Finite Group Databasebeta

← #13151291

Subgroups — #13151291

Order 1728.

1274 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic, complemented
3C9×#939C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721291C211yesmaximal, characteristic, complemented
7#11721288C211yesmaximal, characteristic, complemented
8#11721278C211yesmaximal, characteristic, complemented
9#11721277C211yesmaximal, characteristic, complemented
10#11721275C211yesmaximal, characteristic, complemented
11C2×#88445C211yesmaximal, characteristic, complemented
12#11721051C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720957C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10595308—31nomaximal
17#10589707—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C23×C3⋊D9C2211yescharacteristic, complemented
20C22×D3×D9C2211yescharacteristic, complemented
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic
23C2×#6233C2211yescharacteristic, complemented
24D4×C3⋊D9—24no—
25C2×C4⋊(C3⋊D9)C2211yescharacteristic
26C2×C4×C3⋊D9C2211yescharacteristic, complemented
27C2×C9×#67C2211yescharacteristic, complemented
28C2×C9×#67C2211yescharacteristic, complemented
29C2×C3×#611C2211yescharacteristic, complemented
30C2×C3×#611C2211yescharacteristic, complemented
31C22×C9×Dic3C2211yescharacteristic, complemented
32C22×C3×Dic9C2211yescharacteristic, complemented
33#88668—24no—
34C2×#6195C2211yescharacteristic
35C2×#6195C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×#6192C2211yescharacteristic, complemented
38C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
39C9×#217C2211yescharacteristic, complemented
40C3×#3676C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46#88445C2211yescharacteristic, complemented
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3811—31no—
57C3×#939—31no—
58C3×#939D311yescharacteristic
59#63983—31no—
60#63981—31no—
61#63981—31no—
62#63978—31no—
63#63978—31no—
64#63975—31no—
65C2×#3722—31no—
66#63923—31no—
67#63897—31no—
68#63853—31no—
69#63853—31no—
70C2×D4×D9—31no—
71C2×D4×D9—31no—
72C2×D4×D9—61no—
73C9×#121—31no—
74#63501—31no—
75#63501D311yescharacteristic, complemented
76#63499—31no—
77#63499—31no—
78#63492—31no—
79C2×(C2×D9)⋊C4—31no—
80#63456—31no—
81#63456—31no—
82#63445—31no—
83#63445—31no—
84#63444—31no—
85#63444—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9—41no—
91C22×C3⋊D9—41no—
92C22×C3⋊D9—41no—
93C22×C3⋊D9D414yescomplemented
94C22×C3⋊D9C2311yescharacteristic
95C22×C3⋊D9C2311yescharacteristic
96C22×C3⋊D9C2311yescharacteristic
97C22×D3×C9C2311yescharacteristic
98C22×C3×D9C2311yescharacteristic
99C2×D3×D9—22no—
100C2×D3×D9—41no—
101C2×D3×D9—41no—
102C3×D4×C9—22no—
103C2×C3×C4×C9C2311yescharacteristic
104#6233—22no—
105#6233—22no—
106C2×C3⋊Dic9C2311yescharacteristic
107C4⋊(C3⋊D9)—22no—
108C4×C3⋊D9—22no—
109C9×#67—22no—
110C9×#67—41no—
111C3×#611—22no—
112C3×#611—41no—
113C2×C9×Dic3—41no—
114C2×C9×Dic3C2311yescharacteristic
115C2×C9×Dic3C2311yescharacteristic
116C2×C9×Dic3C2311yescharacteristic
117C2×C3×Dic9—41no—
118C2×C3×Dic9C2311yescharacteristic
119C2×C3×Dic9C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121#6195—22no—
122#6195—41no—
123#6192—22no—
124#6192—41no—
125(C3⋊D9)⋊C4—22no—
126#5605—91no—
