Finite Group Databasebeta

← #13148138

Subgroups — #13148138

Order 1728.

1096 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×D9×#67C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8#11721262C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11#11721033C211yesmaximal, characteristic, complemented
12#11721031C211yesmaximal, characteristic, complemented
13C4×#6192C211yesmaximal, characteristic, complemented
14#11720984C211yesmaximal, characteristic, complemented
15#11720977C211yesmaximal, characteristic, complemented
16#10594280—31nomaximal
17#10589778—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×C3×C4×D9C2211yescharacteristic, complemented
27C2×C9×Dic6C2211yescharacteristic, complemented
28D9×#67—24no—
29C2×#6195C2211yescharacteristic, complemented
30C2×#6194C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×#6192C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic
37#88635—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C3×(C2×D9)⋊C4C2211yescharacteristic
47C4×C9×Dic3C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3799—31no—
57#64093—31no—
58C3×#885D311yescharacteristic
59C3×D3×C22⋊C4—31no—
60#63977—31no—
61#63975—31no—
62#63958—31no—
63#63923—31no—
64#63921—31no—
65#63906—31no—
66#63905—31no—
67C4×#626—31no—
68#63887—31no—
69#63880—31no—
70C2×#3701—31no—
71C2×D4×D9—31no—
72C9×#124—31no—
73#63508—31no—
74#63500—31no—
75#63446—31no—
76#63446—31no—
77#63446—61no—
78#63445—31no—
79#63445—31no—
80#63444—31no—
81#63444—31no—
82C22⋊C4×D9—31no—
83C22⋊C4×D9D311yescharacteristic, complemented
84C4×D36—31no—
85C4×D36—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9—41no—
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C4⋊(C3⋊D9)—22no—
105C4×C3⋊D9—41no—
106C9×#67—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C3×C4×D9—22no—
113C3×C4×D9—41no—
114C9×Dic6—22no—
115#6195—41no—
116#6194—22no—
117#6192—22no—
118#6192—22no—
119#6192D414yescomplemented
120(C3⋊D9)⋊C4—22no—
121(C3⋊D9)⋊C4—22no—
122Dic3×D9—22no—
123#5676—91no—
124#5490—91no—
125C23×C3×D3—31no—
126C22×D32—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4×C3⋊D3—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×Dic6C2×D311yescharacteristic
135D3×#67—64no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×D3×Dic3—31no—
144#3799—64no—
145C23×D9—31no—
146C23×D9C2×D311yescharacteristic
147C32×C22⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3750—31no—
150C3×#217—31no—
151C3×#217C2×D311yescharacteristic
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×C4×Dic3C2×D311yescharacteristic
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C2×Q8×C9—31no—
165C2×D4×C9—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—61no—
171C2×#611—61no—
172#3701—64no—
173D4×D9—64no—
174C2×D36—31no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36—31no—
178C2×D36—61no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×C4×D9C2×D311yescharacteristic, complemented
186C9×C22⋊C4—21no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4C2×D311yescharacteristic, complemented
191C42×C9—31no—
192#3676—31no—
193#3676C2×D311yescharacteristic, complemented
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—61no—
199(C2×D9)⋊C4C2×D311yescharacteristic
200(C2×D9)⋊C4C2×D311yescharacteristic
201C4⋊Dic9—31no—
202C4⋊Dic9—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205Dic9⋊C4—61no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9C2×D412yes—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×C3×D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—44no—
224C2×C3×D9C2×D412yes—
225C2×C3×D9#4112yescomplemented
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3C2×D412yes—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×#67—91no—
237C2×#239—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#124—31no—
241C2×C3×C22⋊C4—91no—
242#953—91no—
243#946—91no—
244#938—91no—
245#930—91no—
246#929—91no—
247C4×#67—91no—
248#885D911yescharacteristic, complemented
249#884—91no—
250#884—91no—
251#884—91no—
252#884—91no—
253#884—181no—
254#883—91no—
255#883—91no—
256#883—91no—
257#882—91no—
258#882—91no—
259#882—91no—
260#67⋊C4—91no—
261D3×C22⋊C4—31no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264#878—91no—
265C4×D12—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—62no—
273C22×C3×D3—62no—
274C22×C3×D3—121no—
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C4⋊(C3⋊D3)—62no—
286C4×C3⋊D3—121no—
287C3×#67—22no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×C4×D3—62no—
294C3×C4×D3—121no—
295C3×Dic6—22no—
296#626—34no—
297#626—62no—
298#626—62no—
299#626—121no—
300#625—62no—
301#624—62no—
