Finite Group Databasebeta

← #13148752

Subgroups — #13148752

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88640C211yesmaximal, characteristic, complemented
2C2×D9×Dic6C211yesmaximal, characteristic, complemented
3#11721752C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63455C211yesmaximal, characteristic, complemented
6#11721042C211yesmaximal, characteristic, complemented
7#11721033C211yesmaximal, characteristic, complemented
8#11721003C211yesmaximal, characteristic, complemented
9#11720983C211yesmaximal, characteristic, complemented
10#11720982C211yesmaximal, characteristic, complemented
11#11720978C211yesmaximal, characteristic, complemented
12#11720976C211yesmaximal, characteristic, complemented
13#11720956C211yesmaximal, characteristic, complemented
14#11720939C211yesmaximal, characteristic, complemented
15#11720901C211yesmaximal, characteristic, complemented
16#10594375—31nomaximal
17#10589735—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic
25C2×#6195C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×#6189C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34#88640—24no—
35D9×Dic6—24no—
36C3×C9×C4⋊C4C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39#88534C2211yescharacteristic
40#88534C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46C9×Dic3⋊C4C2211yescharacteristic
47C3×C4×Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3798—31no—
56C2×D3×Dic6—31no—
57#64105—31no—
58C3×#896D311yescharacteristic
59C3×#893—31no—
60#63913—31no—
61#63907—31no—
62#63906—31no—
63#63886—31no—
64#63885—31no—
65#63881—31no—
66#63879—31no—
67#63852—31no—
68#63851—31no—
69#63837—31no—
70C2×Q8×D9—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63458—31no—
76#63458—31no—
77#63458—61no—
78#63457—31no—
79#63455—31no—
80#63455D311yescharacteristic, complemented
81#63449—31no—
82#63447—31no—
83#63447—31no—
84#63446—31no—
85#63446—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—22no—
97#6226—22no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C4×D3×C9—22no—
104C3×D36—22no—
105C3×C4×D9—22no—
106C3×C4×D9—22no—
107C9×Dic6—22no—
108#6195—22no—
109#6194—22no—
110#6194—22no—
111#6192—22no—
112#6192—22no—
113Dic3×D9—22no—
114Dic3×D9—22no—
115#6189—22no—
116#6189D414yescomplemented
117#5633—91no—
118#5552—91no—
119C2×C4×C3⋊D3—31no—
120C2×#634—31no—
121C2×C3×D12—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×Dic6C2×D311yescharacteristic
126C2×#627—31no—
127C2×#627—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#625—31no—
132C2×#625—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135#3798—64no—
136D3×Dic6—64no—
137C32×C4⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3752—31no—
140#3750—31no—
141#3750—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4C2×D311yescharacteristic
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×C4×Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—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×D36C2×D311yescharacteristic
166C2×C4×D9—31no—
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—61no—
170C2×C4×D9C2×D311yescharacteristic
171C2×C4×D9C2×D311yescharacteristic
172C2×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—61no—
176C9×C4⋊C4—21no—
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4C2×D311yescharacteristic
180C9×C22⋊C4—31no—
181C9×C22⋊C4—31no—
182#3676—31no—
183(C2×D9)⋊C4—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—61no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic
191(C2×D9)⋊C4C2×D311yescharacteristic
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—61no—
196Dic9⋊C4—61no—
197C4×Dic9—31no—
198C4×Dic9—31no—
199C4×Dic9C2×D311yescharacteristic
200C22×C3×C9C2411yescharacteristic
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9#4112yescomplemented
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9C2×D412yes—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3C2×D412yes—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×D3×Q8—91no—
225C2×#235—91no—
226C2×#235—91no—
227C22×Dic6—91no—
