Finite Group Databasebeta

← #13148305

Subgroups — #13148305

Order 1728.

828 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721729C211yesmaximal, characteristic, complemented
2C9×#885C211yesmaximal, characteristic, complemented
3C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
4#11721285C211yesmaximal, characteristic, complemented
5#11721282C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7#11721247C211yesmaximal, characteristic, complemented
8#11721041C211yesmaximal, characteristic, complemented
9#11721033C211yesmaximal, characteristic, complemented
10#11721021C211yesmaximal, characteristic, complemented
11#11721012C211yesmaximal, characteristic, complemented
12#11721003C211yesmaximal, characteristic, complemented
13C4×#6192C211yesmaximal, characteristic, complemented
14#11720947C211yesmaximal, characteristic, complemented
15#11720944C211yesmaximal, characteristic, complemented
16#10594196—31nomaximal
17#10589780—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C9×#67C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic, complemented
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic, complemented
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C3×C9×C22⋊C4C2211yescharacteristic
32#88551C2211yescharacteristic
33#88536C2211yescharacteristic, complemented
34C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
35#88534C2211yescharacteristic, complemented
36C9×#217C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C4×C9×Dic3C2211yescharacteristic, complemented
43#88445C2211yescharacteristic, complemented
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64092—31no—
54C3×#885D311yescharacteristic
55C3×D3×C22⋊C4—31no—
56#63977—31no—
57#63976—31no—
58#63971—31no—
59#63956—31no—
60#63912—31no—
61#63907—31no—
62#63906—31no—
63C4×#626—31no—
64#63891—31no—
65#63879—31no—
66#63859—31no—
67#63856—31no—
68C9×#124—31no—
69#63509—31no—
70#63508—31no—
71#63501—31no—
72#63499—31no—
73#63448—31no—
74#63446—31no—
75#63446—31no—
76#63445—31no—
77#63445—61no—
78#63444—31no—
79#611⋊C4—31no—
80C22⋊C4×D9D311yescharacteristic, complemented
81#63441—31no—
82#63438—31no—
83C4×D36—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9—22no—
88C22×C3×D9—41no—
89C22×C3×D9—41no—
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—41no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4×C3⋊D9—41no—
99C9×#67—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×C4×D9—41no—
106C3×C4×D9—41no—
107C9×Dic6—41no—
108#6195—41no—
109#6194—22no—
110#6194—41no—
111D3×Dic9—41no—
112#6192—22no—
113#6192—41no—
114#5678—91no—
115#5494—91no—
116C23×C3×D3—31no—
117C2×#638—31no—
118C2×C4×C3⋊D3—31no—
119C2×C3×#67C2×D311yescharacteristic
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×Dic6C2×D311yescharacteristic
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#625—31no—
127C2×#625—31no—
128C2×D3×Dic3—31no—
129C23×D9C2×D311yescharacteristic
130C32×C22⋊C4C2×D311yescharacteristic
131#3757—31no—
132#3752—31no—
133C4⋊(C3⋊Dic3)—31no—
134#3750—31no—
135C3×#217—31no—
136C3×#217C2×D311yescharacteristic
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×C4×Dic3C2×D311yescharacteristic
142#3724—31no—
143#3724—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146#3722—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×Q8×C9—31no—
153C2×D4×C9—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—61no—
159C22×Dic9—31no—
160C2×D36—31no—
161C2×D36—31no—
162C2×C4×D9—31no—
163C2×C4×D9—61no—
164C2×C4×D9C2×D311yescharacteristic
165C2×C4×D9C2×D311yescharacteristic
166C9×C22⋊C4—21no—
167C9×C22⋊C4—31no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4C2×D311yescharacteristic
171C42×C9—31no—
172#3676—31no—
173#3676—61no—
174#3676C2×D311yescharacteristic
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—61no—
182(C2×D9)⋊C4C2×D311yescharacteristic
183(C2×D9)⋊C4C2×D311yescharacteristic
184C4⋊Dic9—31no—
185C4⋊Dic9—31no—
186C4⋊Dic9—61no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—61no—
192C4×Dic9—31no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—44no—
209C2×C3×D9#4112yes—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#124—31no—
221C2×C3×C22⋊C4—91no—
222#953—91no—
223#953—91no—
224#947—91no—
225#946—91no—
226#939—91no—