302#624—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9C22×D311yescharacteristic
307C22×D9—22no—
308C22×D9—22no—
309C22×D9—31no—
310C22×D9—31no—
311C22×D9—41no—
312C22×D9—61no—
313C22×D9—61no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—121no—
317C22×D9C22×D311yescharacteristic
318C22×D9C22×D311yescharacteristic
319Q8×C9—62no—
320D4×C9—62no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9C22×D311yescharacteristic
327C2×C4×C9C22×D311yescharacteristic
328#611—62no—
329#611—62no—
330#611—122no—
331#611—121no—
332#611—121no—
333#611—122no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—61no—
337C2×Dic9—61no—
338C2×Dic9C22×D311yescharacteristic
339C2×Dic9C22×D311yescharacteristic
340D36—34no—
341D36—62no—
342D36—62no—
343D36—62no—
344D36—122no—
345C4×D9—22no—
346C4×D9—41no—
347C4×D9—62no—
348C4×D9—62no—
349C4×D9—62no—
350C4×D9—121no—
351C4×D9—122no—
352#546—271noSylow
353C2×C3×C9—41no—
354C2×C3×C9C22×D411yescharacteristic
355C2×C3×C9C2×#4111yescharacteristic
356C2×C3×C9H(5,𝔽2)11yescharacteristic
357C3⋊D9—22no—
358C3⋊D9—41no—
359D3×C9—41no—
360C3×D9—22no—
361C3×D9—22no—
362C24×C3—91no—
363C23×D3—31no—
364C23×D3—91no—
365C23×D3—91no—
366C2×C3×Q8—31no—
367C2×C3×D4—31no—
368C22×C3×C4—91no—
369C22×C3×C4—91no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—181no—
381C2×#67—181no—
382C2×#67—184no—
383C2×#67C2×D911yescharacteristic
384C22×Dic3—91no—
385#239—184no—
386D3×D4—184no—
387#235—184no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—181no—
395C2×C4×D3—31no—
396C2×C4×D3—31no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—181no—
405C2×Dic6C2×D911yescharacteristic, complemented
406C3×C22⋊C4—21no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4C2×D911yescharacteristic, complemented
414C3×C22⋊C4D3211yescharacteristic
415C3×C42—31no—
416#217—31no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217C2×D911yescharacteristic, complemented
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—181no—
431(C2×D3)⋊C4C2×D911yescharacteristic, complemented
432(C2×D3)⋊C4C2×D911yescharacteristic, complemented
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—181no—
442C4×Dic3C2×D911yescharacteristic, complemented
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—32no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—32no—
457C2×C3×D3—32no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—124no—
463D32—124no—
464C32×C4—21no—
465C32×C4—21no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3D3×D412yes—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—41no—
478C22×C9—41no—
479C22×C9—41no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9C23×D311yescharacteristic
484C2×D9—21no—
485C2×D9—21no—
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—32no—
489C2×D9—44no—
490C2×D9—62no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—121no—
497C2×D9—121no—
498C2×D9—121no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—124no—
502C2×D9#23512yescomplemented
503C2×D9D3×D412yes—
504C4×C9—21no—
505C4×C9—21no—
506C4×C9—32no—
507C4×C9—41no—
508C4×C9—41no—
509C4×C9—61no—
510C4×C9—61no—
511Dic9—21no—
512Dic9—21no—
513Dic9—62no—
514Dic9—61no—
515Dic9—61no—
516Dic9—121no—
517C2×#41—271no—
518C22×D4—271no—
519#124—31no—
520#123—271no—
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—91no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—91no—
536C23×C3—91no—
537C23×C3—182no—
538C23×C3—182no—
539C23×C3—361no—
540C23×C3C22×D911yescharacteristic
541C23×C3C2×D3211yescharacteristic
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—121no—
551C22×D3—181no—
552C22×D3—181no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—361no—
558C22×D3—361no—
559C22×D3C22×D911yescharacteristic
560C3×Q8—62no—
561C3×D4—62no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—182no—
570C2×C3×C4—361no—
571C2×C3×C4C22×D911yescharacteristic
572C2×C3×C4C22×D911yescharacteristic
573C2×C3×C4C2×D3211yescharacteristic
574C2×C3×C4C2×D3211yescharacteristic
575#67—22no—
576#67—94no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—362no—
584#67—361no—
585#67—361no—
586#67—361no—
587#67—362no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—181no—
595C2×Dic3—181no—
596C2×Dic3—182no—
597C2×Dic3C22×D911yescharacteristic
598C2×Dic3C22×D911yescharacteristic
599C2×Dic3C22×D911yescharacteristic
600D12—94no—
601D12—182no—
602D12—182no—
603D12—182no—
604D12—182no—
605D12—362no—
606D12—361no—
607C4×D3—62no—
608C4×D3—121no—
609C4×D3—182no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—361no—
615C4×D3—361no—
616C4×D3—362no—
617Dic6—22no—
618C2×C32—41no—
619C2×C32C2×D3×D411yescharacteristic
