Finite Group Databasebeta

← #13148754

Subgroups — #13148754

Order 1728.

964 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88640C211yesmaximal, characteristic, complemented
2C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
3#11721749C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6#11721044C211yesmaximal, characteristic, complemented
7#11721041C211yesmaximal, characteristic, complemented
8#11721039C211yesmaximal, characteristic, complemented
9#11721035C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11#11721005C211yesmaximal, characteristic, complemented
12#11721003C211yesmaximal, characteristic, complemented
13#11721002C211yesmaximal, characteristic, complemented
14#11720923C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16#10594521—31nomaximal
17#10589735—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×D3×C9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C9×Dic6C2211yescharacteristic
24C2×C3×Dic18C2211yescharacteristic
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×#6189C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34#88640—24no—
35(C3⋊D9)⋊Q8—24no—
36C3×C9×C4⋊C4C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39C4×C3⋊Dic9C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3798—31no—
56C2×#3797—31no—
57#64102—31no—
58C3×#896—31no—
59C3×#896D311yescharacteristic
60#63915—31no—
61#63912—31no—
62#63910—31no—
63#63910—31no—
64#63907—31no—
65#63907—31no—
66#63904—31no—
67#63904—31no—
68#63865—31no—
69#63838—31no—
70C2×Q8×D9—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63458—31no—
76#63458D311yescharacteristic, complemented
77#63457—31no—
78#63455—31no—
79#63455—31no—
80#63455—61no—
81#63449—31no—
82#63447—31no—
83#63447—31no—
84#63446—31no—
85#63446—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4⋊(C3⋊D9)—22no—
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
104C4×D3×C9—22no—
105C3×C4×D9—22no—
106C9×Dic6—22no—
107C3×Dic18—22no—
108#6195—22no—
109#6195—22no—
110#6194—22no—
111#6192—22no—
112#6192—22no—
113(C3⋊D9)⋊C4—22no—
114(C3⋊D9)⋊C4—22no—
115#6189—22no—
116#6189D414yescomplemented
117#5633—91no—
118#5633—91no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3C2×D311yescharacteristic
124C2×C3×Dic6—31no—
125C2×C3×Dic6C2×D311yescharacteristic
126C2×#627—31no—
127C2×#627—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#625—31no—
133C2×#624—31no—
134C2×#624—31no—
135#3798—64no—
136#3797—64no—
137C32×C4⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3752—31no—
140C4×C3⋊Dic3—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×Dic3⋊C4C2×D311yescharacteristic
149#3724—31no—
150#3722—31no—
151#3722—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154Dic32—31no—
155Dic32—31no—
156C2×Q8×C9—31no—
157C22×C4×C9—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161Q8×D9—64no—
162#3697—64no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—31no—
166C2×D36—61no—
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—61no—
172C2×C4×D9—61no—
173C2×C4×D9C2×D311yescharacteristic
174C2×Dic18—31no—
175C2×Dic18—31no—
176C2×Dic18C2×D311yescharacteristic
177C9×C4⋊C4—21no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180C9×C4⋊C4C2×D311yescharacteristic
181C9×C22⋊C4—31no—
182C9×C22⋊C4—31no—
183#3676—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4C2×D311yescharacteristic
192(C2×D9)⋊C4C2×D311yescharacteristic
193Dic9⋊C4—31no—
194Dic9⋊C4C2×D311yescharacteristic
195Dic9⋊C4C2×D311yescharacteristic
196C4×Dic9—31no—
197C4×Dic9—31no—
198C4×Dic9—31no—
199C4×Dic9—61no—
200C22×C3×C9C2411yescharacteristic
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9#4112yescomplemented
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×D3×Q8—91no—
225C2×D3×Q8—91no—
226C2×#235—91no—
227C2×#235—91no—
228C3×C22⋊Q8—31no—
229C3×C22⋊Q8—91no—
230#947—91no—
231#947—91no—
232C4×#67—91no—
233C4×#67—91no—
234#896—31no—
235#896—91no—
236#896—91no—
237#896D911yescharacteristic, complemented
238#895—91no—
239#895—91no—
240#893—91no—
241#893—91no—
242#893—91no—
243#893—91no—
244#893—181no—
