Finite Group Databasebeta

← #13151999

Subgroups — #13151999

Order 1728.

882 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88551C211yesmaximal, characteristic, complemented
2C9×#953C211yesmaximal, characteristic, complemented
3C3×#63515C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#67⋊Dic9C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#11721280C211yesmaximal, characteristic, complemented
8#611⋊Dic3C211yesmaximal, characteristic, complemented
9#11721270C211yesmaximal, characteristic, complemented
10#11721269C211yesmaximal, characteristic, complemented
11#11721267C211yesmaximal, characteristic, complemented
12#11721263C211yesmaximal, characteristic, complemented
13#11721257C211yesmaximal, characteristic, complemented
14#11721247C211yesmaximal, characteristic, complemented
15#11721246C211yesmaximal, characteristic, complemented
16#10595508—31nomaximal
17#10589695—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×#6194C2211yescharacteristic, complemented
28C2×D3×Dic9C2211yescharacteristic, complemented
29C2×Dic3×D9C2211yescharacteristic, complemented
30C2×#6189C2211yescharacteristic, complemented
31#88551C2211yescharacteristic
32#88551C2211yescharacteristic
33#88551C2211yescharacteristic
34#88551C2211yescharacteristic
35C9×#217C2211yescharacteristic
36C9×#217C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic, complemented
42(C2×D3)⋊Dic9C2211yescharacteristic, complemented
43(C2×D9)⋊Dic3C2211yescharacteristic, complemented
44(C2×D9)⋊Dic3C2211yescharacteristic, complemented
45Dic3⋊Dic9C2211yescharacteristic, complemented
46Dic3⋊Dic9C2211yescharacteristic, complemented
47#88442C2211yescharacteristic, complemented
48#88442C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C2×#3757—31no—
54C3×#953—31no—
55C3×#953D311yescharacteristic
56#63982—31no—
57#63980—31no—
58#67⋊Dic3—31no—
59#67⋊Dic3—31no—
60#63970—31no—
61#63970—31no—
62#63969—31no—
63#63969—31no—
64#63959—31no—
65#63959—31no—
66#63956—31no—
67#63956—31no—
68C9×#120—31no—
69#63515D311yescharacteristic, complemented
70C2×#3676—31no—
71C2×#3676—61no—
72#63501—31no—
73#63501—31no—
74#63500—31no—
75#63498—31no—
76#63497—31no—
77D4×Dic9—31no—
78#63447—31no—
79#63445—31no—
80#611⋊C4—31no—
81#63441—31no—
82#63441—31no—
83#63440—31no—
84C23×C3×C9—22no—
85C23×C3×C9—41no—
86C23×C3×C9—41no—
87C23×C3×C9C2311yescharacteristic
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3⋊Dic9—41no—
93C2×C3⋊Dic9—41no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C9×#67—22no—
99C9×#67—41no—
100C9×#67—41no—
101C3×#611—22no—
102C3×#611—41no—
103C3×#611—41no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110#6194—41no—
111D3×Dic9—41no—
112Dic3×D9—41no—
113#6189—41no—
114#5593—91no—
115#5593—91no—
116C24×C32C2×D311yescharacteristic
117C22×C3⋊Dic3—31no—
118C22×C3⋊Dic3—31no—
119C2×C3×#67—31no—
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67C2×D311yescharacteristic
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×#67C2×D311yescharacteristic
125C2×#627—31no—
126C2×#625—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129C24×C9—21no—
130C24×C9C2×D311yescharacteristic
131#3757—31no—
132#3757—31no—
133#3757—31no—
134#3757—31no—
135C3×#217—31no—
136C3×#217—31no—
137C3×#217—31no—
138C3×#217C2×D311yescharacteristic
139C3×#217C2×D311yescharacteristic
140C3×#217C2×D311yescharacteristic
141#3724—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152Dic32—31no—
