Finite Group Databasebeta

← #13147990

Subgroups — #13147990

Order 1728.

1064 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3×D9C211yesmaximal, characteristic, complemented
2C2×#88641C211yesmaximal, characteristic, complemented
3#11721724C211yesmaximal, characteristic, complemented
4C9×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#63444C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721285C211yesmaximal, characteristic, complemented
8Dic3×#611C211yesmaximal, characteristic, complemented
9#11720996C211yesmaximal, characteristic, complemented
10Dic3×D36C211yesmaximal, characteristic, complemented
11#11720989C211yesmaximal, characteristic, complemented
12#11720982C211yesmaximal, characteristic, complemented
13#11720981C211yesmaximal, characteristic, complemented
14#11720976C211yesmaximal, characteristic, complemented
15#11720974C211yesmaximal, characteristic, complemented
16#10594054—31nomaximal
17#10589649—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×D36C2211yescharacteristic
26C2×C3×D36C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic, complemented
30C2×Dic3×D9—24no—
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic, complemented
36#88641—24no—
37C3×C9×C22⋊C4C2211yescharacteristic
38#88551C2211yescharacteristic
39C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C4×C9×Dic3C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×D3×Dic3—31no—
56C2×#3795—31no—
57#64087—31no—
58C3×#882—31no—
59C3×#67⋊C4D311yescharacteristic
60#63980—31no—
61#63976—31no—
62Dic3×#67—31no—
63#63896—31no—
64Dic3×D12—31no—
65#63891—31no—
66#63885—31no—
67#63884—31no—
68#63879—31no—
69#63877—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C4×D4×C9—31no—
73#63501—31no—
74#63499—31no—
75C4×#611—31no—
76C4×#611—31no—
77#63458—31no—
78#63456—31no—
79#63446—31no—
80#63445—31no—
81#63444D311yescharacteristic, complemented
82#63440—31no—
83#63440—61no—
84C4×D36—31no—
85#63434—31no—
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9—22no—
89C22×C3×D9—22no—
90C22×C3×D9—22no—
91C22×C3×D9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3⋊Dic9—22no—
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101#6226—22no—
102C9×#67—22no—
103C3×#611—22no—
104C2×C9×Dic3—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C4×D3×C9—22no—
110C3×D36—22no—
111C3×D36—22no—
112#6194—22no—
113#6194—22no—
114#6194—22no—
115Dic3×D9—22no—
116Dic3×D9—22no—
117Dic3×D9—22no—
118Dic3×D9—22no—
119Dic3×D9D414yescomplemented
120#5586—91no—
121#5547—91no—
122C23×C3×D3—31no—
123C22×C3⋊Dic3—31no—
124C2×#634—31no—
125C2×C3×#67—31no—
126C2×C3×#67C2×D311yescharacteristic
127C22×C3×Dic3C2×D311yescharacteristic
128C2×C3×D12—31no—
129C2×C3×D12—31no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×#625—31no—
132C2×#625—31no—
133C2×#625—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—64no—
140#3795—64no—
141C23×D9C2×D311yescharacteristic
142C32×C22⋊C4C2×D311yescharacteristic
143#3757—31no—
144C4⋊(C3⋊Dic3)—31no—
145#3750—31no—
146#3750—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×Dic3⋊C4C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—31no—
153Dic3⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—31no—
160C2×D4×C9—31no—
161C22×C4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611C2×D311yescharacteristic
167C22×Dic9—31no—
168C22×Dic9—61no—
169#3697—64no—
170C2×D36C2×D311yescharacteristic
171C2×D36C2×D311yescharacteristic
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—64no—
178C2×Dic18—31no—
179C2×Dic18—61no—
180C9×C4⋊C4—31no—
