Finite Group Databasebeta

← #13151000

Subgroups — #13151000

Order 1728.

1238 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3C3×#63501C211yesmaximal, characteristic, complemented
4C9×#935C211yesmaximal, characteristic, complemented
5#11721278C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7#11721274C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9C2×#88445C211yesmaximal, characteristic, complemented
10#11721242C211yesmaximal, characteristic, complemented
11#11721241C211yesmaximal, characteristic, complemented
12#11721005C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720978C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10595163—31nomaximal
17#10589756—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C23×C3⋊D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic
23D4×C3⋊D9—24no—
24C2×C4⋊(C3⋊D9)C2211yescharacteristic
25C2×C4×C3⋊D9C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic, complemented
27C2×C3×#611C2211yescharacteristic, complemented
28C22×C9×Dic3C2211yescharacteristic, complemented
29C22×C3×Dic9C2211yescharacteristic, complemented
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35#88658—24no—
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38C9×#217C2211yescharacteristic, complemented
39C9×#217C2211yescharacteristic, complemented
40C9×#217C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3804—31no—
57C3×#939—31no—
58C3×#935D311yescharacteristic
59#63981—31no—
60#63981—31no—
61#63974—31no—
62#63971—31no—
63C2×#3722—31no—
64#63953—31no—
65#63952—31no—
66#63910—31no—
67#63897—31no—
68#63881—31no—
69#63865—31no—
70C2×D4×D9—31no—
71C2×D4×D9—61no—
72C2×#3697—31no—
73C9×#123—31no—
74#63501D311yescharacteristic, complemented
75C2×(C2×D9)⋊C4—31no—
76#63458—31no—
77#63457—31no—
78#63456—31no—
79#63455—31no—
80#63447—31no—
81#63446—31no—
82#63444—31no—
83#63444—31no—
84#611⋊C4—31no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9—22no—
91C22×C3⋊D9—22no—
92C22×C3⋊D9—41no—
93C22×C3⋊D9—41no—
94C22×C3⋊D9C2311yescharacteristic
95C22×C3⋊D9C2311yescharacteristic
96C22×C3⋊D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C3×D4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233D414yescomplemented
102C2×C3⋊Dic9C2311yescharacteristic
103C4⋊(C3⋊D9)—22no—
104C4×C3⋊D9—22no—
105C3×#611—22no—
106C3×#611—41no—
107C2×C9×Dic3—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C3×Dic9—41no—
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116#6192—22no—
117#6192—22no—
118#6192—41no—
119(C3⋊D9)⋊C4—22no—
120(C3⋊D9)⋊C4—41no—
121Dic3×D9—22no—
122#6189—22no—
123#5654—91no—
124#5610—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130D4×C3⋊D3—64no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4×C3⋊D3—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3C2×D311yescharacteristic
137C2×#627—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—
148C23×D9—61no—
149C3×#217—31no—
150C3×#217C2×D311yescharacteristic
151C3×#217C2×D311yescharacteristic
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4C2×D311yescharacteristic
156C3×Dic3⋊C4C2×D311yescharacteristic
157#3724—31no—
158#3722—31no—
159#3722—31no—
160#3722—31no—
161#3722—31no—
162#3722—31no—
163#3722—31no—
164#3722—31no—
165Dic32—31no—
166C2×D4×C9—21no—
167C2×D4×C9C2×D311yescharacteristic