127#5605—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—31no—
130C22×D32—31no—
131C2×C32×D4C2×D311yescharacteristic
132C2×#638—31no—
133C2×#638—31no—
134D4×C3⋊D3—64no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4×C3⋊D3—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67C2×D311yescharacteristic
140C2×C3×#67C2×D311yescharacteristic
141C22×C3×Dic3—31no—
142C22×C3×Dic3C2×D311yescharacteristic
143#3811—64no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#624—31no—
149C23×D9—31no—
150C23×D9—31no—
151C23×D9—31no—
152C23×D9—61no—
153C23×D9—61no—
154C3×#217—31no—
155C3×#217C2×D311yescharacteristic
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4C2×D311yescharacteristic
158C3×Dic3⋊C4—31no—
159C3×Dic3⋊C4C2×D311yescharacteristic
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162#3722—31no—
163#3722—31no—
164#3722—31no—
165#3722—31no—
166#3722—31no—
167#3722—31no—
168(C2×D3)⋊Dic3—31no—
169(C2×D3)⋊Dic3—31no—
170C2×D4×C9—21no—
171C2×D4×C9—31no—
172C2×D4×C9—31no—
173C2×D4×C9C2×D311yescharacteristic, complemented
174C22×C4×C9—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—31no—
179C2×#611—61no—
180C2×#611—61no—
181C2×#611C2×D311yescharacteristic, complemented
182C2×#611C2×D311yescharacteristic, complemented
183C22×Dic9C2×D311yescharacteristic, complemented
184D4×D9—64no—
185D4×D9—64no—
186D4×D9—68no—
187C2×D36—31no—
188C2×D36—31no—
189C2×D36—31no—
190C2×D36—61no—
191C2×C4×D9—31no—
192C2×C4×D9—31no—
193C2×C4×D9—61no—
194C9×C4⋊C4—31no—
195C9×C22⋊C4—31no—
196C9×C22⋊C4—31no—
197#3676—31no—
198#3676C2×D311yescharacteristic, complemented
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4—31no—
204(C2×D9)⋊C4—31no—
205(C2×D9)⋊C4—31no—
206(C2×D9)⋊C4C2×D311yescharacteristic, complemented
207C4⋊Dic9—31no—
208Dic9⋊C4—31no—
209Dic9⋊C4C2×D311yescharacteristic, complemented
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9—21no—
215C22×C3×C9C2×D412yes—
216C22×C3×C9C2411yescharacteristic
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×C3⋊D9—21no—
220C2×C3⋊D9—21no—
221C2×C3⋊D9—21no—
222C2×C3⋊D9—21no—
223C2×C3⋊D9—21no—
224C2×C3⋊D9—44no—
225C2×C3⋊D9—44no—
226C2×C3⋊D9C2×D412yes—
227C2×C3⋊D9C2×D412yes—
228C2×D3×C9—21no—
229C2×D3×C9—21no—
230C2×D3×C9—21no—
231C2×C3×D9—21no—
232C2×C3×D9—21no—
233C2×C3×D9—21no—
234D3×D9—44no—
235C3×C4×C9—21no—
236C3⋊Dic9—21no—
237C9×Dic3—21no—
238C9×Dic3—21no—
239C9×Dic3—21no—
240C3×Dic9—21no—
241C3×Dic9—21no—
242C3×Dic9—21no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C2×D3×D4—91no—
246C2×D3×D4—91no—
247C2×D3×D4—181no—
248C3×#121—31no—
249C3×#121—91no—
250#939—31no—
251#939—91no—
252#939—91no—
253#939D911yescharacteristic, complemented
254#937—91no—
255#937—91no—
256#937—91no—
257#937—91no—
258#930—91no—
259#930—91no—
260C2×(C2×D3)⋊C4—91no—
261C2×(C2×D3)⋊C4—91no—
262#894—91no—
263#894—91no—
264#894—91no—
265#894—91no—
266#883—91no—
267#883—91no—
268#883—91no—
269#883—91no—
270#882—91no—
271#882—91no—
272#882—91no—
273#882—91no—
274C23×C32C22×D311yescharacteristic
275C23×C32C22×D311yescharacteristic
276C22×C3⋊D3—31no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—31no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—121no—
282C22×C3⋊D3—121no—
283C22×C3⋊D3—121no—
284C22×C3⋊D3—121no—
285C22×C3×D3—31no—
