Finite Group Databasebeta

← #13151295

Subgroups — #13151295

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721838C211yesmaximal, characteristic, complemented
2C9×#939C211yesmaximal, characteristic, complemented
3C3×#63501C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721265C211yesmaximal, characteristic, complemented
7#11721263C211yesmaximal, characteristic, complemented
8#11721259C211yesmaximal, characteristic, complemented
9#11721257C211yesmaximal, characteristic, complemented
10#11721241C211yesmaximal, characteristic, complemented
11#11721240C211yesmaximal, characteristic, complemented
12#11721048C211yesmaximal, characteristic, complemented
13#11720965C211yesmaximal, characteristic, complemented
14#11720949C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10595311—31nomaximal
17#10589715—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C9×#67C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C22×C9×Dic3C2211yescharacteristic, complemented
28C22×C3×Dic9C2211yescharacteristic, complemented
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×#6189C2211yescharacteristic, complemented
31#88551C2211yescharacteristic, complemented
32#88551C2211yescharacteristic, complemented
33C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
34C9×#217C2211yescharacteristic, complemented
35C3×#3676C2211yescharacteristic, complemented
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40(C2×D3)⋊Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48#88442C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64147—31no—
54C3×#939—31no—
55C3×#939D311yescharacteristic
56#63983—31no—
57#63983—31no—
58#63961—31no—
59#63961—31no—
60#63959—31no—
61#63959—31no—
62#63952—31no—
63#63952—31no—
64#63921—31no—
65#63865—31no—
66#63861—31no—
67#63861—31no—
68C9×#121—31no—
69#63501D311yescharacteristic, complemented
70#63500—31no—
71#63500—61no—
72#63499—31no—
73#63499—31no—
74#63498—31no—
75#63497—31no—
76#63491—31no—
77C4×#611—31no—
78#63460—31no—
79#63458—31no—
80#63447—31no—
81#611⋊C4—31no—
82C22⋊C4×D9—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C3×D4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95#6233—22no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C4×C3⋊D9—41no—
100C9×#67—41no—
101C9×#67—41no—
102C3×#611—41no—
103C3×#611—41no—
104C2×C9×Dic3—41no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9—41no—
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112(C3⋊D9)⋊C4—41no—
113#6189—41no—
114#5613—91no—
115#5613—91no—
116C22×D32—31no—
117C2×C32×D4C2×D311yescharacteristic
118C2×#638—31no—
119C2×#638—31no—
120C2×C4×C3⋊D3—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×#67C2×D311yescharacteristic
125C22×C3×Dic3—31no—
126C22×C3×Dic3C2×D311yescharacteristic
127C2×#627—31no—
128C2×#624—31no—
129C23×D9—31no—
130#3757—31no—
131#3757—31no—
132C4⋊(C3⋊Dic3)—31no—
133C3×#217—31no—
134C3×#217C2×D311yescharacteristic
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4C2×D311yescharacteristic
139#3724—31no—
140#3724—31no—
141#3724—31no—
142#3722—31no—
143#3722—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150Dic32—31no—
151Dic32—31no—
152C2×D4×C9—21no—
153C2×D4×C9—31no—
154C2×D4×C9—31no—
155C2×D4×C9C2×D311yescharacteristic, complemented
156C22×C4×C9—31no—
157C2×#611—31no—
158C2×#611—31no—
159C2×#611—61no—
160C2×#611—61no—
161C2×#611C2×D311yescharacteristic
162C2×#611C2×D311yescharacteristic
163C22×Dic9C2×D311yescharacteristic, complemented
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C2×Dic18—31no—
168C9×C4⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—31no—
176#3676—61no—
177#3676—61no—
178#3676C2×D311yescharacteristic, complemented
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4C2×D311yescharacteristic
185C4⋊Dic9—31no—
186C4⋊Dic9—61no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4C2×D311yescharacteristic, complemented
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×C9C2411yescharacteristic
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9#4112yes—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209D3×D9—44no—
210C3×C4×C9—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×#121—31no—
221C3×#121—91no—
222#939—31no—
223#939D911yescharacteristic, complemented
224#938—91no—
225#938—91no—
226#938—181no—
227#937—91no—
228#937—91no—
229#937—91no—
230#937—91no—
231#936—91no—
232#936—91no—
233#935—91no—
234#935—91no—
235#929—91no—
236#929—91no—
237C4×#67—91no—
238C4×#67—91no—
239#898—91no—
240#898—91no—
241#896—91no—
242#896—91no—
243#885—91no—
244#885—91no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247D3×C22⋊C4—91no—
