Finite Group Databasebeta

← #13149363

Subgroups — #13149363

Order 1728.

822 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721750C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63459C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic
5#11721048C211yesmaximal, characteristic, complemented
6D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11721035C211yesmaximal, characteristic, complemented
8#11721002C211yesmaximal, characteristic, complemented
9#11720993C211yesmaximal, characteristic, complemented
10#11720988C211yesmaximal, characteristic, complemented
11#11720985C211yesmaximal, characteristic, complemented
12#11720974C211yesmaximal, characteristic, complemented
13#11720962C211yesmaximal, characteristic, complemented
14#11720958C211yesmaximal, characteristic, complemented
15#11720922C211yesmaximal, characteristic, complemented
16#10594654—31nomaximal
17#10589807—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C3×Dic18C2211yescharacteristic, complemented
23C2×#6195C2211yescharacteristic
24C2×#6192C2211yescharacteristic
25C2×(C3⋊D9)⋊C4C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
27C2×Dic3×D9C2211yescharacteristic
28C3×C9×C4⋊C4C2211yescharacteristic, complemented
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic, complemented
31#88536C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33C9×(C2×D3)⋊C4C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C9×C4⋊Dic3C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C4×C9×Dic3C2211yescharacteristic, complemented
41C3×C4⋊Dic9C2211yescharacteristic, complemented
42C3×C4⋊Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64103—31no—
54C3×#898D311yescharacteristic
55C3×#897—31no—
56#63923—31no—
57#63921—31no—
58D3×(C2×D3)⋊C4—31no—
59#63907—31no—
60#63904—31no—
61#63894—31no—
62#63890—31no—
63#63888—31no—
64#63877—31no—
65#63858—31no—
66#63854—31no—
67#63849—31no—
68C9×#126—31no—
69#63459D311yescharacteristic, complemented
70#63458—31no—
71#63456—31no—
72#63456—31no—
73#63456—61no—
74#63455—31no—
75#63454—31no—
76#63447—31no—
77#63445—31no—
78#63444—31no—
79C22⋊C4×D9—31no—
80C22⋊C4×D9—31no—
81#63441—31no—
82C4×D36—31no—
83#63434—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4⋊(C3⋊D9)—22no—
97C4×C3⋊D9—22no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C3×C4×D9—41no—
105C3×Dic18—41no—
106#6195—41no—
107#6192—22no—
108(C3⋊D9)⋊C4—41no—
109(C3⋊D9)⋊C4—41no—
110Dic3×D9—22no—
111#5705—91no—
112#5637—91no—
113C22×D32—31no—
114C2×C4⋊(C3⋊D3)—31no—
115C2×C4×C3⋊D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×Dic6—31no—
118C2×#626—31no—
119C2×#626—31no—
120C2×#624—31no—
121C2×#624—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C32×C4⋊C4C2×D311yescharacteristic
125#3752—31no—
126#3752—31no—
127#3752—31no—
128#3750—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×C4×Dic3C2×D311yescharacteristic
139#3724—31no—
140Dic3⋊Dic3—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147Dic32—31no—
148Dic32—31no—
149C2×#611—31no—
150C2×D36—31no—
151C2×D36—31no—
152C2×D36—61no—
153C2×C4×D9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×C4×D9—61no—
158C2×C4×D9C2×D311yescharacteristic
159C2×Dic18C2×D311yescharacteristic, complemented
160C9×C4⋊C4—21no—
161C9×C4⋊C4—31no—
162C9×C4⋊C4—31no—
163C9×C4⋊C4C2×D311yescharacteristic, complemented
164C9×C22⋊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—31no—
177(C2×D9)⋊C4—61no—
178(C2×D9)⋊C4—61no—
179(C2×D9)⋊C4—61no—
180(C2×D9)⋊C4C2×D311yescharacteristic
181(C2×D9)⋊C4C2×D311yescharacteristic
182C4⋊Dic9C2×D311yescharacteristic, complemented
183C4⋊Dic9C2×D311yescharacteristic, complemented
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—61no—
188C4×Dic9—31no—
189C4×Dic9—31no—
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9#4112yes—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9#4112yes—
203D3×D9—44no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#126—31no—
216C3×C22⋊Q8—91no—
217#947—91no—
218#946—91no—
219C4×#67—91no—
220C2×(C2×D3)⋊C4—91no—
221#898—91no—
222#898D911yescharacteristic, complemented
223#897—31no—
224#896—91no—
225#894—91no—
226#894—91no—
227#894—91no—
228#894—91no—
229#894—181no—
230#893—91no—
231#893—91no—
232#892—91no—
233#892—91no—
234#886—91no—
235#885—91no—
236#883—91no—
237#882—91no—
