Finite Group Databasebeta

← #13148003

Subgroups — #13148003

Order 1728.

1120 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C3×#611⋊C4C211yesmaximal, characteristic, complemented
5C9×#878C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7#11721277C211yesmaximal, characteristic, complemented
8#11721241C211yesmaximal, characteristic, complemented
9#11721005C211yesmaximal, characteristic, complemented
10#11721002C211yesmaximal, characteristic, complemented
11#11720997C211yesmaximal, characteristic, complemented
12#11720992C211yesmaximal, characteristic, complemented
13#11720986C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594066—31nomaximal
17#10589729—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×C9×Dic6C2211yescharacteristic, complemented
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic, complemented
30C2×(C3⋊D9)⋊C4—24no—
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic
34C2×(C3⋊D9)⋊C4C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36#88635—24no—
37C3×C9×C22⋊C4C2211yescharacteristic
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40C9×#217C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C9×C4⋊Dic3C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#624—31no—
56C2×#3799—31no—
57#64091—31no—
58C3×#67⋊C4—31no—
59C3×#878D311yescharacteristic
60#63981—31no—
61#63978—31no—
62#63952—31no—
63#63910—31no—
64#63904—31no—
65#63897—31no—
66#63894—31no—
67#63888—31no—
68#63854—31no—
69#63836—31no—
70C2×#3701—31no—
71C22×C4×D9—31no—
72C9×C22⋊Q8—31no—
73#63508—31no—
74#63492—31no—
75#63457—31no—
76#63456—31no—
77#63456—31no—
78#63455—31no—
79#63455—31no—
80#63454—31no—
81#63444—31no—
82#63444—31no—
83#63444—61no—
84#611⋊C4—31no—
85#611⋊C4D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96#6233—22no—
97C2×C3⋊Dic9C2311yescharacteristic
98C4⋊(C3⋊D9)—22no—
99C4⋊(C3⋊D9)—22no—
100C3×#611—22no—
101C2×C9×Dic3—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9—22no—
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C3×C4×D9—22no—
111C9×Dic6—22no—
112#6192—22no—
113#6192—22no—
114#6192—22no—
115(C3⋊D9)⋊C4—22no—
116(C3⋊D9)⋊C4—22no—
117(C3⋊D9)⋊C4—22no—
118(C3⋊D9)⋊C4—22no—
119(C3⋊D9)⋊C4D414yescomplemented
120#5627—91no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C2×#638—31no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C3×#67—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3C2×D311yescharacteristic
129C2×C3×C4×D3—31no—
130C2×C3×Dic6C2×D311yescharacteristic
131C2×#626—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#624—31no—
135C2×#624—31no—
136C2×#624—31no—
137C2×#624—31no—
138C2×#624—31no—
139C2×#624—64no—
140#3799—64no—
141C23×D9—31no—
142C23×D9—61no—
143C32×C22⋊C4C2×D311yescharacteristic
144#3752—31no—
145#3752—31no—
146C3×#217C2×D311yescharacteristic
147C3×(C2×D3)⋊C4—31no—
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4C2×D311yescharacteristic
151C3×Dic3⋊C4C2×D311yescharacteristic
152C3×C4×Dic3—31no—
153#3724—31no—
154Dic3⋊Dic3—31no—
155#3722—31no—
156#3722—31no—
157#3722—31no—
158#3722—31no—
159(C2×D3)⋊Dic3—31no—
160Dic32—31no—
161C2×Q8×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—61no—
165C2×#611C2×D311yescharacteristic
166C22×Dic9C2×D311yescharacteristic
167#3701—64no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36—31no—
172C2×D36—31no—
173C2×D36—61no—
174C2×D36—61no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—64no—
181C2×C4×D9C2×D311yescharacteristic, complemented
182C9×C4⋊C4—31no—
183C9×C4⋊C4—31no—
184C9×C4⋊C4—31no—
185C9×C22⋊C4—21no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4C2×D311yescharacteristic
188(C2×D9)⋊C4—31no—
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—31no—
195(C2×D9)⋊C4—61no—
196(C2×D9)⋊C4—61no—
197(C2×D9)⋊C4C2×D311yescharacteristic, complemented
198C4⋊Dic9—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4C2×D311yescharacteristic, complemented