245#887—91no—
246#887—91no—
247#885—91no—
248#885—91no—
249#885—91no—
250#885—91no—
251#884—91no—
252#884—91no—
253#884—91no—
254#884—91no—
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C4⋊(C3⋊D3)—62no—
265C4×C3⋊D3—62no—
266C4×C3⋊D3—62no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C3×C4×D3—22no—
274C3×C4×D3—62no—
275C3×Dic6—22no—
276C3×Dic6—62no—
277#627—34no—
278#627—62no—
279#626—62no—
280#626—62no—
281#626—62no—
282#626—62no—
283#625—62no—
284#624—62no—
285#624—62no—
286C23×C9—31no—
287C22×D9—31no—
288C22×D9—31no—
289C22×D9—61no—
290C22×D9—61no—
291C22×D9C22×D311yescharacteristic
292Q8×C9—62no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—62no—
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302C2×C4×C9C22×D311yescharacteristic
303#611—62no—
304#611—62no—
305#611—62no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9C22×D311yescharacteristic
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313D36—62no—
314D36—64no—
315D36—62no—
316D36—62no—
317C4×D9—22no—
318C4×D9—62no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—62no—
322C4×D9—122no—
323C4×D9—122no—
324Dic18—22no—
325Dic18—34no—
326Dic18—62no—
327#548—271noSylow
328C2×C3×C9C22×D411yescharacteristic
329C2×C3×C9C2×#4111yescharacteristic
330C2×C3×C92−1+411yescharacteristic
331C3⋊D9—22no—
332C3⋊D9—41no—
333D3×C9—41no—
334C3×D9—41no—
335C2×C3×Q8—31no—
336C2×C3×Q8—91no—
337C22×C3×C4—31no—
338C22×C3×C4—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345D3×Q8—184no—
346D3×Q8—184no—
347#235—184no—
348#235—184no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—181no—
356C2×C4×D3—31no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—181no—
366C2×C4×D3—181no—
367C2×C4×D3C2×D911yescharacteristic
368C2×Dic6—31no—
369C2×Dic6—91no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C2×Dic6—91no—
373C2×Dic6C2×D911yescharacteristic
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4—91no—
379C3×C4⋊C4C2×D911yescharacteristic
380C3×C4⋊C4D3211yescharacteristic
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385#217—91no—
386#217—91no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—181no—
400(C2×D3)⋊C4—181no—
401(C2×D3)⋊C4C2×D911yescharacteristic
402(C2×D3)⋊C4C2×D911yescharacteristic
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4C2×D911yescharacteristic
408Dic3⋊C4C2×D911yescharacteristic
409C4×Dic3—91no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—181no—
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—32no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C3⋊Dic3—32no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3D3×D412yes—
440C22×C9—21no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9C23×D311yescharacteristic
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—32no—
449C2×D9—62no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—62no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9—121no—
459C2×D9—121no—
460C4×C9—22no—
461C4×C9—21no—
462C4×C9—21no—
463C4×C9—21no—
464C4×C9—32no—
465C4×C9—41no—
466C4×C9—41no—
467C4×C9—61no—
468C4×C9—61no—
469Dic9—21no—
470Dic9—21no—
471Dic9—32no—
472Dic9—62no—
473Dic9—61no—
474Dic9—121no—
475Dic9D3×D412yes—
476C2×#41—271no—
477C22×Q8—271no—
478#124—271no—
479#124—271no—
480#124—271no—
481C22⋊Q8—31no—
482C22⋊Q8—91no—
483C22⋊Q8—271no—
484#121—271no—
485#121—271no—
486#121—271no—
487C4×Q8—271no—
488C4×D4—271no—
489C4×D4—271no—
490C4×D4—271no—
491C3×C9#54811yescharacteristic, complemented, Sylow
492C23×C3—31no—
493C23×C3—91no—
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×Q8—62no—
503C3×Q8—182no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—62no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—182no—
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521#67—182no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—182no—
526#67—182no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3C22×D911yescharacteristic
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539D12—182no—
540D12—182no—
541D12—184no—
542D12—182no—
543D12—182no—
544D12—182no—