227#937—91no—
228#930—91no—
229C4×#67—91no—
230C4×#67—91no—
231#924—91no—
232#886—91no—
233#885—91no—
234#885D911yescharacteristic, complemented
235#884—91no—
236#884—91no—
237#884—91no—
238#884—91no—
239#883—91no—
240#883—91no—
241#883—91no—
242#883—181no—
243#882—91no—
244#67⋊C4—91no—
245D3×C22⋊C4—31no—
246#879—91no—
247#879—91no—
248#879—91no—
249#876—91no—
250C4×D12—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—62no—
256C22×C3×D3—121no—
257C22×C3×D3—121no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—121no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C4×C3⋊D3—121no—
266C3×#67—41no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×C4×D3—121no—
273C3×C4×D3—121no—
274C3×Dic6—41no—
275#626—62no—
276#626—121no—
277#626—121no—
278#625—62no—
279#625—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9C22×D311yescharacteristic
284C22×D9—22no—
285C22×D9—31no—
286C22×D9—41no—
287C22×D9—41no—
288C22×D9—61no—
289C22×D9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291Q8×C9—121no—
292D4×C9—121no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300#611—62no—
301#611—121no—
302#611—121no—
303#611—121no—
304#611—122no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—121no—
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314D36—62no—
315D36—121no—
316C4×D9—41no—
317C4×D9—41no—
318C4×D9—121no—
319C4×D9—122no—
320#538—271noSylow
321C2×C3×C9—41no—
322C2×C3×C9C2×#4111yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C3⋊D9—41no—
326D3×C9—41no—
327C3×D9—22no—
328C3×D9—41no—
329C24×C3—91no—
330C23×D3—31no—
331C2×C3×Q8—31no—
332C2×C3×D4—31no—
333C22×C3×C4—91no—
334C22×C3×C4—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—181no—
345C2×#67C2×D911yescharacteristic
346C22×Dic3—91no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—181no—
356C2×Dic6C2×D911yescharacteristic, complemented
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4C2×D911yescharacteristic
365C3×C22⋊C4D3211yescharacteristic
366C3×C42—31no—
367#217—31no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—181no—
375#217C2×D911yescharacteristic
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—181no—
387(C2×D3)⋊C4C2×D911yescharacteristic, complemented
388(C2×D3)⋊C4C2×D911yescharacteristic, complemented
389C4⋊Dic3—91no—
390C4⋊Dic3—91no—
391C4⋊Dic3—91no—
392C4⋊Dic3—91no—
393C4⋊Dic3—181no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—181no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3C2×D911yescharacteristic, complemented
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—32no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—124no—
423C32×C4—21no—
424C32×C4—21no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—41no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—44no—
450C2×D9—62no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9#23512yes—
457C4×C9—21no—
458C4×C9—21no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—61no—
462C4×C9—61no—
463C4×C9—61no—
464Dic9—21no—
465Dic9—21no—
466Dic9—61no—
467Dic9—61no—
468Dic9—61no—
469Dic9—121no—
470Dic9—121no—
471Dic9—121no—
472#126—271no—
473#126—271no—
474#124—31no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—271no—
480#121—271no—
481#121—271no—
482#120—271no—
483#120—271no—
484C4×D4—271no—
485C4×D4—271no—
486C2×C22⋊C4—91no—
487C3×C9#53811yescharacteristic, complemented, Sylow
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—91no—
491C23×C3—91no—
492C23×C3—182no—
493C23×C3—361no—
494C23×C3—361no—
495C23×C3C22×D911yescharacteristic
496C23×C3C2×D3211yescharacteristic
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—62no—
500C22×D3—91no—
501C22×D3—91no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—181no—
505C22×D3C22×D911yescharacteristic
506C3×Q8—121no—
507C3×D4—121no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—361no—
516C2×C3×C4—361no—
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C22×D911yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521#67—41no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—361no—
526#67—361no—
527#67—361no—
528#67—361no—
529#67—361no—
530#67—361no—
531#67—362no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—361no—
544C2×Dic3C22×D911yescharacteristic
