic, complemented
15#11723507C211yesmaximal, characteristic, complemented
16#10596061—31nomaximal
17#10595287—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic, complemented
19C23×C3×C3⋊D3C2211yescharacteristic, complemented
20C23×C32×D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×C33×D4C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C2×#6312C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C3×D4×C3⋊D3—24no—
29C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
31C2×C32×#67C2211yescharacteristic, complemented
32C2×C32×#67C2211yescharacteristic, complemented
33C3⋊D3×#67—24no—
34D3×#638—24no—
35C2×#6292C2211yescharacteristic, complemented
36C2×#6292C2211yescharacteristic, complemented
37C2×#6291C2211yescharacteristic, complemented
38C2×#6290—24no—
39C2×#6290C2211yescharacteristic
40C2×#6290C2211yescharacteristic, complemented
41C2×#6290C2211yescharacteristic, complemented
42C2×#6290C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
45C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
46#88864C2211yescharacteristic, complemented
47#88859C2211yescharacteristic, complemented
48#88857C2211yescharacteristic, complemented
49C32×#217C2211yescharacteristic, complemented
50C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
52#88807C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55#88803C2211yescharacteristic, complemented
56Dic3×C3⋊Dic3C2211yescharacteristic, complemented
57C22×#638—31no—
58C22×#638—31no—
59C2×D4×C3⋊D3—31no—
60C2×D4×C3⋊D3D311yescharacteristic, complemented
61C2×C3×D3×D4—34no—
62C2×D3×#67—34no—
63C2×D3×#67—34no—
64C22×#625—34no—
65C32×#120—31no—
66#64149—31no—
67#64148—31no—
68#64148—31no—
69#64148—34no—
70#64148—64no—
71#64146—31no—
72#64093—31no—
73#64093—31no—
74#64091—31no—
75#64091—31no—
76#64090—31no—
77#64090—31no—
78C3×#937D314yescomplemented
79#63979—34no—
80#63977—34no—
81#63976—34no—
82#67⋊Dic3—34no—
83#63970—34no—
84#63922—34no—
85#63906—34no—
86#63885—34no—
87#63879—34no—
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3—22no—
92C22×C3×C3⋊D3—22no—
93C22×C3×C3⋊D3—22no—
94C22×C3×C3⋊D3—22no—
95C22×C3×C3⋊D3—41no—
96C22×C3×C3⋊D3—41no—
97C22×C3×C3⋊D3C2311yescharacteristic
98C22×C3×C3⋊D3C2311yescharacteristic
99C22×C3×C3⋊D3C2311yescharacteristic
100C22×C32×D3—22no—
101C22×C32×D3—22no—
102C22×C32×D3—41no—
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×D3×C3⋊D3—22no—
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—41no—
108C33×D4—22no—
109C2×C33×C4C2311yescharacteristic
110#6312—22no—
111#6312—22no—
112C2×C3⋊(C3⋊Dic3)—22no—
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
116C3×#638—22no—
117C3×#638D414yescomplemented
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C3×C4⋊(C3⋊D3)—22no—