201C4×Dic9—31no—
202C4×Dic9C2×D311yescharacteristic, complemented
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9#4112yescomplemented
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—28no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9C2×D412yes—
216C2×C3⋊D9#4112yescomplemented
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3⋊Dic9—21no—
223C9×Dic3—21no—
224C9×Dic3—21no—
225C9×Dic3—21no—
226C9×Dic3C2×D412yes—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9C2×D412yes—
230C2×#239—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×C22⋊Q8—31no—
235C3×C4×D4—91no—
236#946—91no—
237#939—91no—
238#937—91no—
239#930—91no—
240C4×#67—91no—
241C4×#67—91no—
242#896—91no—
243#895—91no—
244#894—91no—
245#894—91no—
246#894—91no—
247#893—91no—
248#893—91no—
249#892—91no—
250#884—91no—
251#883—91no—
252#882—91no—
253#882—91no—
254#882—91no—
255#882—181no—
256#67⋊C4—31no—
257#67⋊C4—91no—
258#878D911yescharacteristic, complemented
259C4×D12—91no—
260#872—91no—
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—62no—
268C22×C3×D3—31no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271#638—62no—
272C2×C3⋊Dic3—31no—
273C4⋊(C3⋊D3)—62no—
274C4⋊(C3⋊D3)—62no—
275C3×#67—62no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C3×C4×D3—62no—
286C3×Dic6—22no—
287#626—62no—
288#626—62no—
289#626—62no—
290#624—34no—
291#624—62no—
292#624—62no—
293#624—62no—
294#624—62no—
295C23×C9—21no—
296C23×C9C22×D311yescharacteristic
297C22×D9—31no—
298C22×D9—31no—
299C22×D9—31no—
300C22×D9—61no—
301C22×D9—61no—
302C22×D9—61no—
303C22×D9—62no—
304C22×D9—62no—
305C22×D9—62no—
306C22×D9—122no—
307C22×D9—122no—
308C22×D9—122no—
309C22×D9C22×D311yescharacteristic
310Q8×C9—62no—
311C2×C4×C9—21no—
312C2×C4×C9—21no—
313C2×C4×C9—31no—
314C2×C4×C9—31no—
315C2×C4×C9—31no—
316C2×C4×C9—31no—
317C2×C4×C9—62no—
318C2×C4×C9C22×D311yescharacteristic
319C2×C4×C9C22×D311yescharacteristic
320#611—22no—
321#611—62no—
322#611—122no—
323C2×Dic9—22no—
324C2×Dic9—31no—
325C2×Dic9—61no—
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328C2×Dic9C22×D311yescharacteristic
329D36—62no—
330D36—62no—
331D36—62no—
332D36—62no—
333D36—62no—
334D36—122no—
335D36—122no—
336C4×D9—22no—
337C4×D9—34no—
338C4×D9—62no—
339C4×D9—62no—
340C4×D9—62no—
341C4×D9—62no—
342#525—271noSylow
343C2×C3×C9—22no—
344C2×C3×C9C22×D411yescharacteristic
345C2×C3×C9C2×#4111yescharacteristic
346C2×C3×C9C2×#4111yescharacteristic
347C3⋊D9—22no—
348C3⋊D9—22no—
349C3⋊D9—41no—
350C3×D9—41no—
351C23×D3—91no—
352C23×D3—91no—
353C23×D3—181no—
354C2×C3×Q8—31no—
355C2×C3×D4—91no—
356C22×C3×C4—31no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—181no—
366C22×Dic3—31no—
367C22×Dic3C2×D911yescharacteristic
368#239—184no—
369#235—184no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—91no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—91no—
376C2×D12—91no—
377C2×D12—181no—
378C2×D12—181no—
379C2×C4×D3—31no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—184no—
391C2×C4×D3—184no—
392C2×Dic6C2×D911yescharacteristic, complemented
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—91no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4C2×D911yescharacteristic
401C3×C22⋊C4D3211yescharacteristic
402C3×C42—91no—
403#217—91no—
404#217C2×D911yescharacteristic
405(C2×D3)⋊C4—31no—
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—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—181no—
420(C2×D3)⋊C4—181no—
421C4⋊Dic3—91no—
422C4⋊Dic3C2×D911yescharacteristic, complemented
423Dic3⋊C4—31no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4C2×D911yescharacteristic, complemented
428Dic3⋊C4C2×D911yescharacteristic, complemented
429C4×Dic3—31no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32#23912yes—
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—32no—
