Finite Group Databasebeta

← #13148421

Subgroups — #13148421

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C9×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#63448C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7C2×#88445C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
10#11721038C211yesmaximal, characteristic, complemented
11#11721020C211yesmaximal, characteristic, complemented
12#11721005C211yesmaximal, characteristic, complemented
13#11720995C211yesmaximal, characteristic, complemented
14#11720993C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594293—31nomaximal
17#10589656—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic, complemented
26C22×C3×Dic9C2211yescharacteristic, complemented
27C2×C4×D3×C9C2211yescharacteristic, complemented
28#88668—24no—
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic, complemented
31#88662—24no—
32C2×D3×Dic9C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic
40#88536C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C4×C9×Dic3C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×C4⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic3⋊Dic9C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3804—31no—
57#64091—31no—
58C3×#886—31no—
59C3×#67⋊C4D311yescharacteristic
60#63978—31no—
61C2×#3722—31no—
62#63923—31no—
63D3×(C2×D3)⋊C4—31no—
64#63910—31no—
65#63909—31no—
66#63895—31no—
67#63894—31no—
68#63890—31no—
69#63852—31no—
70C2×#3699—31no—
71C2×D4×D9—31no—
72C4×D4×C9—31no—
73#63492—31no—
74#63492—31no—
75C2×(C2×D9)⋊C4—31no—
76C2×(C2×D9)⋊C4—31no—
77#63459—31no—
78#63457—31no—
79#63448—31no—
80#63448D311yescharacteristic, complemented
81#63444—31no—
82#63444—31no—
83#63444—61no—
84#63437—31no—
85C4×D36—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
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
100#6233—22no—
101C2×C3⋊Dic9C2311yescharacteristic
102C4⋊(C3⋊D9)—22no—
103C4⋊(C3⋊D9)—41no—
104C9×#67D414yescomplemented
105C3×#611—22no—
106C2×C9×Dic3—41no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9—22no—
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C4×D3×C9—41no—
115#6195—22no—
116#6195—22no—
117D3×Dic9—22no—
118#6192—22no—
119#6192—41no—
120(C3⋊D9)⋊C4—22no—
121(C3⋊D9)⋊C4—22no—
122#6189—22no—
123#5654—91no—
124#5554—91no—
125C23×C3⋊D3—31no—
126C22×D32—31no—
127C2×#638—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C22×C3×Dic3—31no—
133C22×C3×Dic3C2×D311yescharacteristic
134C2×C3×C4×D3C2×D311yescharacteristic
135#3811—64no—
136C2×#627—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#624—31no—
142C2×#624—31no—
143#3804—64no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9—31no—
147C23×D9—61no—
148C32×C22⋊C4C2×D311yescharacteristic
149#3752—31no—
150#3752—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×C4⋊Dic3—31no—
155C3×C4⋊Dic3—31no—
156C3×Dic3⋊C4C2×D311yescharacteristic
157C3×C4×Dic3C2×D311yescharacteristic
158Dic3⋊Dic3—31no—
159#3722—31no—
160#3722—31no—
161#3722—31no—
162#3722—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165C2×D4×C9—31no—
166C22×C4×C9—31no—
167C22×C4×C9—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—61no—
172C2×#611C2×D311yescharacteristic
173C22×Dic9—31no—
174C22×Dic9C2×D311yescharacteristic, complemented
175#3699—64no—
176D4×D9—64no—
177C2×D36—31no—
178C2×D36—31no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—61no—
182C2×D36—61no—
183C2×C4×D9—31no—
184C2×C4×D9—31no—
185C2×Dic18—31no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—21no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4C2×D311yescharacteristic, complemented
190C42×C9—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
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—31no—
199(C2×D9)⋊C4—61no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203C4⋊Dic9—31no—
204C4⋊Dic9C2×D311yescharacteristic, complemented
205C4⋊Dic9C2×D311yescharacteristic, complemented
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9C2×D412yes—
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⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—44no—
219C2×C3⋊D9#4112yescomplemented
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—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3C2×D412yes—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×#237—91no—
237C2×D3×D4—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#123—91no—
241C3×C4×D4—31no—
242#939—91no—
243#930—91no—
244#930—91no—
245C2×(C2×D3)⋊C4—91no—
246C2×(C2×D3)⋊C4—91no—
247C2×(C2×D3)⋊C4—91no—
248#897—91no—
249#896—91no—
250#895—91no—
251#895—91no—
252#894—91no—
253#893—91no—
254#886—31no—
255#886—91no—
256#885—91no—
257#884—91no—
258#882—91no—
259#882—91no—
260#882—91no—
261#882—91no—
262#882—181no—
263#67⋊C4D911yescharacteristic, complemented
264D3×C22⋊C4—91no—
265#875—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3⋊D3—31no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—121no—
274C22×C3×D3—31no—
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282C2×C3⋊Dic3—31no—
