Finite Group Databasebeta

← #13150269

Subgroups — #13150269

Order 1728.

808 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721819C211yesmaximal, characteristic, complemented
2C4×C9×#67C211yesmaximal, characteristic, complemented
3C2×C3×Dic9⋊C4C211yesmaximal, characteristic, complemented
4#11721288C211yesmaximal, characteristic, complemented
5#11721288C211yesmaximal, characteristic, complemented
6#11721241C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic, complemented
8#11721039C211yesmaximal, characteristic, complemented
9#11721030C211yesmaximal, characteristic, complemented
10#11720997C211yesmaximal, characteristic, complemented
11#11720965C211yesmaximal, characteristic, complemented
12#11720954C211yesmaximal, characteristic, complemented
13#11720926C211yesmaximal, characteristic, complemented
14#11720915C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10595028—31nomaximal
17#10589642—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×C4×D3×C9C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30#88536C2211yescharacteristic
31#88536C2211yescharacteristic
32C4⋊(C3⋊Dic9)C2211yescharacteristic
33C9×#217C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C4×C9×Dic3C2211yescharacteristic
37C3×Dic9⋊C4C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×Dic9⋊C4C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64139—31no—
54C3×C4×#67D311yescharacteristic
55C2×C3×Dic3⋊C4—31no—
56#63978—31no—
57#63978—31no—
58#63952—31no—
59#63952—31no—
60#63910—31no—
61#63904—31no—
62#63897—31no—
63#63868—31no—
64#63861—31no—
65#63850—31no—
66#63845—31no—
67#63836—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63501—31no—
71#63492—31no—
72#63492—61no—
73#63491—31no—
74C4×#611—31no—
75C2×Dic9⋊C4D311yescharacteristic, complemented
76#63456—31no—
77#63451—31no—
78#63446—31no—
79#611⋊C4—31no—
80#611⋊C4—31no—
81#63441—31no—
82#63438—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C2×C3×C4×C9—41no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91#6233—22no—
92#6233—22no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4⋊(C3⋊D9)—41no—
96C9×#67—22no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9—22no—
101C2×C3×Dic9—41no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—41no—
107#6195—22no—
108#6195—41no—
109(C3⋊D9)⋊C4—22no—
110(C3⋊D9)⋊C4—41no—
111#5540—91no—
112#5514—91no—
113C22×C32×C4C2×D311yescharacteristic
114C2×#638—31no—
115C2×#638—31no—
116C2×C4⋊(C3⋊D3)—31no—
117C2×C3×#67C2×D311yescharacteristic
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×#626—31no—
122C2×#626—31no—
123C2×#624—31no—
124C2×#624—31no—
125#3752—31no—
126#3752—31no—
127C4⋊(C3⋊Dic3)—31no—
128C3×#217C2×D311yescharacteristic
129C3×(C2×D3)⋊C4C2×D311yescharacteristic
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4—31no—
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×C4×Dic3C2×D311yescharacteristic
136#3724—31no—
137#3724—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140#3722—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146Dic32—31no—
147Dic32—31no—
148C2×D4×C9—31no—
149C22×C4×C9—21no—
150C22×C4×C9—31no—
151C22×C4×C9C2×D311yescharacteristic
152C2×#611—31no—
153C2×#611—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—61no—
157C2×#611—61no—
158C22×Dic9C2×D311yescharacteristic
159C22×Dic9C2×D311yescharacteristic
160C2×D36—31no—
161C2×D36—61no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C9×C4⋊C4—31no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4—31no—
167C42×C9—31no—
168#3676—31no—
169#3676—31no—
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—61no—
177(C2×D9)⋊C4—61no—
178C4⋊Dic9—31no—
179C4⋊Dic9—61no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4C2×D311yescharacteristic
185Dic9⋊C4C2×D311yescharacteristic
186Dic9⋊C4C2×D311yescharacteristic
187Dic9⋊C4C2×D311yescharacteristic
188C4×Dic9—31no—
189C4×Dic9—31no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9#4112yes—
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—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3⋊Dic9—21no—
206C3⋊Dic9—21no—
207C9×Dic3—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C3×Dic9—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9#4112yes—
214C3×C4×D4—31no—
215C2×C3×C4⋊C4—91no—
216#939—91no—
217#939—91no—
218#930—91no—
219#930—91no—
220#930—91no—
221#930—91no—
222#930—181no—