545D12—182no—
546C4×D3—22no—
547C4×D3—62no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—362no—
557C4×D3—362no—
558Dic6—22no—
559Dic6—62no—
560Dic6—94no—
561Dic6—94no—
562Dic6—182no—
563Dic6—182no—
564C2×C32C2×D3×D411yescharacteristic
565C2×C32#100711yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C3⋊D3—62no—
568C3⋊D3—121no—
569C3×D3—41no—
570C3×D3—121no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—121no—
575C2×C9C2×D3×D411yescharacteristic
576C2×C9#100711yescharacteristic
577C2×C9D3×#4111yescharacteristic
578D9—41no—
579D9—62no—
580D9—122no—
581D9—122no—
582D9—121no—
583#41—544no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×Q8—271no—
587C2×Q8—271no—
588C2×Q8—544no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4—271no—
594C2×D4—271no—
595C22×C4—31no—
596C22×C4—91no—
597C22×C4—271no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—271no—
606C4⋊C4D3×D911yescharacteristic
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C42—271no—
619C42—271no—
620C22×C3—21no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3C23×D911yescharacteristic
628C22×C3C22×D3211yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—92no—
636C2×D3—92no—
637C2×D3—182no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—182no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—361no—
650C2×D3—361no—
651C2×D3—361no—
652C2×D3—361no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—92no—
666C3×C4—181no—
667C3×C4—181no—
668Dic3—21no—
669Dic3—21no—
670Dic3—32no—
671Dic3—61no—
672Dic3—61no—
673Dic3—92no—
674Dic3—92no—
675Dic3—182no—
676Dic3—181no—
677Dic3—181no—
678Dic3—361no—
679Dic3D4×D912yes—
680C32#563311yescharacteristic
681C9—21no—
682C9#563311yescharacteristic, complemented
683C23—31no—
684C23—91no—
685C23—271no—
686C23—271no—
687Q8—62no—
688Q8—182no—
689Q8—274no—
690Q8—542no—
691D4—542no—
692D4—542no—
693D4—542no—
694D4—542no—
695D4—542no—
696D4—542no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—62no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—182no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4C2×D3×D911yescharacteristic
712C2×C4C2×D3×D911yescharacteristic
713C2×C4C2×D3×D911yescharacteristic
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—121no—
718C2×C3—361no—
719C2×C3C2×D4×D911yescharacteristic
720C2×C3#6371311yescharacteristic
721C2×C3#41×D911yescharacteristic
722C2×C3#6430611yescharacteristic
723C2×C3D32×D411yescharacteristic
724C2×C3#6431611yescharacteristic
725D3—41no—
726D3—121no—
727D3—182no—
728D3—182no—
729D3—362no—
730D3—362no—
731D3—361no—
732D3—361no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—272no—
740C22—541no—
741C22—541no—
742C22—541no—
743C22—541no—
744C22—541no—
745C22C22×D3×D911yescharacteristic
746C4—21no—
747C4—21no—
748C4—21no—
749C4—32no—
750C4—61no—
751C4—61no—
752C4—92no—
753C4—181no—
754C4—181no—
755C4—272no—
756C4—541no—
757C3—21no—
758C3#1058973511yescharacteristic, complemented
759C3#1059452111yescharacteristic
760C2—121no—
761C2—361no—
762C2—542no—
763C2—1081no—
764C2#1172247511yescharacteristic
765C2D3×D4×D911yescharacteristic
766C2#1172250911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#548
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. C2×#88640C2semidirect
2. C2×(C3⋊D9)⋊Q8C2semidirect
3. #11721749C2semidirect
4. C9×#896C2semidirect
5. C3×#63458C2semidirect
6. #11721044C2semidirect
7. #11721041C2semidirect
8. #11721039C2semidirect
9. #11721035C2semidirect
10. #11721030C2semidirect
11. #11721005C2semidirect
12. #11721003C2semidirect
13. #11721002C2semidirect
14. #11720923C2semidirect
15. #11720902C2semidirect
76. #63458D3semidirect
116. #6189D4semidirect
206. C2×C3⋊D9#41semidirect
237. #896D9semidirect
491. C3×C9#548semidirect
682. C9#5633semidirect
758. C3#10589735semidirect

Maximal subgroups

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

subgroupindex
C2×#886402
C2×(C3⋊D9)⋊Q82
#117217492
C9×#8962
C3×#634582
#117210442
#117210412
#117210392
#117210352
#117210302
#117210052
#117210032
#117210022
#117209232
#117209022
#105945213
#105897353