286C22×C3×D3C22×D311yescharacteristic
287C2×D32—62no—
288C2×D32—121no—
289C2×D32—121no—
290C32×D4—22no—
291C2×C32×C4C22×D311yescharacteristic
292#638—62no—
293#638—62no—
294C2×C3⋊Dic3—31no—
295C4⋊(C3⋊D3)—62no—
296C4×C3⋊D3—62no—
297C3×#67—22no—
298C3×#67—41no—
299C3×#67—62no—
300C3×#67—121no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—41no—
305C2×C3×Dic3—121no—
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D311yescharacteristic
309#626—62no—
310#626—62no—
311#626—121no—
312#626—121no—
313#624—62no—
314C23×C9—21no—
315C23×C9—21no—
316C23×C9—31no—
317C23×C9C22×D311yescharacteristic
318C23×C9C22×D311yescharacteristic
319C22×D9—31no—
320C22×D9—31no—
321C22×D9—34no—
322C22×D9—31no—
323C22×D9—61no—
324C22×D9—61no—
325C22×D9—61no—
326C22×D9—64no—
327C22×D9—62no—
328C22×D9—62no—
329C22×D9—64no—
330C22×D9—121no—
331C22×D9—121no—
332C22×D9—121no—
333C22×D9—121no—
334C22×D9—121no—
335C22×D9—121no—
336C22×D9—122no—
337C22×D9—122no—
338C22×D9—122no—
339C22×D9—122no—
340C22×D9C22×D311yescharacteristic
341D4×C9—24no—
342D4×C9—22no—
343D4×C9—62no—
344D4×C9—121no—
345C2×C4×C9—21no—
346C2×C4×C9—31no—
347C2×C4×C9—31no—
348C2×C4×C9—31no—
349C2×C4×C9—121no—
350C2×C4×C9C22×D311yescharacteristic
351#611—22no—
352#611—41no—
353#611—62no—
354#611—62no—
355#611—64no—
356#611—64no—
357#611—62no—
358#611—121no—
359C2×Dic9—31no—
360C2×Dic9—41no—
361C2×Dic9—61no—
362C2×Dic9C22×D311yescharacteristic
363C2×Dic9C22×D311yescharacteristic
364C2×Dic9C22×D311yescharacteristic
365D36—62no—
366D36—64no—
367D36—62no—
368D36—121no—
369C4×D9—62no—
370C4×D9—62no—
371C4×D9—64no—
372#534—271noSylow
373C2×C3×C9—22no—
374C2×C3×C9—41no—
375C2×C3×C9C22×D411yescharacteristic
376C2×C3×C9H(5,𝔽2)11yescharacteristic
377C2×C3×C9H(5,𝔽2)11yescharacteristic
378C3⋊D9—22no—
379C3⋊D9—22no—
380C3⋊D9—41no—
381D3×C9—41no—
382C3×D9—41no—
383C23×D3—91no—
384C23×D3—91no—
385C23×D3—91no—
386C23×D3—91no—
387C23×D3—91no—
388C23×D3—91no—
389C23×D3—181no—
390C23×D3—181no—
391C2×C3×D4—21no—
392C2×C3×D4—31no—
393C2×C3×D4—31no—
394C2×C3×D4—91no—
395C2×C3×D4—91no—
396C2×C3×D4C2×D911yescharacteristic, complemented
397C2×C3×D4D3211yescharacteristic
398C22×C3×C4—31no—
399C22×C3×C4—91no—
400C2×#67—31no—
401C2×#67—31no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—91no—
406C2×#67—91no—
407C2×#67—91no—
408C2×#67—91no—
409C2×#67—91no—
410C2×#67—181no—
411C2×#67—181no—
412C2×#67C2×D911yescharacteristic, complemented
413C2×#67C2×D911yescharacteristic, complemented
414C22×Dic3—31no—
415C22×Dic3C2×D911yescharacteristic, complemented
416D3×D4—184no—
417D3×D4—184no—
418D3×D4—184no—
419D3×D4—184no—
420D3×D4—188no—
421C2×D12—91no—
422C2×D12—91no—
423C2×D12—91no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—181no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—181no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—91no—
435C3×C22⋊C4—31no—
436C3×C22⋊C4—31no—
437C3×C22⋊C4—91no—
438C3×C22⋊C4—91no—
439#217—31no—
440#217—91no—
441#217—91no—
442#217C2×D911yescharacteristic, complemented
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—91no—
451(C2×D3)⋊C4—91no—
452(C2×D3)⋊C4—91no—
453(C2×D3)⋊C4—91no—
454(C2×D3)⋊C4—91no—
455(C2×D3)⋊C4—91no—
456(C2×D3)⋊C4—91no—
457(C2×D3)⋊C4—91no—
