Finite Group Databasebeta

← #13148375

Subgroups — #13148375

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721727C211yesmaximal, characteristic, complemented
2C9×#882C211yesmaximal, characteristic, complemented
3C3×#63440C211yesmaximal, characteristic, complemented
4#11721288C211yesmaximal, characteristic, complemented
5#11721287C211yesmaximal, characteristic, complemented
6#67⋊Dic9C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
8#11721045C211yesmaximal, characteristic, complemented
9#11721035C211yesmaximal, characteristic, complemented
10#11721017C211yesmaximal, characteristic, complemented
11#11721015C211yesmaximal, characteristic, complemented
12#11720967C211yesmaximal, characteristic, complemented
13#11720966C211yesmaximal, characteristic, complemented
14#11720962C211yesmaximal, characteristic, complemented
15#11720957C211yesmaximal, characteristic, complemented
16#10594173—31nomaximal
17#10589695—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic
25C2×C9×D12C2211yescharacteristic
26C2×C3×Dic18C2211yescharacteristic, complemented
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×#6195C2211yescharacteristic, complemented
30C2×D3×Dic9C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88536C2211yescharacteristic, complemented
33#88534C2211yescharacteristic, complemented
34C4×C3⋊Dic9C2211yescharacteristic, complemented
35C3×#3676C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C3×C4⋊Dic9C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×Dic9⋊C4C2211yescharacteristic, complemented
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64090—31no—
54C3×#882D311yescharacteristic
55C3×#878—31no—
56#63978—31no—
57#63977—31no—
58#67⋊Dic3—31no—
59C2×(C2×D3)⋊Dic3—31no—
60#63916—31no—
61#63907—31no—
62#63886—31no—
63#63884—31no—
64#63863—31no—
65#63862—31no—
66#63858—31no—
67#63853—31no—
68C9×#120—31no—
69#63515—31no—
70C2×#3676—31no—
71#63501—31no—
72#63501—31no—
73#63500—31no—
74#63498—31no—
75#63497—31no—
76D4×Dic9—31no—
77#63447—31no—
78#63445—31no—
79#611⋊C4—31no—
80#611⋊C4—61no—
81#63441—31no—
82#63441—31no—
83#63440D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9—22no—
87C22×D3×C9—41no—
88C22×D3×C9—41no—
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95C2×C3⋊Dic9—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C4×C3⋊D9—41no—
100C9×#67—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9—41no—
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×D12—41no—
108C9×D12—41no—
109C3×Dic18—41no—
110#6195—41no—
111#6195—41no—
112#6195—41no—
113D3×Dic9—41no—
114#5644—91no—
115#5593—91no—
116C23×C3×D3C2×D311yescharacteristic
117C2×#638—31no—
118C22×C3⋊Dic3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C3×#67C2×D311yescharacteristic
121C22×C3×Dic3—31no—
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×D12C2×D311yescharacteristic
124C2×C3×Dic6—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×D3×Dic3—31no—
129C24×C9—31no—
130C32×C22⋊C4C2×D311yescharacteristic
131#3752—31no—
132#3750—31no—
133C4×C3⋊Dic3—31no—
134C3×#217—31no—
135C3×(C2×D3)⋊C4C2×D311yescharacteristic
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×C4⋊Dic3—31no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142#3722—31no—
143(C2×D3)⋊Dic3—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—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×D4×C9—31no—
153C2×D4×C9—31no—
154C2×D4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—31no—
159C2×#611—61no—
160C22×Dic9—31no—
161C22×Dic9—31no—
162C22×Dic9—61no—
163C22×Dic9C2×D311yescharacteristic
164C2×C4×D9—31no—
165C2×C4×D9—61no—
166C2×Dic18C2×D311yescharacteristic, complemented
167C9×C22⋊C4—21no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4C2×D311yescharacteristic
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—31no—
176#3676—31no—
177#3676—31no—
178#3676—31no—
179#3676C2×D311yescharacteristic
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—61no—
183C4⋊Dic9—31no—
184C4⋊Dic9C2×D311yescharacteristic, complemented
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—61no—
188Dic9⋊C4C2×D311yescharacteristic, complemented
189Dic9⋊C4C2×D311yescharacteristic, complemented
190C4×Dic9—31no—
191C4×Dic9—31no—
192C4×Dic9—61no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
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×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—44no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C9×Dic3—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×C22⋊Q8—91no—
221C3×#120—31no—
222#953—91no—
223C2×#217—91no—
224#947—91no—
225#947—91no—
226#939—91no—
