Finite Group Databasebeta

← #13177387

Subgroups — #13177387

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723980C211yesmaximal, characteristic, complemented
4C32×#935C211yesmaximal, characteristic, complemented
5#11723636C211yesmaximal, characteristic, complemented
6#11723636C211yesmaximal, characteristic, complemented
7#11723626C211yesmaximal, characteristic, complemented
8#11723623C211yesmaximal, characteristic, complemented
9C3⋊D3×#217C211yesmaximal, characteristic, complemented
10C2×#88803C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723512C211yesmaximal, characteristic, complemented
13#11723488C211yesmaximal, characteristic, complemented
14#11723482C211yesmaximal, characteristic, complemented
15#11723418C211yesmaximal, characteristic, complemented
16#10596125—31nomaximal
17#10595148—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic
26C3×D4×C3⋊D3—24no—
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
28C2×C3×C4×C3⋊D3C2211yescharacteristic
29C22×C32×Dic3C2211yescharacteristic, complemented
30C2×#6293C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35#89031—24no—
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88857C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42C32×#217C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44C32×Dic3⋊C4C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46#88807C2211yescharacteristic, complemented
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3D311yescharacteristic, complemented
56C2×#3828—31no—
57C2×C3×D3×D4—34no—
58C2×#3804—34no—
59C32×#123—31no—
60#64148—31no—
61#64148—34no—
62#64148—64no—
63C2×#3752—31no—
64#64105—31no—
65#64104—31no—
66#64103—31no—
67#64102—31no—
68#64094—31no—
69#64093—31no—
70#64091—31no—
71#64091—31no—
72#64090—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#935D314yescomplemented
75#63977—34no—
76#63977—34no—
77#67⋊Dic3—34no—
78D3×#217—34no—
79C2×(C2×D3)⋊Dic3—34no—
80#63959—34no—
81#63958—34no—
82#63904—34no—
83#63886—34no—
84#63884—34no—
85#63851—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—22no—
91C22×C3×C3⋊D3—22no—
92C22×C3×C3⋊D3—22no—
93C22×C3×C3⋊D3—41no—
94C22×C3×C3⋊D3—41no—
95C22×C3×C3⋊D3C2311yescharacteristic
96C22×C3×C3⋊D3C2311yescharacteristic
97C22×C3×C3⋊D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312—41no—
102C2×C3⋊(C3⋊Dic3)—41no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C3×#638—22no—
107C3×#638D414yescomplemented
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4⋊(C3⋊D3)—22no—
110C3×C4×C3⋊D3—22no—
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6293—22no—
117#6292—22no—
118#6292—22no—
119#6292—41no—
120#6289—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—41no—
123#5806—91no—
124#5654—94no—
125C23×C3⋊D3C2×D311yescharacteristic
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—34no—
128C23×C3×D3—34no—
129C2×C32×D4—24no—
130C2×C32×D4C2×D314yes—
131C2×C32×D4C2×D311yescharacteristic
132C22×C32×C4—31no—
133C2×#638—31no—
134C2×#638—34no—
135C2×#638—31no—
136C2×#638—34no—
137C2×#638—64no—
138C2×#638—64no—
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—34no—
143C22×C3⋊Dic3—64no—
144D4×C3⋊D3—24no—
145#3828—64no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3C2×D311yescharacteristic
154C2×#634—31no—
155C2×C3×#67—34no—
156C2×C3×#67—34no—