228C3×C22⋊Q8—31no—
229C3×C4×D4—91no—
230#947—91no—
231#939—91no—
232#939—91no—
233#930—91no—
234C4×#67—91no—
235#924—91no—
236#896—91no—
237#896—91no—
238#896—91no—
239#896—181no—
240#896D911yescharacteristic, complemented
241#895—91no—
242#893—31no—
243#893—91no—
244#887—91no—
245#885—91no—
246#885—91no—
247#885—91no—
248#885—91no—
249#884—91no—
250#884—91no—
251#67⋊C4—91no—
252#67⋊C4—91no—
253#875—91no—
254C4×Dic6—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—
264C2×C3⋊Dic3—31no—
265C4×C3⋊D3—62no—
266#634—62no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×D12—62no—
273C3×C4×D3—22no—
274C3×C4×D3—62no—
275C3×C4×D3—62no—
276C3×Dic6—22no—
277#627—34no—
278#627—62no—
279#626—62no—
280#626—62no—
281#626—62no—
282#625—62no—
283#625—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—31no—
287C22×D9—31no—
288C22×D9—61no—
289C22×D9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291Q8×C9—62no—
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—62no—
299C2×C4×C9C22×D311yescharacteristic
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302#611—62no—
303#611—62no—
304#611—62no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313D36—22no—
314D36—62no—
315D36—62no—
316C4×D9—22no—
317C4×D9—22no—
318C4×D9—62no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—122no—
322Dic18—34no—
323Dic18—62no—
324Dic18—62no—
325Dic18—122no—
326#548—271noSylow
327C2×C3×C9C22×D411yescharacteristic
328C2×C3×C9C2×#4111yescharacteristic
329C2×C3×C92−1+411yescharacteristic
330C3⋊D9—41no—
331D3×C9—41no—
332C3×D9—22no—
333C3×D9—41no—
334C2×C3×Q8—31no—
335C2×C3×D4—91no—
336C22×C3×C4—31no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348D3×Q8—184no—
349#235—184no—
350#235—184no—
351C2×D12—31no—
352C2×D12—91no—
353C2×D12—91no—
354C2×D12—91no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—181no—
362C2×C4×D3C2×D911yescharacteristic
363C2×Dic6—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—181no—
370C2×Dic6—184no—
371C2×Dic6C2×D911yescharacteristic
372C3×C4⋊C4—21no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4C2×D911yescharacteristic
376C3×C4⋊C4D3211yescharacteristic
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C42—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
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—181no—
397(C2×D3)⋊C4—181no—
398(C2×D3)⋊C4C2×D911yescharacteristic
399(C2×D3)⋊C4C2×D911yescharacteristic
400C4⋊Dic3—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—181no—
407Dic3⋊C4—181no—
408Dic3⋊C4C2×D911yescharacteristic
409Dic3⋊C4C2×D911yescharacteristic
410C4×Dic3—31no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—32no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C3⋊Dic3—32no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3D3×D412yes—
439C22×C9—21no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—62no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9#23512yescomplemented
456C4×C9—21no—
457C4×C9—21no—
458C4×C9—21no—
459C4×C9—32no—
460C4×C9—41no—
461C4×C9—41no—
462C4×C9—41no—
463C4×C9—61no—
464C4×C9—61no—
465Dic9—21no—
466Dic9—32no—
467Dic9—62no—
468Dic9—61no—
469Dic9—61no—
470Dic9—121no—
471Dic9—121no—
472Dic9D3×D412yes—
473C2×#41—271no—
474C22×Q8—271no—
475#124—271no—
476#124—271no—
477#124—271no—
478C22⋊Q8—31no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481#121—271no—
482#121—271no—
483#121—271no—
484C4×Q8—271no—
485C4×D4—91no—
486C4×D4—271no—
487C4×D4—271no—
488C3×C9#54811yescharacteristic, complemented, Sylow
489C23×C3—31no—
490C23×C3—91no—
491C23×C3—91no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—91no—
495C22×D3—91no—
496C22×D3—181no—
497C22×D3C22×D911yescharacteristic
498C3×Q8—62no—
499C3×D4—182no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—62no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—182no—
510C2×C3×C4—182no—
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517#67—182no—
518#67—182no—
519#67—182no—
520#67—182no—
521#67—182no—
522#67—182no—
523#67—182no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—182no—
