Finite Group Databasebeta

← #13148190

Subgroups — #13148190

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
2C3×#63444C211yesmaximal, characteristic, complemented
3C9×#879C211yesmaximal, characteristic, complemented
4#11721276C211yesmaximal, characteristic, complemented
5#11721271C211yesmaximal, characteristic, complemented
6D9×#217C211yesmaximal, characteristic, complemented
7#11721257C211yesmaximal, characteristic, complemented
8#11721007C211yesmaximal, characteristic, complemented
9#11720999C211yesmaximal, characteristic, complemented
10Dic3×D36C211yesmaximal, characteristic, complemented
11#11720983C211yesmaximal, characteristic, complemented
12#11720981C211yesmaximal, characteristic, complemented
13#11720978C211yesmaximal, characteristic, complemented
14#11720949C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594127—31nomaximal
17#10589806—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C3×#611C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×#6192C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×#6192C2211yescharacteristic, complemented
27C2×Dic3×D9C2211yescharacteristic
28C2×Dic3×D9C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic, complemented
30C2×#6189C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88551C2211yescharacteristic
33#88536C2211yescharacteristic, complemented
34C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
35#88534C2211yescharacteristic, complemented
36C9×#217C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C4×C9×Dic3C2211yescharacteristic, complemented
44#88445C2211yescharacteristic, complemented
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64092—31no—
54C3×#882—31no—
55C3×#879D311yescharacteristic
56#63977—31no—
57#63971—31no—
58D3×#217—31no—
59#63959—31no—
60#63916—31no—
61#63899—31no—
62Dic3×D12—31no—
63#63886—31no—
64#63884—31no—
65#63881—31no—
66#63861—31no—
67#63852—31no—
68C9×#126—31no—
69#63460—31no—
70#63458—31no—
71#63457—31no—
72#63457—31no—
73#63456—31no—
74#63455—31no—
75#63447—31no—
76#63446—31no—
77#63445—31no—
78#63445—61no—
79#63444—31no—
80#63444D311yescharacteristic, complemented
81C22⋊C4×D9—31no—
82#63437—31no—
83C4×D36—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—41no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
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—
99C3×#611—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×D36—22no—
106C3×D36—41no—
107#6192—22no—
108#6192—41no—
109#6192—41no—
110Dic3×D9—41no—
111Dic3×D9—41no—
112Dic3×D9—41no—
113#6189—41no—
114#5704—91no—
115#5593—91no—
116C23×C3×D3—31no—
117C2×#638—31no—
118C2×C4×C3⋊D3—31no—
119C2×C3×#67—31no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×#627—31no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×D3×Dic3—31no—
127C2×D3×Dic3—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×#217C2×D311yescharacteristic
136C3×#217C2×D311yescharacteristic
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×Dic3⋊C4C2×D311yescharacteristic
141C3×Dic3⋊C4C2×D311yescharacteristic
142C3×C4×Dic3C2×D311yescharacteristic
143#3724—31no—
144#3722—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—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×#611—31no—
153C2×#611—61no—
154C2×#611C2×D311yescharacteristic
155C2×D36—31no—
156C2×D36—31no—
157C2×D36—31no—
158C2×D36C2×D311yescharacteristic
159C2×D36C2×D311yescharacteristic
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C2×C4×D9—61no—
165C2×Dic18—31no—
166C9×C4⋊C4—31no—
167C9×C4⋊C4—31no—
168C9×C4⋊C4—31no—
169C9×C22⋊C4—21no—
170C9×C22⋊C4—31no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4C2×D311yescharacteristic
173C42×C9—31no—
174#3676—31no—
175#3676—61no—
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—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—61no—
185(C2×D9)⋊C4C2×D311yescharacteristic
186(C2×D9)⋊C4C2×D311yescharacteristic
187C4⋊Dic9—31no—
188C4⋊Dic9—61no—
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×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—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—