157C22×C3×Dic3C2×D314yescomplemented
158C3×D3×D4—616no—
159C2×C3×D12—34no—
160C2×C3×C4×D3—34no—
161C2×#627—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#624—34no—
166#3804—616no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174#3757—31no—
175#3757—34no—
176#3757—64no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—34no—
186#3752—64no—
187#3750—31no—
188#3750—34no—
189#3750—31no—
190#3750—64no—
191C4×C3⋊Dic3—31no—
192C3×#217C2×D314yescomplemented
193C3×#217C2×D314yescomplemented
194C3×#217C2×D314yescomplemented
195C3×Dic3⋊C4C2×D314yescomplemented
196C3×Dic3⋊C4C2×D314yescomplemented
197Dic3⋊Dic3—34no—
198(C2×D3)⋊Dic3—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33C2×D412yes—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
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—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—44no—
224C2×C3×C3⋊D3—44no—
225C2×C3×C3⋊D3C2×D412yes—
226C2×C3×C3⋊D3#4112yescomplemented
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3C2×D412yes—
232C32×Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×C3×D4—91no—
237C2×#237—91no—
238C2×D3×D4—34no—
239C2×#235—94no—
240C3×#123—34no—
241#953—91no—
242#953—91no—
243C2×#217—91no—
244C2×#217—91no—
245#939—94no—
246#939—91no—
247#939—91no—
248#939—184no—
249#938—91no—
250#936—91no—
251#935—91no—
252#935C3⋊D311yescharacteristic, complemented
253D4×Dic3—91no—
254C4×#67—91no—
255C2×(C2×D3)⋊C4—94no—
256#924—91no—
257#896—94no—
258#895—94no—
259#894—94no—
260#893—94no—
261#885—94no—
262#884—94no—
263#882—94no—
264#882—94no—
265#67⋊C4—94no—
266D3×C22⋊C4—94no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32C22×D314yes—
270C23×C32C22×D314yes—
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—22no—
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—41no—
280C22×C3⋊D3—41no—
281C22×C3⋊D3—64no—
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3⋊D3C22×D311yescharacteristic
284C22×C3⋊D3C22×D311yescharacteristic
285C22×C3×D3—34no—
286C22×C3×D3—34no—
287C22×C3×D3—34no—
288C22×C3×D3—68no—
289C22×C3×D3—68no—
290C22×C3×D3—68no—
291C22×C3×D3—68no—
292C22×C3×D3—124no—
293C22×C3×D3—124no—
294C32×D4—22no—
295C32×D4—28no—
296C32×D4—48no—
297C2×C32×C4—24no—
298C2×C32×C4—31no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—62no—
303C2×C32×C4C22×D314yes—
304C2×C32×C4C22×D311yescharacteristic
305#638—22no—
306#638—62no—
307#638—68no—
308#638—128no—
309#638—121no—
310#638—124no—
311#638—128no—
312#638#6714yescomplemented
313C2×C3⋊Dic3—31no—
314C2×C3⋊Dic3—31no—
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—34no—
318C2×C3⋊Dic3—34no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—121no—
323C2×C3⋊Dic3—124no—
324C2×C3⋊Dic3—128no—
325C2×C3⋊Dic3C22×D311yescharacteristic
326C4⋊(C3⋊D3)—22no—
327C4⋊(C3⋊D3)—62no—
328C4⋊(C3⋊D3)—62no—
329C4⋊(C3⋊D3)—121no—
330C4×C3⋊D3—22no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—121no—
334#634—62no—
335C3×#67—316no—
336C3×#67—68no—
337C2×C3×Dic3—28no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3C22×D314yes—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C2×C3×Dic3C22×D314yes—
343C3×D12—68no—
344C3×C4×D3—68no—
345#627—68no—
346#626—68no—
347#626—68no—
348#626—124no—
349#624—68no—
350D3×Dic3—68no—
351D3×Dic3—124no—
352#546—271noSylow
353C2×C33—22no—