458(C2×D3)⋊C4C2×D911yescharacteristic, complemented
459C4⋊Dic3—91no—
460C4⋊Dic3—91no—
461Dic3⋊C4—31no—
462Dic3⋊C4—91no—
463Dic3⋊C4—91no—
464Dic3⋊C4C2×D911yescharacteristic, complemented
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32D3×D412yes—
471C22×C32C23×D311yescharacteristic
472C2×C3⋊D3—32no—
473C2×C3⋊D3—32no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—61no—
476C2×C3⋊D3—61no—
477C2×C3⋊D3—61no—
478C2×C3⋊D3—61no—
479C2×C3⋊D3—61no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3—124no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
488C2×C3×D3—61no—
489D32—124no—
490C32×C4—21no—
491C3⋊Dic3—61no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C22×C9—21no—
499C22×C9—21no—
500C22×C9—22no—
501C22×C9—21no—
502C22×C9—21no—
503C22×C9—21no—
504C22×C9—21no—
505C22×C9—22no—
506C22×C9—41no—
507C22×C9—41no—
508C22×C9—41no—
509C22×C9—41no—
510C22×C9—61no—
511C22×C9—61no—
512C22×C9—61no—
513C22×C9D3×D412yes—
514C22×C9C23×D311yescharacteristic
515C2×D9—21no—
516C2×D9—21no—
517C2×D9—21no—
518C2×D9—32no—
519C2×D9—32no—
520C2×D9—62no—
521C2×D9—62no—
522C2×D9—62no—
523C2×D9—62no—
524C2×D9—61no—
525C2×D9—61no—
526C2×D9—61no—
527C2×D9—61no—
528C2×D9—62no—
529C2×D9—61no—
530C2×D9—61no—
531C2×D9—61no—
532C2×D9—121no—
533C2×D9—121no—
534C2×D9—121no—
535C2×D9—121no—
536C2×D9—124no—
537C2×D9—124no—
538C2×D9—128no—
539C2×D9—128no—
540C2×D9—124no—
541C4×C9—22no—
542C4×C9—21no—
543C4×C9—61no—
544C4×C9—61no—
545C4×C9—61no—
546Dic9—21no—
547Dic9—21no—
548Dic9—21no—
549Dic9—62no—
550Dic9—61no—
551C22×D4—271no—
552C22×D4—271no—
553#123—271no—
554#123—271no—
555#123—271no—
556#123—271no—
557#121—31no—
558#121—91no—
559#121—271no—
560#121—271no—
561#120—271no—
562#120—271no—
563#120—271no—
564#120—271no—
565C2×C22⋊C4—271no—
566C3×C9#53411yescharacteristic, complemented, Sylow
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—31no—
570C23×C3—91no—
571C23×C3C22×D911yescharacteristic
572C23×C3C22×D911yescharacteristic
573C23×C3C2×D3211yescharacteristic
574C23×C3C2×D3211yescharacteristic
575C22×D3—31no—
576C22×D3—91no—
577C22×D3—91no—
578C22×D3—91no—
579C22×D3—91no—
580C22×D3—94no—
581C22×D3—94no—
582C22×D3—91no—
583C22×D3—91no—
584C22×D3—181no—
585C22×D3—181no—
586C22×D3—181no—
587C22×D3—184no—
588C22×D3—182no—
589C22×D3—182no—
590C22×D3—182no—
591C22×D3—182no—
592C22×D3—184no—
593C22×D3—361no—
594C22×D3—361no—
595C22×D3—361no—
596C22×D3—361no—
597C22×D3—361no—
598C22×D3—361no—
599C22×D3—361no—
600C22×D3—361no—
601C22×D3—361no—
602C22×D3—361no—
603C22×D3—361no—
604C22×D3—361no—
605C22×D3—362no—
606C22×D3—362no—
607C22×D3—362no—
608C22×D3—362no—
609C22×D3C22×D911yescharacteristic
610C3×D4—24no—
611C3×D4—22no—
612C3×D4—22no—
613C3×D4—62no—
614C3×D4—121no—
615C3×D4—182no—
616C3×D4—361no—
617C2×C3×C4—21no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—31no—
621C2×C3×C4—91no—
622C2×C3×C4—91no—
623C2×C3×C4—91no—
624C2×C3×C4—121no—
625C2×C3×C4—361no—
626C2×C3×C4C22×D911yescharacteristic
627C2×C3×C4C2×D3211yescharacteristic
628#67—22no—
629#67—41no—
630#67—62no—
631#67—121no—
632#67—182no—
633#67—182no—
634#67—182no—
635#67—182no—
636#67—184no—
637#67—184no—
638#67—182no—
639#67—182no—
640#67—361no—
641#67—361no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—41no—