218C9×Dic3—21no—
219C3×Dic9—21no—
220C3×#126—31no—
221C3×#120—91no—
222#953—91no—
223C2×#217—91no—
224#939—91no—
225#939—91no—
226#938—91no—
227#936—91no—
228#935—91no—
229D4×Dic3—91no—
230#898—91no—
231#896—91no—
232#895—91no—
233#895—91no—
234#894—91no—
235#893—91no—
236#885—91no—
237#885—91no—
238#884—91no—
239#883—91no—
240#883—91no—
241#883—181no—
242#882—31no—
243#882—91no—
244#67⋊C4—91no—
245D3×C22⋊C4—91no—
246#879—91no—
247#879D911yescharacteristic, complemented
248#878—91no—
249#875—91no—
250C4×D12—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—62no—
257C22×C3×D3—121no—
258C22×C3×D3—121no—
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—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×D12—62no—
273C3×D12—121no—
274#627—121no—
275#626—62no—
276#626—121no—
277#626—121no—
278D3×Dic3—121no—
279D3×Dic3—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9C22×D311yescharacteristic
283C22×D9—22no—
284C22×D9—31no—
285C22×D9—41no—
286C22×D9—41no—
287C22×D9—61no—
288C22×D9C22×D311yescharacteristic
289C22×D9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—31no—
294C2×C4×C9—31no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9C22×D311yescharacteristic
298C2×C4×C9C22×D311yescharacteristic
299#611—41no—
300#611—121no—
301#611—122no—
302C2×Dic9—31no—
303C2×Dic9—31no—
304C2×Dic9—31no—
305C2×Dic9—61no—
306C2×Dic9—61no—
307C2×Dic9—61no—
308C2×Dic9C22×D311yescharacteristic
309D36—22no—
310D36—41no—
311D36—62no—
312D36—121no—
313D36—121no—
314C4×D9—121no—
315C4×D9—121no—
316C4×D9—121no—
317C4×D9—121no—
318C4×D9—122no—
319Dic18—121no—
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—
326C3×D9—22no—
327C3×D9—41no—
328C3×D9—41no—
329C24×C3—91no—
330C23×D3—31no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C2×#67—31no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—181no—
341C22×Dic3—91no—
342C22×Dic3—91no—
343C22×Dic3—91no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—91no—
347C2×D12—91no—
348C2×D12—91no—
349C2×C4×D3—91no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—181no—
355C2×Dic6—91no—
356C2×Dic6—91no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4C2×D911yescharacteristic
366C3×C22⋊C4D3211yescharacteristic
367C3×C42—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—181no—
377#217C2×D911yescharacteristic
378#217C2×D911yescharacteristic
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
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—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—181no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—181no—
395C4⋊Dic3C2×D911yescharacteristic, complemented
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—181no—
401Dic3⋊C4C2×D911yescharacteristic, complemented
402Dic3⋊C4C2×D911yescharacteristic, complemented
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—32no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
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—21no—
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×C9C23×D311yescharacteristic
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
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#23712yes—
457C4×C9—21no—
458C4×C9—21no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—61no—
462C4×C9—61no—
463C4×C9—61no—
464C4×C9—61no—
465Dic9—21no—
466Dic9—61no—
467Dic9—61no—
468Dic9—61no—
469Dic9—121no—
470Dic9—121no—
471Dic9—121no—
472#126—31no—
473#126—271no—
474#124—271no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—271no—
480#121—271no—
481#121—271no—
482#120—91no—
483#120—271no—
484C4×D4—271no—
485C4×D4—271no—
486C2×C22⋊C4—271no—
487C3×C9#53811yescharacteristic, complemented, Sylow
488C23×C3—21no—
489C23×C3—91no—
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—31no—
500C22×D3—62no—
501C22×D3—91no—
502C22×D3—91no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—181no—
506C3×D4—182no—
507C3×D4—361no—
508C3×D4—361no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—91no—
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—121no—
