Finite Group Databasebeta

← #13148094

Subgroups — #13148094

Order 1728.

814 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721727C211yesmaximal, characteristic, complemented
2C9×#883C211yesmaximal, characteristic, complemented
3C3×#63446C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721271C211yesmaximal, characteristic, complemented
7#11721260C211yesmaximal, characteristic, complemented
8#11721034C211yesmaximal, characteristic, complemented
9C4×#6194C211yesmaximal, characteristic, complemented
10#11721007C211yesmaximal, characteristic, complemented
11#11720982C211yesmaximal, characteristic, complemented
12#11720975C211yesmaximal, characteristic, complemented
13#11720957C211yesmaximal, characteristic, complemented
14#11720938C211yesmaximal, characteristic, complemented
15#11720918C211yesmaximal, characteristic, complemented
16#10594151—31nomaximal
17#10589765—31nomaximal
18C2×#6233C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34#88536C2211yescharacteristic
35#88534C2211yescharacteristic
36C4×C3⋊Dic9C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64090—31no—
54C3×#884—31no—
55C3×#883D311yescharacteristic
56#63980—31no—
57#63979—31no—
58#63971—31no—
59#63962—31no—
60#63916—31no—
61#63906—31no—
62C4×#625—31no—
63#63885—31no—
64#63878—31no—
65#63853—31no—
66#63850—31no—
67#63847—31no—
68C9×#123—31no—
69#63502—31no—
70#63501—31no—
71#63492—31no—
72C4×#611—31no—
73#63457—31no—
74#63456—31no—
75#63454—31no—
76#63451—31no—
77#63448—31no—
78#63446—31no—
79#63446—31no—
80#63446D311yescharacteristic, complemented
81#63445—31no—
82#611⋊C4—31no—
83#611⋊C4—61no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91#6233—22no—
92C2×C3⋊Dic9—41no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—41no—
97C9×#67—41no—
98C3×#611—41no—
99C3×#611—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C4×D3×C9—41no—
106C3×D36—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6194—22no—
110#6194—41no—
111#6192—41no—
112#6192—41no—
113Dic3×D9—22no—
114#5663—91no—
115#5615—91no—
116C2×#638—31no—
117C22×C3⋊Dic3—31no—
118C2×C4×C3⋊D3—31no—
119C2×C3×#67—31no—
120C2×C3×#67—31no—
121C2×C3×#67C2×D311yescharacteristic
122C2×C3×D12—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#625—31no—
129C2×#625—31no—
130C2×D3×Dic3—31no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3752—31no—
133#3750—31no—
134C4×C3⋊Dic3—31no—
135C3×#217C2×D311yescharacteristic
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×C4⋊Dic3C2×D311yescharacteristic
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4C2×D311yescharacteristic
141#3724—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145#3722—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150Dic32—31no—
151C2×D4×C9—31no—
152C22×C4×C9—31no—
153C2×#611—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—61no—
158C2×#611C2×D311yescharacteristic
159C2×#611C2×D311yescharacteristic
160C22×Dic9—31no—
161C22×Dic9—61no—
162C2×D36—31no—
163C2×D36—31no—
164C2×D36C2×D311yescharacteristic
165C2×C4×D9—31no—
166C2×C4×D9—31no—
167C2×C4×D9—61no—
168C2×C4×D9C2×D311yescharacteristic
169C9×C4⋊C4—31no—
170C9×C4⋊C4—31no—
171C9×C22⋊C4—21no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4—31no—
174C9×C22⋊C4C2×D311yescharacteristic
175#3676—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—61no—
182(C2×D9)⋊C4C2×D311yescharacteristic
183C4⋊Dic9—31no—
184C4⋊Dic9—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—61no—
189Dic9⋊C4C2×D311yescharacteristic
190C4×Dic9—31no—
191C4×Dic9—31no—
192C4×Dic9—61no—
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×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—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—
209C3×C4×C9—21no—
210C3×C4×C9—21no—
211C3⋊Dic9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9#4112yes—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×#123—31no—
220C3×#121—91no—
221#940—91no—
222#940—91no—
223#939—91no—
224#939—91no—
225#939—91no—
226#939—91no—
227#938—91no—
228#935—91no—
229#930—91no—
230#929—91no—
231C4×#67—91no—
232C4×#67—91no—
233#895—91no—
234#894—91no—
235#894—91no—
236#892—91no—
237#889—91no—
238#889—91no—
239#886—91no—
240#884—31no—
241#884—91no—
242#884—91no—