354C2×C33—41no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4111yescharacteristic
357C2×C33H(5,𝔽2)11yescharacteristic
358C3⋊(C3⋊D3)—41no—
359C3×C3⋊D3—22no—
360C3×C3⋊D3—22no—
361C3×C3⋊D3—41no—
362C24×C3—91no—
363C24×C3—91no—
364C23×D3—34no—
365C23×D3—34no—
366C2×C3×D4—24no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C2×C3×D4—91no—
370C2×C3×D4—184no—
371C2×C3×D4D3214yes—
372C2×C3×D4C2×C3⋊D311yescharacteristic
373C22×C3×C4—34no—
374C22×C3×C4—91no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—94no—
378C2×#67—91no—
379C2×#67—94no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—184no—
385C2×#67—184no—
386C22×Dic3—94no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—184no—
391C22×Dic3C2×C3⋊D311yescharacteristic, complemented
392#237—184no—
393D3×D4—616no—
394#235—1816no—
395C2×D12—34no—
396C2×D12—94no—
397C2×D12—94no—
398C2×D12—94no—
399C2×C4×D3—34no—
400C2×C4×D3—94no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—94no—
404C2×Dic6—94no—
405C2×Dic6—91no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411#217—94no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—184no—
421#217C2×C3⋊D311yescharacteristic, complemented
422#217C2×C3⋊D311yescharacteristic, complemented
423#217C2×C3⋊D311yescharacteristic, complemented
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—94no—
429(C2×D3)⋊C4—94no—
430(C2×D3)⋊C4—94no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—184no—
434C4⋊Dic3—91no—
435Dic3⋊C4—94no—
436Dic3⋊C4—94no—
437Dic3⋊C4—91no—
438Dic3⋊C4—184no—
439Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
440Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
441C4×Dic3—94no—
442C4×Dic3—91no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—24no—
449C22×C32—28no—
450C22×C32—24no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—44no—
456C22×C32—44no—
457C22×C32—44no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32D3×D418yes—
461C22×C32C2×#6712yes—
462C22×C32C23×D314yes—
463C22×C32C23×D311yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—44no—
472C2×C3⋊D3—44no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—61no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—64no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—124no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3#23712yescomplemented
483C2×C3⋊D3C2×#6712yes—
484C2×C3×D3—38no—
485C2×C3×D3—38no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3—64no—
489C2×C3×D3—64no—
490C2×C3×D3—64no—
491C2×C3×D3—64no—
492C2×C3×D3—64no—
493C2×C3×D3—1216no—
494C2×C3×D3—1216no—
495C32×C4—21no—
496C32×C4—24no—
497C32×C4—44no—
498C32×C4—61no—
499C32×C4—61no—
500C32×C4—61no—
501C32×C4—61no—
502C3⋊Dic3—68no—
503C3⋊Dic3—61no—
504C3⋊Dic3—61no—
505C3⋊Dic3—64no—
506C3⋊Dic3—61no—
507C3⋊Dic3—64no—
508C3⋊Dic3—64no—
509C3⋊Dic3—124no—
510C3⋊Dic3—124no—
511C3⋊Dic3C2×#6712yes—
512C3×Dic3—24no—
513C3×Dic3—24no—
514C3×Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3—38no—
517C2×#41—271no—
518C22×D4—91no—
519#124—271no—
520#123—31no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C33#54611yescharacteristic, complemented, Sylow
533C23×C3—24no—
534C23×C3—24no—
535C23×C3—91no—
536C23×C3—91no—
537C23×C3—91no—
538C23×C3—182no—
539C23×C3—182no—
540C23×C3—182no—
541C23×C3—182no—
542C23×C3—361no—
543C23×C3—361no—
544C23×C3C2×D3214yes—
545C23×C3C2×D3214yes—