437C2×C3⋊D3—32no—
438C2×C3⋊D3—68no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3×D3—61no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449C32×C4—21no—
450C32×C4—21no—
451C3⋊Dic3—61no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—32no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3D3×D412yes—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—21no—
462C22×C9—22no—
463C22×C9—41no—
464C22×C9—41no—
465C22×C9#23512yescomplemented
466C22×C9C23×D311yescharacteristic
467C2×D9—21no—
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—32no—
471C2×D9—32no—
472C2×D9—62no—
473C2×D9—62no—
474C2×D9—68no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—61no—
479C2×D9—61no—
480C2×D9—61no—
481C2×D9—61no—
482C2×D9—121no—
483C2×D9—121no—
484C2×D9—121no—
485C2×D9—121no—
486C2×D9—128no—
487C2×D9—121no—
488C2×D9—121no—
489C2×D9—121no—
490C4×C9—21no—
491C4×C9—21no—
492C4×C9—32no—
493C4×C9—41no—
494C4×C9—41no—
495C4×C9—61no—
496C4×C9—61no—
497C4×C9—61no—
498Dic9—21no—
499Dic9—21no—
500Dic9—61no—
501Dic9—121no—
502Dic9D3×D412yes—
503C2×#41—271no—
504C23×C4—271no—
505#123—271no—
506#123—271no—
507C22⋊Q8—31no—
508C22⋊Q8—271no—
509#121—271no—
510#121—271no—
511#120—271no—
512#120—271no—
513C4×D4—91no—
514C4×D4—271no—
515C4×D4—271no—
516C4×D4—271no—
517#117—271no—
518C3×C9#52511yescharacteristic, complemented, Sylow
519C23×C3—21no—
520C23×C3—91no—
521C23×C3C22×D911yescharacteristic
522C23×C3C2×D3211yescharacteristic
523C22×D3—31no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—91no—
530C22×D3—181no—
531C22×D3—181no—
532C22×D3—181no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—182no—
538C22×D3—182no—
539C22×D3—362no—
540C22×D3—362no—
541C22×D3—362no—
542C3×Q8—62no—
543C3×D4—182no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—62no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—182no—
555C2×C3×C4—182no—
556C2×C3×C4C22×D911yescharacteristic
557C2×C3×C4C22×D911yescharacteristic
558C2×C3×C4C2×D3211yescharacteristic
559C2×C3×C4C2×D3211yescharacteristic
560#67—62no—
561#67—182no—
562#67—182no—
563#67—182no—
564#67—182no—
565#67—182no—
566#67—362no—
567C2×Dic3—22no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—62no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—181no—
575C2×Dic3C22×D911yescharacteristic
576C2×Dic3C22×D911yescharacteristic
577C2×Dic3C22×D911yescharacteristic
578C2×Dic3C22×D911yescharacteristic
579D12—182no—
580D12—182no—
581D12—182no—
582D12—182no—
583D12—182no—
584D12—182no—
585D12—182no—
586D12—362no—
587D12—362no—
588C4×D3—62no—
589C4×D3—94no—
590C4×D3—94no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—182no—
594C4×D3—182no—
595C4×D3—182no—
596C4×D3—182no—
597C4×D3—182no—
598C4×D3—182no—
599Dic6—22no—
600C2×C32—22no—
601C2×C32C2×D3×D411yescharacteristic
602C2×C32C2×#23911yescharacteristic
603C2×C32D3×#4111yescharacteristic
604C3⋊D3—62no—
605C3⋊D3—62no—
606C3⋊D3—121no—
607C3×D3—121no—
608C2×C9—22no—
609C2×C9—21no—
610C2×C9—21no—
611C2×C9—21no—
612C2×C9—42no—
613C2×C9C2×#23511yescharacteristic
614C2×C9C2×D3×D411yescharacteristic
615C2×C9D3×#4111yescharacteristic
616D9—41no—
617D9—62no—
618D9—62no—
619D9—122no—
620D9—122no—
621D9—121no—
622D9—241no—
623C24—271no—
624#41—544no—
625C2×Q8—31no—
626C2×D4—91no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C22×C4—31no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4—271no—
641C22×C4—544no—
642C4⋊C4—31no—
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—91no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C22⋊C4—31no—
649C22⋊C4—91no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4D3×D911yescharacteristic
658C42—91no—
659C42—271no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—22no—
665C22×C3—21no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3#370112yescomplemented
672C22×C3C23×D911yescharacteristic