153C2×D4×C9—31no—
154C2×D4×C9—31no—
155C2×D4×C9—31no—
156C2×#611—31no—
157C2×#611C2×D311yescharacteristic
158C2×#611C2×D311yescharacteristic
159C2×#611C2×D311yescharacteristic
160C22×Dic9—31no—
161C22×Dic9—31no—
162C22×Dic9—31no—
163C22×Dic9—61no—
164C22×Dic9—61no—
165C2×C4×D9—31no—
166C2×Dic18—31no—
167C9×C22⋊C4—31no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170#3676—31no—
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—31no—
176#3676—61no—
177#3676—61no—
178#3676—61no—
179#3676—61no—
180#3676C2×D311yescharacteristic
181#3676C2×D311yescharacteristic
182#3676C2×D311yescharacteristic
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185C4⋊Dic9—31no—
186C4⋊Dic9—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191C4×Dic9—31no—
192C4×Dic9—31no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—44no—
202C22×C3×C9#4112yes—
203C22×C3×C9C2411yescharacteristic
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3⋊Dic9—21no—
211C3⋊Dic9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#120—31no—
221C3×#120—91no—
222#953—31no—
223#953D911yescharacteristic, complemented
224C2×#217—91no—
225C2×#217—91no—
226C2×#217—181no—
227#939—91no—
228#939—91no—
229#939—91no—
230#939—91no—
231#938—91no—
232#938—91no—
233#936—91no—
234#936—91no—
235#935—91no—
236#935—91no—
237D4×Dic3—91no—
238D4×Dic3—91no—
239#885—91no—
240#885—91no—
241#883—91no—
242#883—91no—
243#67⋊C4—91no—
244#67⋊C4—91no—
245#879—91no—
246#879—91no—
247#879—91no—
248#879—91no—
249#878—91no—
250#878—91no—
251C23×C32—22no—
252C23×C32—41no—
253C23×C32—41no—
254C23×C32C22×D311yescharacteristic
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—121no—
264C2×C3⋊Dic3—121no—
265C3×#67—22no—
266C3×#67—41no—
267C3×#67—41no—
268C3×#67—62no—
269C3×#67—121no—
270C3×#67—121no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277#627—121no—
278#625—121no—
279D3×Dic3—121no—
280D3×Dic3—121no—
281C23×C9—24no—
282C23×C9—22no—
283C23×C9—21no—
284C23×C9—21no—
285C23×C9—21no—
286C23×C9—31no—
287C23×C9—41no—
288C23×C9—41no—
289C23×C9—42no—
290C23×C9—42no—
291C23×C9C22×D311yescharacteristic
292C23×C9C22×D311yescharacteristic
293C23×C9C22×D311yescharacteristic
294C22×D9C22×D311yescharacteristic
295D4×C9—62no—
296D4×C9—121no—
297D4×C9—121no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301#611—22no—
302#611—41no—
303#611—41no—
304#611—121no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9—121no—
314C2×Dic9—121no—
315C2×Dic9—121no—
316C2×Dic9—122no—
317C2×Dic9—122no—
318C2×Dic9C22×D311yescharacteristic
319C2×Dic9C22×D311yescharacteristic
320C2×Dic9C22×D311yescharacteristic
321C4×D9—121no—
322Dic18—121no—
323#538—271noSylow
324C2×C3×C9—22no—
325C2×C3×C9—41no—
326C2×C3×C9—41no—
327C2×C3×C9C2×#4111yescharacteristic
328C2×C3×C9H(5,𝔽2)11yescharacteristic
329C2×C3×C9H(5,𝔽2)11yescharacteristic
330D3×C9—41no—
331C3×D9—41no—
332C24×C3—21no—
333C24×C3C2×D911yescharacteristic
334C24×C3D3211yescharacteristic
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4—91no—
341C2×#67—31no—
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67C2×D911yescharacteristic
347C2×#67C2×D911yescharacteristic
348C2×#67C2×D911yescharacteristic
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C22×Dic3—91no—
355C22×Dic3—181no—
356C22×Dic3—181no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×Dic6—91no—
360C2×Dic6—91no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367#217—31no—
368#217—31no—