168C22×C4×C9—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—61no—
172C2×#611—61no—
173C2×#611C2×D311yescharacteristic, complemented
174C2×#611C2×D311yescharacteristic, complemented
175C22×Dic9C2×D311yescharacteristic, complemented
176D4×D9—64no—
177D4×D9—68no—
178#3697—64no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—31no—
182C2×D36—31no—
183C2×D36—61no—
184C2×C4×D9—31no—
185C2×C4×D9—31no—
186C2×C4×D9—31no—
187C2×C4×D9—31no—
188C2×C4×D9—61no—
189C2×Dic18—31no—
190C9×C4⋊C4—31no—
191C9×C4⋊C4—31no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195#3676C2×D311yescharacteristic, complemented
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205Dic9⋊C4C2×D311yescharacteristic, complemented
206C4×Dic9—31no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C2×D412yes—
213C22×C3×C9C2411yescharacteristic
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×C3⋊D9—21no—
220C2×C3⋊D9—21no—
221C2×C3⋊D9—44no—
222C2×C3⋊D9—44no—
223C2×C3⋊D9C2×D412yes—
224C2×C3⋊D9#4112yescomplemented
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9C2×D412yes—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C3×Dic9—21no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C2×D3×D4—91no—
240C2×D3×D4—181no—
241C2×#235—91no—
242C3×#123—31no—
243C3×#121—91no—
244#939—31no—
245#939—91no—
246#937—91no—
247#937—91no—
248#935D911yescharacteristic, complemented
249C4×#67—91no—
250C2×(C2×D3)⋊C4—91no—
251C2×(C2×D3)⋊C4—91no—
252#896—91no—
253#896—91no—
254#895—91no—
255#894—91no—
256#894—91no—
257#893—91no—
258#885—91no—
259#885—91no—
260#884—91no—
261#884—91no—
262#882—91no—
263#882—91no—
264#67⋊C4—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267D3×C22⋊C4—91no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3—31no—
271C22×C3⋊D3—31no—
272C22×C3⋊D3—31no—
273C22×C3⋊D3—62no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3⋊D3—62no—
277C22×C3⋊D3—121no—
278C22×C3⋊D3—121no—
279C22×C3×D3—31no—
280C32×D4—22no—
281C2×C32×C4C22×D311yescharacteristic
282#638—34no—
283#638—62no—
284C2×C3⋊Dic3—31no—
285C4⋊(C3⋊D3)—62no—
286C4×C3⋊D3—62no—
287C3×#67—62no—
288C3×#67—121no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—121no—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298#627—62no—
299#626—62no—
300#626—62no—
301#626—121no—
302#624—62no—
303#624—121no—
304D3×Dic3—62no—
305C23×C9—21no—
306C23×C9—21no—
307C23×C9C22×D311yescharacteristic
308C23×C9C22×D311yescharacteristic
309C22×D9—31no—
310C22×D9—31no—
311C22×D9—31no—
312C22×D9—61no—
313C22×D9—61no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—62no—
318C22×D9—64no—
319C22×D9—64no—
320C22×D9—62no—
321C22×D9—122no—
322C22×D9—122no—
323C22×D9—121no—
324C22×D9—121no—
325C22×D9—122no—
326C22×D9—122no—
327C22×D9C22×D311yescharacteristic
328D4×C9—24no—
329D4×C9—22no—
330C2×C4×C9—21no—
331C2×C4×C9—31no—
332C2×C4×C9—31no—
333C2×C4×C9—31no—
334C2×C4×C9—31no—
335C2×C4×C9—62no—
336C2×C4×C9C22×D311yescharacteristic
337#611—22no—
338#611—34no—
339#611—41no—
340#611—64no—
341#611—62no—
342#611—64no—
343C2×Dic9—31no—
344C2×Dic9—41no—
345C2×Dic9—61no—
346C2×Dic9C22×D311yescharacteristic
347C2×Dic9C22×D311yescharacteristic
348C2×Dic9C22×D311yescharacteristic
349D36—62no—
350D36—64no—
351D36—62no—
352D36—62no—
353D36—121no—
354C4×D9—62no—
