Finite Group Databasebeta

← #13147992

Subgroups — #13147992

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88658C211yesmaximal, characteristic, complemented
2C2×C4×D3×D9C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#63445C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721282C211yesmaximal, characteristic, complemented
8#11721240C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11#11721026C211yesmaximal, characteristic, complemented
12#11720993C211yesmaximal, characteristic, complemented
13#11720974C211yesmaximal, characteristic, complemented
14#11720938C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10594266—31nomaximal
17#10589649—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic, complemented
26C2×C4×D3×C9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×D3×Dic9C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33#88658—24no—
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic, complemented
36C4×D3×D9—24no—
37C3×C9×C22⋊C4C2211yescharacteristic, complemented
38#88536C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C3×#3676C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C4×C9×Dic3C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52#88442C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3804—31no—
56C2×C4×D32—31no—
57#64093—31no—
58C3×#883—31no—
59C3×#67⋊C4D311yescharacteristic
60#63983—31no—
61#63971—31no—
62#63952—31no—
63#63923—31no—
64#63904—31no—
65#63899—31no—
66#63894—31no—
67#63877—31no—
68#63865—31no—
69#63850—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C4×D4×C9—31no—
73#63501—31no—
74#63499—31no—
75C4×#611—31no—
76C4×#611—31no—
77#63458—31no—
78#63456—31no—
79#63446—31no—
80#63446—61no—
81#63445D311yescharacteristic, complemented
82#63444—31no—
83#63440—31no—
84C4×D36—31no—
85#63434—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×D3×D9—22no—
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96#6233—22no—
97#6233—22no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C4⋊(C3⋊D9)—22no—
101C4×C3⋊D9—22no—
102C9×#67—22no—
103C3×#611—22no—
104C2×C9×Dic3—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C4×D3×C9—22no—
112C3×C4×D9—22no—
113#6195—22no—
114D3×Dic9—22no—
115#6192—22no—
116(C3⋊D9)⋊C4—22no—
117(C3⋊D9)⋊C4—22no—
118Dic3×D9D414yescomplemented
119#6189—22no—
120#5656—91no—
121#5547—91no—
122C22×D32—31no—
123C2×#638—31no—
124C2×#638—31no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C4×C3⋊D3—31no—
127C2×C3×#67—31no—
128C2×C3×#67C2×D311yescharacteristic
129C22×C3×Dic3C2×D311yescharacteristic
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×#627—31no—
133C2×#626—31no—
134C2×#626—31no—
135C2×#624—31no—
136C2×#624—31no—
137#3804—64no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C4×D32—64no—
141C23×D9—31no—
142C32×C22⋊C4C2×D311yescharacteristic
143#3752—31no—
144#3750—31no—
145C3×#217—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4C2×D311yescharacteristic
148C3×C4⋊Dic3—31no—
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—31no—
153#3724—31no—
154#3722—31no—
155#3722—31no—
156#3722—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—31no—
160C2×D4×C9—31no—
161C22×C4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—61no—
167C2×#611—61no—
168C2×#611C2×D311yescharacteristic
169C22×Dic9—31no—
170#3697—64no—
171C2×D36—31no—
172C2×D36—31no—
173C2×D36—61no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—64no—
179C2×C4×D9—61no—
180C2×C4×D9C2×D311yescharacteristic
181C2×Dic18—31no—
182C9×C4⋊C4—31no—
183C9×C22⋊C4—21no—
184C9×C22⋊C4—31no—
185C9×C22⋊C4C2×D311yescharacteristic, complemented
186C42×C9—31no—
187#3676—31no—
188#3676C2×D311yescharacteristic, complemented
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—61no—