646C2×Dic3—91no—
647C2×Dic3—91no—
648C2×Dic3—121no—
649C2×Dic3—181no—
650C2×Dic3C22×D911yescharacteristic
651C2×Dic3C22×D911yescharacteristic
652C2×Dic3C22×D911yescharacteristic
653D12—182no—
654D12—182no—
655D12—184no—
656D12—182no—
657D12—182no—
658D12—361no—
659D12—361no—
660C4×D3—182no—
661C4×D3—182no—
662C4×D3—182no—
663C4×D3—182no—
664C4×D3—184no—
665C2×C32—22no—
666C2×C32—41no—
667C2×C32C2×D3×D411yescharacteristic
668C2×C32#100411yescharacteristic
669C2×C32#100911yescharacteristic
670C3⋊D3—62no—
671C3⋊D3—62no—
672C3⋊D3—121no—
673C3×D3—41no—
674C3×D3—121no—
675C2×C9—22no—
676C2×C9—21no—
677C2×C9—21no—
678C2×C9—21no—
679C2×C9—42no—
680C2×C9—42no—
681C2×C9—41no—
682C2×C9—121no—
683C2×C9C2×D3×D411yescharacteristic
684C2×C9#100411yescharacteristic
685C2×C9#100911yescharacteristic
686D9—41no—
687D9—64no—
688D9—62no—
689D9—62no—
690D9—122no—
691D9—122no—
692D9—121no—
693C24—271no—
694C24—271no—
695C24—271no—
696C2×D4—31no—
697C2×D4—31no—
698C2×D4—91no—
699C2×D4—91no—
700C2×D4—271no—
701C2×D4—271no—
702C2×D4—271no—
703C2×D4—271no—
704C2×D4—271no—
705C2×D4—271no—
706C2×D4—271no—
707C2×D4—544no—
708C2×D4—544no—
709C2×D4D3×D911yescharacteristic, complemented
710C22×C4—31no—
711C22×C4—91no—
712C22×C4—271no—
713C22×C4—271no—
714C4⋊C4—31no—
715C4⋊C4—91no—
716C4⋊C4—271no—
717C4⋊C4—271no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—91no—
721C22⋊C4—91no—
722C22⋊C4—271no—
723C22⋊C4—271no—
724C22⋊C4—271no—
725C22⋊C4—271no—
726C22⋊C4—271no—
727C22⋊C4—271no—
728C22⋊C4—271no—
729C22⋊C4—271no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—181no—
751C22×C3—181no—
752C22×C3—181no—
753C22×C3D4×D912yes—
754C22×C3C23×D911yescharacteristic
755C22×C3#381112yes—
756C22×C3C22×D3211yescharacteristic
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—92no—
764C2×D3—92no—
765C2×D3—92no—
766C2×D3—92no—
767C2×D3—182no—
768C2×D3—182no—
769C2×D3—182no—
770C2×D3—182no—
771C2×D3—181no—
772C2×D3—181no—
773C2×D3—181no—
774C2×D3—181no—
775C2×D3—181no—
776C2×D3—181no—
777C2×D3—181no—
778C2×D3—181no—
779C2×D3—182no—
780C2×D3—181no—
781C2×D3—181no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—181no—
785C2×D3—181no—
786C2×D3—361no—
787C2×D3—361no—
788C2×D3—361no—
789C2×D3—361no—
790C2×D3—364no—
791C2×D3—364no—
792C2×D3—364no—
793C2×D3—364no—
794C2×D3—364no—
795C2×D3—368no—
796C2×D3—368no—
797C2×D3—364no—
798C3×C4—22no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—61no—
804C3×C4—181no—
805C3×C4—181no—
806C3×C4—181no—
807Dic3—21no—
808Dic3—21no—
809Dic3—21no—
810Dic3—61no—
811Dic3—61no—
812Dic3—61no—
813Dic3—182no—
814Dic3—181no—
815Dic3—181no—
816C32#560511yescharacteristic
817C9—21no—
818C9#560511yescharacteristic, complemented
819C23—31no—
820C23—91no—
821C23—271no—
822C23—271no—
823C23—274no—
824C23—271no—
825C23—542no—
826C23—542no—
827C23—1081no—
828C23—1081no—
829C23—1081no—
830C23—1081no—
831C23—1081no—
832C23—1081no—
833C23C2×D3×D911yescharacteristic
834C23C2×D3×D911yescharacteristic
835D4—22no—
836D4—62no—
837D4—121no—
838D4—182no—
839D4—361no—
840D4—542no—
841D4—542no—
842D4—542no—
843D4—542no—
844D4—542no—
845D4—1081no—
846D4—1081no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—91no—
851C2×C4—91no—
852C2×C4—91no—
853C2×C4—121no—
