Finite Group Databasebeta

← #13148997

Subgroups — #13148997

Order 1728.

798 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721750C211yesmaximal, characteristic, complemented
2C9×#892C211yesmaximal, characteristic, complemented
3C3×#63456C211yesmaximal, characteristic, complemented
4#11721041C211yesmaximal, characteristic, complemented
5#11721039C211yesmaximal, characteristic, complemented
6#11721034C211yesmaximal, characteristic, complemented
7#11721034C211yesmaximal, characteristic, complemented
8#11721033C211yesmaximal, characteristic, complemented
9#11721006C211yesmaximal, characteristic, complemented
10C4×#6192C211yesmaximal, characteristic, complemented
11#11720988C211yesmaximal, characteristic, complemented
12#11720982C211yesmaximal, characteristic, complemented
13#11720977C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720925C211yesmaximal, characteristic, complemented
16#10594546—31nomaximal
17#10589637—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×#6195C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C3×C9×C4⋊C4C2211yescharacteristic
34#88536C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88534C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×C4⋊Dic3C2211yescharacteristic
44C4×C9×Dic3C2211yescharacteristic
45C4×C9×Dic3C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53#64103—31no—
54C3×#894—31no—
55C3×#892D311yescharacteristic
56#63912—31no—
57#63911—31no—
58#63910—31no—
59#63906—31no—
60#63906—31no—
61#63906—31no—
62C4×#626—31no—
63#63890—31no—
64#63885—31no—
65#63880—31no—
66#63867—31no—
67#63854—31no—
68C9×#117—31no—
69#63492—31no—
70#63492—31no—
71#63456—31no—
72#63456—31no—
73#63456—31no—
74#63456—61no—
75#63456D311yescharacteristic, complemented
76#63446—31no—
77#63446—31no—
78#63446—31no—
79#63446—31no—
80#63436—31no—
81C4×D36—31no—
82C4×D36—31no—
83#63432—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C4⋊(C3⋊D9)—41no—
95C4×C3⋊D9—41no—
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C4×D3×C9—22no—
102C3×D36—41no—
103C3×C4×D9—41no—
104#6195—41no—
105#6195—41no—
106#6194—41no—
107#6194—41no—
108#6192—22no—
109#6192—22no—
110#6192—41no—
111#6192—41no—
112(C3⋊D9)⋊C4—41no—
113Dic3×D9—41no—
114#5663—91no—
115#5535—91no—
116C2×C4⋊(C3⋊D3)—31no—
117C2×C4×C3⋊D3—31no—
118C2×C3×D12—31no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×#626—31no—
122C2×#626—31no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#625—31no—
128C2×#625—31no—
129C2×#624—31no—
130C2×D3×Dic3—31no—
131C32×C4⋊C4C2×D311yescharacteristic
132#3752—31no—
133#3752—31no—
134#3752—31no—
135#3750—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×Dic3⋊C4—31no—
143C3×C4×Dic3C2×D311yescharacteristic
144C3×C4×Dic3C2×D311yescharacteristic
145#3724—31no—
146Dic3⋊Dic3—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149#3722—31no—
150(C2×D3)⋊Dic3—31no—
151C22×C4×C9—31no—
152C2×#611—31no—
153C2×#611—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×D36—31no—
157C2×D36—31no—
158C2×D36—31no—
159C2×D36—31no—
160C2×D36—31no—
161C2×D36—61no—
162C2×D36C2×D311yescharacteristic
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C2×C4×D9C2×D311yescharacteristic
168C9×C4⋊C4—21no—
169C9×C4⋊C4—31no—
170C9×C4⋊C4C2×D311yescharacteristic
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C42×C9—31no—
174C42×C9—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—61no—
181(C2×D9)⋊C4—61no—
182(C2×D9)⋊C4—61no—
183(C2×D9)⋊C4C2×D311yescharacteristic
184(C2×D9)⋊C4C2×D311yescharacteristic
185(C2×D9)⋊C4C2×D311yescharacteristic
186C4⋊Dic9—31no—
187C4⋊Dic9—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—61no—
192Dic9⋊C4C2×D311yescharacteristic
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
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×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3#4112yes—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×#123—91no—
220C3×#117—31no—
221#940—91no—
222#939—91no—
223#930—91no—
224#930—91no—
225#930—91no—
226C4×#67—91no—
227#895—91no—
228#894—31no—
229#894—91no—
230#894—91no—
231#894—91no—
232#894—91no—
233#894—181no—
234#892D911yescharacteristic, complemented
235#889—91no—
236#886—91no—
237#884—91no—
238#884—91no—
239#884—91no—
240#884—91no—
241#884—91no—
242#884—91no—
243#884—91no—
244#883—91no—