369#217—31no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—91no—
378#217—91no—
379#217—91no—
380#217—91no—
381#217—91no—
382#217—181no—
383#217—181no—
384#217—181no—
385#217—181no—
386#217C2×D911yescharacteristic
387#217C2×D911yescharacteristic
388#217C2×D911yescharacteristic
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405C4×Dic3—91no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C4×Dic3—91no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—44no—
418C22×C32#23712yes—
419C22×C32C23×D311yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3⋊Dic3—61no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C3×Dic3—61no—
436C22×C9—22no—
437C22×C9—22no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—22no—
441C22×C9—22no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—21no—
446C22×C9—21no—
447C22×C9—21no—
448C22×C9—21no—
449C22×C9—22no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9—41no—
453C22×C9—41no—
454C22×C9—48no—
455C22×C9—44no—
456C22×C9—61no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9#23712yes—
460C22×C9C23×D311yescharacteristic
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—21no—
464C4×C9—61no—
465C4×C9—61no—
466C4×C9—61no—
467Dic9—21no—
468Dic9—21no—
469Dic9—21no—
470Dic9—61no—
471Dic9—61no—
472Dic9—61no—
473Dic9—61no—
474Dic9—121no—
475Dic9—121no—
476Dic9—121no—
477Dic9—121no—
478#126—271no—
479#126—271no—
480#124—271no—
481#124—271no—
482#123—271no—
483#123—271no—
484C22⋊Q8—271no—
485#121—271no—
486#121—271no—
487#121—271no—
488#120—31no—
489#120—91no—
490C4×D4—271no—
491C4×D4—271no—
492C2×C22⋊C4—271no—
493C3×C9#53811yescharacteristic, complemented, Sylow
494C23×C3—24no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—31no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—42no—
506C23×C3—42no—
507C23×C3—91no—
508C23×C3C22×D911yescharacteristic
509C23×C3C22×D911yescharacteristic
510C23×C3C22×D911yescharacteristic
511C23×C3C2×D3211yescharacteristic
512C23×C3C2×D3211yescharacteristic
513C23×C3C2×D3211yescharacteristic
514C22×D3—31no—
515C22×D3C22×D911yescharacteristic
516C3×D4—62no—
517C3×D4—121no—
518C3×D4—121no—
519C3×D4—182no—
520C3×D4—361no—
521C3×D4—361no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528#67—22no—
529#67—41no—
530#67—41no—
531#67—62no—
532#67—121no—
533#67—121no—
534#67—361no—
535#67—361no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—181no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—361no—
552C2×Dic3—361no—
553C2×Dic3—361no—
554C2×Dic3—361no—
555C2×Dic3—361no—
556C2×Dic3—361no—
557C2×Dic3—362no—
558C2×Dic3—362no—
559C2×Dic3C22×D911yescharacteristic
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562C4×D3—361no—
563C4×D3—361no—
564Dic6—361no—
565Dic6—361no—
566C2×C32—22no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32C2×#23711yescharacteristic
570C2×C32#100411yescharacteristic
571C2×C32#100411yescharacteristic
572C3×D3—41no—
573C3×D3—121no—
574C2×C9—24no—
575C2×C9—22no—
576C2×C9—21no—
577C2×C9—21no—
578C2×C9—21no—
579C2×C9—42no—
580C2×C9—42no—
581C2×C9—41no—
582C2×C9—41no—
583C2×C9—121no—
584C2×C9C2×#23711yescharacteristic
585C2×C9#100411yescharacteristic
586C2×C9#100411yescharacteristic
587D9—41no—
588C24D3×D911yescharacteristic
589C2×Q8—271no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—31no—
593C2×D4—91no—
594C2×D4—91no—
595C2×D4—91no—