243#884—91no—
244#883—91no—
245#883D911yescharacteristic, complemented
246#67⋊C4—91no—
247#67⋊C4—91no—
248#67⋊C4—181no—
249#877—91no—
250C23×C32C22×D311yescharacteristic
251C22×C3⋊D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257#638—62no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—121no—
262C4×C3⋊D3—121no—
263C3×#67—41no—
264C3×#67—121no—
265C3×#67—121no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C3×D12—121no—
272C3×C4×D3—41no—
273C3×C4×D3—121no—
274#626—121no—
275#626—121no—
276#626—121no—
277#625—62no—
278#625—121no—
279D3×Dic3—62no—
280C23×C9—21no—
281C23×C9—31no—
282C23×C9C22×D311yescharacteristic
283C22×D9—31no—
284C22×D9—61no—
285C22×D9C22×D311yescharacteristic
286C22×D9C22×D311yescharacteristic
287D4×C9—121no—
288C2×C4×C9—21no—
289C2×C4×C9—21no—
290C2×C4×C9—31no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—121no—
294C2×C4×C9C22×D311yescharacteristic
295C2×C4×C9C22×D311yescharacteristic
296#611—41no—
297#611—41no—
298#611—62no—
299#611—62no—
300#611—64no—
301#611—121no—
302#611—121no—
303C2×Dic9—31no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—61no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—121no—
310C2×Dic9—122no—
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313D36—41no—
314D36—121no—
315D36—121no—
316C4×D9—41no—
317C4×D9—62no—
318C4×D9—121no—
319C4×D9—122no—
320#540—271noSylow
321C2×C3×C9—41no—
322C2×C3×C9C2×#4111yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C3⋊D9—41no—
326D3×C9—41no—
327C3×D9—41no—
328C3×D9—41no—
329C2×C3×D4—31no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C22×C3×C4—31no—
334C22×C3×C4—91no—
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—181no—
347C2×#67C2×D911yescharacteristic
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—181no—
352C2×D12—31no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×C4×D3—31no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—181no—
361C2×C4×D3C2×D911yescharacteristic
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—91no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4C2×D911yescharacteristic
370C3×C22⋊C4D3211yescharacteristic
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217C2×D911yescharacteristic
376(C2×D3)⋊C4—31no—
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—181no—
386(C2×D3)⋊C4C2×D911yescharacteristic
387C4⋊Dic3—91no—
388C4⋊Dic3—91no—
389C4⋊Dic3C2×D911yescharacteristic
390Dic3⋊C4—31no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—181no—
400Dic3⋊C4C2×D911yescharacteristic
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—181no—
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—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C32×C4—21no—
423C32×C4—21no—
424C3⋊Dic3—32no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C22×C9—22no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—61no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9C23×D311yescharacteristic
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—62no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—121no—
454C2×D9—121no—
455C4×C9—21no—
456C4×C9—21no—
457C4×C9—41no—
458C4×C9—41no—
459C4×C9—61no—
460C4×C9—61no—
461C4×C9—61no—
462Dic9—21no—
463Dic9—21no—
464Dic9—32no—
465Dic9—62no—
466Dic9—62no—
467Dic9—61no—
468Dic9—61no—
469Dic9—121no—
470#127—271no—
471#125—271no—
472#123—31no—
473#123—271no—
474#123—271no—
475#123—271no—
476#121—91no—
477#121—271no—
478#121—271no—
479#121—271no—
480#121—271no—
481#121—271no—
482C4×D4—271no—
483C4×D4—271no—
484#117—271no—
485C3×C9#54011yescharacteristic, complemented, Sylow
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—91no—
489C23×C3—91no—
490C23×C3C22×D911yescharacteristic
491C23×C3C2×D3211yescharacteristic
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—91no—
495C22×D3—91no—
496C22×D3—181no—
497C22×D3C22×D911yescharacteristic
498C3×D4—121no—
499C3×D4—361no—
500C3×D4—361no—
501C3×D4—361no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—121no—
510C2×C3×C4—361no—
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515#67—41no—
516#67—121no—
517#67—121no—
518#67—182no—
519#67—182no—
520#67—182no—
521#67—182no—
522#67—184no—
523#67—361no—
524#67—361no—
525#67—361no—