245#67⋊C4—91no—
246#874—91no—
247C4×D12—91no—
248C4×D12—91no—
249#870—91no—
250C22×C3⋊D3—31no—
251C22×C3⋊D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C4⋊(C3⋊D3)—121no—
261C4×C3⋊D3—121no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×D12—121no—
268C3×C4×D3—22no—
269C3×C4×D3—121no—
270#626—62no—
271#626—62no—
272#626—121no—
273#626—121no—
274#626—121no—
275#626—121no—
276#625—121no—
277#625—121no—
278#624—121no—
279D3×Dic3—121no—
280C23×C9—31no—
281C22×D9—31no—
282C22×D9—31no—
283C22×D9—61no—
284C22×D9—61no—
285C22×D9C22×D311yescharacteristic
286C22×D9C22×D311yescharacteristic
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9—21no—
290C2×C4×C9—31no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—62no—
294C2×C4×C9C22×D311yescharacteristic
295C2×C4×C9C22×D311yescharacteristic
296C2×C4×C9C22×D311yescharacteristic
297#611—121no—
298#611—121no—
299#611—121no—
300#611—121no—
301C2×Dic9—31no—
302C2×Dic9—31no—
303C2×Dic9—61no—
304C2×Dic9—61no—
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307D36—41no—
308D36—62no—
309D36—62no—
310D36—121no—
311D36—122no—
312D36—121no—
313D36—121no—
314C4×D9—41no—
315C4×D9—121no—
316C4×D9—121no—
317C4×D9—121no—
318C4×D9—122no—
319#540—271noSylow
320C2×C3×C9C2×#4111yescharacteristic
321C2×C3×C9H(5,𝔽2)11yescharacteristic
322C2×C3×C9H(5,𝔽2)11yescharacteristic
323C3⋊D9—41no—
324C3⋊D9—41no—
325D3×C9—41no—
326C3×D9—41no—
327C3×D9—41no—
328C2×C3×D4—91no—
329C22×C3×C4—31no—
330C22×C3×C4—91no—
331C2×#67—91no—
332C2×#67—91no—
333C2×#67—91no—
334C2×#67—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C22×Dic3—91no—
342C2×D12—31no—
343C2×D12—91no—
344C2×D12—91no—
345C2×D12—91no—
346C2×D12—91no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—181no—
352C2×C4×D3—31no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—181no—
359C2×C4×D3C2×D911yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4C2×D911yescharacteristic
364C3×C4⋊C4D3211yescharacteristic
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4—91no—
370C3×C42—31no—
371C3×C42—31no—
372#217—91no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—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—181no—
386(C2×D3)⋊C4—181no—
387(C2×D3)⋊C4—181no—
388(C2×D3)⋊C4C2×D911yescharacteristic
389(C2×D3)⋊C4C2×D911yescharacteristic
390C4⋊Dic3—91no—
391C4⋊Dic3—91no—
392C4⋊Dic3—91no—
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×Dic3C2×D911yescharacteristic
404C4×Dic3C2×D911yescharacteristic
405C22×C32C23×D311yescharacteristic
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3#23512yes—
431C22×C9—21no—
432C22×C9—61no—
433C22×C9—61no—
434C22×C9—61no—
435C22×C9C23×D311yescharacteristic
436C2×D9—21no—
437C2×D9—21no—
438C2×D9—21no—
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—62no—
443C2×D9—61no—
444C2×D9—61no—
445C2×D9—61no—
446C2×D9—61no—
447C2×D9—61no—
448C2×D9—61no—
449C2×D9—121no—
450C2×D9—121no—
451C2×D9—121no—
452C2×D9—121no—
453C2×D9—121no—
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—21no—
457C4×C9—32no—
458C4×C9—41no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—61no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—21no—
465Dic9—61no—
466Dic9—61no—
467Dic9—121no—
468Dic9—121no—
469#127—271no—
470#125—271no—
471#123—91no—
472#123—271no—
473#123—271no—
474#123—271no—
475#121—271no—
476#121—271no—
477#121—271no—
478#121—271no—
479#121—271no—
480#121—271no—
481C4×D4—271no—
482C4×D4—271no—
483#117—31no—
484C3×C9#54011yescharacteristic, complemented, Sylow
485C23×C3—31no—
486C23×C3—91no—
487C23×C3—91no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—91no—
491C22×D3—91no—
492C22×D3—91no—
493C22×D3—91no—
494C22×D3—181no—
495C22×D3—181no—
496C22×D3C22×D911yescharacteristic
497C3×D4—361no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—62no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—361no—
508C2×C3×C4C22×D911yescharacteristic
509C2×C3×C4C22×D911yescharacteristic
510C2×C3×C4C22×D911yescharacteristic
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C2×D3211yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514#67—182no—
515#67—182no—
516#67—361no—
517#67—361no—
518#67—361no—
519#67—361no—
520#67—361no—
521#67—361no—
522#67—361no—
523#67—361no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—181no—
