Finite Group Databasebeta

← #13148182

Subgroups — #13148182

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
2C3×#63444C211yesmaximal, characteristic, complemented
3C9×#878C211yesmaximal, characteristic, complemented
4#11721277C211yesmaximal, characteristic, complemented
5#11721276C211yesmaximal, characteristic, complemented
6#611⋊Dic3C211yesmaximal, characteristic, complemented
7C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
8#11721007C211yesmaximal, characteristic, complemented
9#11721003C211yesmaximal, characteristic, complemented
10#11720983C211yesmaximal, characteristic, complemented
11#11720981C211yesmaximal, characteristic, complemented
12#11720951C211yesmaximal, characteristic, complemented
13#11720950C211yesmaximal, characteristic, complemented
14#11720946C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10594173—31nomaximal
17#10589746—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C9×Dic6C2211yescharacteristic, complemented
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic, complemented
30C2×Dic3×D9C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88536C2211yescharacteristic, complemented
33#88534C2211yescharacteristic, complemented
34C4×C3⋊Dic9C2211yescharacteristic, complemented
35C9×#217C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C9×C4⋊Dic3C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C9×Dic3⋊C4C2211yescharacteristic, complemented
41#88445C2211yescharacteristic, complemented
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64090—31no—
54C3×#882—31no—
55C3×#878D311yescharacteristic
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×C22⋊Q8—31no—
69#63509—31no—
70#63509—31no—
71#63492—31no—
72C2×(C2×D9)⋊C4—31no—
73#63460—31no—
74#63460—31no—
75#63457—31no—
76#63457—31no—
77#63456—31no—
78#63456—31no—
79#63444—31no—
80#63444D311yescharacteristic, complemented
81#611⋊C4—31no—
82#611⋊C4—31no—
83#611⋊C4—61no—
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—22no—
95C2×C3⋊Dic9—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C4×C3⋊D9—41no—
100C3×#611—22no—
101C2×C9×Dic3—41no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×D36—41no—
108C3×D36—41no—
109C9×Dic6—41no—
110#6192—41no—
111#6192—41no—
112#6192—41no—
113Dic3×D9—41no—
114#5644—91no—
115#5593—91no—
116C23×C3×D3—31no—
117C2×#638—31no—
118C22×C3⋊Dic3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C3×#67—31no—
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×D12—31no—
123C2×C3×D12—31no—
124C2×C3×Dic6C2×D311yescharacteristic
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×D3×Dic3—31no—
129C23×D9C2×D311yescharacteristic
130C32×C22⋊C4C2×D311yescharacteristic
131#3752—31no—
132#3750—31no—
133C4×C3⋊Dic3—31no—
134C3×#217C2×D311yescharacteristic
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×Dic3⋊C4C2×D311yescharacteristic
139C3×Dic3⋊C4C2×D311yescharacteristic
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×Q8×C9—31no—
153C22×C4×C9—31no—
154C2×#611—31no—
155C2×#611—61no—
156C2×#611C2×D311yescharacteristic
157C22×Dic9—31no—
158C22×Dic9—61no—
159C2×D36—31no—
160C2×D36—31no—
161C2×D36—31no—
162C2×D36C2×D311yescharacteristic
163C2×D36C2×D311yescharacteristic
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C9×C4⋊C4—31no—
168C9×C4⋊C4—31no—
169C9×C4⋊C4—31no—
170C9×C22⋊C4—21no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4C2×D311yescharacteristic
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
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—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4C2×D311yescharacteristic
185(C2×D9)⋊C4C2×D311yescharacteristic
186C4⋊Dic9—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—61no—
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×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—21no—
209C2×C3×D9—44no—
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×C22⋊Q8—31no—
221C3×#120—91no—
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—31no—
243#882—91no—
244#67⋊C4—91no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247#67⋊C4—181no—
248#879—91no—
249#879—91no—
250#878D911yescharacteristic, complemented
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—62no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—121no—
266C4×C3⋊D3—121no—
267C3×#67—62no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C3×D12—121no—
275C3×D12—121no—
276C3×Dic6—41no—
277#626—121no—
278#626—121no—
279#626—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
291Q8×C9—121no—
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—31no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—121no—
299C2×C4×C9C22×D311yescharacteristic
300C2×C4×C9C22×D311yescharacteristic
301#611—22no—
302#611—64no—
303#611—62no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—121no—
311C2×Dic9—122no—
312C2×Dic9C22×D311yescharacteristic
313D36—41no—
314D36—41no—
315D36—121no—
316D36—121no—
317D36—121no—
318C4×D9—121no—
319C4×D9—122no—
320C4×D9—121no—
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—
327C3×D9—41no—
328C3×D9—41no—
329C3×D9—41no—
330C24×C3—91no—
331C23×D3—31no—
332C2×C3×Q8—31no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C22×C3×C4—31no—
337C2×#67—31no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—181no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C22×Dic3—181no—
348C22×Dic3C2×D911yescharacteristic
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—181no—
358C2×Dic6C2×D911yescharacteristic, complemented
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4C2×D911yescharacteristic
367C3×C22⋊C4D3211yescharacteristic
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#217C2×D911yescharacteristic
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
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—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—181no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3C2×D911yescharacteristic, complemented
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—181no—
400Dic3⋊C4C2×D911yescharacteristic, complemented
