Finite Group Databasebeta

← #13148300

Subgroups — #13148300

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×#88639C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#63447C211yesmaximal, characteristic, complemented
6#11721291C211yesmaximal, characteristic, complemented
7#11721281C211yesmaximal, characteristic, complemented
8#11721280C211yesmaximal, characteristic, complemented
9#11721050C211yesmaximal, characteristic, complemented
10D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12C4×#6195C211yesmaximal, characteristic, complemented
13#11721013C211yesmaximal, characteristic, complemented
14#11720985C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10594285—31nomaximal
17#10589712—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic
25C2×C9×D12C2211yescharacteristic, complemented
26C2×C4×D3×C9C2211yescharacteristic, complemented
27C2×C3×Dic18C2211yescharacteristic, complemented
28#88668—24no—
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic, complemented
33C2×D3×Dic9C2211yescharacteristic, complemented
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×#6192C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic
37#88639—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88551C2211yescharacteristic, complemented
40#88536C2211yescharacteristic
41#88536C2211yescharacteristic
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3796—31no—
57C22⋊C4×C3⋊D3—31no—
58C3×#885—31no—
59C3×#884D311yescharacteristic
60#63981—31no—
61#63970—31no—
62#63969—31no—
63#63922—31no—
64D3×(C2×D3)⋊C4—31no—
65#63912—31no—
66C4×#626—31no—
67#63888—31no—
68#63880—31no—
69#63853—31no—
70C2×#3699—31no—
71C2×D4×D9—31no—
72C9×#121—31no—
73#63501—31no—
74#63499—31no—
75#63499—31no—
76#63497—31no—
77C4×#611—31no—
78C2×(C2×D9)⋊C4—31no—
79#63458—31no—
80#63456—31no—
81#63447D311yescharacteristic, complemented
82#63446—31no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9—61no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C4×C3⋊D9—22no—
103C4×C3⋊D9—41no—
104C9×#67—22no—
105C9×#67—41no—
106C3×#611—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C9×D12—22no—
113C4×D3×C9—41no—
114C3×Dic18—22no—
115#6195—22no—
116#6195—22no—
117#6195D414yescomplemented
118#6194—41no—
119D3×Dic9—22no—
120D3×Dic9—22no—
121#6192—22no—
122(C3⋊D9)⋊C4—22no—
123#5676—91no—
124#5610—91no—
125C23×C3⋊D3—31no—
126C22×D32—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×#67—31no—
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×D12C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×Dic6—31no—
135#3811—64no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144#3796—64no—
145C23×D9—31no—
146C23×D9—31no—
147C23×D9—61no—
148C32×C22⋊C4C2×D311yescharacteristic
149#3757—31no—
150#3752—31no—
151#3752—31no—
152C3×#217—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×Dic3⋊C4C2×D311yescharacteristic
157C3×C4×Dic3—31no—
158#3724—31no—
159Dic3⋊Dic3—31no—
160Dic3⋊Dic3—31no—
161#3722—31no—
162#3722—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9—31no—
168C22×C4×C9—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611C2×D311yescharacteristic
174C22×Dic9—31no—
175C22×Dic9—31no—
176#3699—64no—
177D4×D9—64no—
178C2×D36—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—61no—
183C2×C4×D9—61no—
184C2×Dic18C2×D311yescharacteristic, complemented
185C9×C4⋊C4—31no—
186C9×C22⋊C4—21no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4C2×D311yescharacteristic, complemented
189#3676—31no—
190#3676—31no—
191#3676—61no—
192#3676C2×D311yescharacteristic, complemented
193(C2×D9)⋊C4—31no—
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)⋊C4—61no—
200(C2×D9)⋊C4C2×D311yescharacteristic, complemented