531C2×Dic3—181no—
532C2×Dic3—361no—
533C2×Dic3C22×D911yescharacteristic
534C2×Dic3C22×D911yescharacteristic
535C2×Dic3C22×D911yescharacteristic
536D12—121no—
537D12—182no—
538D12—182no—
539D12—361no—
540D12—361no—
541D12—362no—
542D12—361no—
543D12—361no—
544D12—361no—
545D12—361no—
546C4×D3—22no—
547C4×D3—121no—
548C4×D3—361no—
549C4×D3—361no—
550C4×D3—361no—
551C4×D3—361no—
552C4×D3—361no—
553C4×D3—362no—
554C2×C32C2×#23511yescharacteristic
555C2×C32#100911yescharacteristic
556C2×C32#100911yescharacteristic
557C3⋊D3—121no—
558C3⋊D3—121no—
559C3×D3—41no—
560C3×D3—121no—
561C3×D3—121no—
562C2×C9—21no—
563C2×C9—21no—
564C2×C9—21no—
565C2×C9—121no—
566C2×C9#100411yescharacteristic
567C2×C9D3×#4111yescharacteristic
568C2×C9#100911yescharacteristic
569D9—41no—
570D9—41no—
571D9—122no—
572D9—121no—
573D9—121no—
574D9—241no—
575C2×D4—91no—
576C2×D4—271no—
577C2×D4—271no—
578C2×D4—271no—
579C2×D4—271no—
580C2×D4—271no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4—271no—
585C22×C4—31no—
586C22×C4—91no—
587C22×C4—271no—
588C22×C4—271no—
589C22×C4—271no—
590C4⋊C4—31no—
591C4⋊C4—91no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4D3×D911yescharacteristic
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4—91no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C42—31no—
609C42—31no—
610C22×C3—21no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3C23×D911yescharacteristic
621C22×C3C22×D3211yescharacteristic
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—182no—
632C2×D3—181no—
633C2×D3—181no—
634C2×D3—181no—
635C2×D3—181no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—361no—
645C2×D3—361no—
646C2×D3—361no—
647C2×D3—361no—
648C2×D3—361no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—181no—
662C3×C4—181no—
663Dic3—21no—
664Dic3—21no—
665Dic3—61no—
666Dic3—61no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—361no—
672Dic3—361no—
673Dic3#369712yes—
674C32#553511yescharacteristic
675C9—21no—
676C9#566311yescharacteristic, complemented
677C23—31no—
678C23—91no—
679C23—91no—
680C23—271no—
681C23—271no—
682D4—361no—
683D4—542no—
684D4—542no—
685D4—1081no—
686D4—1081no—
687D4—1081no—
688D4—1081no—
689D4—1081no—
690D4—1081no—
691D4—1081no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—62no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—361no—
701C2×C4—1081no—
702C2×C4—1081no—
703C2×C4—1081no—
704C2×C4C2×D3×D911yescharacteristic
705C2×C4C2×D3×D911yescharacteristic
706C2×C4C2×D3×D911yescharacteristic
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—121no—
711C2×C3—361no—
712C2×C3—361no—
713C2×C3C2×#369711yescharacteristic
714C2×C3#6371511yescharacteristic
715C2×C3#6371511yescharacteristic
716C2×C3D3×#23511yescharacteristic
717C2×C3#6431411yescharacteristic
718C2×C3#6432011yescharacteristic
719D3—41no—
720D3—121no—
721D3—121no—
722D3—362no—
723D3—361no—
724D3—361no—
725D3—361no—
726D3—361no—
727D3—721no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—541no—
738C22—541no—
739C22—541no—
740C22—541no—
741C22—541no—
742C22—541no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—32no—
748C4—61no—
749C4—61no—
750C4—181no—
751C4—181no—
752C4—541no—
753C4—541no—
754C3—21no—
755C3#1058963711yescharacteristic, complemented
756C3#1059454611yescharacteristic
757C2—121no—
758C2—361no—
759C2—361no—
760C2—1081no—
761C2—1081no—
762C2D3×#369711yescharacteristic
763C2#1172250111yescharacteristic
764C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#540
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11721750C2semidirect
2. C9×#892C2semidirect
3. C3×#63456C2semidirect
4. #11721041C2semidirect
5. #11721039C2semidirect
6. #11721034C2semidirect
7. #11721034C2semidirect
8. #11721033C2semidirect
9. #11721006C2semidirect
10. C4×#6192C2semidirect
11. #11720988C2semidirect
12. #11720982C2semidirect
13. #11720977C2semidirect
14. #11720942C2semidirect
15. #11720925C2semidirect
75. #63456D3semidirect
234. #892D9semidirect
484. C3×C9#540semidirect
676. C9#5663semidirect
755. C3#10589637semidirect

Maximal subgroups

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

subgroupindex
#117217502
C9×#8922
C3×#634562
#117210412
#117210392
#117210342
#117210332
#117210062
C4×#61922
#117209882
#117209822
#117209772
#117209422
#117209252
#105945463
#105896373