355C4×D9—62no—
356C4×D9—62no—
357C4×D9—64no—
358C4×D9—121no—
359Dic18—62no—
360#546—271noSylow
361C2×C3×C9—22no—
362C2×C3×C9—41no—
363C2×C3×C9C22×D411yescharacteristic
364C2×C3×C9C2×#4111yescharacteristic
365C2×C3×C9H(5,𝔽2)11yescharacteristic
366C3⋊D9—22no—
367C3⋊D9—22no—
368C3⋊D9—41no—
369C3×D9—41no—
370C23×D3—91no—
371C23×D3—91no—
372C23×D3—91no—
373C23×D3—91no—
374C23×D3—181no—
375C23×D3—181no—
376C2×C3×D4—21no—
377C2×C3×D4—91no—
378C2×C3×D4—91no—
379C2×C3×D4C2×D911yescharacteristic
380C2×C3×D4D3211yescharacteristic
381C22×C3×C4—31no—
382C22×C3×C4—91no—
383C2×#67—31no—
384C2×#67—31no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—181no—
393C2×#67—181no—
394C22×Dic3—31no—
395C22×Dic3—91no—
396C22×Dic3C2×D911yescharacteristic, complemented
397#237—184no—
398D3×D4—184no—
399D3×D4—184no—
400D3×D4—188no—
401#235—184no—
402C2×D12—91no—
403C2×D12—91no—
404C2×D12—91no—
405C2×D12—91no—
406C2×D12—91no—
407C2×D12—181no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—181no—
416C2×Dic6—91no—
417C2×Dic6—91no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—31no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426#217—31no—
427#217C2×D911yescharacteristic, complemented
428#217C2×D911yescharacteristic, complemented
429#217C2×D911yescharacteristic, complemented
430(C2×D3)⋊C4—31no—
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—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445Dic3⋊C4—31no—
446Dic3⋊C4—91no—
447Dic3⋊C4—91no—
448Dic3⋊C4C2×D911yescharacteristic, complemented
449Dic3⋊C4C2×D911yescharacteristic, complemented
450C4×Dic3—91no—
451C4×Dic3—91no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32D3×D412yes—
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—32no—
460C2×C3⋊D3—32no—
461C2×C3⋊D3—61no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—124no—
469C2×C3⋊D3—124no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C32×C4—21no—
474C3⋊Dic3—32no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C22×C9—21no—
483C22×C9—21no—
484C22×C9—22no—
485C22×C9—21no—
486C22×C9—21no—
487C22×C9—21no—
488C22×C9—21no—
489C22×C9—22no—
490C22×C9—41no—
491C22×C9—41no—
492C22×C9—41no—
493C22×C9—41no—
494C22×C9D3×D412yes—
495C22×C9C23×D311yescharacteristic
496C2×D9—21no—
497C2×D9—21no—
498C2×D9—21no—
499C2×D9—32no—
500C2×D9—32no—
501C2×D9—62no—
502C2×D9—62no—
503C2×D9—62no—
504C2×D9—62no—
505C2×D9—61no—
506C2×D9—61no—
507C2×D9—61no—
508C2×D9—61no—
509C2×D9—62no—
510C2×D9—61no—
511C2×D9—61no—
512C2×D9—61no—
513C2×D9—121no—
514C2×D9—121no—
515C2×D9—121no—
516C2×D9—121no—
517C2×D9—124no—
518C2×D9—124no—
519C2×D9—128no—
520C2×D9—128no—
521C4×C9—22no—
522C4×C9—21no—
523C4×C9—61no—
524C4×C9—61no—
525C4×C9—61no—
526C4×C9—61no—
527Dic9—21no—
528Dic9—21no—
529Dic9—21no—
530Dic9—32no—
531Dic9—62no—
532C2×#41—271no—
533C22×D4—271no—
534#124—271no—
535#123—31no—
536#123—271no—
537C22⋊Q8—271no—
538#121—91no—
539#121—271no—
540#121—271no—
541#120—271no—
542#120—271no—
543C4×D4—271no—
544C4×D4—271no—
545C2×C22⋊C4—271no—
546C2×C22⋊C4—271no—
547C3×C9#54611yescharacteristic, complemented, Sylow
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—91no—
551C23×C3C22×D911yescharacteristic
552C23×C3C22×D911yescharacteristic
553C23×C3C2×D3211yescharacteristic
554C23×C3C2×D3211yescharacteristic
