Finite Group Databasebeta

← #13148102

Subgroups — #13148102

Order 1728.

874 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721728C211yesmaximal, characteristic
2C9×#878C211yesmaximal, characteristic, complemented
3C3×#63439C211yesmaximal, characteristic, complemented
4#11721274C211yesmaximal, characteristic, complemented
5C2×#88445C211yesmaximal, characteristic, complemented
6#11721255C211yesmaximal, characteristic, complemented
7#11721240C211yesmaximal, characteristic, complemented
8#11720997C211yesmaximal, characteristic, complemented
9#11720997C211yesmaximal, characteristic, complemented
10#11720992C211yesmaximal, characteristic, complemented
11#11720986C211yesmaximal, characteristic, complemented
12#11720953C211yesmaximal, characteristic, complemented
13#11720934C211yesmaximal, characteristic, complemented
14#11720920C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594166—31nomaximal
17#10589739—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic, complemented
25C2×(C3⋊D9)⋊C4C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
28C3×C9×C22⋊C4C2211yescharacteristic
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic
31C9×#217C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C9×C4⋊Dic3C2211yescharacteristic, complemented
34C9×Dic3⋊C4C2211yescharacteristic, complemented
35C9×Dic3⋊C4C2211yescharacteristic, complemented
36C3×Dic9⋊C4C2211yescharacteristic, complemented
37C3×Dic9⋊C4C2211yescharacteristic, complemented
38C3×C4×Dic9C2211yescharacteristic, complemented
39C3×C4×Dic9C2211yescharacteristic, complemented
40#88445C2211yescharacteristic
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic, complemented
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64091—31no—
54C3×#878D311yescharacteristic
55C3×#877—31no—
56#63974—31no—
57#63966—31no—
58C2×#3722—31no—
59#63952—31no—
60#63897—31no—
61#63897—31no—
62#63894—31no—
63#63888—31no—
64#63868—31no—
65#63864—31no—
66#63848—31no—
67#63836—31no—
68C9×C22⋊Q8—31no—
69#63509—31no—
70#63508—31no—
71C4×#611—31no—
72C2×(C2×D9)⋊C4—31no—
73#63460—31no—
74#63460—31no—
75#63456—31no—
76#63456—31no—
77#63455—31no—
78#63454—31no—
79#63448—31no—
80#63444—31no—
81#63444—61no—
82C22⋊C4×D9—31no—
83#63439D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—22no—
86C22×C3⋊D9—22no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93#6233—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C4⋊(C3⋊D9)—22no—
96C4⋊(C3⋊D9)—41no—
97C2×C9×Dic3—41no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9—22no—
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×Dic6—41no—
108(C3⋊D9)⋊C4—22no—
109(C3⋊D9)⋊C4—41no—
110(C3⋊D9)⋊C4—41no—
111#5637—91no—
112#5527—91no—
113C23×C3⋊D3—31no—
114C2×#638—31no—
115C2×C4⋊(C3⋊D3)—31no—
116C2×C4⋊(C3⋊D3)—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3C2×D311yescharacteristic
119C2×C3×Dic6C2×D311yescharacteristic
120C2×#624—31no—
121C2×#624—31no—
122C2×#624—31no—
123C23×D9—31no—
124C23×D9—61no—
125C32×C22⋊C4C2×D311yescharacteristic
126#3752—31no—
127#3752—31no—
128C3×#217—31no—
129C3×#217C2×D311yescharacteristic
130C3×C4⋊Dic3C2×D311yescharacteristic
131C3×Dic3⋊C4—31no—
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4C2×D311yescharacteristic
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×C4×Dic3—31no—
136C3×C4×Dic3—31no—
137#3724—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140#3722—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145#3722—31no—
146#3722—31no—
147#3722—31no—
148#3722—31no—
149Dic32—31no—
150C2×Q8×C9—31no—
151C22×C4×C9—31no—
152C2×#611—31no—
153C2×#611—61no—