223#929—91no—
224C4×#67—91no—
225C4×#67—91no—
226C4×#67—91no—
227C4×#67D911yescharacteristic, complemented
228C2×Dic3⋊C4—31no—
229#898—91no—
230#898—91no—
231#895—91no—
232#894—91no—
233#894—91no—
234#894—91no—
235#893—91no—
236#892—91no—
237#890—91no—
238#889—91no—
239#884—91no—
240#67⋊C4—91no—
241#67⋊C4—91no—
242#879—91no—
243#876—91no—
244#872—91no—
245C23×C32C22×D311yescharacteristic
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3×D3C22×D311yescharacteristic
249C2×C32×C4—41no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252#638—62no—
253#638—62no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C4⋊(C3⋊D3)—121no—
257C3×#67—22no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3—121no—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×C4×D3—41no—
268#626—62no—
269#626—121no—
270#624—62no—
271#624—121no—
272C23×C9—21no—
273C23×C9—31no—
274C23×C9C22×D311yescharacteristic
275C22×D9—31no—
276C22×D9—31no—
277C22×D9—61no—
278C22×D9—61no—
279D4×C9—62no—
280C2×C4×C9—21no—
281C2×C4×C9—21no—
282C2×C4×C9—31no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9—41no—
286C2×C4×C9—42no—
287C2×C4×C9—121no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—62no—
291#611—62no—
292#611—62no—
293#611—122no—
294#611—122no—
295#611—121no—
296C2×Dic9—22no—
297C2×Dic9—31no—
298C2×Dic9—31no—
299C2×Dic9—41no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306D36—121no—
307D36—122no—
308C4×D9—62no—
309C4×D9—121no—
310#553—271noSylow
311C2×C3×C9—22no—
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9C2×#4111yescharacteristic
314C2×C3×C9H(5,𝔽2)11yescharacteristic
315C3⋊D9—41no—
316C3⋊D9—41no—
317D3×C9—41no—
318C2×C3×D4—31no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C22×C3×C4C2×D911yescharacteristic
324C22×C3×C4D3211yescharacteristic
325C2×#67—91no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—91no—
331C2×#67—181no—
332C2×#67—181no—
333C2×#67C2×D911yescharacteristic
334C22×Dic3—31no—
335C22×Dic3—31no—
336C2×D12—91no—
337C2×D12—91no—
338C2×D12—91no—
339C2×D12—91no—
340C2×D12—181no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×C4×D3—91no—
345C2×C4×D3C2×D911yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C42—31no—
354#217—91no—
355#217—91no—
356#217C2×D911yescharacteristic
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—181no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4C2×D911yescharacteristic
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—181no—
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4C2×D911yescharacteristic
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3C2×D911yescharacteristic
395C22×C32—21no—
396C22×C32—21no—
397C22×C32#23512yes—
398C22×C32C23×D311yescharacteristic
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3⋊D3—61no—
402C2×C3⋊D3—61no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—32no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—22no—
423C22×C9—41no—
424C22×C9—41no—
425C22×C9—61no—
426C22×C9—61no—
427C22×C9—61no—
428C22×C9#23912yes—
429C22×C9C23×D311yescharacteristic
430C2×D9—61no—
431C2×D9—61no—
432C2×D9—61no—
433C2×D9—61no—
434C2×D9—61no—
435C2×D9—61no—
436C2×D9—121no—
437C2×D9—121no—
438C2×D9—121no—
439C2×D9—121no—
440C2×D9—121no—
441C2×D9—121no—
442C4×C9—22no—
443C4×C9—21no—
444C4×C9—21no—
445C4×C9—41no—
446C4×C9—61no—
447C4×C9—61no—
448C4×C9—61no—
449Dic9—21no—
450Dic9—21no—
451Dic9—21no—
452Dic9—61no—
453Dic9—61no—
454Dic9—121no—
455Dic9—121no—
456Dic9#23512yes—
457#126—271no—
458#126—271no—
459#125—271no—
460#123—271no—
461#123—271no—
462#121—271no—
463#121—271no—
464#121—271no—
465#121—271no—
466C4×D4—31no—
467C4×D4—271no—
468C4×D4—271no—
469C4×D4—271no—
470#117—271no—
471C2×C4⋊C4—91no—
472C3×C9#55311yescharacteristic, complemented, Sylow
473C23×C3—21no—
474C23×C3—31no—
475C23×C3C22×D911yescharacteristic
476C23×C3C2×D3211yescharacteristic
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—91no—
480C22×D3—91no—
481C22×D3—181no—
482C22×D3—181no—
483C22×D3C22×D911yescharacteristic
484C3×D4—62no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—42no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—121no—
498C2×C3×C4—182no—
499C2×C3×C4—361no—
500C2×C3×C4C22×D911yescharacteristic
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504#67—22no—
505#67—182no—
506#67—182no—
507#67—182no—
508#67—182no—
509#67—182no—