401Dic3⋊C4C2×D911yescharacteristic, complemented
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—181no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32#23912yes—
410C22×C32C23×D311yescharacteristic
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—61no—
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—61no—
423C2×C3×D3—124no—
424C32×C4—21no—
425C32×C4—21no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—61no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—22no—
438C22×C9—41no—
439C22×C9—41no—
440C22×C9#23712yes—
441C22×C9C23×D311yescharacteristic
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—44no—
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—
463C4×C9—61no—
464C4×C9—61no—
465C4×C9—61no—
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—31no—
480#121—271no—
481#121—271no—
482#121—271no—
483#120—91no—
484#120—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C22⋊C4—271no—
488C3×C9#53811yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—91no—
491C23×C3—91no—
492C23×C3—91no—
493C23×C3—182no—
494C23×C3—361no—
495C23×C3—361no—
496C23×C3C22×D911yescharacteristic
497C23×C3C2×D3211yescharacteristic
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—62no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—181no—
507C3×Q8—121no—
508C3×D4—182no—
509C3×D4—361no—
510C3×D4—361no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—91no—
518C2×C3×C4—121no—
519C2×C3×C4C22×D911yescharacteristic
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523#67—62no—
524#67—184no—
525#67—182no—
526#67—182no—
527#67—361no—
528#67—361no—
529#67—361no—
530C2×Dic3—31no—
531C2×Dic3—41no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—181no—
539C2×Dic3—181no—
540C2×Dic3—181no—
541C2×Dic3—361no—
542C2×Dic3—361no—
543C2×Dic3—361no—
544C2×Dic3—362no—
545C2×Dic3C22×D911yescharacteristic
546C2×Dic3C22×D911yescharacteristic
547C2×Dic3C22×D911yescharacteristic
548C2×Dic3C22×D911yescharacteristic
549D12—121no—
550D12—121no—
551D12—361no—
552D12—361no—
553D12—361no—
554C4×D3—361no—
555C4×D3—361no—
556C4×D3—362no—
557C4×D3—361no—
558Dic6—41no—
559C2×C32—22no—
560C2×C32#100411yescharacteristic
561C2×C32C2×#23911yescharacteristic
562C2×C32#100911yescharacteristic
563C3⋊D3—121no—
564C3×D3—121no—
565C3×D3—121no—
566C3×D3—121no—
567C2×C9—22no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—42no—
572C2×C9C2×#23711yescharacteristic
573C2×C9#100411yescharacteristic
574C2×C9#100411yescharacteristic
575D9—41no—
576D9—41no—
577D9—41no—
578D9—122no—
579D9—121no—
580C24—91no—
581C2×Q8—31no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—91no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—31no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4—271no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—91no—
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—181no—
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×C3#370112yes—
634C22×C3C23×D911yescharacteristic
635C22×C3#379612yes—
636C22×C3C22×D3211yescharacteristic
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—124no—
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—61no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—181no—
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—61no—
672Dic3—182no—
673Dic3—182no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—181no—
680Dic3—361no—
681C32#564411yescharacteristic
682C9—21no—
683C9#559311yescharacteristic, complemented
684C23—91no—
685C23—91no—
686C23—91no—
687C23—182no—
688C23—271no—
689C23—361no—
690C23—361no—
691C23C2×D3×D911yescharacteristic
692Q8—121no—
693D4—182no—
694D4—361no—
695D4—361no—
696D4—542no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—91no—
705C2×C4—121no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—271no—
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—361no—
721C2×C3—361no—
722C2×C3—361no—
723C2×C3#6371011yescharacteristic
724C2×C3C2×#370111yescharacteristic
725C2×C3#6371511yescharacteristic
726C2×C3C2×#379611yescharacteristic
727C2×C3#6431311yescharacteristic
728C2×C3#6431411yescharacteristic
729D3—121no—
730D3—121no—
731D3—121no—
732D3—362no—
733D3—361no—
734D3—361no—
735C22—21no—
736C22—21no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—181no—
746C22—364no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22#8863412yes—
751C22C22×D3×D911yescharacteristic
752C4—21no—
753C4—21no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—181no—
759C4—541no—
760C4—541no—
761C4—541no—
762C3—21no—
763C3#1058974611yescharacteristic, complemented
764C3#1059417311yescharacteristic
765C2—22no—
766C2—361no—
767C2—361no—
768C2—361no—
769C2—1081no—
770C2C2×#8863411yescharacteristic
771C2#1172249911yescharacteristic
772C2#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. #11721727C2semidirect
2. C3×#63444C2semidirect
3. C9×#878C2semidirect
4. #11721277C2semidirect
5. #11721276C2semidirect
6. #611⋊Dic3C2semidirect
7. C2×(C2×D9)⋊Dic3C2semidirect
8. #11721007C2semidirect
9. #11721003C2semidirect
10. #11720983C2semidirect
11. #11720981C2semidirect
12. #11720951C2semidirect
13. #11720950C2semidirect
14. #11720946C2semidirect
15. #11720941C2semidirect
21. C2×C4×C3⋊D9C22semidirect
26. C2×C9×Dic6C22semidirect
29. C2×#6192C22semidirect
30. C2×Dic3×D9C22semidirect
32. #88536C22semidirect
33. #88534C22semidirect
34. C4×C3⋊Dic9C22semidirect
38. C9×C4⋊Dic3C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C9×Dic3⋊C4C22semidirect
41. #88445C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
80. #63444D3semidirect
250. #878D9semidirect
358. C2×Dic6C2×D9semidirect
394. C4⋊Dic3C2×D9semidirect
400. Dic3⋊C4C2×D9semidirect
401. Dic3⋊C4C2×D9semidirect
488. C3×C9#538semidirect
683. C9#5593semidirect
763. C3#10589746semidirect

Maximal subgroups

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

subgroupindex
#117217272
C3×#634442
C9×#8782
#117212772
#117212762
#611⋊Dic32
C2×(C2×D9)⋊Dic32
#117210072
#117210032
#117209832
#117209812
#117209512
#117209502
#117209462
#117209412
#105941733
#105897463