526#67—361no—
527#67—361no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—181no—
537C2×Dic3—181no—
538C2×Dic3—181no—
539C2×Dic3—182no—
540C2×Dic3—361no—
541C2×Dic3—361no—
542C2×Dic3—362no—
543C2×Dic3C22×D911yescharacteristic
544C2×Dic3C22×D911yescharacteristic
545C2×Dic3C22×D911yescharacteristic
546D12—121no—
547D12—361no—
548D12—361no—
549D12—361no—
550C4×D3—41no—
551C4×D3—121no—
552C4×D3—182no—
553C4×D3—361no—
554C4×D3—361no—
555C4×D3—362no—
556C2×C32—41no—
557C2×C32#100411yescharacteristic
558C2×C32D3×#4111yescharacteristic
559C2×C32#100911yescharacteristic
560C3⋊D3—121no—
561C3×D3—41no—
562C3×D3—121no—
563C3×D3—121no—
564C2×C9—21no—
565C2×C9—21no—
566C2×C9—21no—
567C2×C9—42no—
568C2×C9—41no—
569C2×C9—121no—
570C2×C9#100411yescharacteristic
571C2×C9#100411yescharacteristic
572C2×C9D3×#4111yescharacteristic
573D9—41no—
574D9—41no—
575D9—122no—
576D9—121no—
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—91no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—31no—
588C22×C4—91no—
589C22×C4—271no—
590C22×C4—271no—
591C22×C4—271no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—91no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—91no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4D3×D911yescharacteristic
610C42—271no—
611C42—271no—
612C22×C3—22no—
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—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3C23×D911yescharacteristic
632C22×C3C22×D3211yescharacteristic
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—182no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—361no—
650C2×D3—361no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—181no—
661C3×C4—181no—
662Dic3—21no—
663Dic3—21no—
664Dic3—21no—
665Dic3—61no—
666Dic3—61no—
667Dic3—92no—
668Dic3—92no—
669Dic3—182no—
670Dic3—182no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—361no—
676C32#566311yescharacteristic
677C9—21no—
678C9#561511yescharacteristic, complemented
679C23—31no—
680C23—91no—
681C23—91no—
682C23—271no—
683C23C2×D3×D911yescharacteristic
684D4—121no—
685D4—361no—
686D4—361no—
687D4—361no—
688D4—542no—
689D4—542no—
690D4—1081no—
691D4—1081no—
692D4—1081no—
693D4—1081no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—121no—
700C2×C4—271no—
701C2×C4—271no—
702C2×C4—271no—
703C2×C4—361no—
704C2×C4—542no—
705C2×C4—1081no—
706C2×C4—1081no—
707C2×C4C2×D3×D911yescharacteristic
708C2×C4C2×D3×D911yescharacteristic
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—42no—
713C2×C3—41no—
714C2×C3—41no—
715C2×C3—121no—
716C2×C3—361no—
717C2×C3—361no—
718C2×C3#6371011yescharacteristic
719C2×C3#41×D911yescharacteristic
720C2×C3#6371511yescharacteristic
721C2×C3#6430611yescharacteristic
722C2×C3#6431311yescharacteristic
723C2×C3#6431411yescharacteristic
724D3—41no—
725D3—121no—
726D3—121no—
727D3—362no—
728D3—361no—
729D3—361no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—541no—
743C22—541no—
744C22—541no—
745C22C22×D3×D911yescharacteristic
746C4—21no—
747C4—21no—
748C4—61no—
749C4—61no—
750C4—61no—
751C4—181no—
752C4—181no—
753C4—272no—
754C4—541no—
755C4—541no—
756C3—21no—
757C3#1058976511yescharacteristic, complemented
758C3#1059415111yescharacteristic
759C2—41no—
760C2—121no—
761C2—361no—
762C2—361no—
763C2—1081no—
764C2#1172247511yescharacteristic
765C2#1172249911yescharacteristic
766C2#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#540
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×#883C2semidirect
3. C3×#63446C2semidirect
4. #11721290C2semidirect
5. #11721289C2semidirect
6. #11721271C2semidirect
7. #11721260C2semidirect
8. #11721034C2semidirect
9. C4×#6194C2semidirect
10. #11721007C2semidirect
11. #11720982C2semidirect
12. #11720975C2semidirect
13. #11720957C2semidirect
14. #11720938C2semidirect
15. #11720918C2semidirect
80. #63446D3semidirect
245. #883D9semidirect
485. C3×C9#540semidirect
678. C9#5615semidirect
757. C3#10589765semidirect

Maximal subgroups

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

subgroupindex
#117217272
C9×#8832
C3×#634462
#117212902
#117212892
#117212712
#117212602
#117210342
C4×#61942
#117210072
#117209822
#117209752
#117209572
#117209382
#117209182
#105941513
#105897653