545C2×Dic3C22×D911yescharacteristic
546C2×Dic3C22×D911yescharacteristic
547D12—182no—
548D12—361no—
549D12—361no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3—361no—
553C4×D3—361no—
554C4×D3—361no—
555C4×D3—362no—
556Dic6—41no—
557C2×C32—41no—
558C2×C32#100411yescharacteristic
559C2×C32D3×#4111yescharacteristic
560C2×C32#100911yescharacteristic
561C3⋊D3—121no—
562C3×D3—41no—
563C3×D3—62no—
564C3×D3—121no—
565C2×C9—21no—
566C2×C9—21no—
567C2×C9—21no—
568C2×C9—41no—
569C2×C9—81no—
570C2×C9—121no—
571C2×C9C2×#23511yescharacteristic
572C2×C9#100411yescharacteristic
573C2×C9#100411yescharacteristic
574D9—22no—
575D9—41no—
576D9—122no—
577D9—121no—
578C24—91no—
579C2×Q8—31no—
580C2×D4—31no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—271no—
590C22×C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4—91no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4D3×D911yescharacteristic
611C42—31no—
612C42—271no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—92no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—364no—
633C22×C3C23×D911yescharacteristic
634C22×C3C22×D3211yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—32no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—124no—
645C2×D3—182no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—361no—
653C2×D3—361no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—61no—
669Dic3—61no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—361no—
677Dic3—361no—
678Dic3—361no—
679C32#567811yescharacteristic
680C9—21no—
681C9#549411yescharacteristic, complemented
682C23—31no—
683C23—91no—
684C23—91no—
685C23—182no—
686C23—271no—
687C23—361no—
688C23—361no—
689C23C2×D3×D911yescharacteristic
690Q8—121no—
691D4—121no—
692D4—542no—
693D4—542no—
694D4—1081no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—361no—
707C2×C4—361no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4C2×D3×D911yescharacteristic
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—81no—
718C2×C3—121no—
719C2×C3—182no—
720C2×C3—361no—
721C2×C3#6371011yescharacteristic
722C2×C3#41×D911yescharacteristic
723C2×C3#6371511yescharacteristic
724C2×C3D3×#23511yescharacteristic
725C2×C3#6431311yescharacteristic
726C2×C3#6431411yescharacteristic
727D3—41no—
728D3—62no—
729D3—121no—
730D3—362no—
731D3—361no—
732D3—361no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—92no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—364no—
746C22—541no—
747C22—541no—
748C22—541no—
749C22C22×D3×D911yescharacteristic
750C4—21no—
751C4—21no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—181no—
756C4—181no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—21no—
761C3#1058978011yescharacteristic, complemented
762C3#1059419611yescharacteristic
763C2—41no—
764C2—121no—
765C2—182no—
766C2—361no—
767C2—1081no—
768C2D9×#23511yescharacteristic
769C2#1172249911yescharacteristic
770C2#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#538
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. #11721729C2semidirect
2. C9×#885C2semidirect
3. C3×C22⋊C4×D9C2semidirect
4. #11721285C2semidirect
5. #11721282C2semidirect
6. #11721276C2semidirect
7. #11721247C2semidirect
8. #11721041C2semidirect
9. #11721033C2semidirect
10. #11721021C2semidirect
11. #11721012C2semidirect
12. #11721003C2semidirect
13. C4×#6192C2semidirect
14. #11720947C2semidirect
15. #11720944C2semidirect
20. C2×C4×C3⋊D9C22semidirect
24. C2×C9×Dic6C22semidirect
25. C2×#6195C22semidirect
28. C2×D3×Dic9C22semidirect
33. #88536C22semidirect
34. C4⋊(C3⋊Dic9)C22semidirect
35. #88534C22semidirect
38. C9×(C2×D3)⋊C4C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
42. C4×C9×Dic3C22semidirect
43. #88445C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
80. C22⋊C4×D9D3semidirect
234. #885D9semidirect
356. C2×Dic6C2×D9semidirect
387. (C2×D3)⋊C4C2×D9semidirect
388. (C2×D3)⋊C4C2×D9semidirect
405. C4×Dic3C2×D9semidirect
487. C3×C9#538semidirect
681. C9#5494semidirect
761. C3#10589780semidirect

Maximal subgroups

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

subgroupindex
#117217292
C9×#8852
C3×C22⋊C4×D92
#117212852
#117212822
#117212762
#117212472
#117210412
#117210332
#117210212
#117210122
#117210032
C4×#61922
#117209472
#117209442
#105941963
#105897803