673C22×C3#379912yes—
674C22×C3C22×D3211yescharacteristic
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—92no—
679C2×D3—92no—
680C2×D3—92no—
681C2×D3—92no—
682C2×D3—182no—
683C2×D3—182no—
684C2×D3—188no—
685C2×D3—188no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—361no—
701C2×D3—361no—
702C2×D3—361no—
703C2×D3—361no—
704C2×D3—368no—
705C2×D3—361no—
706C2×D3—361no—
707C2×D3—361no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—32no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—92no—
719C3×C4—181no—
720C3×C4—181no—
721Dic3—21no—
722Dic3—21no—
723Dic3—21no—
724Dic3—32no—
725Dic3—61no—
726Dic3—61no—
727Dic3—181no—
728Dic3—181no—
729Dic3—361no—
730Dic3D4×D912yes—
731C32#562711yescharacteristic
732C9—21no—
733C9#554711yescharacteristic, complemented
734C23—91no—
735C23—271no—
736C23—271no—
737C23—271no—
738C23—542no—
739C23—542no—
740C23—542no—
741C23C2×D3×D911yescharacteristic
742Q8—62no—
743D4—182no—
744D4—542no—
745D4—542no—
746D4—542no—
747D4—542no—
748D4—542no—
749D4—542no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—62no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—182no—
759C2×C4—182no—
760C2×C4—274no—
761C2×C4—271no—
762C2×C4—542no—
763C2×C4—542no—
764C2×C4—542no—
765C2×C4—542no—
766C2×C4C2×D3×D911yescharacteristic
767C2×C4C2×D3×D911yescharacteristic
768C2×C3—22no—
769C2×C3—22no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—42no—
774C2×C3—361no—
775C2×C3C2×D4×D911yescharacteristic
776C2×C3C2×#370111yescharacteristic
777C2×C3#41×D911yescharacteristic
778C2×C3C2×#379911yescharacteristic
779C2×C3D32×D411yescharacteristic
780C2×C3#6431211yescharacteristic
781D3—121no—
782D3—182no—
783D3—182no—
784D3—182no—
785D3—182no—
786D3—362no—
787D3—362no—
788D3—361no—
789D3—361no—
790D3—721no—
791C22—21no—
792C22—21no—
793C22—181no—
794C22—181no—
795C22—181no—
796C22—272no—
797C22—272no—
798C22—548no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22#8863512yescomplemented
807C22C22×D3×D911yescharacteristic
808C4—21no—
809C4—21no—
810C4—32no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—92no—
815C4—181no—
816C4—181no—
817C4—541no—
818C3—21no—
819C3#1058972911yescharacteristic, complemented
820C3#1059406611yescharacteristic
821C2—22no—
822C2—361no—
823C2—542no—
824C2—542no—
825C2—1081no—
826C2C2×#8863511yescharacteristic
827C2D3×D4×D911yescharacteristic
828C2#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. C22×(C3⋊D9)⋊C4C2semidirect
2. C2×#88635C2semidirect
3. #11721728C2semidirect
4. C3×#611⋊C4C2semidirect
5. C9×#878C2semidirect
6. #11721278C2semidirect
7. #11721277C2semidirect
8. #11721241C2semidirect
9. #11721005C2semidirect
10. #11721002C2semidirect
11. #11720997C2semidirect
12. #11720992C2semidirect
13. #11720986C2semidirect
14. #11720942C2semidirect
15. #11720899C2semidirect
25. C2×C3×C4×D9C22semidirect
26. C2×C9×Dic6C22semidirect
29. C2×#6192C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C9×C4⋊Dic3C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×C4×Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
85. #611⋊C4D3semidirect
119. (C3⋊D9)⋊C4D4semidirect
181. C2×C4×D9C2×D3semidirect
197. (C2×D9)⋊C4C2×D3semidirect
200. Dic9⋊C4C2×D3semidirect
202. C4×Dic9C2×D3semidirect
205. C22×C3×C9#41semidirect
216. C2×C3⋊D9#41semidirect
258. #878D9semidirect
392. C2×Dic6C2×D9semidirect
422. C4⋊Dic3C2×D9semidirect
427. Dic3⋊C4C2×D9semidirect
428. Dic3⋊C4C2×D9semidirect
465. C22×C9#235semidirect
518. C3×C9#525semidirect
671. C22×C3#3701semidirect
733. C9#5547semidirect
806. C22#88635semidirect
819. C3#10589729semidirect

Maximal subgroups

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

subgroupindex
C22×(C3⋊D9)⋊C42
C2×#886352
#117217282
C3×#611⋊C42
C9×#8782
#117212782
#117212772
#117212412
#117210052
#117210022
#117209972
#117209922
#117209862
#117209422
#117208992
#105940663
#105897293