536C2×Dic3—182no—
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539C2×Dic3C22×D911yescharacteristic
540D12—62no—
541D12—182no—
542D12—182no—
543D12—182no—
544C4×D3—22no—
545C4×D3—62no—
546C4×D3—62no—
547C4×D3—182no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—362no—
552Dic6—22no—
553Dic6—94no—
554Dic6—94no—
555Dic6—182no—
556Dic6—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—362no—
560C2×C32C2×D3×D411yescharacteristic
561C2×C32#100711yescharacteristic
562C2×C32D3×#4111yescharacteristic
563C3⋊D3—121no—
564C3×D3—41no—
565C3×D3—62no—
566C3×D3—121no—
567C2×C9—21no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—121no—
571C2×C9C2×#23511yescharacteristic
572C2×C9C2×D3×D411yescharacteristic
573C2×C9#101011yescharacteristic
574D9—22no—
575D9—41no—
576D9—122no—
577D9—121no—
578#41—544no—
579C2×Q8—31no—
580C2×Q8—271no—
581C2×Q8—271no—
582C2×Q8—271no—
583C2×Q8—544no—
584C2×D4—91no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C22×C4—31no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4D3×D911yescharacteristic
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C42—91no—
613C42—271no—
614C42—271no—
615C22×C3—21no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—92no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3C23×D911yescharacteristic
626C22×C3C22×D3211yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—32no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—182no—
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—361no—
644C2×D3—361no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—92no—
658C3×C4—181no—
659Dic3—21no—
660Dic3—21no—
661Dic3—32no—
662Dic3—61no—
663Dic3—92no—
664Dic3—92no—
665Dic3—182no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—361no—
671Dic3—361no—
672Dic3D4×D912yes—
673C32#563311yescharacteristic
674C9—21no—
675C9#555211yescharacteristic, complemented
676C23—31no—
677C23—91no—
678C23—91no—
679C23—271no—
680Q8—62no—
681Q8—274no—
682Q8—542no—
683Q8—542no—
684D4—182no—
685D4—542no—
686D4—542no—
687D4—542no—
688D4—542no—
689D4—542no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—62no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—182no—
697C2×C4—182no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—542no—
702C2×C4—542no—
703C2×C4—542no—
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—182no—
712C2×C3—361no—
713C2×C3C2×D4×D911yescharacteristic
714C2×C3#6371311yescharacteristic
715C2×C3#41×D911yescharacteristic
716C2×C3D3×#23511yescharacteristic
717C2×C3D32×D411yescharacteristic
718C2×C3#6431511yescharacteristic
719D3—41no—
720D3—62no—
721D3—121no—
722D3—362no—
723D3—361no—
724D3—361no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—92no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—541no—
735C22—541no—
736C22—541no—
737C22C22×D3×D911yescharacteristic
738C4—21no—
739C4—21no—
740C4—21no—
741C4—32no—
742C4—61no—
743C4—61no—
744C4—92no—
745C4—181no—
746C4—272no—
747C4—541no—
748C4—541no—
749C3—21no—
750C3#1058973511yescharacteristic, complemented
751C3#1059437511yescharacteristic
752C2—121no—
753C2—182no—
754C2—361no—
755C2—1081no—
756C2D9×#23511yescharacteristic
757C2D3×D4×D911yescharacteristic
758C2#1172251011yescharacteristic
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×D9×Dic6C2semidirect
3. #11721752C2semidirect
4. C9×#896C2semidirect
5. C3×#63455C2semidirect
6. #11721042C2semidirect
7. #11721033C2semidirect
8. #11721003C2semidirect
9. #11720983C2semidirect
10. #11720982C2semidirect
11. #11720978C2semidirect
12. #11720976C2semidirect
13. #11720956C2semidirect
14. #11720939C2semidirect
15. #11720901C2semidirect
80. #63455D3semidirect
116. #6189D4semidirect
212. C2×C3×D9#41semidirect
240. #896D9semidirect
455. C2×D9#235semidirect
488. C3×C9#548semidirect
675. C9#5552semidirect
750. 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×D9×Dic62
#117217522
C9×#8962
C3×#634552
#117210422
#117210332
#117210032
#117209832
#117209822
#117209782
#117209762
#117209562
#117209392
#117209012
#105943753
#105897353