154C22×Dic9C2×D311yescharacteristic
155C2×D36—31no—
156C2×D36—31no—
157C2×D36—61no—
158C2×D36—61no—
159C2×C4×D9—31no—
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C9×C4⋊C4—31no—
163C9×C4⋊C4—31no—
164C9×C4⋊C4—31no—
165C9×C22⋊C4—21no—
166C9×C22⋊C4—31no—
167C9×C22⋊C4C2×D311yescharacteristic
168#3676C2×D311yescharacteristic
169(C2×D9)⋊C4—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—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—61no—
181(C2×D9)⋊C4—61no—
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4C2×D311yescharacteristic, complemented
186Dic9⋊C4C2×D311yescharacteristic, complemented
187C4×Dic9—31no—
188C4×Dic9C2×D311yescharacteristic, complemented
189C4×Dic9C2×D311yescharacteristic, complemented
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×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—44no—
203C2×C3⋊D9#4112yes—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C9×Dic3—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×C22⋊Q8—31no—
216C3×#117—91no—
217#947—91no—
218#946—91no—
219#929—91no—
220C4×#67—91no—
221C2×(C2×D3)⋊C4—91no—
222C2×(C2×D3)⋊C4—91no—
223#898—91no—
224#898—91no—
225#898—91no—
226#896—91no—
227#894—91no—
228#894—91no—
229#894—91no—
230#894—91no—
231#893—91no—
232#892—91no—
233#886—91no—
234#882—91no—
235#882—91no—
236#882—181no—
237#67⋊C4—91no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240#878D911yescharacteristic, complemented
241#877—31no—
242#876—91no—
243#875—91no—
244C4×D12—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3⋊D3—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—31no—
250C22×C3⋊D3—62no—
251C22×C3⋊D3—62no—
252C22×C3⋊D3—121no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255#638—62no—
256C2×C3⋊Dic3—31no—
257C4⋊(C3⋊D3)—62no—
258C4⋊(C3⋊D3)—121no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×Dic6—41no—
270#624—62no—
271#624—121no—
272#624—121no—
273C23×C9—21no—
274C23×C9C22×D311yescharacteristic
275C22×D9—31no—
276C22×D9—31no—
277C22×D9—31no—
278C22×D9—61no—
279C22×D9—61no—
280C22×D9—61no—
281C22×D9—62no—
282C22×D9—62no—
283C22×D9—122no—
284C22×D9—122no—
285C22×D9—121no—
286C22×D9—122no—
287Q8×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—31no—
294C2×C4×C9—121no—
295C2×C4×C9C22×D311yescharacteristic
296C2×C4×C9C22×D311yescharacteristic
297#611—62no—
298#611—122no—
299C2×Dic9—22no—
300C2×Dic9—31no—
301C2×Dic9—61no—
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306D36—62no—
307D36—122no—
308D36—121no—
309D36—122no—
310C4×D9—62no—
311C4×D9—121no—
312C4×D9—121no—
313#551—271noSylow
314C2×C3×C9—22no—
315C2×C3×C9C2×#4111yescharacteristic
316C2×C3×C9C2×#4111yescharacteristic
317C2×C3×C9H(5,𝔽2)11yescharacteristic
318C3⋊D9—22no—
319C3⋊D9—41no—
320C3⋊D9—41no—
321C23×D3—91no—
322C23×D3—91no—
323C23×D3—181no—
324C2×C3×Q8—31no—
325C22×C3×C4—31no—
326C22×C3×C4—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—181no—
330C22×Dic3—31no—
331C22×Dic3C2×D911yescharacteristic
332C2×D12—91no—
333C2×D12—91no—
334C2×D12—91no—
335C2×D12—91no—
336C2×D12—181no—
337C2×D12—181no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×Dic6C2×D911yescharacteristic, complemented
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4C2×D911yescharacteristic
354C3×C22⋊C4D3211yescharacteristic
355C3×C42—91no—
356C3×C42—91no—
357#217—31no—
358#217C2×D911yescharacteristic
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—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
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—181no—
382(C2×D3)⋊C4—181no—
383C4⋊Dic3—91no—
384C4⋊Dic3—91no—
385C4⋊Dic3C2×D911yescharacteristic, complemented