555C22×D3—31no—
556C22×D3—91no—
557C22×D3—91no—
558C22×D3—91no—
559C22×D3—91no—
560C22×D3—91no—
561C22×D3—91no—
562C22×D3—181no—
563C22×D3—181no—
564C22×D3—181no—
565C22×D3—182no—
566C22×D3—182no—
567C22×D3—182no—
568C22×D3—182no—
569C22×D3—182no—
570C22×D3—182no—
571C22×D3—184no—
572C22×D3—184no—
573C22×D3—182no—
574C22×D3—182no—
575C22×D3—362no—
576C22×D3—362no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—362no—
582C22×D3—362no—
583C3×D4—24no—
584C3×D4—22no—
585C3×D4—22no—
586C3×D4—182no—
587C3×D4—361no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—62no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—361no—
598C2×C3×C4C22×D911yescharacteristic
599C2×C3×C4C2×D3211yescharacteristic
600#67—62no—
601#67—94no—
602#67—94no—
603#67—121no—
604#67—184no—
605#67—182no—
606#67—182no—
607#67—182no—
608#67—182no—
609#67—184no—
610#67—361no—
611C2×Dic3—22no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—91no—
616C2×Dic3—91no—
617C2×Dic3—121no—
618C2×Dic3—181no—
619C2×Dic3—182no—
620C2×Dic3C22×D911yescharacteristic
621C2×Dic3C22×D911yescharacteristic
622C2×Dic3C22×D911yescharacteristic
623C2×Dic3C22×D911yescharacteristic
624D12—182no—
625D12—182no—
626D12—184no—
627D12—182no—
628D12—182no—
629D12—361no—
630C4×D3—182no—
631C4×D3—182no—
632C4×D3—182no—
633C4×D3—182no—
634C4×D3—182no—
635C4×D3—184no—
636C4×D3—361no—
637C4×D3—361no—
638Dic6—182no—
639Dic6—182no—
640C2×C32—22no—
641C2×C32—41no—
642C2×C32C2×D3×D411yescharacteristic
643C2×C32D3×#4111yescharacteristic
644C2×C32#100911yescharacteristic
645C3⋊D3—62no—
646C3⋊D3—62no—
647C3⋊D3—121no—
648C3×D3—121no—
649C2×C9—22no—
650C2×C9—21no—
651C2×C9—21no—
652C2×C9—21no—
653C2×C9—42no—
654C2×C9—42no—
655C2×C9—41no—
656C2×C9C2×D3×D411yescharacteristic
657C2×C9#100411yescharacteristic
658C2×C9D3×#4111yescharacteristic
659D9—41no—
660D9—64no—
661D9—62no—
662D9—62no—
663D9—122no—
664D9—122no—
665D9—121no—
666C24—271no—
667C24—271no—
668#41—544no—
669C2×Q8—271no—
670C2×D4—91no—
671C2×D4—91no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—544no—
679C2×D4D3×D911yescharacteristic
680C22×C4—31no—
681C22×C4—91no—
682C22×C4—271no—
683C22×C4—271no—
684C22×C4—271no—
685C22×C4—271no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—91no—
689C4⋊C4—271no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C42—271no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—22no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3D4×D912yes—
724C22×C3C23×D911yescharacteristic
725C22×C3#381112yes—
726C22×C3C22×D3211yescharacteristic
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—92no—
731C2×D3—92no—
732C2×D3—92no—
733C2×D3—92no—
734C2×D3—182no—
735C2×D3—182no—
736C2×D3—182no—
737C2×D3—182no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3—181no—
741C2×D3—181no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—182no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—361no—
754C2×D3—361no—
755C2×D3—361no—
756C2×D3—361no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3—364no—
761C2×D3—368no—
762C2×D3—368no—
763C3×C4—22no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—61no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773Dic3—21no—
774Dic3—21no—
775Dic3—21no—
776Dic3—21no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—92no—