227#939—91no—
228#938—91no—
229#936—91no—
230#935—91no—
231D4×Dic3—91no—
232#930—91no—
233C2×(C2×D3)⋊C4—91no—
234#898—91no—
235#898—91no—
236#895—91no—
237#895—91no—
238#894—91no—
239#894—91no—
240#885—91no—
241#883—91no—
242#882—91no—
243#882D911yescharacteristic, complemented
244#67⋊C4—91no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247#67⋊C4—181no—
248#879—91no—
249#879—91no—
250#878—31no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3×D3—22no—
254C22×C3×D3—41no—
255C22×C3×D3—41no—
256C22×C3×D3C22×D311yescharacteristic
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—121no—
266C4×C3⋊D3—121no—
267C3×#67—22no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—121no—
273C2×C3×Dic3C22×D311yescharacteristic
274C3×D12—41no—
275C3×D12—41no—
276C3×Dic6—121no—
277#626—121no—
278#626—121no—
279#626—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9—31no—
284C23×C9—31no—
285C23×C9—62no—
286C23×C9—121no—
287C23×C9—121no—
288C23×C9C22×D311yescharacteristic
289C22×D9—31no—
290C22×D9—61no—
291D4×C9—62no—
292D4×C9—121no—
293D4×C9—121no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—31no—
297C2×C4×C9C22×D311yescharacteristic
298C2×C4×C9C22×D311yescharacteristic
299#611—64no—
300#611—62no—
301#611—121no—
302#611—121no—
303#611—121no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—41no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—121no—
312C2×Dic9—121no—
313C2×Dic9—122no—
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317C2×Dic9C22×D311yescharacteristic
318C4×D9—121no—
319C4×D9—122no—
320Dic18—41no—
321#538—271noSylow
322C2×C3×C9—22no—
323C2×C3×C9C2×#4111yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C2×C3×C9H(5,𝔽2)11yescharacteristic
326C3⋊D9—41no—
327D3×C9—41no—
328D3×C9—41no—
329D3×C9—41no—
330C24×C3—31no—
331C23×D3C2×D911yescharacteristic
332C2×C3×Q8—91no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C22×C3×C4—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—181no—
343C2×#67C2×D911yescharacteristic
344C22×Dic3—31no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348C22×Dic3—181no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12C2×D911yescharacteristic
353C2×D12C2×D911yescharacteristic
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—181no—
358C2×Dic6—31no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4—91no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4C2×D911yescharacteristic
367C3×C22⋊C4D3211yescharacteristic
368#217—31no—
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(C2×D3)⋊C4—91no—
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—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—181no—
390(C2×D3)⋊C4C2×D911yescharacteristic
391(C2×D3)⋊C4C2×D911yescharacteristic
392C4⋊Dic3—31no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—181no—
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—181no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32#23712yes—
410C22×C32C23×D311yescharacteristic
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—61no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—44no—
424C32×C4—21no—
425C32×C4—21no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—22no—
438C22×C9—41no—
439C22×C9—41no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9—61no—
445C22×C9—61no—
446C22×C9—61no—
447C22×C9—61no—
448C22×C9—61no—
449C22×C9—124no—
450C22×C9#23912yes—
451C22×C9C23×D311yescharacteristic
452C2×D9—62no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—121no—
457C2×D9—121no—
458C4×C9—21no—
459C4×C9—21no—
460C4×C9—41no—
461C4×C9—41no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—21no—
465Dic9—21no—
466Dic9—21no—
467Dic9—62no—
468Dic9—62no—
469Dic9—61no—
470Dic9—61no—
471Dic9—61no—
472Dic9—121no—
473#126—271no—
474#126—271no—
475#124—271no—
476#124—271no—
477#123—271no—
478#123—271no—
479C22⋊Q8—91no—
480#121—271no—
481#121—271no—
482#121—271no—
483#120—31no—
484#120—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C22⋊C4—271no—
488C3×C9#53811yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—62no—
494C23×C3—121no—
495C23×C3—121no—
496C23×C3C22×D911yescharacteristic
497C23×C3C2×D3211yescharacteristic
498C22×D3—22no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—91no—
502C22×D3—91no—
503C22×D3—181no—
504C22×D3C22×D911yescharacteristic
505C22×D3C22×D911yescharacteristic
506C22×D3C22×D911yescharacteristic
507C3×Q8—361no—
508C3×D4—62no—
509C3×D4—121no—
510C3×D4—121no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—361no—
519C2×C3×C4C22×D911yescharacteristic
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523#67—22no—
524#67—184no—
