Finite Group Databasebeta

← #13148420

Subgroups — #13148420

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×#88658C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C9×#886C211yesmaximal, characteristic, complemented
5C3×#611⋊C4C211yesmaximal, characteristic, complemented
6#11721288C211yesmaximal, characteristic, complemented
7C2×#88445C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721039C211yesmaximal, characteristic, complemented
11#11721004C211yesmaximal, characteristic, complemented
12#11720994C211yesmaximal, characteristic, complemented
13#11720992C211yesmaximal, characteristic, complemented
14#11720988C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16#10594293—31nomaximal
17#10589756—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×C3×C4×D9C2211yescharacteristic, complemented
28#88668—24no—
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35#88658—24no—
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic
40#88536C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C9×C4⋊Dic3C2211yescharacteristic, complemented
45C9×C4⋊Dic3C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53#88445C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3804—31no—
57#64091—31no—
58C3×#886D311yescharacteristic
59C3×#67⋊C4—31no—
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×D4×D9—31no—
71C2×#3697—31no—
72C9×#123—31no—
73#63501—31no—
74C2×(C2×D9)⋊C4—31no—
75#63458—31no—
76#63457—31no—
77#63456—31no—
78#63455—31no—
79#63447—31no—
80#63446—31no—
81#63444—31no—
82#63444—31no—
83#63444—61no—
84#611⋊C4D311yescharacteristic, complemented
85C22⋊C4×D9—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×#67—22no—
105C3×#611D414yescomplemented
106C2×C9×Dic3—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9—41no—
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C3×C4×D9—41no—
115#6195—22no—
116#6195—41no—
117#6192—22no—
118#6192—22no—
119(C3⋊D9)⋊C4—22no—
120(C3⋊D9)⋊C4—22no—
121Dic3×D9—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×D3—31no—
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)⋊C4C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×C4⋊Dic3C2×D311yescharacteristic
155C3×C4⋊Dic3C2×D311yescharacteristic
156C3×Dic3⋊C4—31no—
157C3×C4×Dic3—31no—
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—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—61no—
171C2×#611C2×D311yescharacteristic
172C22×Dic9C2×D311yescharacteristic, complemented
173D4×D9—64no—
174#3697—64no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36—31no—
178C2×D36—31no—
179C2×D36—61no—
180C2×D36—61no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×Dic18—31no—
186C9×C4⋊C4—31no—
187C9×C4⋊C4—31no—
188C9×C22⋊C4—21no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4—31no—
191C9×C22⋊C4C2×D311yescharacteristic, complemented
192#3676—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—31no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203Dic9⋊C4—31no—
204Dic9⋊C4C2×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×C9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9C2×D412yes—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×#237—91no—
237C2×D3×D4—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#123—31no—
241C3×C4×D4—91no—
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—91no—
255#886D911yescharacteristic, complemented
256#885—91no—
257#884—91no—
258#882—91no—
259#882—91no—
260#882—91no—
261#882—91no—
262#882—181no—
263#67⋊C4—31no—
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—22no—
286C3×#67—34no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—121no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C3×C4×D3—121no—
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—62no—
324C2×C4×C9—21no—
325C2×C4×C9—21no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—62no—
330C2×C4×C9C22×D311yescharacteristic
331C2×C4×C9C22×D311yescharacteristic
332#611—62no—
333#611—62no—
334#611—122no—
335#611—121no—
336#611D1214yescomplemented
337C2×Dic9—31no—
338C2×Dic9—41no—
339C2×Dic9—61no—
340C2×Dic9C22×D311yescharacteristic
341C2×Dic9C22×D311yescharacteristic
342C2×Dic9C22×D311yescharacteristic
343D36—62no—
344D36—62no—
345D36—62no—
346D36—122no—
347D36—121no—
348D36—122no—
349C4×D9—41no—
350C4×D9—62no—
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—41no—
363C3×D9—22no—
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—91no—
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—31no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×Dic6—91no—
407C2×Dic6—91no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—91no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4C2×D911yescharacteristic, complemented
416C3×C22⋊C4D3211yescharacteristic
417C3×C42—91no—
418#217—91no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—91no—
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—181no—
436(C2×D3)⋊C4—181no—
437(C2×D3)⋊C4C2×D911yescharacteristic, complemented
438(C2×D3)⋊C4C2×D911yescharacteristic, complemented
439C4⋊Dic3—91no—
440C4⋊Dic3C2×D911yescharacteristic, complemented
441C4⋊Dic3C2×D911yescharacteristic, complemented
442Dic3⋊C4—31no—
443Dic3⋊C4—91no—
444C4×Dic3—31no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32D3×D412yes—
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—21no—
462C2×C3×D3—32no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465D32—124no—
466C32×C4—21no—
467C32×C4—21no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—32no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—22no—
479C22×C9—41no—
480C22×C9—41no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9C2×D1212yes—
