Finite Group Databasebeta

← #13148359

Subgroups — #13148359

Order 1728.

814 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721730C211yesmaximal, characteristic, complemented
2C9×#886C211yesmaximal, characteristic, complemented
3C3×#63445C211yesmaximal, characteristic, complemented
4#11721289C211yesmaximal, characteristic, complemented
5#11721282C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7#11721240C211yesmaximal, characteristic, complemented
8#11721041C211yesmaximal, characteristic, complemented
9#11721039C211yesmaximal, characteristic, complemented
10#11721020C211yesmaximal, characteristic, complemented
11#11721012C211yesmaximal, characteristic, complemented
12#11721004C211yesmaximal, characteristic, complemented
13#11720942C211yesmaximal, characteristic, complemented
14#11720922C211yesmaximal, characteristic, complemented
15#11720918C211yesmaximal, characteristic, complemented
16#10594161—31nomaximal
17#10589765—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×D3×Dic9C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34#88536C2211yescharacteristic
35#88534C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic
41C9×C4⋊Dic3C2211yescharacteristic
42C3×C4⋊Dic9C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64093—31no—
54C3×#886D311yescharacteristic
55C3×#883—31no—
56#63979—31no—
57#63978—31no—
58#63971—31no—
59#63952—31no—
60#63912—31no—
61#63910—31no—
62#63909—31no—
63#63890—31no—
64#63879—31no—
65#63854—31no—
66#63849—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#63446—31no—
81#63446—61no—
82#63445D311yescharacteristic, complemented
83#611⋊C4—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91#6233—22no—
92#6233—41no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4⋊(C3⋊D9)—41no—
96C4×C3⋊D9—22no—
97C9×#67—41no—
98C3×#611—41no—
99C2×C9×Dic3—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×C4×D9—41no—
107#6195—41no—
108#6195—41no—
109#6194—22no—
110D3×Dic9—41no—
111#6192—41no—
112#6192—41no—
113(C3⋊D9)⋊C4—41no—
114#5663—91no—
115#5663—91no—
116C2×#638—31no—
117C2×#638—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4×C3⋊D3—31no—
120C2×C3×#67—31no—
121C2×C3×#67C2×D311yescharacteristic
122C22×C3×Dic3C2×D311yescharacteristic
123C2×C3×C4×D3—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#625—31no—
129C2×#624—31no—
130C2×D3×Dic3—31no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3752—31no—
133#3750—31no—
134C3×#217—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—31no—
142#3724—31no—
143#3724—31no—
144Dic3⋊Dic3—31no—
145#3722—31no—
146#3722—31no—
147#3722—31no—
148(C2×D3)⋊Dic3—31no—
149Dic32—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—31no—
158C2×#611—61no—
159C2×#611—61no—
160C2×#611C2×D311yescharacteristic
161C22×Dic9—31no—
162C2×D36—31no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—61no—
166C2×C4×D9—31no—
167C2×C4×D9—31no—
168C2×C4×D9—61no—
169C2×C4×D9C2×D311yescharacteristic
170C9×C4⋊C4—31no—
171C9×C4⋊C4—31no—
172C9×C22⋊C4—21no—
173C9×C22⋊C4—31no—
174C9×C22⋊C4—31no—
175C9×C22⋊C4C2×D311yescharacteristic
176#3676C2×D311yescharacteristic
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—61no—
183(C2×D9)⋊C4C2×D311yescharacteristic
184C4⋊Dic9—31no—
185C4⋊Dic9C2×D311yescharacteristic
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—61no—
190Dic9⋊C4C2×D311yescharacteristic
191C4×Dic9—31no—
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×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—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#4112yes—
213C9×Dic3—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×#123—31no—
220C3×#123—91no—
221#940—91no—
222#940—91no—
223#939—91no—
224#939—91no—
225#930—91no—
226#930—91no—
227C4×#67—91no—
228C4×#67—91no—
229#895—91no—
230#895—91no—
231#894—91no—
232#894—91no—
233#892—91no—
234#892—91no—
235#889—91no—
236#889—91no—
237#886—91no—
238#886D911yescharacteristic, complemented
239#884—91no—
240#884—91no—
241#884—91no—
242#884—91no—
243#884—91no—