781Dic3—92no—
782Dic3—182no—
783C32#565411yescharacteristic
784C9—21no—
785C9#561011yescharacteristic, complemented
786C23—91no—
787C23—271no—
788C23—271no—
789C23—271no—
790C23—542no—
791C23—542no—
792C23—542no—
793C23—542no—
794C23—1081no—
795C23—1081no—
796C23C2×D3×D911yescharacteristic
797C23C2×D3×D911yescharacteristic
798Q8—542no—
799D4—22no—
800D4—182no—
801D4—274no—
802D4—361no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—62no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—271no—
817C2×C4—361no—
818C2×C4—542no—
819C2×C4—542no—
820C2×C4—542no—
821C2×C4—1081no—
822C2×C4C2×D3×D911yescharacteristic
823C2×C3—22no—
824C2×C3—22no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—42no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—361no—
833C2×C3C2×D4×D911yescharacteristic
834C2×C3#41×D911yescharacteristic
835C2×C3#6371511yescharacteristic
836C2×C3#6431211yescharacteristic
837C2×C3#6431411yescharacteristic
838C2×C3C2×#381111yescharacteristic
839D3—121no—
840D3—184no—
841D3—182no—
842D3—182no—
843D3—182no—
844D3—182no—
845D3—362no—
846D3—362no—
847D3—361no—
848D3—361no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22—272no—
858C22—272no—
859C22—541no—
860C22—541no—
861C22—541no—
862C22—541no—
863C22—541no—
864C22—541no—
865C22—541no—
866C22—1084no—
867C22—1084no—
868C22#8866812yes—
869C22C22×D3×D911yescharacteristic
870C4—21no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—61no—
875C4—181no—
876C4—181no—
877C4—181no—
878C4—272no—
879C3—21no—
880C3#1058975611yescharacteristic, complemented
881C3#1059516311yescharacteristic
882C2—22no—
883C2—41no—
884C2—361no—
885C2—542no—
886C2—542no—
887C2—1081no—
888C2#1172249811yescharacteristic
889C2#1172250111yescharacteristic
890C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊D9C2semidirect
2. C2×#88658C2semidirect
3. C3×#63501C2semidirect
4. C9×#935C2semidirect
5. #11721278C2semidirect
6. #11721278C2semidirect
7. #11721274C2semidirect
8. #11721271C2semidirect
9. C2×#88445C2semidirect
10. #11721242C2semidirect
11. #11721241C2semidirect
12. #11721005C2semidirect
13. #11720997C2semidirect
14. #11720978C2semidirect
15. #11720923C2semidirect
26. C2×C3×#611C22semidirect
27. C2×C3×#611C22semidirect
28. C22×C9×Dic3C22semidirect
29. C22×C3×Dic9C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
38. C9×#217C22semidirect
39. C9×#217C22semidirect
40. C9×#217C22semidirect
41. C3×#3676C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C3×Dic9⋊C4C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
74. #63501D3semidirect
101. #6233D4semidirect
173. C2×#611C2×D3semidirect
174. C2×#611C2×D3semidirect
175. C22×Dic9C2×D3semidirect
195. #3676C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
205. Dic9⋊C4C2×D3semidirect
224. C2×C3⋊D9#41semidirect
248. #935D9semidirect
396. C22×Dic3C2×D9semidirect
427. #217C2×D9semidirect
428. #217C2×D9semidirect
429. #217C2×D9semidirect
448. Dic3⋊C4C2×D9semidirect
449. Dic3⋊C4C2×D9semidirect
547. C3×C9#546semidirect
785. C9#5610semidirect
880. C3#10589756semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊D92
C2×#886582
C3×#635012
C9×#9352
#117212782
#117212742
#117212712
C2×#884452
#117212422
#117212412
#117210052
#117209972
#117209782
#117209232
#105951633
#105897563