283C4⋊(C3⋊D3)—62no—
284C4⋊(C3⋊D3)—121no—
285C3×#67—62no—
286C3×#67D1214yes—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—41no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C3×C4×D3—41no—
296#627—62no—
297#626—62no—
298#626—62no—
299#626—62no—
300#626—121no—
301#624—62no—
302#624—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9C22×D311yescharacteristic
307C22×D9—31no—
308C22×D9—31no—
309C22×D9—31no—
310C22×D9—61no—
311C22×D9—61no—
312C22×D9—61no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—122no—
318C22×D9—122no—
319C22×D9—121no—
320C22×D9—121no—
321C22×D9—122no—
322C22×D9C22×D311yescharacteristic
323D4×C9—34no—
324C2×C4×C9—21no—
325C2×C4×C9—21no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—121no—
330C2×C4×C9—121no—
331C2×C4×C9C22×D311yescharacteristic
332C2×C4×C9C22×D311yescharacteristic
333#611—22no—
334#611—62no—
335#611—62no—
336#611—62no—
337#611—122no—
338C2×Dic9—22no—
339C2×Dic9—31no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345D36—62no—
346D36—62no—
347D36—122no—
348D36—121no—
349D36—122no—
350D36—121no—
351C4×D9—62no—
352C4×D9—62no—
353Dic18—62no—
354#546—271noSylow
355C2×C3×C9—22no—
356C2×C3×C9C22×D411yescharacteristic
357C2×C3×C9C2×#4111yescharacteristic
358C2×C3×C9H(5,𝔽2)11yescharacteristic
359C3⋊D9—22no—
360C3⋊D9—41no—
361C3⋊D9—41no—
362D3×C9—22no—
363C3×D9—41no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—181no—
369C2×C3×D4—31no—
370C2×C3×D4—91no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—91no—
374C2×#67—31no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—181no—
382C2×#67C2×D911yescharacteristic
383C22×Dic3—31no—
384C22×Dic3—91no—
385C22×Dic3C2×D911yescharacteristic, complemented
386#237—184no—
387D3×D4—184no—
388D3×D4—184no—
389#235—184no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—91no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—181no—
399C2×D12—181no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3C2×D911yescharacteristic, complemented
406C2×Dic6—91no—
407C2×Dic6—91no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—91no—
410C3×C4⋊C4—91no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4C2×D911yescharacteristic, complemented
416C3×C22⋊C4D3211yescharacteristic
417C3×C42—31no—
418#217—91no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
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—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—181no—
437(C2×D3)⋊C4—181no—
438(C2×D3)⋊C4C2×D911yescharacteristic, complemented
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—91no—
442Dic3⋊C4—91no—
443Dic3⋊C4C2×D911yescharacteristic, complemented
444C4×Dic3C2×D911yescharacteristic, complemented
445C22×C32—21no—
446C22×C32—21no—
447C22×C32C2×D1212yes—
448C22×C32C23×D311yescharacteristic
449C2×C3⋊D3—32no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—124no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3C2×D1212yes—
465D32—124no—
466C32×C4—21no—
467C32×C4—21no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3C2×D1212yes—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—22no—
479C22×C9—32no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9D3×D412yes—
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—32no—
490C2×D9—62no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—62no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—121no—
507C2×D9—124no—
508C2×D9—124no—
509C2×D9—128no—
510C4×C9—21no—
511C4×C9—21no—
512C4×C9—32no—
513C4×C9—41no—
514C4×C9—41no—
515C4×C9—61no—
516C4×C9—61no—
517Dic9—21no—
518Dic9—21no—
519Dic9—21no—
520Dic9—61no—
521Dic9—121no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—91no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—31no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—91no—
541C23×C3C22×D911yescharacteristic
542C23×C3C2×D3211yescharacteristic
543C22×D3—31no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—181no—
551C22×D3—181no—
552C22×D3—181no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3—361no—
564C22×D3—361no—
565C22×D3—361no—
566C22×D3—361no—
567C22×D3—362no—
568C22×D3C22×D911yescharacteristic
569C3×D4—34no—
570C3×D4—182no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—121no—
580C2×C3×C4—121no—
581C2×C3×C4—182no—
582C2×C3×C4C22×D911yescharacteristic
583C2×C3×C4C22×D911yescharacteristic
584C2×C3×C4C2×D3211yescharacteristic
585C2×C3×C4C2×D3211yescharacteristic
586#67—62no—
587#67—182no—
588#67—182no—
589#67—182no—
590#67—182no—
591#67—182no—
592#67—362no—
593#67—361no—
594#67D3614yescomplemented
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—41no—
599C2×Dic3—62no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—181no—
603C2×Dic3—182no—
604C2×Dic3C22×D911yescharacteristic
605C2×Dic3C22×D911yescharacteristic
606C2×Dic3C22×D911yescharacteristic
607D12—182no—
608D12—182no—
609D12—182no—
610D12—182no—
611D12—182no—
612D12—362no—
613D12—361no—
614D12—361no—
615D12—362no—
616D12—361no—