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—32no—
489C2×D9—62no—
490C2×D9—61no—
491C2×D9—61no—
492C2×D9—62no—
493C2×D9—61no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—124no—
507C2×D9—124no—
508C2×D9—128no—
509C2×D9C2×D1212yes—
510C4×C9—21no—
511C4×C9—21no—
512C4×C9—41no—
513C4×C9—41no—
514C4×C9—61no—
515C4×C9—61no—
516C4×C9—61no—
517Dic9—21no—
518Dic9—21no—
519Dic9—61no—
520Dic9—121no—
521Dic9C2×D1212yes—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—31no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—91no—
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—62no—
570C3×D4—94no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—62no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—361no—
581C2×C3×C4—361no—
582C2×C3×C4C22×D911yescharacteristic
583C2×C3×C4C22×D911yescharacteristic
584C2×C3×C4C2×D3211yescharacteristic
585C2×C3×C4C2×D3211yescharacteristic
586#67—22no—
587#67—34no—
588#67—182no—
589#67—182no—
590#67—182no—
591#67—182no—
592#67—182no—
593#67—362no—
594#67—361no—
595C2×Dic3—22no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—121no—
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—121no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—182no—
623Dic6—182no—
624Dic6—182no—
625C2×C32—22no—
626C2×C32C2×D3×D411yescharacteristic
627C2×C32D3×#4111yescharacteristic
628C2×C32#100911yescharacteristic
629C3⋊D3—62no—
630C3⋊D3—121no—
631C3⋊D3—121no—
632C3×D3—41no—
633C3×D3—62no—
634C2×C9—22no—
635C2×C9—21no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—42no—
639C2×C9—121no—
640C2×C9C22×D1211yescharacteristic
641C2×C9#100411yescharacteristic
642C2×C9D3×#4111yescharacteristic
643D9—22no—
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—91no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—91no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
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—91no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—92no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3D4×D912yes—
702C22×C3C23×D911yescharacteristic
703C22×C3D3×D1212yes—
704C22×C3C22×D3211yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—32no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—182no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
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—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—361no—
732C2×D3—361no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—361no—
738C2×D3—364no—
739C2×D3—364no—
740C2×D3—364no—
741C2×D3—364no—
742C2×D3—368no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—92no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—32no—
759Dic3—61no—
760Dic3—61no—
761Dic3—181no—
762Dic3—181no—
763Dic3—361no—
764C32#565411yescharacteristic
765C9—21no—
766C9#555411yescharacteristic, 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—62no—
781D4—94no—
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—62no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—271no—
797C2×C4—361no—
798C2×C4—361no—
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—121no—
811C2×C3—182no—
812C2×C3C2×D4×D911yescharacteristic
813C2×C3#41×D911yescharacteristic
814C2×C3#6371511yescharacteristic
815C2×C3C2×D3×D1211yescharacteristic
816C2×C3#6431211yescharacteristic
817C2×C3#6431411yescharacteristic
818D3—41no—
819D3—62no—
820D3—182no—
821D3—182no—
822D3—362no—
823D3—362no—
824D3—361no—
825D3—361no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—92no—
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—
848C22D9×D1212yes—
849C22C22×D3×D911yescharacteristic
850C4—21no—
851C4—21no—
852C4—61no—
853C4—61no—
854C4—61no—
855C4—92no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—21no—
860C3#1058975611yescharacteristic, complemented
861C3#1059429311yescharacteristic
862C2—22no—
863C2—121no—
864C2—182no—
865C2—542no—
866C2—1081no—
867C2—1081no—
868C2C2×D9×D1211yescharacteristic
869C2#1172249811yescharacteristic
870C2#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×#88668C2semidirect
2. C2×#88658C2semidirect
3. #11721728C2semidirect
4. C9×#886C2semidirect
5. C3×#611⋊C4C2semidirect
6. #11721288C2semidirect
7. C2×#88445C2semidirect
8. #11721051C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721039C2semidirect
11. #11721004C2semidirect
12. #11720994C2semidirect
13. #11720992C2semidirect
14. #11720988C2semidirect
15. #11720956C2semidirect
20. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
25. C22×C9×Dic3C22semidirect
26. C22×C3×Dic9C22semidirect
27. C2×C3×C4×D9C22semidirect
30. C2×#6195C22semidirect
32. C2×#6192C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
40. #88536C22semidirect
41. C9×(C2×D3)⋊C4C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C9×C4⋊Dic3C22semidirect
45. C9×C4⋊Dic3C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. #88445C22semidirect
54. Dic9⋊Dic3C22semidirect
84. #611⋊C4D3semidirect
105. C3×#611D4semidirect
172. C22×Dic9C2×D3semidirect
184. C2×C4×D9C2×D3semidirect
191. C9×C22⋊C4C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
205. C4×Dic9C2×D3semidirect
219. C2×C3⋊D9#41semidirect
255. #886D9semidirect
336. #611D12semidirect
385. C22×Dic3C2×D9semidirect
415. C3×C22⋊C4C2×D9semidirect
437. (C2×D3)⋊C4C2×D9semidirect
438. (C2×D3)⋊C4C2×D9semidirect
440. C4⋊Dic3C2×D9semidirect
441. C4⋊Dic3C2×D9semidirect
537. C3×C9#546semidirect
685. C22⋊C4D3×D9semidirect
766. C9#5554semidirect
860. C3#10589756semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886582
#117217282
C9×#8862
C3×#611⋊C42
#117212882
C2×#884452
#117210512
D9×(C2×D3)⋊C42
#117210392
#117210042
#117209942
#117209922
#117209882
#117209562
#105942933
#105897563