248D3×C22⋊C4—91no—
249#879—91no—
250#879—91no—
251C23×C32C22×D311yescharacteristic
252C23×C32C22×D311yescharacteristic
253C22×C3⋊D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3C22×D311yescharacteristic
256C2×D32—62no—
257C2×D32—121no—
258C2×D32—121no—
259C32×D4—41no—
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262#638—62no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C4×C3⋊D3—121no—
267C3×#67—41no—
268C3×#67—41no—
269C3×#67—121no—
270C3×#67—121no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—41no—
275C2×C3×Dic3—121no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279#627—121no—
280#624—121no—
281C23×C9—21no—
282C23×C9—21no—
283C23×C9—31no—
284C23×C9C22×D311yescharacteristic
285C23×C9C22×D311yescharacteristic
286C22×D9—31no—
287C22×D9—61no—
288C22×D9—62no—
289C22×D9—121no—
290C22×D9—121no—
291C22×D9C22×D311yescharacteristic
292D4×C9—41no—
293D4×C9—42no—
294D4×C9—121no—
295D4×C9—121no—
296C2×C4×C9—21no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—121no—
301C2×C4×C9C22×D311yescharacteristic
302#611—41no—
303#611—41no—
304#611—62no—
305#611—62no—
306#611—122no—
307#611—122no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—31no—
311C2×Dic9—41no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9—61no—
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317C2×Dic9C22×D311yescharacteristic
318C4×D9—121no—
319C4×D9—121no—
320C4×D9—122no—
321Dic18—121no—
322#538—271noSylow
323C2×C3×C9—41no—
324C2×C3×C9—41no—
325C2×C3×C9C2×#4111yescharacteristic
326C2×C3×C9H(5,𝔽2)11yescharacteristic
327C2×C3×C9H(5,𝔽2)11yescharacteristic
328C3⋊D9—22no—
329D3×C9—41no—
330C3×D9—41no—
331C23×D3—91no—
332C23×D3—91no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4C2×D911yescharacteristic, complemented
339C2×C3×D4D3211yescharacteristic
340C22×C3×C4—31no—
341C22×C3×C4—91no—
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—181no—
349C2×#67—181no—
350C2×#67C2×D911yescharacteristic
351C2×#67C2×D911yescharacteristic
352C22×Dic3—31no—
353C22×Dic3C2×D911yescharacteristic, complemented
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—181no—
359C2×Dic6—91no—
360C2×Dic6—91no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—91no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367#217—31no—
368#217—91no—
369#217—91no—
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—181no—
379#217—181no—
380#217C2×D911yescharacteristic, complemented
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4C2×D911yescharacteristic
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—181no—
396Dic3⋊C4—31no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4C2×D911yescharacteristic, complemented
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32C23×D311yescharacteristic
415C2×C3⋊D3—32no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424D32—124no—
425C32×C4—21no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—41no—
443C22×C9—41no—
444C22×C9—41no—
445C22×C9—41no—
446C22×C9—41no—
447C22×C9—41no—
448C22×C9—61no—
449C22×C9—61no—
450C22×C9—61no—
451C22×C9C23×D311yescharacteristic
452C2×D9—21no—
453C2×D9—21no—
454C2×D9—21no—
455C2×D9—32no—
456C2×D9—62no—
457C2×D9—61no—
458C2×D9—61no—
459C2×D9—121no—
460C2×D9—121no—
461C2×D9—124no—
462C4×C9—22no—
463C4×C9—21no—
464C4×C9—61no—
465C4×C9—61no—
466C4×C9—61no—
467Dic9—21no—
468Dic9—21no—
469Dic9—21no—
470Dic9—61no—
471Dic9—61no—
472Dic9—61no—
473Dic9—121no—
474Dic9—121no—
475Dic9—121no—
476#126—271no—
477#126—271no—
478#124—271no—
479#124—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483#121—31no—
484#121—91no—
485#121—271no—
486#120—271no—
487#120—271no—
488C4×D4—271no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C3×C9#53811yescharacteristic, complemented, Sylow
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—91no—
496C23×C3C22×D911yescharacteristic
497C23×C3C22×D911yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C23×C3C2×D3211yescharacteristic
500C22×D3—31no—
501C22×D3—91no—
502C22×D3—91no—
503C22×D3—181no—
504C22×D3—182no—
505C22×D3—182no—
506C22×D3—361no—
507C22×D3—361no—
508C22×D3—361no—
509C22×D3—361no—
510C22×D3C22×D911yescharacteristic
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—42no—
514C3×D4—121no—
515C3×D4—121no—
516C3×D4—361no—
517C3×D4—361no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—121no—
526C2×C3×C4—361no—
527C2×C3×C4C22×D911yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529#67—41no—
530#67—41no—
531#67—121no—
532#67—121no—
533#67—182no—
534#67—182no—
535#67—182no—
536#67—182no—
537#67—362no—