617C4×D3—41no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—182no—
623Dic6—182no—
624Dic6—182no—
625C2×C32—22no—
626C2×C32C22×D1211yescharacteristic
627C2×C32#100411yescharacteristic
628C2×C32D3×#4111yescharacteristic
629C3⋊D3—62no—
630C3⋊D3—121no—
631C3⋊D3—121no—
632C3×D3—22no—
633C3×D3—121no—
634C2×C9—22no—
635C2×C9—21no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—42no—
639C2×C9—62no—
640C2×C9C2×D3×D411yescharacteristic
641C2×C9D3×#4111yescharacteristic
642C2×C9#100911yescharacteristic
643D9—41no—
644D9—62no—
645D9—122no—
646D9—122no—
647D9—121no—
648D9—121no—
649D9—241no—
650C24—271no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—91no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—91no—
672C4⋊C4—91no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4D3×D911yescharacteristic, complemented
686C42—31no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—32no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3C2×D3612yes—
702C22×C3C23×D911yescharacteristic
703C22×C3D3×D1212yes—
704C22×C3C22×D3211yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—92no—
711C2×D3—92no—
712C2×D3—182no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—182no—
718C2×D3—181no—
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—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—361no—
731C2×D3—361no—
732C2×D3—361no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—364no—
738C2×D3—364no—
739C2×D3—364no—
740C2×D3—364no—
741C2×D3—368no—
742C2×D3C2×D3612yes—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—32no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—181no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—181no—
761Dic3—181no—
762Dic3—361no—
763Dic3C2×D3612yes—
764C32#555411yescharacteristic
765C9—21no—
766C9#565411yescharacteristic, complemented
767C23—31no—
768C23—91no—
769C23—271no—
770C23—271no—
771C23—271no—
772C23—542no—
773C23—542no—
774C23—542no—
775C23—542no—
776C23—1081no—
777C23—1081no—
778C23C2×D3×D911yescharacteristic
779Q8—542no—
780D4—34no—
781D4—182no—
782D4—542no—
783D4—542no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—182no—
798C2×C4—271no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—542no—
802C2×C4C2×D3×D911yescharacteristic
803C2×C4C2×D3×D911yescharacteristic
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—42no—
810C2×C3—62no—
811C2×C3—361no—
812C2×C3C22×D3611yescharacteristic
813C2×C3#6371011yescharacteristic
814C2×C3#41×D911yescharacteristic
815C2×C3C2×D3×D1211yescharacteristic
816C2×C3#6431211yescharacteristic
817C2×C3#6431411yescharacteristic
818D3—22no—
819D3—121no—
820D3—182no—
821D3—182no—
822D3—362no—
823D3—362no—
824D3—361no—
825D3—361no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—32no—
832C22—61no—
833C22—61no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—272no—
838C22—541no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—1084no—
847C22—1084no—
848C22D3×D3612yes—
849C22C22×D3×D911yescharacteristic
850C4—21no—
851C4—21no—
852C4—32no—
853C4—61no—
854C4—61no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—21no—
860C3#1058965611yescharacteristic, complemented
861C3#1059429311yescharacteristic
862C2—22no—
863C2—62no—
864C2—361no—
865C2—542no—
866C2—1081no—
867C2—1081no—
868C2C2×D3×D3611yescharacteristic
869C2#1172249811yescharacteristic
870C2#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×#88662C2semidirect
3. #11721728C2semidirect
4. C9×#67⋊C4C2semidirect
5. C3×#63448C2semidirect
6. #11721277C2semidirect
7. C2×#88445C2semidirect
8. #11721051C2semidirect
9. D3×(C2×D9)⋊C4C2semidirect
10. #11721038C2semidirect
11. #11721020C2semidirect
12. #11721005C2semidirect
13. #11720995C2semidirect
14. #11720993C2semidirect
15. #11720940C2semidirect
20. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
25. C22×C9×Dic3C22semidirect
26. C22×C3×Dic9C22semidirect
27. C2×C4×D3×C9C22semidirect
30. C2×#6195C22semidirect
32. C2×D3×Dic9C22semidirect
34. C2×#6192C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
40. #88536C22semidirect
41. C9×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C4×C9×Dic3C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×C4⋊Dic9C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic3⋊Dic9C22semidirect
80. #63448D3semidirect
104. C9×#67D4semidirect
174. C22×Dic9C2×D3semidirect
189. C9×C22⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
204. C4⋊Dic9C2×D3semidirect
205. C4⋊Dic9C2×D3semidirect
219. C2×C3⋊D9#41semidirect
263. #67⋊C4D9semidirect
385. C22×Dic3C2×D9semidirect
405. C2×C4×D3C2×D9semidirect
415. C3×C22⋊C4C2×D9semidirect
438. (C2×D3)⋊C4C2×D9semidirect
443. Dic3⋊C4C2×D9semidirect
444. C4×Dic3C2×D9semidirect
537. C3×C9#546semidirect
594. #67D36semidirect
685. C22⋊C4D3×D9semidirect
766. C9#5654semidirect
860. C3#10589656semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886622
#117217282
C9×#67⋊C42
C3×#634482
#117212772
C2×#884452
#117210512
D3×(C2×D9)⋊C42
#117210382
#117210202
#117210052
#117209952
#117209932
#117209402
#105942933
#105896563