181C9×C22⋊C4—21no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4C2×D311yescharacteristic
184C42×C9—31no—
185#3676—31no—
186#3676—31no—
187#3676—61no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4C2×D311yescharacteristic
193(C2×D9)⋊C4C2×D311yescharacteristic
194C4⋊Dic9—31no—
195C4⋊Dic9—61no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—61no—
201Dic9⋊C4—61no—
202C4×Dic9—31no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9#4112yescomplemented
206C22×C3×C9C2411yescharacteristic
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—28no—
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×D9C2×D412yes—
219C2×C3×D9#4112yescomplemented
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C3⋊Dic9C2×D412yes—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C9×Dic3C2×D412yes—
229C3×Dic9—21no—
230C23×Dic3—91no—
231C2×#237—91no—
232C2×#235—91no—
233C22×C4×D3—91no—
234C3×#120—91no—
235C3×C4×D4—31no—
236#953—91no—
237#939—91no—
238#939—91no—
239#939—91no—
240#937—91no—
241#935—91no—
242D4×Dic3—91no—
243D4×Dic3—91no—
244C4×#67—91no—
245C4×#67—91no—
246#896—91no—
247#894—91no—
248#886—91no—
249#884—91no—
250#883—91no—
251#882—31no—
252#67⋊C4—91no—
253#67⋊C4D911yescharacteristic, complemented
254#878—91no—
255#878—91no—
256#878—91no—
257#878—181no—
258#877—91no—
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×D3C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—62no—
276#634—62no—
277C3×#67—22no—
278C3×#67—62no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C3×D12—62no—
285C3×D12—62no—
286C3×C4×D3—22no—
287#625—62no—
288#625—62no—
289#625—62no—
290D3×Dic3—34no—
291D3×Dic3—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9—31no—
297C23×C9C22×D311yescharacteristic
298C22×D9—22no—
299C22×D9—22no—
300C22×D9—22no—
301C22×D9C22×D311yescharacteristic
302C22×D9C22×D311yescharacteristic
303C22×D9C22×D311yescharacteristic
304D4×C9—62no—
305C2×C4×C9—21no—
306C2×C4×C9—21no—
307C2×C4×C9—31no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—62no—
311C2×C4×C9—62no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314#611—22no—
315#611—62no—
316#611—62no—
317#611—62no—
318C2×Dic9—31no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—62no—
327C2×Dic9—122no—
328C2×Dic9C22×D311yescharacteristic
329D36—22no—
330D36—22no—
331C4×D9—34no—
332C4×D9—62no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—62no—
336Dic18—62no—
337Dic18—122no—
338#525—271noSylow
339C2×C3×C9—22no—
340C2×C3×C9C22×D411yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343D3×C9—41no—
344C3×D9—22no—
345C3×D9—22no—
346C3×D9—41no—
347C24×C3—91no—
348C23×D3—31no—
349C2×C3×D4—31no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C2×#67—31no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67C2×D911yescharacteristic
363C22×Dic3—91no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369C22×Dic3—91no—
370C22×Dic3—181no—
371C22×Dic3—184no—
372C22×Dic3C2×D911yescharacteristic
373#237—184no—
374#235—184no—
375C2×D12—31no—
376C2×D12—31no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—184no—
383C2×C4×D3C2×D911yescharacteristic, complemented
384C2×Dic6—91no—
385C2×Dic6—91no—
386C2×Dic6—181no—
387C3×C4⋊C4—31no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4C2×D911yescharacteristic
393C3×C22⋊C4D3211yescharacteristic
394C3×C42—31no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—91no—
402#217—181no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—31no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4C2×D911yescharacteristic, complemented
411C4⋊Dic3—91no—