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205C4×Dic9C2×D311yescharacteristic, complemented
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—44no—
215C2×C3⋊D9C2×D412yes—
216C2×C3⋊D9#4112yescomplemented
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9C2×D412yes—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×#239—91no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C2×D3×D4—91no—
240C3×#124—91no—
241C3×#121—31no—
242#946—91no—
243#939—91no—
244#938—91no—
245#937—91no—
246#937—91no—
247#935—91no—
248C4×#67—91no—
249C2×(C2×D3)⋊C4—91no—
250#896—91no—
251#894—91no—
252#885—31no—
253#884—91no—
254#884—91no—
255#884D911yescharacteristic, complemented
256#883—91no—
257#883—91no—
258#882—91no—
259#882—91no—
260#67⋊C4—91no—
261D3×C22⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—181no—
265C4×D12—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—121no—
273C22×C3×D3—31no—
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—121no—
285C3×#67—22no—
286C3×#67—41no—
287C3×#67—62no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×D12—22no—
294C3×C4×D3—41no—
295C3×Dic6—62no—
296#626—34no—
297#626—62no—
298#626—62no—
299#626—62no—
300#625—121no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9C22×D311yescharacteristic
308C22×D9—31no—
309C22×D9—31no—
310C22×D9—61no—
311C22×D9—61no—
312C22×D9—62no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—64no—
317C22×D9—122no—
318C22×D9—121no—
319C22×D9—121no—
320C22×D9—122no—
321C22×D9C22×D311yescharacteristic
322D4×C9—62no—
323D4×C9—62no—
324D4×C9—121no—
325C2×C4×C9—21no—
326C2×C4×C9—21no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—121no—
330C2×C4×C9C22×D311yescharacteristic
331C2×C4×C9C22×D311yescharacteristic
332#611—22no—
333#611—34no—
334#611—62no—
335#611—62no—
336#611—121no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9—62no—
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345C2×Dic9C22×D311yescharacteristic
346D36—62no—
347C4×D9—62no—
348C4×D9—62no—
349C4×D9—122no—
350C4×D9—121no—
351C4×D9—122no—
352Dic18—22no—
353#546—271noSylow
354C2×C3×C9—41no—
355C2×C3×C9C22×D411yescharacteristic
356C2×C3×C9C2×#4111yescharacteristic
357C2×C3×C9H(5,𝔽2)11yescharacteristic
358C3⋊D9—22no—
359C3⋊D9—22no—
360D3×C9—22no—
361D3×C9—41no—
362C3×D9—41no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—181no—
368C2×C3×Q8—91no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—91no—
373C22×C3×C4—31no—
374C2×#67—31no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67C2×D911yescharacteristic
382C2×#67C2×D911yescharacteristic, complemented
383C22×Dic3—91no—
384C22×Dic3—91no—
385#239—184no—
386#237—184no—
387D3×D4—184no—
388D3×D4—184no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12C2×D911yescharacteristic, complemented
394C2×C4×D3—91no—
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—181no—
403C2×C4×D3—181no—
404C2×C4×D3C2×D911yescharacteristic, complemented
405C2×Dic6—31no—
406C3×C4⋊C4—31no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4C2×D911yescharacteristic, complemented
413C3×C22⋊C4D3211yescharacteristic
414C3×C42—91no—
415#217—31no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—181no—
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—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—181no—
434(C2×D3)⋊C4—181no—
435(C2×D3)⋊C4C2×D911yescharacteristic, complemented
436C4⋊Dic3—91no—
437C4⋊Dic3—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4C2×D911yescharacteristic, complemented
443C4×Dic3—31no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32C23×D311yescharacteristic
448C2×C3⋊D3—32no—
449C2×C3⋊D3—32no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—124no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3D3×D412yes—
