Finite Group Databasebeta

← #13150472

Subgroups — #13150472

Order 1728.

1226 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3C4×C9×#67C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#11721291C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721278C211yesmaximal, characteristic, complemented
8#11721267C211yesmaximal, characteristic, complemented
9#11721041C211yesmaximal, characteristic, complemented
10C4×#6195C211yesmaximal, characteristic, complemented
11C4×#6192C211yesmaximal, characteristic, complemented
12#11720957C211yesmaximal, characteristic, complemented
13#11720941C211yesmaximal, characteristic, complemented
14#11720931C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10595016—31nomaximal
17#10589649—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C4×C3⋊D9—24no—
22C2×C4×C3⋊D9C2211yescharacteristic
23C2×C4×C3⋊D9C2211yescharacteristic
24C2×C4×C3⋊D9C2211yescharacteristic
25C2×C4×C3⋊D9C2211yescharacteristic
26C2×C9×#67C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C4×D3×C9C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic, complemented
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6194C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×#6189C2211yescharacteristic, complemented
36#88640—24no—
37C9×#217C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C4×C9×Dic3C2211yescharacteristic, complemented
43C3×Dic9⋊C4C2211yescharacteristic, complemented
44C3×C4×Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C22×C4×C3⋊D3—31no—
56C2×#3798—31no—
57C3×C4×#67—31no—
58C3×C4×#67D311yescharacteristic
59#63982—31no—
60#63981—31no—
61#63981—31no—
62#63980—31no—
63#63912—31no—
64C4×#626—31no—
65C4×#626—31no—
66#63874—31no—
67#63865—31no—
68#63853—31no—
69#63853—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C22×C4×D9—61no—
73C4×D4×C9—31no—
74#63501—31no—
75#63499—31no—
76C4×#611—31no—
77C4×#611D311yescharacteristic, complemented
78#63458—31no—
79#63456—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#63440—31no—
84C4×D36—31no—
85#63434—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×C3×C4×C9—22no—
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3⋊Dic9—22no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C4×C3⋊D9—22no—
101C4×C3⋊D9—22no—
102C4×C3⋊D9—22no—
103C4×C3⋊D9D414yescomplemented
104C9×#67—22no—
105C3×#611—22no—
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C4×D3×C9—22no—
113C3×C4×D9—22no—
114#6195—22no—
115#6195—22no—
116#6194—22no—
117#6192—22no—
118#6192—22no—
119#6189—22no—
120#5547—91no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C22×C32×C4C2×D311yescharacteristic
124C22×C3⋊Dic3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—64no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×#627—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140#3798—64no—
141C23×D9—31no—
142C23×D9—61no—
143C3×#217—31no—
144C3×#217C2×D311yescharacteristic
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4C2×D311yescharacteristic
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4C2×D311yescharacteristic
149C3×C4×Dic3—31no—
150C3×C4×Dic3C2×D311yescharacteristic
151#3724—31no—
152#3724—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155#3722—31no—
156#3722—31no—