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414C4⋊Dic3—181no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—181no—
423Dic3⋊C4—181no—
424Dic3⋊C4C2×D911yescharacteristic, complemented
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3C2×D911yescharacteristic, complemented
428C22×C32—21no—
429C22×C32—21no—
430C22×C32#23512yes—
431C22×C32C23×D311yescharacteristic
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—32no—
436C2×C3×D3—32no—
437C2×C3×D3—68no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3—61no—
445C32×C4—21no—
446C32×C4—21no—
447C3⋊Dic3—32no—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—61no—
454C3×Dic3D3×D412yes—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—22no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9#23712yescomplemented
465C22×C9C23×D311yescharacteristic
466C2×D9—28no—
467C2×D9—21no—
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—21no—
472C2×D9—21no—
473C2×D9—21no—
474C2×D9D3×D412yes—
475C2×D9#23712yescomplemented
476C4×C9—21no—
477C4×C9—21no—
478C4×C9—32no—
479C4×C9—41no—
480C4×C9—41no—
481C4×C9—61no—
482C4×C9—61no—
483Dic9—21no—
484Dic9—32no—
485Dic9—62no—
486Dic9—61no—
487Dic9—61no—
488Dic9—61no—
489Dic9—121no—
490Dic9—121no—
491Dic9—121no—
492C2×#41—271no—
493C23×C4—271no—
494#123—271no—
495#123—271no—
496C22⋊Q8—271no—
497C22⋊Q8—271no—
498#121—271no—
499#121—271no—
500#120—91no—
501#120—271no—
502C4×D4—31no—
503C4×D4—271no—
504C4×D4—271no—
505C4×D4—271no—
506#117—271no—
507C3×C9#52511yescharacteristic, complemented, Sylow
508C23×C3—21no—
509C23×C3—31no—
510C23×C3—91no—
511C23×C3—91no—
512C23×C3—91no—
513C23×C3—182no—
514C23×C3—182no—
515C23×C3—182no—
516C23×C3C22×D911yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C22×D3—31no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—62no—
524C22×D3C22×D911yescharacteristic
525C3×D4—62no—
526C3×D4—182no—
527C3×D4—182no—
528C3×D4—182no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—62no—
535C2×C3×C4—62no—
536C2×C3×C4—91no—
537C2×C3×C4C22×D911yescharacteristic
538C2×C3×C4C22×D911yescharacteristic
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541#67—22no—
542#67—62no—
543#67—182no—
544#67—182no—
545#67—182no—
546#67—182no—
547#67—182no—
548#67—182no—
549C2×Dic3—22no—
550C2×Dic3—31no—
551C2×Dic3—91no—
552C2×Dic3—91no—
553C2×Dic3—94no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—181no—
564C2×Dic3—182no—
565C2×Dic3—182no—
566C2×Dic3—182no—
567C2×Dic3—182no—
568C2×Dic3—182no—
569C2×Dic3—182no—
570C2×Dic3—362no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573C2×Dic3C22×D911yescharacteristic
574D12—62no—
575D12—62no—
576C4×D3—22no—
577C4×D3—94no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—182no—
582Dic6—182no—
583Dic6—182no—
584Dic6—362no—
585C2×C32—22no—
586C2×C32C2×#23511yescharacteristic
587C2×C32C2×D3×D411yescharacteristic
588C2×C32D3×#4111yescharacteristic
589C3×D3—41no—
590C3×D3—62no—
591C3×D3—62no—
592C3×D3—121no—
593C2×C9—22no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—42no—
598C2×C9—121no—
599C2×C9C2×D3×D411yescharacteristic
600C2×C9C2×#23711yescharacteristic
601C2×C9C2×#23711yescharacteristic
602D9—22no—
603D9—22no—
604D9—41no—
605C24—91no—
606#41—544no—
607C2×Q8—271no—
608C2×D4—31no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—271no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—544no—
624C4⋊C4—31no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C22⋊C4—31no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4D3×D911yescharacteristic
640C42—31no—
641C42—271no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—92no—
654C22×C3—92no—