238#882—91no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—91no—
241D3×C22⋊C4—91no—
242#879—91no—
243#877—91no—
244C4×D12—91no—
245#872—91no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3C22×D311yescharacteristic
250C2×D32—62no—
251C2×D32—62no—
252C2×D32—121no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C4⋊(C3⋊D3)—62no—
259C4×C3⋊D3—62no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C3×C4×D3—121no—
267C3×Dic6—121no—
268#626—62no—
269#626—121no—
270#624—121no—
271#624—121no—
272D3×Dic3—62no—
273C23×C9—31no—
274C22×D9—31no—
275C22×D9—31no—
276C22×D9—61no—
277C22×D9—61no—
278C22×D9—62no—
279C22×D9—62no—
280C22×D9—121no—
281C22×D9C22×D311yescharacteristic
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291#611—121no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9C22×D311yescharacteristic
297C2×Dic9C22×D311yescharacteristic
298C2×Dic9C22×D311yescharacteristic
299D36—62no—
300D36—62no—
301D36—122no—
302C4×D9—41no—
303C4×D9—62no—
304C4×D9—62no—
305C4×D9—122no—
306C4×D9—121no—
307C4×D9—121no—
308Dic18—41no—
309#551—271noSylow
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9H(5,𝔽2)11yescharacteristic
313C3⋊D9—22no—
314C3⋊D9—41no—
315D3×C9—41no—
316C3×D9—22no—
317C23×D3—91no—
318C23×D3—91no—
319C2×C3×Q8—91no—
320C22×C3×C4—91no—
321C2×#67—91no—
322C2×#67—91no—
323C22×Dic3—91no—
324C2×D12—91no—
325C2×D12—91no—
326C2×D12—91no—
327C2×D12—91no—
328C2×D12—181no—
329C2×C4×D3—31no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—181no—
338C2×Dic6—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4C2×D911yescharacteristic, complemented
345C3×C4⋊C4D3211yescharacteristic
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C42—31no—
352#217—91no—
353#217—91no—
354#217—91no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
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—91no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4—181no—
374(C2×D3)⋊C4—181no—
375(C2×D3)⋊C4C2×D911yescharacteristic
376(C2×D3)⋊C4C2×D911yescharacteristic
377(C2×D3)⋊C4C2×D911yescharacteristic
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—91no—
381C4⋊Dic3C2×D911yescharacteristic, complemented
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—181no—
388Dic3⋊C4C2×D911yescharacteristic, complemented
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3C2×D911yescharacteristic, complemented
394C22×C32C23×D311yescharacteristic
395C2×C3⋊D3—32no—
396C2×C3⋊D3—61no—
397C2×C3⋊D3—61no—
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—32no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407D32—124no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—61no—
421C22×C9—61no—
422C22×C9—61no—
423C22×C9C23×D311yescharacteristic
424C2×D9—21no—
425C2×D9—21no—
426C2×D9—32no—
427C2×D9—62no—
428C2×D9—61no—
429C2×D9—61no—
430C2×D9—61no—
431C2×D9—61no—
432C2×D9—61no—
433C2×D9—121no—
434C2×D9—121no—
435C2×D9—121no—
436C2×D9—121no—
437C2×D9—121no—
438C2×D9—124no—
439C2×D9#23912yes—
440C4×C9—21no—
441C4×C9—21no—
442C4×C9—21no—
443C4×C9—41no—
444C4×C9—41no—
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—
456#126—31no—
457#126—271no—
458#124—271no—
459#123—271no—
460#123—271no—
461#123—271no—
462C22⋊Q8—91no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—271no—
468#117—271no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C3×C9#55111yescharacteristic, complemented, Sylow
472C23×C3—31no—
473C23×C3—91no—
474C22×D3—31no—
475C22×D3—91no—
476C22×D3—91no—
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—181no—
480C22×D3—181no—
481C22×D3—182no—
482C22×D3—182no—
483C22×D3—182no—
484C22×D3—182no—
485C22×D3—361no—
486C22×D3—361no—
487C22×D3C22×D911yescharacteristic
488C3×Q8—361no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—361no—
499C2×C3×C4C22×D911yescharacteristic
500C2×C3×C4C22×D911yescharacteristic
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505#67—182no—
506#67—361no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—182no—
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519C2×Dic3C22×D911yescharacteristic
520D12—182no—
521D12—182no—
522D12—182no—
523D12—362no—
524D12—361no—
525C4×D3—121no—
526C4×D3—182no—
527C4×D3—182no—
528C4×D3—182no—
529C4×D3—362no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—361no—
533C4×D3—361no—
534Dic6—121no—