120C3×C4×C3⋊D3—22no—
121C32×#67—22no—
122C32×#67—41no—
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6292—22no—
126#6292—41no—
127#6291—22no—
128#6290—22no—
129#6290—22no—
130#6290—22no—
131#6290—22no—
132#6290D414yescomplemented
133Dic3×C3⋊D3—22no—
134D3×C3⋊Dic3—22no—
135D4×#67—91no—
136#5590—94no—
137C24×C32—31no—
138C23×C3⋊D3—31no—
139C23×C3⋊D3C2×D311yescharacteristic, complemented
140C23×C3⋊D3C2×D311yescharacteristic, complemented
141C23×C3×D3—34no—
142C23×C3×D3—34no—
143C23×C3×D3C2×D314yescomplemented
144C22×D32—34no—
145C2×C32×D4—24no—
146C2×C32×D4—31no—
147C2×C32×D4—31no—
148C2×C32×D4C2×D314yescomplemented
149C2×C32×D4C2×D311yescharacteristic, complemented
150C2×#638—31no—
151C2×#638—31no—
152C2×#638—31no—
153C2×#638—34no—
154C2×#638—34no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—64no—
161C2×#638—64no—
162C2×#638—64no—
163C2×#638—64no—
164C2×#638C2×D311yescharacteristic
165C2×#638C2×D311yescharacteristic, complemented
166C22×C3⋊Dic3—31no—
167C22×C3⋊Dic3—34no—
168C22×C3⋊Dic3—31no—
169C22×C3⋊Dic3—64no—
170D4×C3⋊D3—24no—
171D4×C3⋊D3—64no—
172C2×C4⋊(C3⋊D3)—31no—
173C2×C4⋊(C3⋊D3)—31no—
174C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
175C2×C4×C3⋊D3—31no—
176C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
177C2×C3×#67—34no—
178C2×C3×#67—34no—
179C2×C3×#67C2×D314yescomplemented
180C2×C3×#67C2×D314yescomplemented
181C3×D3×D4—616no—
182C2×C3×D12—34no—
183C2×C3×C4×D3—34no—
184D3×#67—616no—
185D3×#67—616no—
186C2×#626—34no—
187C2×#626—34no—
188C2×#626—34no—
189C2×#625—34no—
190C2×#625—34no—
191C2×#625—34no—
192C2×#625—34no—
193C2×#625—34no—
194C2×#625—616no—
195C2×D3×Dic3—34no—
196C2×D3×Dic3—34no—
197C32×C22⋊C4—31no—
198C32×C22⋊C4—31no—
199C32×C22⋊C4—31no—
200#3757—31no—
201#3757—34no—
202#3757—64no—
203#3752—31no—
204#3752—31no—
205#3752—31no—
206#3752—31no—
207#3752—34no—
208#3752—64no—
209#3750—31no—
210#3750—34no—
211#3750—31no—
212#3750—64no—
213C4×C3⋊Dic3—31no—
214C3×#217C2×D314yescomplemented
215C3×(C2×D3)⋊C4C2×D314yescomplemented
216C3×(C2×D3)⋊C4C2×D314yescomplemented
217Dic3⋊Dic3—34no—
218(C2×D3)⋊Dic3—34no—
219(C2×D3)⋊Dic3—34no—
220(C2×D3)⋊Dic3—34no—
221Dic32—34no—
222C22×C33—21no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33—21no—
226C22×C33—21no—
227C22×C33C2×D412yescomplemented
228C22×C33C2411yescharacteristic
229C2×C3⋊(C3⋊D3)—21no—
230C2×C3⋊(C3⋊D3)—21no—
231C2×C3⋊(C3⋊D3)—21no—
232C2×C3×C3⋊D3—21no—
233C2×C3×C3⋊D3—21no—
234C2×C3×C3⋊D3—21no—
235C2×C3×C3⋊D3—21no—
236C2×C3×C3⋊D3—21no—
237C2×C3×C3⋊D3—21no—
238C2×C3×C3⋊D3—21no—
239C2×C3×C3⋊D3—44no—
240C2×C3×C3⋊D3—44no—
241C2×C3×C3⋊D3C2×D412yescomplemented
242C2×C3×C3⋊D3C2×D412yescomplemented
243C2×C32×D3—21no—