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4C2×D911yescharacteristic, complemented
393Dic3⋊C4C2×D911yescharacteristic, complemented
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32#23912yes—
401C22×C32C23×D311yescharacteristic
402C2×C3⋊D3—32no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—124no—
412C32×C4—21no—
413C32×C4—21no—
414C3⋊Dic3—61no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—61no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C3×Dic3—61no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—22no—
427C22×C9—41no—
428C22×C9—41no—
429C22×C9#23512yes—
430C22×C9C23×D311yescharacteristic
431C2×D9—32no—
432C2×D9—62no—
433C2×D9—61no—
434C2×D9—61no—
435C2×D9—62no—
436C2×D9—61no—
437C2×D9—61no—
438C2×D9—61no—
439C2×D9—61no—
440C2×D9—61no—
441C2×D9—61no—
442C2×D9—121no—
443C2×D9—121no—
444C2×D9—121no—
445C2×D9—121no—
446C2×D9—121no—
447C2×D9—121no—
448C2×D9—121no—
449C2×D9—124no—
450C2×D9—128no—
451C4×C9—21no—
452C4×C9—21no—
453C4×C9—41no—
454C4×C9—41no—
455C4×C9—61no—
456C4×C9—61no—
457C4×C9—61no—
458C4×C9—61no—
459Dic9—21no—
460Dic9—21no—
461Dic9—21no—
462Dic9—21no—
463Dic9—61no—
464Dic9—121no—
465#126—271no—
466#126—271no—
467#124—271no—
468#123—271no—
469#123—271no—
470#123—271no—
471C22⋊Q8—31no—
472C22⋊Q8—271no—
473#120—271no—
474C4×D4—271no—
475C4×D4—271no—
476#117—91no—
477#117—271no—
478C2×C22⋊C4—271no—
479C2×C22⋊C4—271no—
480C3×C9#55111yescharacteristic, complemented, Sylow
481C23×C3—21no—
482C23×C3C22×D911yescharacteristic
483C23×C3C2×D3211yescharacteristic
484C22×D3—91no—
485C22×D3—91no—
486C22×D3—91no—
487C22×D3—91no—
488C22×D3—91no—
489C22×D3—91no—
490C22×D3—181no—
491C22×D3—181no—
492C22×D3—181no—
493C22×D3—182no—
494C22×D3—182no—
495C22×D3—182no—
496C22×D3—182no—
497C22×D3—362no—
498C22×D3—362no—
499C22×D3—361no—
500C22×D3—361no—
501C22×D3—362no—
502C3×Q8—121no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
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—91no—
513C2×C3×C4—121no—
514C2×C3×C4—182no—
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—182no—
520#67—182no—
521#67—362no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—41no—
527C2×Dic3—62no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—181no—
531C2×Dic3C22×D911yescharacteristic
532C2×Dic3C22×D911yescharacteristic
533C2×Dic3C22×D911yescharacteristic
534C2×Dic3C22×D911yescharacteristic
535D12—182no—
536D12—182no—
537D12—362no—
538D12—361no—
539D12—361no—
540D12—362no—
541C4×D3—182no—
542C4×D3—182no—
543C4×D3—361no—
544C4×D3—361no—
545C4×D3—361no—
546C4×D3—361no—
547Dic6—41no—
548C2×C32—22no—
549C2×C32#100411yescharacteristic
550C2×C32C2×#23911yescharacteristic
551C2×C32D3×#4111yescharacteristic
552C3⋊D3—62no—
553C3⋊D3—121no—
554C3⋊D3—121no—
555C2×C9—22no—
556C2×C9—21no—
557C2×C9—21no—
558C2×C9—21no—
559C2×C9—42no—
560C2×C9C2×#23511yescharacteristic
561C2×C9D3×#4111yescharacteristic
562C2×C9#100911yescharacteristic
563D9—62no—
564D9—122no—
565D9—122no—
566D9—121no—
567D9—121no—
568D9—241no—
569C24—271no—
570C2×Q8—31no—
571C2×D4—271no—
572C2×D4—271no—
573C2×D4—271no—
574C22×C4—31no—
575C22×C4—91no—
576C22×C4—271no—
577C22×C4—271no—
578C22×C4—271no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C22⋊C4—31no—
588C22⋊C4—91no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4D3×D911yescharacteristic
601C42—91no—
602C42—91no—
603C42—271no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3#370112yes—
613C22×C3C23×D911yescharacteristic
614C22×C3#379912yes—
615C22×C3C22×D3211yescharacteristic
616C2×D3—92no—
617C2×D3—92no—
618C2×D3—182no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—181no—