538#67—362no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—41no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—121no—
550C2×Dic3—181no—
551C2×Dic3—181no—
552C2×Dic3—181no—
553C2×Dic3C22×D911yescharacteristic
554C2×Dic3C22×D911yescharacteristic
555C2×Dic3C22×D911yescharacteristic
556C4×D3—361no—
557C4×D3—361no—
558C4×D3—361no—
559C4×D3—361no—
560C4×D3—362no—
561Dic6—361no—
562Dic6—361no—
563C2×C32—41no—
564C2×C32—41no—
565C2×C32#100411yescharacteristic
566C2×C32#100411yescharacteristic
567C2×C32D3×#4111yescharacteristic
568C3⋊D3—62no—
569C3×D3—41no—
570C3×D3—121no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—41no—
575C2×C9—41no—
576C2×C9—81no—
577C2×C9—81no—
578C2×C9—121no—
579C2×C9#100411yescharacteristic
580C2×C9#100411yescharacteristic
581C2×C9D3×#4111yescharacteristic
582D9—41no—
583D9—62no—
584D9—122no—
585C24—271no—
586C2×Q8—271no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—91no—
590C2×D4—91no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4D3×D911yescharacteristic, complemented
594C22×C4—31no—
595C22×C4—91no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—91no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C42—271no—
619C42—271no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3C23×D911yescharacteristic
646C22×C3C22×D3211yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—92no—
654C2×D3—92no—
655C2×D3—182no—
656C2×D3—181no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—361no—
661C2×D3—361no—
662C2×D3—364no—
663C2×D3—364no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—181no—
671C3×C4—181no—
672C3×C4—181no—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—181no—
680Dic3—181no—
681Dic3—181no—
682Dic3—181no—
683Dic3—181no—
684Dic3—181no—
685Dic3—361no—
686Dic3—361no—
687Dic3—361no—
688C32#561311yescharacteristic
689C9—21no—
690C9#561311yescharacteristic, complemented
691C23—31no—
692C23—91no—
693C23—271no—
694C23—542no—
695C23—1081no—
696C23—1081no—
697C23C2×D3×D911yescharacteristic
698C23C2×D3×D911yescharacteristic
699Q8—1081no—
700D4—41no—
701D4—121no—
702D4—121no—
703D4—361no—
704D4—361no—
705D4—542no—
706D4—542no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—121no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—271no—
717C2×C4—361no—
718C2×C4—1081no—
719C2×C4—1081no—
720C2×C4C2×D3×D911yescharacteristic
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—81no—
729C2×C3—81no—
730C2×C3—121no—
731C2×C3—361no—
732C2×C3#6371011yescharacteristic
733C2×C3#6371011yescharacteristic
734C2×C3#41×D911yescharacteristic
735C2×C3#6431211yescharacteristic
736C2×C3#6431311yescharacteristic
737C2×C3#6433011yescharacteristic
738D3—41no—
739D3—121no—
740D3—182no—
741D3—182no—
742D3—362no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—272no—
756C22—541no—
757C22—541no—
758C22—1084no—
759C22C22×D3×D911yescharacteristic
760C4—21no—
761C4—61no—
762C4—61no—
763C4—61no—
764C4—181no—
765C4—181no—
766C4—181no—
767C4—541no—
768C4—541no—
769C4—541no—
770C3—21no—
771C3#1058971511yescharacteristic, complemented
772C3#1059531111yescharacteristic
773C2—41no—
774C2—41no—
775C2—121no—
776C2—361no—
777C2—542no—
778C2#1172249811yescharacteristic
779C2#1172249911yescharacteristic
780C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11721838C2semidirect
2. C9×#939C2semidirect
3. C3×#63501C2semidirect
4. #11721292C2semidirect
5. #11721292C2semidirect
6. #11721265C2semidirect
7. #11721263C2semidirect
8. #11721259C2semidirect
9. #11721257C2semidirect
10. #11721241C2semidirect
11. #11721240C2semidirect
12. #11721048C2semidirect
13. #11720965C2semidirect
14. #11720949C2semidirect
15. #11720923C2semidirect
19. C2×C3×D4×C9C22semidirect
27. C22×C9×Dic3C22semidirect
28. C22×C3×Dic9C22semidirect
30. C2×#6189C22semidirect
31. #88551C22semidirect
32. #88551C22semidirect
33. C4⋊(C3⋊Dic9)C22semidirect
34. C9×#217C22semidirect
35. C3×#3676C22semidirect
38. C9×Dic3⋊C4C22semidirect
39. C3×Dic9⋊C4C22semidirect
48. #88442C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
69. #63501D3semidirect
155. C2×D4×C9C2×D3semidirect
163. C22×Dic9C2×D3semidirect
178. #3676C2×D3semidirect
190. Dic9⋊C4C2×D3semidirect
223. #939D9semidirect
338. C2×C3×D4C2×D9semidirect
353. C22×Dic3C2×D9semidirect
380. #217C2×D9semidirect
403. Dic3⋊C4C2×D9semidirect
491. C3×C9#538semidirect
593. C2×D4D3×D9semidirect
690. C9#5613semidirect
771. C3#10589715semidirect

Maximal subgroups

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

subgroupindex
#117218382
C9×#9392
C3×#635012
#117212922
#117212652
#117212632
#117212592
#117212572
#117212412
#117212402
#117210482
#117209652
#117209492
#117209232
#105953113
#105897153