546C23×C3C22×C3⋊D311yescharacteristic
547C23×C3C22×C3⋊D311yescharacteristic
548C22×D3—34no—
549C22×D3—34no—
550C22×D3—34no—
551C22×D3—68no—
552C22×D3—68no—
553C22×D3—68no—
554C22×D3—68no—
555C22×D3—94no—
556C22×D3—91no—
557C22×D3—124no—
558C22×D3—124no—
559C22×D3—184no—
560C3×D4—28no—
561C3×D4—22no—
562C3×D4—48no—
563C3×D4—94no—
564C3×D4—182no—
565C3×D4—182no—
566C2×C3×C4—24no—
567C2×C3×C4—34no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—34no—
571C2×C3×C4—68no—
572C2×C3×C4—91no—
573C2×C3×C4—182no—
574C2×C3×C4C2×D3214yes—
575C2×C3×C4C22×C3⋊D311yescharacteristic
576#67—316no—
577#67—68no—
578#67—182no—
579#67—182no—
580#67—188no—
581#67—182no—
582#67—368no—
583#67—361no—
584#67—364no—
585#67—361no—
586#67—368no—
587C2×Dic3—22no—
588C2×Dic3—34no—
589C2×Dic3—94no—
590C2×Dic3—94no—
591C2×Dic3—94no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—184no—
596C2×Dic3—184no—
597C2×Dic3—184no—
598C2×Dic3—182no—
599C2×Dic3—361no—
600C2×Dic3—364no—
601C2×Dic3—361no—
602C2×Dic3—368no—
603C2×Dic3C22×C3⋊D311yescharacteristic
604C2×Dic3C22×C3⋊D311yescharacteristic
605C2×Dic3C22×C3⋊D311yescharacteristic
606C2×Dic3C22×C3⋊D311yescharacteristic
607D12—68no—
608D12—188no—
609D12—188no—
610D12—364no—
611C4×D3—68no—
612C4×D3—182no—
613C4×D3—188no—
614C4×D3—188no—
615C4×D3—364no—
616Dic6—182no—
617Dic6—188no—
618C2×C32—22no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—24no—
622C2×C32—28no—
623C2×C32—48no—
624C2×C32—41no—
625C2×C32—44no—
626C2×C32—84no—
627C2×C32C2×D3×D414yes—
628C2×C32C2×#23711yescharacteristic
629C2×C32#100411yescharacteristic
630C2×C32D3×#4114yes—
631C2×C32#100914yes—
632C2×C32C22×#6711yescharacteristic
633C3⋊D3—22no—
634C3⋊D3—22no—
635C3⋊D3—41no—
636C3⋊D3—121no—
637C3⋊D3—124no—
638C3⋊D3—244no—
639C3×D3—68no—
640C3×D3—68no—
641C3×D3—124no—
642C24—91no—
643C24—91no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—91no—
647C2×D4—91no—
648C2×D4—91no—
649C2×D4—184no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4D3×C3⋊D311yescharacteristic
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—271no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—24no—
690C22×C3—28no—
691C22×C3—44no—
692C22×C3—44no—
693C22×C3—44no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—92no—
697C22×C3—92no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3—364no—
706C22×C3—364no—
707C22×C3D3×#6718yes—
708C22×C3D4×C3⋊D312yes—
709C22×C3C22×D3214yes—
710C22×C3C23×C3⋊D311yescharacteristic
711C2×D3—38no—
712C2×D3—38no—
713C2×D3—64no—
714C2×D3—64no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—64no—
719C2×D3—64no—
720C2×D3—1216no—
721C2×D3—1216no—
722C2×D3—184no—
723C2×D3—184no—
724C2×D3—184no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3—364no—
731C3×C4—24no—
732C3×C4—21no—
733C3×C4—44no—
734C3×C4—64no—
735C3×C4—64no—
736C3×C4—64no—
737C3×C4—64no—
738C3×C4—92no—
739Dic3—21no—
740Dic3—21no—
741Dic3—21no—
742Dic3—21no—
743Dic3—38no—
744Dic3—188no—
745Dic3—184no—
746Dic3—184no—
747Dic3—184no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—364no—
752Dic3—364no—
753C32—24no—
754C32#565414yescomplemented
755C32#580611yescharacteristic, complemented
756C23—91no—
757C23—91no—
758C23—91no—
759C23—182no—
760C23—182no—
761C23—182no—
762C23—182no—
763C23—271no—
764C23—361no—
765C23—361no—
766C23C2×D3×C3⋊D311yescharacteristic