622C2×D3—181no—
623C2×D3—182no—
624C2×D3—181no—
625C2×D3—181no—
626C2×D3—181no—
627C2×D3—181no—
628C2×D3—181no—
629C2×D3—181no—
630C2×D3—181no—
631C2×D3—181no—
632C2×D3—181no—
633C2×D3—181no—
634C2×D3—181no—
635C2×D3—181no—
636C2×D3—361no—
637C2×D3—361no—
638C2×D3—361no—
639C2×D3—361no—
640C2×D3—361no—
641C2×D3—361no—
642C2×D3—361no—
643C2×D3—364no—
644C2×D3—364no—
645C2×D3—368no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—181no—
659C3×C4—181no—
660Dic3—21no—
661Dic3—21no—
662Dic3—21no—
663Dic3—21no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—61no—
668Dic3—181no—
669Dic3—181no—
670Dic3—361no—
671C32#563711yescharacteristic
672C9—21no—
673C9#552711yescharacteristic, complemented
674C23—271no—
675C23—271no—
676C23—271no—
677C23—542no—
678C23—542no—
679C23—1081no—
680C23C2×D3×D911yescharacteristic
681Q8—121no—
682D4—542no—
683D4—542no—
684D4—1081no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—121no—
694C2×C4—182no—
695C2×C4—271no—
696C2×C4—542no—
697C2×C4—1081no—
698C2×C4—1081no—
699C2×C4C2×D3×D911yescharacteristic
700C2×C4C2×D3×D911yescharacteristic
701C2×C3—22no—
702C2×C3—22no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—42no—
707C2×C3#6371011yescharacteristic
708C2×C3C2×#370111yescharacteristic
709C2×C3#41×D911yescharacteristic
710C2×C3C2×#379911yescharacteristic
711C2×C3#6431211yescharacteristic
712C2×C3#6431411yescharacteristic
713D3—182no—
714D3—182no—
715D3—362no—
716D3—362no—
717D3—361no—
718D3—361no—
719D3—361no—
720D3—361no—
721D3—721no—
722C22—21no—
723C22—21no—
724C22—272no—
725C22—541no—
726C22—541no—
727C22—541no—
728C22—541no—
729C22—541no—
730C22—541no—
731C22—541no—
732C22—541no—
733C22—1084no—
734C22#8863512yes—
735C22C22×D3×D911yescharacteristic
736C4—21no—
737C4—21no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—61no—
742C4—181no—
743C4—181no—
744C4—181no—
745C4—181no—
746C4—541no—
747C3—21no—
748C3#1058973911yescharacteristic, complemented
749C3#1059416611yescharacteristic
750C2—22no—
751C2—542no—
752C2—1081no—
753C2—1081no—
754C2C2×#8863511yescharacteristic
755C2#1172249811yescharacteristic
756C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721728C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#551
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C9×#878C2semidirect
3. C3×#63439C2semidirect
4. #11721274C2semidirect
5. C2×#88445C2semidirect
6. #11721255C2semidirect
7. #11721240C2semidirect
8. #11720997C2semidirect
9. #11720997C2semidirect
10. #11720992C2semidirect
11. #11720986C2semidirect
12. #11720953C2semidirect
13. #11720934C2semidirect
14. #11720920C2semidirect
15. #11720899C2semidirect
24. C2×C9×Dic6C22semidirect
27. C2×(C3⋊D9)⋊C4C22semidirect
33. C9×C4⋊Dic3C22semidirect
34. C9×Dic3⋊C4C22semidirect
35. C9×Dic3⋊C4C22semidirect
36. C3×Dic9⋊C4C22semidirect
37. C3×Dic9⋊C4C22semidirect
38. C3×C4×Dic9C22semidirect
39. C3×C4×Dic9C22semidirect
46. #88445C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
83. #63439D3semidirect
185. Dic9⋊C4C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
188. C4×Dic9C2×D3semidirect
189. C4×Dic9C2×D3semidirect
240. #878D9semidirect
344. C2×Dic6C2×D9semidirect
385. C4⋊Dic3C2×D9semidirect
392. Dic3⋊C4C2×D9semidirect
393. Dic3⋊C4C2×D9semidirect
480. C3×C9#551semidirect
673. C9#5527semidirect
748. C3#10589739semidirect

Maximal subgroups

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

subgroupindex
#117217282
C9×#8782
C3×#634392
#117212742
C2×#884452
#117212552
#117212402
#117209972
#117209922
#117209862
#117209532
#117209342
#117209202
#117208992
#105941663
#105897393