464D32—124no—
465C32×C4—21no—
466C32×C4—21no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—32no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C22×C9—22no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—32no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9—61no—
487C22×C9C23×D311yescharacteristic
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—32no—
492C2×D9—32no—
493C2×D9—62no—
494C2×D9—62no—
495C2×D9—62no—
496C2×D9—62no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—61no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—124no—
504C2×D9—124no—
505C2×D9—128no—
506C4×C9—21no—
507C4×C9—21no—
508C4×C9—41no—
509C4×C9—41no—
510C4×C9—61no—
511C4×C9—61no—
512Dic9—21no—
513Dic9—21no—
514Dic9—61no—
515Dic9—61no—
516Dic9—121no—
517Dic9—121no—
518Dic9D3×D412yes—
519C2×#41—271no—
520C22×D4—271no—
521#124—91no—
522#123—271no—
523#123—271no—
524C22⋊Q8—271no—
525#121—31no—
526#121—271no—
527#121—271no—
528#120—271no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C3×C9#54611yescharacteristic, complemented, Sylow
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—31no—
538C23×C3—91no—
539C23×C3C22×D911yescharacteristic
540C23×C3C2×D3211yescharacteristic
541C22×D3—31no—
542C22×D3—91no—
543C22×D3—91no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—181no—
547C22×D3—181no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—184no—
556C22×D3—182no—
557C22×D3—362no—
558C22×D3—361no—
559C22×D3—361no—
560C22×D3—361no—
561C22×D3—361no—
562C22×D3—362no—
563C22×D3C22×D911yescharacteristic
564C22×D3C22×D911yescharacteristic
565C3×Q8—182no—
566C3×D4—62no—
567C3×D4—62no—
568C3×D4—121no—
569C3×D4—182no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—121no—
578C2×C3×C4C22×D911yescharacteristic
579C2×C3×C4C22×D911yescharacteristic
580C2×C3×C4C2×D3211yescharacteristic
581C2×C3×C4C2×D3211yescharacteristic
582#67—22no—
583#67—41no—
584#67—62no—
585#67—94no—
586#67—182no—
587#67—182no—
588#67—182no—
589#67—361no—
590#67—361no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—181no—
599C2×Dic3—181no—
600C2×Dic3—182no—
601C2×Dic3—182no—
602C2×Dic3C22×D911yescharacteristic
603C2×Dic3C22×D911yescharacteristic
604D12—22no—
605D12—94no—
606D12—182no—
607D12—182no—
608D12—182no—
609C4×D3—41no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—182no—
616C4×D3—362no—
617C4×D3—361no—
618C4×D3—361no—
619C4×D3—362no—
620Dic6—62no—
621C2×C32—41no—
622C2×C32C2×D3×D411yescharacteristic
623C2×C32#100411yescharacteristic
624C2×C32D3×#4111yescharacteristic
625C3⋊D3—62no—
626C3⋊D3—62no—
627C3×D3—22no—
628C3×D3—41no—
629C3×D3—121no—
630C2×C9—21no—
631C2×C9—21no—
632C2×C9—21no—
633C2×C9—42no—
634C2×C9—41no—
635C2×C9—62no—
636C2×C9—121no—
637C2×C9C2×D3×D411yescharacteristic
638C2×C9D3×#4111yescharacteristic
639C2×C9#100911yescharacteristic
640D9—41no—
641D9—64no—
642D9—62no—
643D9—62no—
644D9—122no—
645C24—271no—
646C24—271no—
647#41—544no—
648C2×Q8—91no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—91no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—544no—
659C22×C4—31no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C4⋊C4—31no—
666C4⋊C4—271no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4D3×D911yescharacteristic, complemented
681C42—91no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—32no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3C23×D911yescharacteristic
702C22×C3C22×D3211yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—92no—
715C2×D3—182no—
716C2×D3—182no—
717C2×D3—182no—
718C2×D3—182no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—361no—
728C2×D3—361no—
729C2×D3—364no—
730C2×D3—364no—
731C2×D3—364no—