157#3722—31no—
158#3722—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161C2×D4×C9—31no—
162C22×C4×C9—21no—
163C22×C4×C9—31no—
164C22×C4×C9C2×D311yescharacteristic
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611C2×D311yescharacteristic
169C22×Dic9—31no—
170C22×Dic9—61no—
171#3697—64no—
172C2×D36—31no—
173C2×D36—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—64no—
179C2×C4×D9—61no—
180C2×C4×D9—61no—
181C2×C4×D9—61no—
182C2×C4×D9—61no—
183C2×C4×D9—68no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×Dic18—31no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C42×C9—31no—
190#3676—31no—
191#3676C2×D311yescharacteristic
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)⋊C4C2×D311yescharacteristic, complemented
198C4⋊Dic9—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4C2×D311yescharacteristic, complemented
203C4×Dic9C2×D311yescharacteristic, complemented
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9#4112yescomplemented
207C22×C3×C9C2411yescharacteristic
208C2×C3⋊D9—28no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9C2×D412yes—
214C2×C3⋊D9#4112yescomplemented
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C2×C3×D9—21no—
221C3×C4×C9—21no—
222C3×C4×C9C2×D412yes—
223C3⋊Dic9—21no—
224C3⋊Dic9C2×D412yes—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C3×Dic9—21no—
231C2×#235—91no—
232C2×#235—91no—
233C22×C4×D3—91no—
234C22×C4×D3—91no—
235C22×C4×D3—181no—
236C3×C4×D4—31no—
237C3×C4×D4—91no—
238#939—91no—
239#939—91no—
240#937—91no—
241#937—91no—
242C4×#67—31no—
243C4×#67—91no—
244C4×#67—91no—
245C4×#67D911yescharacteristic, complemented
246#896—91no—
247#896—91no—
248#894—91no—
249#894—91no—
250#884—91no—
251#884—91no—
252#883—91no—
253#883—91no—
254#882—91no—
255#882—91no—
256#878—91no—
257#878—91no—
258C4×D12—91no—
259C4×D12—91no—
260#872—91no—
261#872—91no—
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—62no—
268C22×C3×D3—31no—
269C22×C3×D3C22×D311yescharacteristic
270C2×C32×C4—22no—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—62no—
276C4×C3⋊D3—34no—
277C4×C3⋊D3—62no—
278C4×C3⋊D3—62no—
279C4×C3⋊D3—62no—
280C3×#67—22no—
281C3×#67—62no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C3×C4×D3—22no—
289C3×C4×D3—62no—
290#627—62no—
291#626—62no—
292#626—62no—
293#626—62no—
294#626—62no—
295#625—62no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C22×D9—31no—
300C22×D9—31no—
301C22×D9—61no—
302C22×D9—61no—
303C22×D9—62no—
304C22×D9—62no—
305C22×D9—64no—
306C22×D9—64no—
307C22×D9—64no—
308C22×D9—62no—
309C22×D9C22×D311yescharacteristic
310D4×C9—62no—
311C2×C4×C9—24no—
312C2×C4×C9—22no—
313C2×C4×C9—21no—
314C2×C4×C9—21no—
315C2×C4×C9—31no—
316C2×C4×C9—31no—
317C2×C4×C9—31no—
318C2×C4×C9—62no—
319C2×C4×C9C22×D311yescharacteristic
320C2×C4×C9C22×D311yescharacteristic
321#611—22no—
322#611—62no—
323#611—62no—
324#611—62no—
325C2×Dic9—31no—
326C2×Dic9—31no—
327C2×Dic9—61no—
328C2×Dic9—61no—
329C2×Dic9—62no—
330C2×Dic9—64no—
331C2×Dic9C22×D311yescharacteristic
332C2×Dic9C22×D311yescharacteristic
333C2×Dic9C22×D311yescharacteristic
334D36—62no—
335D36—62no—
336C4×D9—22no—
337C4×D9—34no—
338C4×D9—64no—
339C4×D9—62no—
340C4×D9—62no—
341C4×D9—64no—
342C4×D9—64no—
343C4×D9—64no—
344C4×D9—62no—