854C2×C4—271no—
855C2×C4—361no—
856C2×C4—542no—
857C2×C4—542no—
858C2×C4C2×D3×D911yescharacteristic
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—42no—
865C2×C3—42no—
866C2×C3—41no—
867C2×C3—41no—
868C2×C3—121no—
869C2×C3—361no—
870C2×C3C2×D4×D911yescharacteristic
871C2×C3#6371011yescharacteristic
872C2×C3#6371511yescharacteristic
873C2×C3#6431411yescharacteristic
874C2×C3#6431411yescharacteristic
875C2×C3C2×#381111yescharacteristic
876D3—41no—
877D3—121no—
878D3—184no—
879D3—182no—
880D3—182no—
881D3—182no—
882D3—182no—
883D3—362no—
884D3—362no—
885D3—361no—
886D3—361no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—61no—
893C22—61no—
894C22—61no—
895C22—181no—
896C22—181no—
897C22—181no—
898C22—272no—
899C22—272no—
900C22—541no—
901C22—541no—
902C22—541no—
903C22—541no—
904C22—541no—
905C22—541no—
906C22—541no—
907C22—1084no—
908C22—1084no—
909C22—1084no—
910C22#8866812yes—
911C22C22×D3×D911yescharacteristic
912C4—21no—
913C4—61no—
914C4—61no—
915C4—61no—
916C4—181no—
917C4—181no—
918C4—181no—
919C4—541no—
920C3—21no—
921C3#1058970711yescharacteristic, complemented
922C3#1059530811yescharacteristic
923C2—22no—
924C2—41no—
925C2—121no—
926C2—361no—
927C2—542no—
928C2—542no—
929C2—1081no—
930C2#1172250011yescharacteristic
931C2#1172250111yescharacteristic
932C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#534
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊D9C2semidirect
2. C2×#88668C2semidirect
3. C9×#939C2semidirect
4. C3×#63501C2semidirect
5. #11721292C2semidirect
6. #11721291C2semidirect
7. #11721288C2semidirect
8. #11721278C2semidirect
9. #11721277C2semidirect
10. #11721275C2semidirect
11. C2×#88445C2semidirect
12. #11721051C2semidirect
13. #11720997C2semidirect
14. #11720957C2semidirect
15. #11720941C2semidirect
19. C23×C3⋊D9C22semidirect
20. C22×D3×D9C22semidirect
21. C2×C3×D4×C9C22semidirect
23. C2×#6233C22semidirect
26. C2×C4×C3⋊D9C22semidirect
27. C2×C9×#67C22semidirect
28. C2×C9×#67C22semidirect
29. C2×C3×#611C22semidirect
30. C2×C3×#611C22semidirect
31. C22×C9×Dic3C22semidirect
32. C22×C3×Dic9C22semidirect
35. C2×#6195C22semidirect
37. C2×#6192C22semidirect
38. C2×(C3⋊D9)⋊C4C22semidirect
39. C9×#217C22semidirect
40. C3×#3676C22semidirect
41. C9×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C3×Dic9⋊C4C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. #88445C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic9⋊Dic3C22semidirect
75. #63501D3semidirect
93. C22×C3⋊D9D4semidirect
173. C2×D4×C9C2×D3semidirect
181. C2×#611C2×D3semidirect
182. C2×#611C2×D3semidirect
183. C22×Dic9C2×D3semidirect
198. #3676C2×D3semidirect
206. (C2×D9)⋊C4C2×D3semidirect
209. Dic9⋊C4C2×D3semidirect
253. #939D9semidirect
396. C2×C3×D4C2×D9semidirect
412. C2×#67C2×D9semidirect
413. C2×#67C2×D9semidirect
415. C22×Dic3C2×D9semidirect
442. #217C2×D9semidirect
458. (C2×D3)⋊C4C2×D9semidirect
464. Dic3⋊C4C2×D9semidirect
566. C3×C9#534semidirect
709. C2×D4D3×D9semidirect
818. C9#5605semidirect
921. C3#10589707semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊D92
C2×#886682
C9×#9392
C3×#635012
#117212922
#117212912
#117212882
#117212782
#117212772
#117212752
C2×#884452
#117210512
#117209972
#117209572
#117209412
#105953083
#105897073