195(C2×D9)⋊C4C2×D311yescharacteristic
196C4⋊Dic9C2×D311yescharacteristic, complemented
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—61no—
201Dic9⋊C4C2×D311yescharacteristic, complemented
202C4×Dic9—31no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9#4112yescomplemented
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9#4112yescomplemented
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9C2×D412yes—
219D3×D9—28no—
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9C2×D412yes—
224C9×Dic3—21no—
225C9×Dic3—21no—
226C9×Dic3C2×D412yes—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C2×#237—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×#123—91no—
235C3×C4×D4—31no—
236#939—91no—
237#937—91no—
238#937—91no—
239#929—91no—
240C4×#67—91no—
241C4×#67—91no—
242#896—91no—
243#896—91no—
244#896—91no—
245#894—91no—
246#893—91no—
247#893—91no—
248#884—91no—
249#884—91no—
250#884—91no—
251#884—181no—
252#883—31no—
253#882—91no—
254#882—91no—
255#67⋊C4—91no—
256#67⋊C4D911yescharacteristic, complemented
257#878—91no—
258#877—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3⋊D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3C22×D311yescharacteristic
266C2×D32—62no—
267C2×D32—62no—
268C2×D32—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271#638—62no—
272#638—62no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C4⋊(C3⋊D3)—62no—
276C4×C3⋊D3—62no—
277C3×#67—22no—
278C3×#67—62no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C3×C4×D3—22no—
287C3×C4×D3—62no—
288#627—62no—
289#626—62no—
290#626—62no—
291#624—62no—
292#624—62no—
293D3×Dic3—34no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9—31no—
297C23×C9C22×D311yescharacteristic
298C22×D9—31no—
299C22×D9—31no—
300C22×D9—61no—
301C22×D9—61no—
302C22×D9—62no—
303C22×D9—62no—
304C22×D9—62no—
305C22×D9C22×D311yescharacteristic
306D4×C9—62no—
307C2×C4×C9—21no—
308C2×C4×C9—21no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—62no—
313C2×C4×C9—62no—
314C2×C4×C9C22×D311yescharacteristic
315C2×C4×C9C22×D311yescharacteristic
316#611—22no—
317#611—62no—
318#611—62no—
319#611—62no—
320#611—122no—
321#611—122no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—62no—
327C2×Dic9C22×D311yescharacteristic
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330D36—62no—
331D36—62no—
332D36—122no—
333C4×D9—22no—
334C4×D9—34no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—62no—
338C4×D9—122no—
339Dic18—62no—
340#525—271noSylow
341C2×C3×C9—41no—
342C2×C3×C9C22×D411yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C2×C3×C9C2×#4111yescharacteristic
345C3⋊D9—22no—
346C3⋊D9—41no—
347D3×C9—22no—
348C3×D9—22no—
349C23×D3—91no—
350C23×D3—91no—
351C2×C3×D4—31no—
352C2×C3×D4—91no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—91no—
356C2×#67—31no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—181no—
364C2×#67—181no—
365C2×#67C2×D911yescharacteristic
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3C2×D911yescharacteristic, complemented
369#237—184no—
370#235—184no—
371C2×D12—91no—
372C2×D12—91no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—181no—
376C2×C4×D3—31no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—181no—
386C2×C4×D3—184no—
387C2×C4×D3—184no—
388C2×C4×D3C2×D911yescharacteristic
389C2×Dic6—91no—
390C2×Dic6—91no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—91no—
393C3×C4⋊C4—91no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4C2×D911yescharacteristic, complemented
399C3×C22⋊C4D3211yescharacteristic
400C3×C42—31no—
401#217—31no—
402#217—91no—
403#217—91no—
404(C2×D3)⋊C4—31no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—181no—
416(C2×D3)⋊C4C2×D911yescharacteristic
417C4⋊Dic3—31no—