596C2×D4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—91no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C22⋊C4—271no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C42—271no—
622C42—271no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—44no—
650C22×C3—48no—
651C22×C3—44no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3#369912yes—
659C22×C3C23×D911yescharacteristic
660C22×C3#380512yes—
661C22×C3C22×D3211yescharacteristic
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—181no—
672C3×C4—181no—
673C3×C4—181no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—181no—
681Dic3—181no—
682Dic3—181no—
683Dic3—181no—
684Dic3—181no—
685Dic3—181no—
686Dic3—181no—
687Dic3—181no—
688Dic3—361no—
689Dic3—361no—
690Dic3—361no—
691Dic3—361no—
692C32#559311yescharacteristic
693C9—21no—
694C9#559311yescharacteristic, complemented
695C23—22no—
696C23—31no—
697C23—41no—
698C23—41no—
699C23—91no—
700C23C2×D3×D911yescharacteristic
701C23C2×D3×D911yescharacteristic
702C23C2×D3×D911yescharacteristic
703Q8—1081no—
704D4—62no—
705D4—121no—
706D4—121no—
707D4—182no—
708D4—361no—
709D4—361no—
710D4—1081no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—271no—
718C2×C4—271no—
719C2×C4—271no—
720C2×C4—271no—
721C2×C4—1081no—
722C2×C4—1081no—
723C2×C4—1081no—
724C2×C4—1081no—
725C2×C3—24no—
726C2×C3—22no—
727C2×C3—22no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—121no—
738C2×C3—361no—
739C2×C3C2×#369911yescharacteristic
740C2×C3#6371011yescharacteristic
741C2×C3#6371011yescharacteristic
742C2×C3C2×#380511yescharacteristic
743C2×C3#6433011yescharacteristic
744C2×C3#6433011yescharacteristic
745D3—41no—
746D3—121no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—44no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—181no—
760C22—181no—
761C22—181no—
762C22#8866312yes—
763C22C22×D3×D911yescharacteristic
764C4—61no—
765C4—61no—
766C4—61no—
767C4—181no—
768C4—181no—
769C4—181no—
770C4—541no—
771C4—541no—
772C4—541no—
773C4—541no—
774C3—21no—
775C3#1058969511yescharacteristic, complemented
776C3#1059550811yescharacteristic
777C2—22no—
778C2—41no—
779C2—41no—
780C2—121no—
781C2—361no—
782C2C2×#8866311yescharacteristic
783C2#1172253511yescharacteristic
784C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
hypercenterC24D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C2×#88551C2semidirect
2. C9×#953C2semidirect
3. C3×#63515C2semidirect
4. #11721290C2semidirect
5. #67⋊Dic9C2semidirect
6. #11721281C2semidirect
7. #11721280C2semidirect
8. #611⋊Dic3C2semidirect
9. #11721270C2semidirect
10. #11721269C2semidirect
11. #11721267C2semidirect
12. #11721263C2semidirect
13. #11721257C2semidirect
14. #11721247C2semidirect
15. #11721246C2semidirect
27. C2×#6194C22semidirect
28. C2×D3×Dic9C22semidirect
29. C2×Dic3×D9C22semidirect
30. C2×#6189C22semidirect
41. (C2×D3)⋊Dic9C22semidirect
42. (C2×D3)⋊Dic9C22semidirect
43. (C2×D9)⋊Dic3C22semidirect
44. (C2×D9)⋊Dic3C22semidirect
45. Dic3⋊Dic9C22semidirect
46. Dic3⋊Dic9C22semidirect
47. #88442C22semidirect
48. #88442C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
69. #63515D3semidirect
223. #953D9semidirect
493. C3×C9#538semidirect
694. C9#5593semidirect
775. C3#10589695semidirect

Maximal subgroups

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

subgroupindex
C2×#885512
C9×#9532
C3×#635152
#117212902
#67⋊Dic92
#117212812
#117212802
#611⋊Dic32
#117212702
#117212692
#117212672
#117212632
#117212572
#117212472
#117212462
#105955083
#105896953