244C2×C32×D3—21no—
245C2×C32×D3—21no—
246C2×C32×D3—21no—
247C2×C32×D3—21no—
248C2×C32×D3—44no—
249C2×C32×D3C2×D412yescomplemented
250D3×C3⋊D3—44no—
251C33×C4—21no—
252C3⋊(C3⋊Dic3)—21no—
253C3⋊(C3⋊Dic3)—21no—
254C3⋊(C3⋊Dic3)C2×D412yescomplemented
255C3×C3⋊Dic3C2×D412yescomplemented
256C32×Dic3—21no—
257C32×Dic3—21no—
258C22×C3×D4—91no—
259C22×#67—94no—
260C22×#67—94no—
261C22×#67—91no—
262C22×#67—91no—
263C2×D3×D4—34no—
264C2×D3×D4—94no—
265C2×D3×D4—91no—
266C3×#120—34no—
267#953—91no—
268#953—91no—
269#940—94no—
270#940—91no—
271#939—94no—
272#939—94no—
273#939—91no—
274#939—91no—
275#939—184no—
276#938—91no—
277#937—94no—
278#937—91no—
279#937C3⋊D311yescharacteristic, complemented
280D4×Dic3—91no—
281#930—91no—
282C4×#67—91no—
283#884—94no—
284#884—94no—
285#882—94no—
286#882—94no—
287#67⋊C4—94no—
288#67⋊C4—94no—
289C23×C32—24no—
290C23×C32—24no—
291C23×C32—31no—
292C23×C32—31no—
293C23×C32—62no—
294C23×C32—62no—
295C23×C32—121no—
296C23×C32C22×D314yes—
297C23×C32C22×D314yes—
298C23×C32C22×D311yescharacteristic
299C23×C32C22×D311yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3—31no—
305C22×C3⋊D3—34no—
306C22×C3⋊D3—41no—
307C22×C3⋊D3—41no—
308C22×C3⋊D3—64no—
309C22×C3⋊D3—62no—
310C22×C3⋊D3—62no—
311C22×C3⋊D3—121no—
312C22×C3⋊D3C22×D311yescharacteristic
313C22×C3⋊D3C22×D311yescharacteristic
314C22×C3⋊D3C22×D311yescharacteristic
315C22×C3×D3—28no—
316C22×C3×D3—28no—
317C22×C3×D3—34no—
318C22×C3×D3—34no—
319C22×C3×D3—34no—
320C22×C3×D3—44no—
321C22×C3×D3—68no—
322C22×C3×D3—68no—
323C22×C3×D3—68no—
324C22×C3×D3—68no—
325C22×C3×D3—124no—
326C22×C3×D3—124no—
327C22×C3×D3C22×D314yes—
328C22×C3×D3C22×D314yes—
329C2×D32—68no—
330C2×D32—68no—
331C2×D32—124no—
332C32×D4—22no—
333C32×D4—28no—
334C32×D4—48no—
335C32×D4—62no—
336C32×D4—121no—
337C2×C32×C4—24no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4C22×D314yes—
341C2×C32×C4C22×D311yescharacteristic
342#638—22no—
343#638—34no—
344#638—62no—
345#638—62no—
346#638—62no—
347#638—62no—
348#638—62no—
349#638—62no—
350#638—62no—
351#638—68no—
352#638—68no—
353#638—128no—
354#638—128no—
355#638#6714yescomplemented
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—31no—
359C2×C3⋊Dic3—34no—
360C2×C3⋊Dic3—34no—
361C2×C3⋊Dic3—34no—
362C2×C3⋊Dic3—64no—
363C2×C3⋊Dic3—64no—
364C2×C3⋊Dic3—64no—
365C2×C3⋊Dic3—62no—
366C2×C3⋊Dic3—62no—
367C2×C3⋊Dic3—68no—
368C2×C3⋊Dic3—128no—
369C2×C3⋊Dic3C22×D311yescharacteristic
370C4⋊(C3⋊D3)—22no—
371C4⋊(C3⋊D3)—62no—
372C4⋊(C3⋊D3)—121no—
373C4×C3⋊D3—22no—
374C4×C3⋊D3—62no—
375C3×#67—28no—
376C3×#67—316no—
377C3×#67—44no—
378C3×#67—68no—
379C2×C3×Dic3—34no—
380C2×C3×Dic3C22×D314yes—
381C2×C3×Dic3C22×D314yes—
382C3×D12—68no—
383C3×C4×D3—68no—
384#626—68no—