525#67—182no—
526#67—182no—
527#67—361no—
528#67—361no—
529#67—361no—
530C2×Dic3—31no—
531C2×Dic3—31no—
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—121no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—181no—
544C2×Dic3—361no—
545C2×Dic3—361no—
546C2×Dic3—361no—
547C2×Dic3—362no—
548C2×Dic3C22×D911yescharacteristic
549D12—41no—
550D12—41no—
551D12—361no—
552D12—361no—
553D12—361no—
554C4×D3—361no—
555C4×D3—361no—
556C4×D3—362no—
557C4×D3—361no—
558Dic6—121no—
559C2×C32—22no—
560C2×C32C2×#23711yescharacteristic
561C2×C32#100411yescharacteristic
562C2×C32#100411yescharacteristic
563C3⋊D3—121no—
564C3×D3—41no—
565C3×D3—41no—
566C3×D3—41no—
567C2×C9—22no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—42no—
572C2×C9—121no—
573C2×C9—121no—
574C2×C9—121no—
575C2×C9#100411yescharacteristic
576C2×C9C2×#23911yescharacteristic
577C2×C9#100911yescharacteristic
578D9—122no—
579D9—121no—
580C24—31no—
581C2×Q8—91no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—91no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4—271no—
593C4⋊C4—91no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—91no—
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⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4D3×D911yescharacteristic
613C42—271no—
614C42—271no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—124no—
633C22×C3#369912yes—
634C22×C3C23×D911yescharacteristic
635C22×C3#379612yes—
636C22×C3C22×D3211yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—44no—
647C2×D3—182no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—361no—
655C2×D3—361no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—181no—
664C3×C4—181no—
665C3×C4—181no—
666C3×C4—181no—
667Dic3—21no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—182no—
673Dic3—182no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—181no—
680Dic3—361no—
681C32#559311yescharacteristic
682C9—21no—
683C9#564411yescharacteristic, complemented
684C23—31no—
685C23—31no—
686C23—31no—
687C23—62no—
688C23—121no—
689C23—121no—
690C23—271no—
691C23C2×D3×D911yescharacteristic
692Q8—361no—
693D4—62no—
694D4—121no—
695D4—121no—
696D4—542no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—361no—
709C2×C4—1081no—
710C2×C4—1081no—
711C2×C4—1081no—
712C2×C4C2×D3×D911yescharacteristic
713C2×C4C2×D3×D911yescharacteristic
714C2×C3—22no—
715C2×C3—22no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—121no—
721C2×C3—121no—
722C2×C3—121no—
723C2×C3C2×#369911yescharacteristic
724C2×C3#6371011yescharacteristic
725C2×C3#6371011yescharacteristic
726C2×C3C2×#379611yescharacteristic
727C2×C3#6431311yescharacteristic
728C2×C3#6431411yescharacteristic
729D3—41no—
730D3—41no—
731D3—41no—
732D3—362no—
733D3—361no—
734D3—361no—
735C22—21no—
736C22—21no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—124no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22#8863912yes—
751C22C22×D3×D911yescharacteristic
752C4—21no—
753C4—21no—
754C4—61no—
755C4—181no—
756C4—181no—
757C4—181no—
758C4—181no—
759C4—541no—
760C4—541no—
761C4—541no—
762C3—21no—
763C3#1058969511yescharacteristic, complemented
764C3#1059417311yescharacteristic
765C2—22no—
766C2—121no—
767C2—121no—
768C2—121no—
769C2—1081no—
770C2C2×#8863911yescharacteristic
771C2#1172249911yescharacteristic
772C2#1172250011yescharacteristic
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. #11721727C2semidirect
2. C9×#882C2semidirect
3. C3×#63440C2semidirect
4. #11721288C2semidirect
5. #11721287C2semidirect
6. #67⋊Dic9C2semidirect
7. C2×(C2×D3)⋊Dic9C2semidirect
8. #11721045C2semidirect
9. #11721035C2semidirect
10. #11721017C2semidirect
11. #11721015C2semidirect
12. #11720967C2semidirect
13. #11720966C2semidirect
14. #11720962C2semidirect
15. #11720957C2semidirect
21. C2×C4×C3⋊D9C22semidirect
26. C2×C3×Dic18C22semidirect
29. C2×#6195C22semidirect
30. C2×D3×Dic9C22semidirect
32. #88536C22semidirect
33. #88534C22semidirect
34. C4×C3⋊Dic9C22semidirect
38. C3×C4⋊Dic9C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×Dic9⋊C4C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
83. #63440D3semidirect
166. C2×Dic18C2×D3semidirect
184. C4⋊Dic9C2×D3semidirect
188. Dic9⋊C4C2×D3semidirect
189. Dic9⋊C4C2×D3semidirect
243. #882D9semidirect
488. C3×C9#538semidirect
683. C9#5644semidirect
763. C3#10589695semidirect

Maximal subgroups

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

subgroupindex
#117217272
C9×#8822
C3×#634402
#117212882
#117212872
#67⋊Dic92
C2×(C2×D3)⋊Dic92
#117210452
#117210352
#117210172
#117210152
#117209672
#117209662
#117209622
#117209572
#105941733
#105896953