418Dic3⋊C4—31no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—181no—
426Dic3⋊C4C2×D911yescharacteristic, complemented
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3C2×D911yescharacteristic, complemented
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32C23×D311yescharacteristic
434C2×C3⋊D3—32no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—61no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—32no—
443C2×C3×D3—61no—
444C2×C3×D3—61no—
445C2×C3×D3#23512yes—
446D32—68no—
447C32×C4—21no—
448C32×C4—21no—
449C3⋊Dic3—32no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3D3×D412yes—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—32no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—41no—
465C22×C9—61no—
466C22×C9—61no—
467C22×C9C23×D311yescharacteristic
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—32no—
471C2×D9—62no—
472C2×D9—68no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—121no—
482C2×D9—121no—
483C2×D9D3×D412yes—
484C4×C9—21no—
485C4×C9—21no—
486C4×C9—32no—
487C4×C9—41no—
488C4×C9—41no—
489C4×C9—61no—
490C4×C9—61no—
491Dic9—21no—
492Dic9—21no—
493Dic9—21no—
494Dic9—32no—
495Dic9—62no—
496Dic9—61no—
497Dic9—121no—
498C2×#41—271no—
499C23×C4—271no—
500#123—91no—
501#123—271no—
502C22⋊Q8—271no—
503C22⋊Q8—271no—
504#121—271no—
505#121—271no—
506#120—271no—
507#120—271no—
508C4×D4—31no—
509C4×D4—271no—
510C4×D4—271no—
511C4×D4—271no—
512#117—271no—
513C3×C9#52511yescharacteristic, complemented, Sylow
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—91no—
517C23×C3C22×D911yescharacteristic
518C23×C3C2×D3211yescharacteristic
519C22×D3—31no—
520C22×D3—91no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—181no—
525C22×D3—181no—
526C22×D3—182no—
527C22×D3—182no—
528C22×D3—182no—
529C22×D3—182no—
530C22×D3—182no—
531C22×D3—182no—
532C22×D3C22×D911yescharacteristic
533C3×D4—62no—
534C3×D4—182no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—182no—
546C2×C3×C4C22×D911yescharacteristic
547C2×C3×C4C22×D911yescharacteristic
548C2×C3×C4C2×D3211yescharacteristic
549C2×C3×C4C2×D3211yescharacteristic
550#67—22no—
551#67—62no—
552#67—182no—
553#67—182no—
554#67—182no—
555#67—182no—
556#67—182no—
557#67—182no—
558#67—362no—
559#67—362no—
560C2×Dic3—22no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—94no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3—182no—
572C2×Dic3C22×D911yescharacteristic
573C2×Dic3C22×D911yescharacteristic
574C2×Dic3C22×D911yescharacteristic
575D12—182no—
576D12—182no—
577D12—182no—
578D12—182no—
579D12—362no—
580C4×D3—22no—
581C4×D3—62no—
582C4×D3—94no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—182no—
590C4×D3—362no—
591Dic6—182no—
592Dic6—182no—
593C2×C32—41no—
594C2×C32C2×#23511yescharacteristic
595C2×C32C2×D3×D411yescharacteristic
596C2×C32D3×#4111yescharacteristic
597C3⋊D3—62no—
598C3⋊D3—121no—
599C3×D3—22no—
600C3×D3—62no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—41no—
605C2×C9—62no—
606C2×C9—81no—
607C2×C9C2×D3×D411yescharacteristic
608C2×C9D3×#4111yescharacteristic
609C2×C9D3×#4111yescharacteristic
610D9—22no—
611D9—62no—
612D9—122no—
613D9—121no—
614D9—241no—
615C24—271no—
616#41—544no—
617C2×Q8—271no—
618C2×D4—31no—
619C2×D4—91no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—91no—
628C22×C4—271no—
629C22×C4—271no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C22×C4—544no—
634C4⋊C4—31no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C4⋊C4—271no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4D3×D911yescharacteristic, complemented
650C42—31no—
651C42—271no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—92no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—32no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—92no—
676C2×D3—92no—
677C2×D3—182no—