385#626—68no—
386#626—124no—
387#625—316no—
388#625—68no—
389#625—68no—
390#625—68no—
391#625—68no—
392D3×Dic3—68no—
393D3×Dic3—68no—
394D42—271noSylow
395C2×C33—22no—
396C2×C33—41no—
397C2×C33C22×D411yescharacteristic
398C2×C33C22×D411yescharacteristic
399C2×C33H(5,𝔽2)11yescharacteristic
400C3⋊(C3⋊D3)—41no—
401C3×C3⋊D3—22no—
402C3×C3⋊D3—22no—
403C3×C3⋊D3—41no—
404C32×D3—22no—
405C32×D3—41no—
406C24×C3—34no—
407C24×C3—91no—
408C24×C3—91no—
409C23×D3—34no—
410C23×D3—34no—
411C23×D3—94no—
412C23×D3—91no—
413C23×D3C2×C3⋊D311yescharacteristic, complemented
414C2×C3×D4—24no—
415C2×C3×D4—34no—
416C2×C3×D4—34no—
417C2×C3×D4—91no—
418C2×C3×D4—91no—
419C2×C3×D4—91no—
420C2×C3×D4—184no—
421C2×C3×D4D3214yescomplemented
422C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
423C22×C3×C4—91no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—94no—
427C2×#67—94no—
428C2×#67—91no—
429C2×#67—94no—
430C2×#67—94no—
431C2×#67—94no—
432C2×#67—94no—
433C2×#67—94no—
434C2×#67—94no—
435C2×#67—91no—
436C2×#67—91no—
437C2×#67—91no—
438C2×#67—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—184no—
444C2×#67—184no—
445C2×#67—184no—
446C2×#67—1816no—
447C2×#67—184no—
448C2×#67—1816no—
449C2×#67C2×C3⋊D311yescharacteristic, complemented
450C2×#67C2×C3⋊D311yescharacteristic, complemented
451C22×Dic3—94no—
452C22×Dic3—94no—
453C22×Dic3—91no—
454C22×Dic3—91no—
455C22×Dic3—184no—
456D3×D4—616no—
457D3×D4—1816no—
458D3×D4—184no—
459C2×D12—34no—
460C2×D12—94no—
461C2×D12—91no—
462C2×D12—94no—
463C2×C4×D3—34no—
464C2×C4×D3—94no—
465C2×C4×D3—91no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469#217—94no—
470#217—91no—
471#217—91no—
472#217—91no—
473#217—91no—
474#217—184no—
475#217C2×C3⋊D311yescharacteristic, complemented
476(C2×D3)⋊C4—94no—
477(C2×D3)⋊C4—94no—
478(C2×D3)⋊C4—94no—
479(C2×D3)⋊C4—94no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—184no—
482(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
483(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
484C4⋊Dic3—91no—
485Dic3⋊C4—94no—
486Dic3⋊C4—94no—
487Dic3⋊C4—91no—
488Dic3⋊C4—184no—
489C4×Dic3—94no—
490C4×Dic3—91no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—24no—
497C22×C32—28no—
498C22×C32—24no—
499C22×C32—24no—
500C22×C32—24no—
501C22×C32—24no—
502C22×C32—24no—
503C22×C32—32no—
504C22×C32—44no—
505C22×C32—44no—
506C22×C32—44no—
507C22×C32—44no—
508C22×C32—44no—
509C22×C32—61no—
510C22×C32—61no—
511C22×C32—61no—
512C22×C32—61no—
513C22×C32—61no—
514C22×C32—124no—
515C22×C32D3×D418yescomplemented
516C22×C32C2×#6712yescomplemented
517C22×C32C23×D314yes—
518C22×C32C23×D311yescharacteristic
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—21no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—21no—