510#67—362no—
511#67—362no—
512#67—361no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—62no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—121no—
523C2×Dic3—181no—
524C2×Dic3—181no—
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527C2×Dic3C22×D911yescharacteristic
528D12—182no—
529D12—361no—
530D12—361no—
531D12—362no—
532D12—361no—
533C4×D3—41no—
534C4×D3—182no—
535C4×D3—182no—
536C4×D3—361no—
537C4×D3—361no—
538C2×C32—22no—
539C2×C32C2×#23511yescharacteristic
540C2×C32#100411yescharacteristic
541C2×C32D3×#4111yescharacteristic
542C3⋊D3—121no—
543C3⋊D3—121no—
544C3×D3—41no—
545C2×C9—22no—
546C2×C9—21no—
547C2×C9—21no—
548C2×C9—21no—
549C2×C9—42no—
550C2×C9—121no—
551C2×C9C2×#23511yescharacteristic
552C2×C9#100411yescharacteristic
553C2×C9C2×#23911yescharacteristic
554D9—121no—
555D9—121no—
556D9—241no—
557D9—241no—
558C2×D4—31no—
559C2×D4—271no—
560C2×D4—271no—
561C2×D4—271no—
562C2×D4—271no—
563C2×D4—271no—
564C22×C4—31no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—271no—
568C22×C4—271no—
569C22×C4D3×D911yescharacteristic
570C4⋊C4—31no—
571C4⋊C4—91no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—91no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C22⋊C4—31no—
581C22⋊C4—31no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C42—31no—
591C42—271no—
592C42—271no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3#369712yes—
605C22×C3C23×D911yescharacteristic
606C22×C3#379912yes—
607C22×C3C22×D3211yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—181no—
622C2×D3—181no—
623C2×D3—361no—
624C2×D3—361no—
625C2×D3—361no—
626C2×D3—361no—
627C2×D3—361no—
628C2×D3—361no—
629C3×C4—22no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—92no—
639C3×C4—181no—
640C3×C4—181no—
641C3×C4—181no—
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3—32no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—181no—
650Dic3—181no—
651Dic3—181no—
652Dic3—181no—
653Dic3—361no—
654Dic3—361no—
655C32#554011yescharacteristic
656C9—21no—
657C9#551411yescharacteristic, complemented
658C23—31no—
659C23—271no—
660C23—271no—
661C23C2×D3×D911yescharacteristic
662D4—62no—
663D4—542no—
664D4—542no—
665D4—542no—
666D4—1081no—
667D4—1081no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—41no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—121no—
677C2×C4—182no—
678C2×C4—271no—
679C2×C4—271no—
680C2×C4—361no—
681C2×C4—542no—
682C2×C4—1081no—
683C2×C4C2×D3×D911yescharacteristic
684C2×C4C2×D3×D911yescharacteristic
685C2×C3—22no—
686C2×C3—22no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—42no—
691C2×C3—121no—
692C2×C3C2×#369711yescharacteristic
693C2×C3#6371011yescharacteristic
694C2×C3#41×D911yescharacteristic
695C2×C3C2×#379911yescharacteristic
696C2×C3D3×#23511yescharacteristic
697C2×C3#6433011yescharacteristic
698D3—41no—
699D3—361no—
700D3—361no—
701D3—361no—
702D3—361no—
703D3—721no—
704D3—721no—
705C22—21no—
706C22—21no—
707C22—61no—
708C22—61no—
709C22—61no—
710C22—541no—
711C22—541no—
712C22—541no—
713C22—541no—
714C22—541no—
715C22—541no—
716C22#8864212yes—
717C22C22×D3×D911yescharacteristic
718C4—21no—
719C4—21no—
720C4—61no—
721C4—61no—
722C4—61no—
723C4—92no—
724C4—181no—
725C4—181no—
726C4—181no—
727C4—541no—
728C4—541no—
729C3—21no—
730C3#1058964211yescharacteristic, complemented
731C3#1059502811yescharacteristic
732C2—22no—
733C2—121no—
734C2—1081no—
735C2—1081no—
736C2C2×#8864211yescharacteristic
737C2D9×#23511yescharacteristic
738C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#553
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. #11721819C2semidirect
2. C4×C9×#67C2semidirect
3. C2×C3×Dic9⋊C4C2semidirect
4. #11721288C2semidirect
5. #11721288C2semidirect
6. #11721241C2semidirect
7. #11721241C2semidirect
8. #11721039C2semidirect
9. #11721030C2semidirect
10. #11720997C2semidirect
11. #11720965C2semidirect
12. #11720954C2semidirect
13. #11720926C2semidirect
14. #11720915C2semidirect
15. #11720898C2semidirect
75. C2×Dic9⋊C4D3semidirect
227. C4×#67D9semidirect
472. C3×C9#553semidirect
657. C9#5514semidirect
730. C3#10589642semidirect

Maximal subgroups

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

subgroupindex
#117218192
C4×C9×#672
C2×C3×Dic9⋊C42
#117212882
#117212412
#117210392
#117210302
#117209972
#117209652
#117209542
#117209262
#117209152
#117208982
#105950283
#105896423