620C2×C32D3×#4111yescharacteristic
621C2×C32#100911yescharacteristic
622C3⋊D3—62no—
623C3⋊D3—121no—
624C3×D3—41no—
625C3×D3—62no—
626C3×D3—62no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—41no—
631C2×C9—81no—
632C2×C9—121no—
633C2×C9C2×#23511yescharacteristic
634C2×C9C2×D3×D411yescharacteristic
635C2×C9#100411yescharacteristic
636D9—22no—
637D9—22no—
638D9—62no—
639D9—122no—
640D9—121no—
641D9—241no—
642C24—91no—
643C24—271no—
644#41—544no—
645C2×Q8—31no—
646C2×D4—31no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—544no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4D3×D911yescharacteristic, complemented
678C42—31no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—92no—
693C22×C3—92no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—364no—
699C22×C3C23×D911yescharacteristic
700C22×C3C22×D3211yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—32no—
705C2×D3—32no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—92no—
711C2×D3—92no—
712C2×D3—124no—
713C2×D3—182no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—361no—
725C2×D3—361no—
726C2×D3—361no—
727C2×D3—361no—
728C2×D3—361no—
729C2×D3—364no—
730C2×D3—364no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—32no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—21no—
743Dic3—21no—
744Dic3—61no—
745Dic3—61no—
746Dic3—182no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3D4×D912yes—
753C32#567611yescharacteristic
754C9—21no—
755C9#549011yescharacteristic, complemented
756C23—31no—
757C23—91no—
758C23—91no—
759C23—182no—
760C23—182no—
761C23—271no—
762C23—271no—
763C23—361no—
764C23—542no—
765C23—542no—
766C23—1081no—
767C23C2×D3×D911yescharacteristic
768Q8—62no—
769D4—62no—
770D4—274no—
771D4—542no—
772D4—542no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—182no—
784C2×C4—271no—
785C2×C4—271no—
786C2×C4—361no—
787C2×C4—542no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4C2×D3×D911yescharacteristic
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—41no—
797C2×C3—41no—
798C2×C3—81no—
799C2×C3—121no—
800C2×C3—182no—
801C2×C3—182no—
802C2×C3C2×D4×D911yescharacteristic
803C2×C3#41×D911yescharacteristic
804C2×C3#6371511yescharacteristic
805C2×C3D3×#23511yescharacteristic
806C2×C3D32×D411yescharacteristic
807C2×C3#6431411yescharacteristic
808D3—41no—
809D3—62no—
810D3—62no—
811D3—182no—
812D3—182no—
813D3—362no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—92no—
824C22—92no—
825C22—181no—
826C22—181no—
827C22—181no—
828C22—181no—
829C22—272no—
830C22—364no—
831C22—541no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—1084no—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—21no—
840C4—32no—
841C4—61no—
842C4—61no—
843C4—181no—
844C4—181no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058977811yescharacteristic, complemented
849C3#1059428011yescharacteristic
850C2—41no—
851C2—121no—
852C2—182no—
853C2—182no—
854C2—542no—
855C2—1081no—
856C2D9×#23511yescharacteristic
857C2D3×D4×D911yescharacteristic
858C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D9×#67C2semidirect
2. C2×#88635C2semidirect
3. #11721730C2semidirect
4. C9×#885C2semidirect
5. C3×C22⋊C4×D9C2semidirect
6. #11721276C2semidirect
7. #11721275C2semidirect
8. #11721262C2semidirect
9. #11721051C2semidirect
10. #11721048C2semidirect
11. #11721033C2semidirect
12. #11721031C2semidirect
13. C4×#6192C2semidirect
14. #11720984C2semidirect
15. #11720977C2semidirect
21. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
23. C2×C4×C3⋊D9C22semidirect
25. C2×C3×C4×D9C22semidirect
26. C2×C3×C4×D9C22semidirect
27. C2×C9×Dic6C22semidirect
29. C2×#6195C22semidirect
33. C2×#6192C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C9×#217C22semidirect
42. C3×#3676C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
47. C4×C9×Dic3C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic9⋊Dic3C22semidirect
83. C22⋊C4×D9D3semidirect
119. #6192D4semidirect
184. C2×C4×D9C2×D3semidirect
185. C2×C4×D9C2×D3semidirect
190. C9×C22⋊C4C2×D3semidirect
193. #3676C2×D3semidirect
225. C2×C3×D9#41semidirect
248. #885D9semidirect
405. C2×Dic6C2×D9semidirect
413. C3×C22⋊C4C2×D9semidirect
420. #217C2×D9semidirect
431. (C2×D3)⋊C4C2×D9semidirect
432. (C2×D3)⋊C4C2×D9semidirect
442. C4×Dic3C2×D9semidirect
502. C2×D9#235semidirect
532. C3×C9#546semidirect
677. C22⋊C4D3×D9semidirect
755. C9#5490semidirect
848. C3#10589778semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×#886352
#117217302
C9×#8852
C3×C22⋊C4×D92
#117212762
#117212752
#117212622
#117210512
#117210482
#117210332
#117210312
C4×#61922
#117209842
#117209772
#105942803
#105897783