526C2×C3⋊D3—44no—
527C2×C3⋊D3—44no—
528C2×C3⋊D3—61no—
529C2×C3⋊D3—61no—
530C2×C3⋊D3—61no—
531C2×C3⋊D3—64no—
532C2×C3⋊D3—64no—
533C2×C3⋊D3—64no—
534C2×C3⋊D3—124no—
535C2×C3⋊D3—124no—
536C2×C3⋊D3—124no—
537C2×C3⋊D3—124no—
538C2×C3⋊D3D3×D412yescomplemented
539C2×C3⋊D3C2×#6712yescomplemented
540C2×C3×D3—24no—
541C2×C3×D3—24no—
542C2×C3×D3—24no—
543C2×C3×D3—24no—
544C2×C3×D3—24no—
545C2×C3×D3—38no—
546C2×C3×D3—38no—
547C2×C3×D3—416no—
548C2×C3×D3—64no—
549C2×C3×D3—64no—
550C2×C3×D3—64no—
551C2×C3×D3—64no—
552C2×C3×D3—64no—
553C2×C3×D3—64no—
554C2×C3×D3—64no—
555C2×C3×D3—1216no—
556C2×C3×D3—1216no—
557C2×C3×D3D3×D418yescomplemented
558D32—1216no—
559C32×C4—21no—
560C32×C4—24no—
561C32×C4—44no—
562C32×C4—61no—
563C32×C4—61no—
564C3⋊Dic3—32no—
565C3⋊Dic3—38no—
566C3⋊Dic3—68no—
567C3⋊Dic3—61no—
568C3⋊Dic3—61no—
569C3⋊Dic3—64no—
570C3⋊Dic3—64no—
571C3⋊Dic3—124no—
572C3⋊Dic3—124no—
573C3⋊Dic3C2×#6712yescomplemented
574C3×Dic3—24no—
575C3×Dic3—24no—
576C3×Dic3—38no—
577C22×D4—91no—
578C22×D4—271no—
579C22×D4—271no—
580C22×D4—271no—
581#127—271no—
582#121—271no—
583#121—271no—
584#121—271no—
585#121—271no—
586#120—31no—
587#120—271no—
588#120—271no—
589#120—271no—
590C4×D4—271no—
591C4×D4—271no—
592C33D4211yescharacteristic, complemented, Sylow
593C23×C3—24no—
594C23×C3—24no—
595C23×C3—34no—
596C23×C3—34no—
597C23×C3—68no—
598C23×C3—68no—
599C23×C3—91no—
600C23×C3—91no—
601C23×C3—91no—
602C23×C3—124no—
603C23×C3—182no—
604C23×C3—182no—
605C23×C3—182no—
606C23×C3—182no—
607C23×C3—361no—
608C23×C3—361no—
609C23×C3C2×D3214yes—
610C23×C3C2×D3214yes—
611C23×C3C22×C3⋊D311yescharacteristic
612C23×C3C22×C3⋊D311yescharacteristic
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—34no—
616C22×D3—34no—
617C22×D3—34no—
618C22×D3—41no—
619C22×D3—68no—
620C22×D3—68no—
621C22×D3—68no—
622C22×D3—68no—
623C22×D3—94no—
624C22×D3—91no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—184no—
628C22×D3—182no—
629C22×D3—188no—
630C22×D3—188no—
631C22×D3—182no—
632C22×D3—361no—
633C22×D3—364no—
634C22×D3C22×C3⋊D311yescharacteristic
635C22×D3C22×C3⋊D311yescharacteristic
636C3×D4—28no—
637C3×D4—22no—
638C3×D4—48no—
639C3×D4—68no—
640C3×D4—94no—
641C3×D4—124no—
642C3×D4—182no—
643C3×D4—182no—
644C2×C3×C4—24no—
645C2×C3×C4—34no—
646C2×C3×C4—34no—
647C2×C3×C4—91no—
648C2×C3×C4—182no—
649C2×C3×C4C2×D3214yes—
650C2×C3×C4C22×C3⋊D311yescharacteristic
651#67—22no—
652#67—316no—
653#67—41no—
654#67—68no—
655#67—916no—
656#67—94no—
657#67—182no—
658#67—188no—
659#67—182no—
660#67—188no—
661#67—182no—
662#67—188no—
663#67—182no—
664#67—182no—
665#67—188no—
666#67—188no—
667#67—188no—
668#67—188no—
669#67—182no—
670#67—182no—
671#67—368no—