767C23C2×D3×C3⋊D311yescharacteristic
768Q8—542no—
769D4—22no—
770D4—94no—
771D4—182no—
772D4—182no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—62no—
783C2×C4—91no—
784C2×C4—182no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—271no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4—1081no—
792C2×C4C2×D3×C3⋊D311yescharacteristic
793C2×C3—22no—
794C2×C3—28no—
795C2×C3—24no—
796C2×C3—24no—
797C2×C3—24no—
798C2×C3—48no—
799C2×C3—41no—
800C2×C3—44no—
801C2×C3—84no—
802C2×C3—182no—
803C2×C3—182no—
804C2×C3—361no—
805C2×C3D3×#23714yes—
806C2×C3#6431414yes—
807C2×C3C2×D3×#6714yes—
808C2×C3C2×D4×C3⋊D311yescharacteristic
809C2×C3#41×C3⋊D311yescharacteristic
810C2×C3#6436611yescharacteristic
811D3—68no—
812D3—68no—
813D3—124no—
814D3—361no—
815D3—364no—
816D3—724no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—92no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—181no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—364no—
832C22—364no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22C3⋊D3×#6712yes—
837C22C22×D3×C3⋊D311yescharacteristic
838C4—21no—
839C4—61no—
840C4—61no—
841C4—61no—
842C4—61no—
843C4—92no—
844C4—541no—
845C4—541no—
846C4—541no—
847C3—24no—
848C3#1059514814yescomplemented
849C3#1059612511yescharacteristic, complemented
850C2—22no—
851C2—41no—
852C2—182no—
853C2—182no—
854C2—361no—
855C2—1081no—
856C2C3⋊D3×#23711yescharacteristic
857C2#1172458911yescharacteristic
858C2C2×C3⋊D3×#6711yescharacteristic
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×C3×D4×C3⋊D3C2semidirect
2. C2×#89031C2semidirect
3. #11723980C2semidirect
4. C32×#935C2semidirect
5. #11723636C2semidirect
6. #11723636C2semidirect
7. #11723626C2semidirect
8. #11723623C2semidirect
9. C3⋊D3×#217C2semidirect
10. C2×#88803C2semidirect
11. #11723591C2semidirect
12. #11723512C2semidirect
13. #11723488C2semidirect
14. #11723482C2semidirect
15. #11723418C2semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
23. C22×C3⋊(C3⋊Dic3)C22semidirect
29. C22×C32×Dic3C22semidirect
30. C2×#6293C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6289C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. #88864C22semidirect
39. #88859C22semidirect
40. #88857C22semidirect
41. C32×#217C22semidirect
42. C32×#217C22semidirect
43. C32×#217C22semidirect
44. C32×Dic3⋊C4C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. #88807C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. C2×D4×C3⋊D3D3semidirect
74. C3×#935D3semidirect
107. C3×#638D4semidirect
157. C22×C3×Dic3C2×D3semidirect
192. C3×#217C2×D3semidirect
193. C3×#217C2×D3semidirect
194. C3×#217C2×D3semidirect
195. C3×Dic3⋊C4C2×D3semidirect
196. C3×Dic3⋊C4C2×D3semidirect
226. C2×C3×C3⋊D3#41semidirect
252. #935C3⋊D3semidirect
312. #638#67semidirect
391. C22×Dic3C2×C3⋊D3semidirect
421. #217C2×C3⋊D3semidirect
422. #217C2×C3⋊D3semidirect
423. #217C2×C3⋊D3semidirect
439. Dic3⋊C4C2×C3⋊D3semidirect
440. Dic3⋊C4C2×C3⋊D3semidirect
482. C2×C3⋊D3#237semidirect
532. C33#546semidirect
754. C32#5654semidirect
755. C32#5806semidirect
848. C3#10595148semidirect
849. C3#10596125semidirect

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×#890312
#117239802
C32×#9352
#117236362
#117236262
#117236232
C3⋊D3×#2172
C2×#888032
#117235912
#117235122
#117234882
#117234822
#117234182
#105961253
#105951483