244#884—91no—
245#884—181no—
246#883—31no—
247#883—91no—
248#67⋊C4—91no—
249#67⋊C4—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—
258#638—121no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C4⋊(C3⋊D3)—121no—
262C4×C3⋊D3—62no—
263C3×#67—41no—
264C3×#67—121no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—41no—
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×C4×D3—121no—
273#626—121no—
274#626—121no—
275#626—121no—
276#626—121no—
277#625—62no—
278#624—121no—
279D3×Dic3—121no—
280C23×C9—21no—
281C23×C9—31no—
282C23×C9C22×D311yescharacteristic
283C22×D9—31no—
284C22×D9—31no—
285C22×D9—61no—
286C22×D9—61no—
287C22×D9C22×D311yescharacteristic
288D4×C9—121no—
289C2×C4×C9—21no—
290C2×C4×C9—21no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—31no—
294C2×C4×C9—121no—
295C2×C4×C9C22×D311yescharacteristic
296C2×C4×C9C22×D311yescharacteristic
297#611—41no—
298#611—62no—
299#611—62no—
300#611—122no—
301#611—121no—
302#611—121no—
303#611—121no—
304#611—122no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—121no—
310C2×Dic9C22×D311yescharacteristic
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313D36—121no—
314D36—122no—
315D36—121no—
316D36—121no—
317C4×D9—41no—
318C4×D9—62no—
319C4×D9—122no—
320C4×D9—121no—
321#540—271noSylow
322C2×C3×C9—41no—
323C2×C3×C9C2×#4111yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C2×C3×C9H(5,𝔽2)11yescharacteristic
326C3⋊D9—41no—
327C3⋊D9—41no—
328D3×C9—41no—
329C3×D9—41no—
330C2×C3×D4—31no—
331C2×C3×D4—91no—
332C22×C3×C4—31no—
333C22×C3×C4—91no—
334C2×#67—31no—
335C2×#67—91no—
336C2×#67—91no—
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—181no—
346C2×#67—181no—
347C2×#67C2×D911yescharacteristic
348C22×Dic3—91no—
349C22×Dic3C2×D911yescharacteristic
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×D12—181no—
357C2×C4×D3—31no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—181no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4C2×D911yescharacteristic
374C3×C22⋊C4D3211yescharacteristic
375#217—31no—
376#217—91no—
377(C2×D3)⋊C4—31no—
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—181no—
388(C2×D3)⋊C4C2×D911yescharacteristic
389(C2×D3)⋊C4C2×D911yescharacteristic
390C4⋊Dic3—31no—
391C4⋊Dic3—91no—
392C4⋊Dic3C2×D911yescharacteristic
393C4⋊Dic3C2×D911yescharacteristic
394Dic3⋊C4—31no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—181no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—91no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
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—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C32×C4—21no—
424C32×C4—21no—
425C3⋊Dic3—32no—
426C3⋊Dic3—61no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—61no—
431C3×Dic3—61no—
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×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—62no—
448C2×D9—61no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9—121no—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—41no—
462C4×C9—41no—
463C4×C9—61no—
464C4×C9—61no—
465C4×C9—61no—
466Dic9—21no—
467Dic9—21no—
468Dic9—21no—
469Dic9—32no—
470Dic9—62no—
471Dic9—61no—
472Dic9—121no—
473#127—271no—
474#125—271no—
475#123—31no—
476#123—91no—
477#123—271no—
478#123—271no—
479#121—271no—
480#121—271no—
481#121—271no—
482#121—271no—
483#121—271no—
484#121—271no—
485C4×D4—271no—
486C4×D4—271no—
487#117—271no—
488C3×C9#54011yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—91no—
492C23×C3C22×D911yescharacteristic
493C23×C3C2×D3211yescharacteristic
494C22×D3—31no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—91no—
498C22×D3—91no—
499C22×D3—181no—
500C22×D3—181no—
501C22×D3C22×D911yescharacteristic
502C3×D4—121no—
503C3×D4—361no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—121no—
513C2×C3×C4—361no—
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518#67—41no—
519#67—121no—
520#67—182no—
521#67—182no—
522#67—182no—
523#67—182no—
524#67—362no—
525#67—361no—
526#67—361no—
527#67—361no—