672#67—368no—
673#67—361no—
674C2×Dic3—34no—
675C2×Dic3—94no—
676C2×Dic3—91no—
677C2×Dic3—94no—
678C2×Dic3—94no—
679C2×Dic3—91no—
680C2×Dic3—91no—
681C2×Dic3—184no—
682C2×Dic3—184no—
683C2×Dic3—184no—
684C2×Dic3—182no—
685C2×Dic3—188no—
686C2×Dic3—182no—
687C2×Dic3—188no—
688C2×Dic3—368no—
689C2×Dic3C22×C3⋊D311yescharacteristic
690C2×Dic3C22×C3⋊D311yescharacteristic
691D12—68no—
692D12—188no—
693D12—182no—
694D12—364no—
695C4×D3—68no—
696C4×D3—188no—
697C4×D3—182no—
698C2×C32—22no—
699C2×C32—24no—
700C2×C32—24no—
701C2×C32—24no—
702C2×C32—28no—
703C2×C32—48no—
704C2×C32—41no—
705C2×C32—44no—
706C2×C32—62no—
707C2×C32—84no—
708C2×C32—121no—
709C2×C32C2×D3×D414yes—
710C2×C32C2×D3×D414yes—
711C2×C32C2×D3×D411yescharacteristic
712C2×C32#100414yes—
713C2×C32#100411yescharacteristic
714C2×C32C22×#6711yescharacteristic
715C3⋊D3—22no—
716C3⋊D3—22no—
717C3⋊D3—41no—
718C3⋊D3—121no—
719C3⋊D3—124no—
720C3⋊D3—244no—
721C3×D3—28no—
722C3×D3—44no—
723C3×D3—68no—
724C3×D3—68no—
725C3×D3—124no—
726C24—31no—
727C24—91no—
728C24—91no—
729C24—271no—
730C2×D4—31no—
731C2×D4—31no—
732C2×D4—91no—
733C2×D4—91no—
734C2×D4—91no—
735C2×D4—184no—
736C2×D4—271no—
737C2×D4—271no—
738C2×D4—271no—
739C2×D4—271no—
740C2×D4—271no—
741C2×D4—271no—
742C2×D4—271no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—544no—
747C2×D4—544no—
748C2×D4—544no—
749C2×D4D3×C3⋊D311yescharacteristic, complemented
750C22×C4—91no—
751C22×C4—271no—
752C22×C4—271no—
753C22×C4—271no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—31no—
757C22⋊C4—31no—
758C22⋊C4—31no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C22⋊C4—271no—
763C22⋊C4—271no—
764C42—271no—
765C22×C3—24no—
766C22×C3—24no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—24no—
770C22×C3—24no—
771C22×C3—24no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—24no—
776C22×C3—28no—
777C22×C3—38no—
778C22×C3—44no—
779C22×C3—44no—
780C22×C3—44no—
781C22×C3—44no—
782C22×C3—44no—
783C22×C3—64no—
784C22×C3—64no—
785C22×C3—64no—
786C22×C3—64no—
787C22×C3—64no—
788C22×C3—92no—
789C22×C3—92no—
790C22×C3—1216no—
791C22×C3—181no—
792C22×C3—181no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—364no—
799C22×C3—364no—
800C22×C3D3×#6718yescomplemented
801C22×C3D4×C3⋊D312yescomplemented
802C22×C3C22×D3214yes—
803C22×C3C23×C3⋊D311yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—21no—
807C2×D3—21no—
808C2×D3—21no—
809C2×D3—38no—
810C2×D3—38no—
811C2×D3—44no—
812C2×D3—64no—
813C2×D3—64no—
814C2×D3—64no—
815C2×D3—64no—
816C2×D3—64no—
817C2×D3—64no—
818C2×D3—64no—
819C2×D3—1216no—
820C2×D3—1216no—
821C2×D3—184no—
822C2×D3—184no—
823C2×D3—184no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—181no—
827C2×D3—364no—