345Dic18—62no—
346#525—271noSylow
347C2×C3×C9—22no—
348C2×C3×C9C22×D411yescharacteristic
349C2×C3×C9C2×#4111yescharacteristic
350C2×C3×C9C2×#4111yescharacteristic
351C3⋊D9—22no—
352C3⋊D9—22no—
353D3×C9—41no—
354C3×D9—41no—
355C23×D3—91no—
356C23×D3—91no—
357C23×D3—181no—
358C2×C3×D4—31no—
359C2×C3×D4—91no—
360C22×C3×C4—21no—
361C22×C3×C4—31no—
362C22×C3×C4—91no—
363C22×C3×C4C2×D911yescharacteristic
364C22×C3×C4D3211yescharacteristic
365C2×#67—31no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67C2×D911yescharacteristic
373C22×Dic3—91no—
374C22×Dic3—91no—
375C22×Dic3—181no—
376#235—184no—
377#235—184no—
378C2×D12—91no—
379C2×D12—91no—
380C2×D12—91no—
381C2×D12—91no—
382C2×C4×D3—31no—
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—91no—
391C2×C4×D3—181no—
392C2×C4×D3—181no—
393C2×C4×D3—181no—
394C2×C4×D3—181no—
395C2×C4×D3—184no—
396C2×C4×D3—184no—
397C2×C4×D3—188no—
398C2×C4×D3C2×D911yescharacteristic, complemented
399C2×Dic6—91no—
400C2×Dic6—91no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—91no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—91no—
406C3×C22⋊C4—91no—
407C3×C42—31no—
408C3×C42—91no—
409#217—31no—
410#217—91no—
411#217—91no—
412#217C2×D911yescharacteristic
413(C2×D3)⋊C4—31no—
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—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4C2×D911yescharacteristic, complemented
425C4⋊Dic3—91no—
426C4⋊Dic3—91no—
427Dic3⋊C4—31no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4C2×D911yescharacteristic, complemented
435C4×Dic3—31no—
436C4×Dic3C2×D911yescharacteristic, complemented
437C22×C32—21no—
438C22×C32—21no—
439C22×C32#23512yes—
440C22×C32C23×D311yescharacteristic
441C2×C3⋊D3—32no—
442C2×C3⋊D3—32no—
443C2×C3⋊D3—68no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C32×C4—21no—
455C32×C4D3×D412yes—
456C3⋊Dic3—32no—
457C3⋊Dic3—61no—
458C3×Dic3—21no—
459C3×Dic3—21no—
460C3×Dic3—21no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C22×C9—22no—
465C22×C9—22no—
466C22×C9—21no—
467C22×C9—21no—
468C22×C9—21no—
469C22×C9—22no—
470C22×C9—61no—
471C22×C9—61no—
472C22×C9—61no—
473C22×C9#23512yescomplemented
474C22×C9C23×D311yescharacteristic
475C2×D9—21no—
476C2×D9—21no—
477C2×D9—21no—
478C2×D9—32no—
479C2×D9—32no—
480C2×D9—62no—
481C2×D9—62no—
482C2×D9—62no—
483C2×D9—616no—
484C2×D9—68no—
485C2×D9—62no—
486C2×D9—62no—
487C2×D9—62no—
488C2×D9—61no—
489C2×D9—61no—
490C2×D9—61no—
491C2×D9—61no—
492C4×C9—22no—
493C4×C9—21no—
494C4×C9—22no—
495C4×C9—61no—
496C4×C9—61no—
497C4×C9—61no—
498C4×C9D3×D412yes—
499Dic9—21no—
500Dic9—21no—
501Dic9—21no—
502Dic9—32no—
503Dic9—62no—
504Dic9—62no—
505Dic9—61no—
506C2×#41—271no—
507C23×C4—271no—
508#123—271no—
509#123—271no—
510C22⋊Q8—271no—
511C22⋊Q8—271no—
512#121—271no—
513#121—271no—
514#120—271no—
515#120—271no—
516C4×D4—31no—
517C4×D4—91no—
518C4×D4—271no—
519C4×D4—271no—
520#117—271no—
521C3×C9#52511yescharacteristic, complemented, Sylow
522C23×C3—21no—
523C23×C3—31no—
524C23×C3—91no—
525C23×C3C22×D911yescharacteristic
526C23×C3C2×D3211yescharacteristic
527C22×D3—31no—
528C22×D3—91no—
529C22×D3—91no—
530C22×D3—91no—
531C22×D3—91no—
532C22×D3—181no—
533C22×D3—181no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—182no—
538C22×D3—184no—