528#67—361no—
529#67—361no—
530#67—361no—
531#67—362no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—41no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—361no—
543C2×Dic3C22×D911yescharacteristic
544C2×Dic3C22×D911yescharacteristic
545C2×Dic3C22×D911yescharacteristic
546D12—361no—
547D12—361no—
548D12—362no—
549D12—361no—
550D12—361no—
551D12—361no—
552D12—361no—
553C4×D3—121no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—362no—
557C4×D3—361no—
558C4×D3—361no—
559C4×D3—361no—
560C2×C32—41no—
561C2×C32#100411yescharacteristic
562C2×C32D3×#4111yescharacteristic
563C2×C32#100911yescharacteristic
564C3⋊D3—121no—
565C3⋊D3—121no—
566C3×D3—41no—
567C3×D3—121no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—41no—
572C2×C9—81no—
573C2×C9—121no—
574C2×C9#100411yescharacteristic
575C2×C9D3×#4111yescharacteristic
576C2×C9#100911yescharacteristic
577D9—41no—
578D9—122no—
579D9—121no—
580D9—121no—
581D9—241no—
582C2×D4—31no—
583C2×D4—91no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C22×C4—31no—
593C22×C4—91no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4D3×D911yescharacteristic
615C42—271no—
616C42—271no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3C23×D911yescharacteristic
634C22×C3C22×D3211yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—182no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—361no—
655C2×D3—361no—
656C2×D3—361no—
657C2×D3—361no—
658C2×D3—361no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—181no—
669C3×C4—181no—
670C3×C4—181no—
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—92no—
678Dic3—92no—
679Dic3—182no—
680Dic3—181no—
681Dic3—181no—
682Dic3—361no—
683C32#566311yescharacteristic
684C9—21no—
685C9#566311yescharacteristic, complemented
686C23—31no—
687C23—91no—
688C23—271no—
689C23—271no—
690C23C2×D3×D911yescharacteristic
691D4—121no—
692D4—361no—
693D4—542no—
694D4—542no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700D4—1081no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—121no—
708C2×C4—271no—
709C2×C4—271no—
710C2×C4—361no—
711C2×C4—542no—
712C2×C4—1081no—
713C2×C4—1081no—
714C2×C4C2×D3×D911yescharacteristic
715C2×C4C2×D3×D911yescharacteristic
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—41no—
720C2×C3—41no—
721C2×C3—81no—
722C2×C3—121no—
723C2×C3—361no—
724C2×C3#6371011yescharacteristic
725C2×C3#41×D911yescharacteristic
726C2×C3#6371511yescharacteristic
727C2×C3#6430711yescharacteristic
728C2×C3#6431211yescharacteristic
729C2×C3#6431411yescharacteristic
730D3—41no—
731D3—121no—
732D3—362no—
733D3—361no—
734D3—361no—
735D3—361no—
736D3—361no—
737D3—721no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—181no—
745C22—181no—
746C22—181no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22—541no—
751C22—541no—
752C22—541no—
753C22C22×D3×D911yescharacteristic
754C4—21no—
755C4—21no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—272no—
763C4—541no—
764C3—21no—
765C3#1058976511yescharacteristic, complemented
766C3#1059416111yescharacteristic
767C2—41no—
768C2—121no—
769C2—361no—
770C2—1081no—
771C2—1081no—
772C2#1172247611yescharacteristic
773C2#1172249811yescharacteristic
774C2#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. #11721730C2semidirect
2. C9×#886C2semidirect
3. C3×#63445C2semidirect
4. #11721289C2semidirect
5. #11721282C2semidirect
6. #11721277C2semidirect
7. #11721240C2semidirect
8. #11721041C2semidirect
9. #11721039C2semidirect
10. #11721020C2semidirect
11. #11721012C2semidirect
12. #11721004C2semidirect
13. #11720942C2semidirect
14. #11720922C2semidirect
15. #11720918C2semidirect
82. #63445D3semidirect
238. #886D9semidirect
488. C3×C9#540semidirect
685. C9#5663semidirect
765. C3#10589765semidirect

Maximal subgroups

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

subgroupindex
#117217302
C9×#8862
C3×#634452
#117212892
#117212822
#117212772
#117212402
#117210412
#117210392
#117210202
#117210122
#117210042
#117209422
#117209222
#117209182
#105941613
#105897653