655C22×C3—188no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3#369712yescomplemented
664C22×C3C23×D911yescharacteristic
665C22×C3#379512yes—
666C22×C3C22×D3211yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—32no—
671C2×D3—32no—
672C2×D3—68no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—32no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—181no—
690Dic3—21no—
691Dic3—21no—
692Dic3—61no—
693Dic3—92no—
694Dic3—92no—
695Dic3—182no—
696Dic3—181no—
697Dic3—181no—
698Dic3—181no—
699Dic3—181no—
700Dic3—181no—
701Dic3—181no—
702Dic3—361no—
703Dic3—361no—
704Dic3—361no—
705Dic3D4×D912yes—
706C32#554711yescharacteristic
707C9—21no—
708C9#558611yescharacteristic, complemented
709C23—31no—
710C23—91no—
711C23—91no—
712C23—91no—
713C23—182no—
714C23—182no—
715C23—182no—
716C23C2×D3×D911yescharacteristic
717Q8—542no—
718D4—62no—
719D4—182no—
720D4—182no—
721D4—182no—
722D4—542no—
723D4—542no—
724D4—542no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—91no—
731C2×C4—274no—
732C2×C4—271no—
733C2×C4—271no—
734C2×C4—271no—
735C2×C4—271no—
736C2×C4—542no—
737C2×C4—542no—
738C2×C4—542no—
739C2×C4—542no—
740C2×C4—542no—
741C2×C4C2×D3×D911yescharacteristic
742C2×C4C2×D3×D911yescharacteristic
743C2×C3—22no—
744C2×C3—22no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—121no—
750C2×C3—182no—
751C2×C3—182no—
752C2×C3—361no—
753C2×C3C2×#369711yescharacteristic
754C2×C3C2×D4×D911yescharacteristic
755C2×C3#41×D911yescharacteristic
756C2×C3C2×#379511yescharacteristic
757C2×C3D32×D411yescharacteristic
758C2×C3D3×#23711yescharacteristic
759D3—41no—
760D3—62no—
761D3—62no—
762D3—121no—
763C22—21no—
764C22—21no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—92no—
769C22—92no—
770C22—188no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22#8864112yescomplemented
779C22C22×D3×D911yescharacteristic
780C4—21no—
781C4—21no—
782C4—32no—
783C4—61no—
784C4—61no—
785C4—181no—
786C4—272no—
787C4—541no—
788C4—541no—
789C4—541no—
790C3—21no—
791C3#1058964911yescharacteristic, complemented
792C3#1059405411yescharacteristic
793C2—22no—
794C2—121no—
795C2—182no—
796C2—182no—
797C2—361no—
798C2C2×#8864111yescharacteristic
799C2D3×D4×D911yescharacteristic
800C2D9×#23711yescharacteristic
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×Dic3×D9C2semidirect
2. C2×#88641C2semidirect
3. #11721724C2semidirect
4. C9×#67⋊C4C2semidirect
5. C3×#63444C2semidirect
6. #11721290C2semidirect
7. #11721285C2semidirect
8. Dic3×#611C2semidirect
9. #11720996C2semidirect
10. Dic3×D36C2semidirect
11. #11720989C2semidirect
12. #11720982C2semidirect
13. #11720981C2semidirect
14. #11720976C2semidirect
15. #11720974C2semidirect
20. C2×#6226C22semidirect
24. C2×C4×D3×C9C22semidirect
29. C2×#6194C22semidirect
35. C2×Dic3×D9C22semidirect
39. C4⋊(C3⋊Dic9)C22semidirect
40. #88534C22semidirect
41. #88534C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C4×C9×Dic3C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
81. #63444D3semidirect
119. Dic3×D9D4semidirect
205. C22×C3×C9#41semidirect
219. C2×C3×D9#41semidirect
253. #67⋊C4D9semidirect
383. C2×C4×D3C2×D9semidirect
410. (C2×D3)⋊C4C2×D9semidirect
424. Dic3⋊C4C2×D9semidirect
427. C4×Dic3C2×D9semidirect
464. C22×C9#237semidirect
475. C2×D9#237semidirect
507. C3×C9#525semidirect
663. C22×C3#3697semidirect
708. C9#5586semidirect
778. C22#88641semidirect
791. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3×D92
C2×#886412
#117217242
C9×#67⋊C42
C3×#634442
#117212902
#117212852
Dic3×#6112
#117209962
Dic3×D362
#117209892
#117209822
#117209812
#117209762
#117209742
#105940543
#105896493