732C2×D3—364no—
733C2×D3—368no—
734C2×D3D4×D912yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—92no—
744C3×C4—181no—
745C3×C4—181no—
746Dic3—21no—
747Dic3—21no—
748Dic3—32no—
749Dic3—61no—
750Dic3—61no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754Dic3—181no—
755Dic3—361no—
756Dic3—361no—
757C32#561011yescharacteristic
758C9—21no—
759C9#567611yescharacteristic, complemented
760C23—31no—
761C23—31no—
762C23—91no—
763C23—271no—
764C23—271no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23—542no—
769C23—1081no—
770C23—1081no—
771C23C2×D3×D911yescharacteristic
772Q8—182no—
773D4—62no—
774D4—62no—
775D4—121no—
776D4—182no—
777D4—274no—
778D4—542no—
779D4—542no—
780D4—542no—
781D4—1081no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—121no—
788C2×C4—271no—
789C2×C4—271no—
790C2×C4—542no—
791C2×C4—542no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4—1081no—
795C2×C4C2×D3×D911yescharacteristic
796C2×C4C2×D3×D911yescharacteristic
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—42no—
801C2×C3—41no—
802C2×C3—41no—
803C2×C3—62no—
804C2×C3—121no—
805C2×C3—361no—
806C2×C3C2×D4×D911yescharacteristic
807C2×C3#6371011yescharacteristic
808C2×C3#41×D911yescharacteristic
809C2×C3#6430611yescharacteristic
810C2×C3D32×D411yescharacteristic
811C2×C3#6431411yescharacteristic
812D3—22no—
813D3—41no—
814D3—121no—
815D3—184no—
816D3—182no—
817D3—182no—
818D3—182no—
819D3—182no—
820D3—362no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—32no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—272no—
834C22—272no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—541no—
839C22—1084no—
840C22—1084no—
841C22C22×D3×D911yescharacteristic
842C4—21no—
843C4—21no—
844C4—61no—
845C4—61no—
846C4—92no—
847C4—181no—
848C4—181no—
849C4—541no—
850C4—541no—
851C3—21no—
852C3#1058971211yescharacteristic, complemented
853C3#1059428511yescharacteristic
854C2—41no—
855C2—62no—
856C2—121no—
857C2—361no—
858C2—542no—
859C2—542no—
860C2#1172247511yescharacteristic
861C2D3×D4×D911yescharacteristic
862C2#1172250011yescharacteristic
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×#88668C2semidirect
2. C2×#88639C2semidirect
3. C22⋊C4×C3⋊D9C2semidirect
4. C9×#884C2semidirect
5. C3×#63447C2semidirect
6. #11721291C2semidirect
7. #11721281C2semidirect
8. #11721280C2semidirect
9. #11721050C2semidirect
10. D3×(C2×D9)⋊C4C2semidirect
11. #11721041C2semidirect
12. C4×#6195C2semidirect
13. #11721013C2semidirect
14. #11720985C2semidirect
15. #11720941C2semidirect
20. C2×C4×C3⋊D9C22semidirect
21. C2×C4×C3⋊D9C22semidirect
23. C2×C9×#67C22semidirect
25. C2×C9×D12C22semidirect
26. C2×C4×D3×C9C22semidirect
27. C2×C3×Dic18C22semidirect
31. C2×#6195C22semidirect
32. C2×#6194C22semidirect
33. C2×D3×Dic9C22semidirect
34. C2×D3×Dic9C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88551C22semidirect
42. C3×#3676C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
81. #63447D3semidirect
117. #6195D4semidirect
184. C2×Dic18C2×D3semidirect
188. C9×C22⋊C4C2×D3semidirect
192. #3676C2×D3semidirect
200. (C2×D9)⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
205. C4×Dic9C2×D3semidirect
216. C2×C3⋊D9#41semidirect
255. #884D9semidirect
382. C2×#67C2×D9semidirect
393. C2×D12C2×D9semidirect
404. C2×C4×D3C2×D9semidirect
412. C3×C22⋊C4C2×D9semidirect
435. (C2×D3)⋊C4C2×D9semidirect
442. Dic3⋊C4C2×D9semidirect
534. C3×C9#546semidirect
680. C22⋊C4D3×D9semidirect
759. C9#5676semidirect
852. C3#10589712semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886392
C22⋊C4×C3⋊D92
C9×#8842
C3×#634472
#117212912
#117212812
#117212802
#117210502
D3×(C2×D9)⋊C42
#117210412
C4×#61952
#117210132
#117209852
#117209412
#105942853
#105897123