535C2×C32D3×#4111yescharacteristic
536C2×C32D3×#4111yescharacteristic
537C2×C32#100911yescharacteristic
538C3⋊D3—62no—
539C3⋊D3—121no—
540C3×D3—41no—
541C3×D3—62no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—121no—
546C2×C9#100411yescharacteristic
547C2×C9C2×#23911yescharacteristic
548C2×C9D3×#4111yescharacteristic
549D9—22no—
550D9—62no—
551D9—122no—
552D9—121no—
553D9—241no—
554C24—271no—
555C2×Q8—91no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—91no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4D3×D911yescharacteristic, complemented
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C42—31no—
587C42—271no—
588C42—271no—
589C22×C3—21no—
590C22×C3—61no—
591C22×C3—61no—
592C22×C3—61no—
593C22×C3—92no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3C23×D911yescharacteristic
597C22×C3C22×D3211yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—32no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—92no—
605C2×D3—92no—
606C2×D3—182no—
607C2×D3—181no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—361no—
618C2×D3—361no—
619C2×D3—361no—
620C2×D3—361no—
621C2×D3—361no—
622C2×D3—364no—
623C2×D3—364no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—181no—
646Dic3—181no—
647Dic3—181no—
648Dic3—181no—
649Dic3—361no—
650Dic3—361no—
651C32#570511yescharacteristic
652C9—21no—
653C9#563711yescharacteristic, complemented
654C23—31no—
655C23—91no—
656C23—271no—
657C23—271no—
658C23—542no—
659C23—542no—
660C23—1081no—
661Q8—361no—
662D4—542no—
663D4—542no—
664D4—1081no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—271no—
672C2×C4—271no—
673C2×C4—361no—
674C2×C4—542no—
675C2×C4—542no—
676C2×C4—1081no—
677C2×C4—1081no—
678C2×C4C2×D3×D911yescharacteristic
679C2×C4C2×D3×D911yescharacteristic
680C2×C4C2×D3×D911yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—121no—
685C2×C3—182no—
686C2×C3#41×D911yescharacteristic
687C2×C3#41×D911yescharacteristic
688C2×C3#6371511yescharacteristic
689C2×C3#6430711yescharacteristic
690C2×C3#6431211yescharacteristic
691C2×C3D3×#23911yescharacteristic
692D3—41no—
693D3—62no—
694D3—182no—
695D3—182no—
696D3—362no—
697D3—361no—
698D3—361no—
699D3—721no—
700C22—61no—
701C22—61no—
702C22—61no—
703C22—92no—
704C22—181no—
705C22—181no—
706C22—272no—
707C22—541no—
708C22—541no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—1084no—
713C22C22×D3×D911yescharacteristic
714C4—21no—
715C4—21no—
716C4—21no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—541no—
724C4—541no—
725C3—21no—
726C3#1058980711yescharacteristic, complemented
727C3#1059465411yescharacteristic
728C2—121no—
729C2—182no—
730C2—542no—
731C2—1081no—
732C2#1172247711yescharacteristic
733C2#1172249811yescharacteristic
734C2D9×#23911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radical#11721051C2
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#551
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×#898C2semidirect
3. C3×#63459C2semidirect
5. #11721048C2semidirect
6. D9×(C2×D3)⋊C4C2semidirect
7. #11721035C2semidirect
8. #11721002C2semidirect
9. #11720993C2semidirect
10. #11720988C2semidirect
11. #11720985C2semidirect
12. #11720974C2semidirect
13. #11720962C2semidirect
14. #11720958C2semidirect
15. #11720922C2semidirect
22. C2×C3×Dic18C22semidirect
26. C2×(C3⋊D9)⋊C4C22semidirect
28. C3×C9×C4⋊C4C22semidirect
30. #88536C22semidirect
31. #88536C22semidirect
32. #88534C22semidirect
38. C9×C4⋊Dic3C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C4×C9×Dic3C22semidirect
41. C3×C4⋊Dic9C22semidirect
42. C3×C4⋊Dic9C22semidirect
47. #88445C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
69. #63459D3semidirect
159. C2×Dic18C2×D3semidirect
163. C9×C4⋊C4C2×D3semidirect
182. C4⋊Dic9C2×D3semidirect
183. C4⋊Dic9C2×D3semidirect
222. #898D9semidirect
344. C3×C4⋊C4C2×D9semidirect
381. C4⋊Dic3C2×D9semidirect
388. Dic3⋊C4C2×D9semidirect
393. C4×Dic3C2×D9semidirect
471. C3×C9#551semidirect
571. C4⋊C4D3×D9semidirect
653. C9#5637semidirect
726. C3#10589807semidirect

Maximal subgroups

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

subgroupindex
#117217502
C9×#8982
C3×#634592
#117210512
#117210482
D9×(C2×D3)⋊C42
#117210352
#117210022
#117209932
#117209882
#117209852
#117209742
#117209622
#117209582
#117209222
#105946543
#105898073