539C22×D3—184no—
540C22×D3—184no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3C22×D911yescharacteristic
544C3×D4—62no—
545C3×D4—182no—
546C2×C3×C4—24no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—62no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—182no—
559C2×C3×C4C22×D911yescharacteristic
560C2×C3×C4C22×D911yescharacteristic
561C2×C3×C4C2×D3211yescharacteristic
562C2×C3×C4C2×D3211yescharacteristic
563#67—22no—
564#67—62no—
565#67—182no—
566#67—182no—
567#67—182no—
568#67—182no—
569#67—182no—
570#67—182no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—91no—
575C2×Dic3—91no—
576C2×Dic3—91no—
577C2×Dic3—91no—
578C2×Dic3—181no—
579C2×Dic3—181no—
580C2×Dic3—182no—
581C2×Dic3—182no—
582C2×Dic3—184no—
583C2×Dic3C22×D911yescharacteristic
584C2×Dic3C22×D911yescharacteristic
585C2×Dic3C22×D911yescharacteristic
586D12—182no—
587D12—182no—
588D12—182no—
589D12—182no—
590C4×D3—22no—
591C4×D3—62no—
592C4×D3—94no—
593C4×D3—94no—
594C4×D3—184no—
595C4×D3—182no—
596C4×D3—182no—
597C4×D3—182no—
598C4×D3—182no—
599C4×D3—184no—
600C4×D3—184no—
601C4×D3—184no—
602C4×D3—182no—
603C4×D3—182no—
604Dic6—182no—
605Dic6—182no—
606C2×C32—22no—
607C2×C32C2×#23511yescharacteristic
608C2×C32C2×D3×D411yescharacteristic
609C2×C32D3×#4111yescharacteristic
610C3⋊D3—62no—
611C3⋊D3—62no—
612C3×D3—41no—
613C3×D3—121no—
614C2×C9—24no—
615C2×C9—22no—
616C2×C9—21no—
617C2×C9—21no—
618C2×C9—21no—
619C2×C9—121no—
620C2×C9C2×#23511yescharacteristic
621C2×C9C2×D3×D411yescharacteristic
622C2×C9D3×#4111yescharacteristic
623D9—41no—
624D9—64no—
625D9—64no—
626D9—62no—
627D9—62no—
628C24—271no—
629#41—544no—
630C2×Q8—271no—
631C2×D4—31no—
632C2×D4—91no—
633C2×D4—271no—
634C2×D4—271no—
635C2×D4—271no—
636C2×D4—271no—
637C2×D4—271no—
638C22×C4—31no—
639C22×C4—91no—
640C22×C4—271no—
641C22×C4—271no—
642C22×C4—271no—
643C22×C4—271no—
644C22×C4—271no—
645C22×C4—544no—
646C22×C4D3×D911yescharacteristic
647C4⋊C4—31no—
648C4⋊C4—91no—
649C4⋊C4—271no—
650C4⋊C4—271no—
651C4⋊C4—271no—
652C4⋊C4—271no—
653C22⋊C4—31no—
654C22⋊C4—31no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—271no—
658C22⋊C4—271no—
659C22⋊C4—271no—
660C22⋊C4—271no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C42—31no—
664C42—91no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—21no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—181no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3#369712yescomplemented
680C22×C3C23×D911yescharacteristic
681C22×C3#379812yes—
682C22×C3C22×D3211yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—92no—
690C2×D3—92no—
691C2×D3—92no—
692C2×D3—92no—
693C2×D3—182no—
694C2×D3—182no—
695C2×D3—182no—
696C2×D3—188no—
697C2×D3—1816no—
698C2×D3—188no—
699C2×D3—182no—
700C2×D3—182no—
701C2×D3—182no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—181no—
708C2×D3—181no—
709C2×D3—181no—
710C3×C4—22no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—22no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—181no—
718C3×C4—181no—
719C3×C4—181no—
720C3×C4D4×D912yes—
721C3×C4#381112yes—
722Dic3—21no—
723Dic3—21no—
724Dic3—21no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—92no—
729Dic3—92no—
730Dic3—182no—
731Dic3—182no—
732Dic3—181no—
733Dic3—181no—