828C2×D3—364no—
829C2×D3—364no—
830C2×D3—364no—
831C2×D3—3616no—
832C2×D3D4×C3⋊D312yescomplemented
833C3×C4—24no—
834C3×C4—21no—
835C3×C4—44no—
836C3×C4—64no—
837C3×C4—64no—
838C3×C4—92no—
839Dic3—21no—
840Dic3—21no—
841Dic3—38no—
842Dic3—98no—
843Dic3—92no—
844Dic3—188no—
845Dic3—184no—
846Dic3—184no—
847Dic3—181no—
848Dic3—181no—
849Dic3—364no—
850Dic3—364no—
851C32—24no—
852C32#559014yescomplemented
853C32D4×#6711yescharacteristic, complemented
854C23—31no—
855C23—31no—
856C23—62no—
857C23—62no—
858C23—91no—
859C23—91no—
860C23—91no—
861C23—121no—
862C23—182no—
863C23—182no—
864C23—182no—
865C23—182no—
866C23—271no—
867C23—361no—
868C23—361no—
869C23—542no—
870C23—542no—
871C23—1081no—
872C23C2×D3×C3⋊D311yescharacteristic
873C23C2×D3×C3⋊D311yescharacteristic
874D4—22no—
875D4—62no—
876D4—94no—
877D4—121no—
878D4—182no—
879D4—182no—
880D4—274no—
881D4—542no—
882D4—542no—
883D4—542no—
884D4—542no—
885D4—542no—
886D4—542no—
887D4—542no—
888D4—542no—
889D4—1081no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—91no—
893C2×C4—182no—
894C2×C4—271no—
895C2×C4—271no—
896C2×C4—271no—
897C2×C4—542no—
898C2×C4—542no—
899C2×C4—542no—
900C2×C4C2×D3×C3⋊D311yescharacteristic
901C2×C3—28no—
902C2×C3—22no—
903C2×C3—24no—
904C2×C3—24no—
905C2×C3—24no—
906C2×C3—48no—
907C2×C3—44no—
908C2×C3—41no—
909C2×C3—68no—
910C2×C3—84no—
911C2×C3—124no—
912C2×C3—182no—
913C2×C3—182no—
914C2×C3—361no—
915C2×C3D32×D414yes—
916C2×C3#6431314yes—
917C2×C3C2×D3×#6714yes—
918C2×C3C2×D4×C3⋊D311yescharacteristic
919C2×C3C2×D4×C3⋊D311yescharacteristic
920C2×C3#6436111yescharacteristic
921D3—22no—
922D3—41no—
923D3—68no—
924D3—68no—
925D3—124no—
926D3—364no—
927D3—361no—
928D3—724no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—32no—
935C22—61no—
936C22—61no—
937C22—61no—
938C22—61no—
939C22—61no—
940C22—92no—
941C22—92no—
942C22—124no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—181no—
950C22—364no—
951C22—364no—
952C22—541no—
953C22—541no—
954C22—541no—
955C22—1084no—
956C22C3⋊D3×#6712yescomplemented
957C22C22×D3×C3⋊D311yescharacteristic
958C4—21no—
959C4—61no—
960C4—61no—
961C4—92no—
962C4—272no—
963C4—541no—
964C4—541no—
965C3—24no—
966C3#1059528714yescomplemented
967C3#1059606111yescharacteristic, complemented
968C2—22no—
969C2—41no—
970C2—62no—
971C2—121no—
972C2—182no—
973C2—182no—
974C2—361no—
975C2—1081no—
976C2D3×D4×C3⋊D311yescharacteristic
977C2#1172458711yescharacteristic
978C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×D3×#638C2semidirect
4. C22×#6290C2semidirect
5. #11723980C2semidirect
6. C32×#937C2semidirect
7. #11723636C2semidirect
8. #11723634C2semidirect
9. #11723633C2semidirect
10. #11723626C2semidirect
11. #11723615C2semidirect