521#67—182no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—361no—
526#67—362no—
527C2×Dic3—31no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—361no—
538C2×Dic3—361no—
539C2×Dic3—361no—
540C2×Dic3C22×D911yescharacteristic
541C2×Dic3C22×D911yescharacteristic
542C2×Dic3C22×D911yescharacteristic
543C2×Dic3C22×D911yescharacteristic
544D12—62no—
545D12—121no—
546D12—182no—
547D12—361no—
548D12—361no—
549C4×D3—361no—
550C4×D3—361no—
551C4×D3—361no—
552C4×D3—361no—
553C4×D3—361no—
554C4×D3—362no—
555Dic6—361no—
556Dic6—361no—
557C2×C32—41no—
558C2×C32D3×#4111yescharacteristic
559C2×C32#100911yescharacteristic
560C2×C32#100911yescharacteristic
561C3⋊D3—121no—
562C3×D3—62no—
563C3×D3—121no—
564C3×D3—121no—
565C2×C9—21no—
566C2×C9—21no—
567C2×C9—21no—
568C2×C9—41no—
569C2×C9—81no—
570C2×C9C2×#23711yescharacteristic
571C2×C9#100411yescharacteristic
572C2×C9#100411yescharacteristic
573D9—22no—
574D9—41no—
575D9—41no—
576D9—122no—
577D9—121no—
578C24—91no—
579C2×Q8—271no—
580C2×D4—91no—
581C2×D4—91no—
582C2×D4—91no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—271no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—271no—
602C22⋊C4—271no—
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—92no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
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—32no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
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—61no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—61no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—361no—
677Dic3—361no—
678Dic3—361no—
679C32#570411yescharacteristic
680C9—21no—
681C9#559311yescharacteristic, complemented
682C23—91no—
683C23—91no—
684C23—91no—
685C23—182no—
686C23—271no—
687C23—361no—
688C23—361no—
689C23C2×D3×D911yescharacteristic
690Q8—1081no—
691D4—182no—
692D4—361no—
693D4—361no—
694D4—542no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—91no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—1081no—
707C2×C4—1081no—
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—182no—
719C2×C3—361no—
720C2×C3—361no—
721C2×C3#41×D911yescharacteristic
722C2×C3#6371511yescharacteristic
723C2×C3#6371511yescharacteristic
724C2×C3#6430711yescharacteristic
725C2×C3D3×#23711yescharacteristic
726C2×C3#6431411yescharacteristic
727D3—62no—
728D3—121no—
729D3—121no—
730D3—362no—
731D3—361no—
732D3—361no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—92no—
737C22—181no—
738C22—181no—
739C22—181no—
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—61no—
756C4—181no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—21no—
761C3#1058980611yescharacteristic, complemented
762C3#1059412711yescharacteristic
763C2—41no—
764C2—182no—
765C2—361no—
766C2—361no—
767C2—1081no—
768C2#1172247711yescharacteristic
769C2D9×#23711yescharacteristic
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. C3×#63444C2semidirect
3. C9×#879C2semidirect
4. #11721276C2semidirect
5. #11721271C2semidirect
6. D9×#217C2semidirect
7. #11721257C2semidirect
8. #11721007C2semidirect
9. #11720999C2semidirect
10. Dic3×D36C2semidirect
11. #11720983C2semidirect
12. #11720981C2semidirect
13. #11720978C2semidirect
14. #11720949C2semidirect
15. #11720940C2semidirect
20. C2×C4×C3⋊D9C22semidirect
26. C2×#6192C22semidirect
29. C2×Dic3×D9C22semidirect
30. C2×#6189C22semidirect
33. #88536C22semidirect
34. C4⋊(C3⋊Dic9)C22semidirect
35. #88534C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C4×C9×Dic3C22semidirect
44. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
80. #63444D3semidirect
247. #879D9semidirect
395. C4⋊Dic3C2×D9semidirect
401. Dic3⋊C4C2×D9semidirect
402. Dic3⋊C4C2×D9semidirect
405. C4×Dic3C2×D9semidirect
487. C3×C9#538semidirect
681. C9#5593semidirect
761. C3#10589806semidirect

Maximal subgroups

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

subgroupindex
#117217292
C3×#634442
C9×#8792
#117212762
#117212712
D9×#2172
#117212572
#117210072
#117209992
Dic3×D362
#117209832
#117209812
#117209782
#117209492
#117209402
#105941273
#105898063