678C2×D3—188no—
679C2×D3—188no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—361no—
691C2×D3—361no—
692C2×D3—361no—
693C2×D3—361no—
694C2×D3—361no—
695C2×D3#369712yescomplemented
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—32no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—181no—
706C3×C4—181no—
707C3×C4—181no—
708Dic3—21no—
709Dic3—21no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—92no—
714Dic3—92no—
715Dic3—182no—
716Dic3—181no—
717Dic3—181no—
718Dic3—361no—
719Dic3D4×D912yes—
720C32#554711yescharacteristic
721C9—21no—
722C9#565611yescharacteristic, complemented
723C23—31no—
724C23—91no—
725C23—271no—
726C23—271no—
727C23—542no—
728C23—542no—
729C23—542no—
730C23C2×D3×D911yescharacteristic
731Q8—542no—
732D4—62no—
733D4—182no—
734D4—542no—
735D4—542no—
736D4—542no—
737D4—542no—
738D4—542no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—182no—
748C2×C4—274no—
749C2×C4—271no—
750C2×C4—271no—
751C2×C4—542no—
752C2×C4—542no—
753C2×C4—542no—
754C2×C4—542no—
755C2×C4C2×D3×D911yescharacteristic
756C2×C4C2×D3×D911yescharacteristic
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—62no—
763C2×C3—81no—
764C2×C3—182no—
765C2×C3C2×#369711yescharacteristic
766C2×C3C2×D4×D911yescharacteristic
767C2×C3#41×D911yescharacteristic
768C2×C3D3×#23511yescharacteristic
769C2×C3D32×D411yescharacteristic
770C2×C3#6431211yescharacteristic
771D3—22no—
772D3—62no—
773D3—182no—
774D3—182no—
775D3—362no—
776D3—361no—
777D3—361no—
778D3—721no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—32no—
783C22—61no—
784C22—61no—
785C22—92no—
786C22—181no—
787C22—181no—
788C22—272no—
789C22—548no—
790C22—541no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—541no—
795C22C22×D3×D911yescharacteristic
796C4—21no—
797C4—21no—
798C4—32no—
799C4—61no—
800C4—61no—
801C4—181no—
802C4—181no—
803C4—181no—
804C4—272no—
805C4—541no—
806C3—21no—
807C3#1058964911yescharacteristic, complemented
808C3#1059426611yescharacteristic
809C2—41no—
810C2—62no—
811C2—182no—
812C2—542no—
813C2—1081no—
814C2D3×#369711yescharacteristic
815C2D3×D4×D911yescharacteristic
816C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#525
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×#88658C2semidirect
2. C2×C4×D3×D9C2semidirect
3. #11721730C2semidirect
4. C9×#67⋊C4C2semidirect
5. C3×#63445C2semidirect
6. #11721292C2semidirect
7. #11721282C2semidirect
8. #11721240C2semidirect
9. #11721051C2semidirect
10. #11721030C2semidirect
11. #11721026C2semidirect
12. #11720993C2semidirect
13. #11720974C2semidirect
14. #11720938C2semidirect
15. #11720923C2semidirect
20. C2×#6233C22semidirect
25. C22×C9×Dic3C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×#6189C22semidirect
37. C3×C9×C22⋊C4C22semidirect
38. #88536C22semidirect
39. #88534C22semidirect
40. C3×#3676C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C4×C9×Dic3C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×Dic9⋊C4C22semidirect
50. #88445C22semidirect
52. #88442C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
81. #63445D3semidirect
118. Dic3×D9D4semidirect
185. C9×C22⋊C4C2×D3semidirect
188. #3676C2×D3semidirect
196. C4⋊Dic9C2×D3semidirect
201. Dic9⋊C4C2×D3semidirect
212. C2×C3⋊D9#41semidirect
215. C2×D3×C9#41semidirect
256. #67⋊C4D9semidirect
368. C22×Dic3C2×D9semidirect
398. C3×C22⋊C4C2×D9semidirect
426. Dic3⋊C4C2×D9semidirect
429. C4×Dic3C2×D9semidirect
513. C3×C9#525semidirect
649. C22⋊C4D3×D9semidirect
695. C2×D3#3697semidirect
722. C9#5656semidirect
807. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C2×#886582
C2×C4×D3×D92
#117217302
C9×#67⋊C42
C3×#634452
#117212922
#117212822
#117212402
#117210512
#117210302
#117210262
#117209932
#117209742
#117209382
#117209232
#105942663
#105896493