734C32#554711yescharacteristic
735C9—21no—
736C9#554711yescharacteristic, complemented
737C23—31no—
738C23—91no—
739C23—271no—
740C23—271no—
741C23—542no—
742C23—542no—
743C23—542no—
744C23C2×D3×D911yescharacteristic
745Q8—542no—
746D4—62no—
747D4—182no—
748D4—542no—
749D4—542no—
750D4—542no—
751D4—542no—
752D4—542no—
753C2×C4—22no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—62no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—182no—
762C2×C4—271no—
763C2×C4—274no—
764C2×C4—271no—
765C2×C4—542no—
766C2×C4—542no—
767C2×C4—542no—
768C2×C4—542no—
769C2×C4C2×D3×D911yescharacteristic
770C2×C4C2×D3×D911yescharacteristic
771C2×C3—24no—
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—121no—
778C2×C3—361no—
779C2×C3C2×#369711yescharacteristic
780C2×C3C2×D4×D911yescharacteristic
781C2×C3#41×D911yescharacteristic
782C2×C3C2×#379811yescharacteristic
783C2×C3#6430611yescharacteristic
784C2×C3C2×#381111yescharacteristic
785D3—41no—
786D3—121no—
787D3—184no—
788D3—184no—
789D3—182no—
790D3—182no—
791D3—182no—
792D3—182no—
793C22—21no—
794C22—21no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—181no—
799C22—181no—
800C22—181no—
801C22—272no—
802C22—272no—
803C22—548no—
804C22—541no—
805C22—541no—
806C22—541no—
807C22—541no—
808C22#8864012yescomplemented
809C22C22×D3×D911yescharacteristic
810C4—21no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—181no—
815C4—181no—
816C4—181no—
817C4—272no—
818C4—541no—
819C4#8866812yes—
820C3—21no—
821C3#1058964911yescharacteristic, complemented
822C3#1059501611yescharacteristic
823C2—22no—
824C2—121no—
825C2—361no—
826C2—542no—
827C2—542no—
828C2C2×#8864011yescharacteristic
829C2#1172247511yescharacteristic
830C2C2×#8866811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#525
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊D9C2semidirect
2. C2×#88640C2semidirect
3. C4×C9×#67C2semidirect
4. C3×C4×#611C2semidirect
5. #11721291C2semidirect
6. #11721290C2semidirect
7. #11721278C2semidirect
8. #11721267C2semidirect
9. #11721041C2semidirect
10. C4×#6195C2semidirect
11. C4×#6192C2semidirect
12. #11720957C2semidirect
13. #11720941C2semidirect
14. #11720931C2semidirect
15. #11720923C2semidirect
28. C2×C4×D3×C9C22semidirect
29. C2×C3×C4×D9C22semidirect
32. C2×#6194C22semidirect
35. C2×#6189C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C4×C9×Dic3C22semidirect
43. C3×Dic9⋊C4C22semidirect
44. C3×C4×Dic9C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. #88442C22semidirect
54. Dic9⋊Dic3C22semidirect
77. C4×#611D3semidirect
103. C4×C3⋊D9D4semidirect
184. C2×C4×D9C2×D3semidirect
197. (C2×D9)⋊C4C2×D3semidirect
202. Dic9⋊C4C2×D3semidirect
203. C4×Dic9C2×D3semidirect
206. C22×C3×C9#41semidirect
214. C2×C3⋊D9#41semidirect
245. C4×#67D9semidirect
398. C2×C4×D3C2×D9semidirect
424. (C2×D3)⋊C4C2×D9semidirect
434. Dic3⋊C4C2×D9semidirect
436. C4×Dic3C2×D9semidirect
473. C22×C9#235semidirect
521. C3×C9#525semidirect
679. C22×C3#3697semidirect
736. C9#5547semidirect
808. C22#88640semidirect
821. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D92
C2×#886402
C4×C9×#672
C3×C4×#6112
#117212912
#117212902
#117212782
#117212672
#117210412
C4×#61952
C4×#61922
#117209572
#117209412
#117209312
#117209232
#105950163
#105896493