12. #11723541C2semidirect
13. #11723520C2semidirect
14. #11723519C2semidirect
15. #11723507C2semidirect
18. C23×C3×C3⋊D3C22semidirect
19. C23×C3×C3⋊D3C22semidirect
20. C23×C32×D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×C33×D4C22semidirect
23. C2×#6312C22semidirect
24. C2×#6312C22semidirect
25. C22×C3⋊(C3⋊Dic3)C22semidirect
27. C2×C3×#638C22semidirect
29. C2×C3×C4⋊(C3⋊D3)C22semidirect
30. C2×C3×C4×C3⋊D3C22semidirect
31. C2×C32×#67C22semidirect
32. C2×C32×#67C22semidirect
35. C2×#6292C22semidirect
36. C2×#6292C22semidirect
37. C2×#6291C22semidirect
40. C2×#6290C22semidirect
41. C2×#6290C22semidirect
42. C2×#6290C22semidirect
43. C2×#6290C22semidirect
44. C2×Dic3×C3⋊D3C22semidirect
45. C2×D3×C3⋊Dic3C22semidirect
46. #88864C22semidirect
47. #88859C22semidirect
48. #88857C22semidirect
49. C32×#217C22semidirect
50. C32×(C2×D3)⋊C4C22semidirect
51. C32×(C2×D3)⋊C4C22semidirect
52. #88807C22semidirect
53. #88803C22semidirect
54. #88803C22semidirect
55. #88803C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
60. C2×D4×C3⋊D3D3semidirect
78. C3×#937D3semidirect
117. C3×#638D4semidirect
132. #6290D4semidirect
139. C23×C3⋊D3C2×D3semidirect
140. C23×C3⋊D3C2×D3semidirect
143. C23×C3×D3C2×D3semidirect
148. C2×C32×D4C2×D3semidirect
149. C2×C32×D4C2×D3semidirect
165. C2×#638C2×D3semidirect
174. C2×C4⋊(C3⋊D3)C2×D3semidirect
176. C2×C4×C3⋊D3C2×D3semidirect
179. C2×C3×#67C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
214. C3×#217C2×D3semidirect
215. C3×(C2×D3)⋊C4C2×D3semidirect
216. C3×(C2×D3)⋊C4C2×D3semidirect
227. C22×C33C2×D4semidirect
241. C2×C3×C3⋊D3C2×D4semidirect
242. C2×C3×C3⋊D3C2×D4semidirect
249. C2×C32×D3C2×D4semidirect
254. C3⋊(C3⋊Dic3)C2×D4semidirect
255. C3×C3⋊Dic3C2×D4semidirect
279. #937C3⋊D3semidirect
355. #638#67semidirect
413. C23×D3C2×C3⋊D3semidirect
421. C2×C3×D4D32semidirect
422. C2×C3×D4C2×C3⋊D3semidirect
449. C2×#67C2×C3⋊D3semidirect
450. C2×#67C2×C3⋊D3semidirect
475. #217C2×C3⋊D3semidirect
482. (C2×D3)⋊C4C2×C3⋊D3semidirect
483. (C2×D3)⋊C4C2×C3⋊D3semidirect
515. C22×C32D3×D4semidirect
516. C22×C32C2×#67semidirect
538. C2×C3⋊D3D3×D4semidirect
539. C2×C3⋊D3C2×#67semidirect
557. C2×C3×D3D3×D4semidirect
573. C3⋊Dic3C2×#67semidirect
592. C33D42semidirect
749. C2×D4D3×C3⋊D3semidirect
800. C22×C3D3×#67semidirect
801. C22×C3D4×C3⋊D3semidirect
832. C2×D3D4×C3⋊D3semidirect
852. C32#5590semidirect
853. C32D4×#67semidirect
956. C22C3⋊D3×#67semidirect
966. C3#10595287semidirect
967. C3#10596061semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C3⋊D3×#672
C2×D3×#6382
C22×#62902
#117239802
C32×#9372
#117236362
#117236342
#117236332
#117236262
#117236152
#117235412
#117235202
#117235192
#117235072
#105960613
#105952873