Finite Group Databasebeta

← #13148982

Subgroups — #13148982

Order 1728.

954 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88635C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3#11721750C211yesmaximal, characteristic, complemented
4C3×#63456C211yesmaximal, characteristic, complemented
5C9×#888C211yesmaximal, characteristic, complemented
6#11721005C211yesmaximal, characteristic, complemented
7#11720988C211yesmaximal, characteristic, complemented
8#11720986C211yesmaximal, characteristic, complemented
9#11720984C211yesmaximal, characteristic, complemented
10#11720983C211yesmaximal, characteristic, complemented
11#11720980C211yesmaximal, characteristic, complemented
12#11720977C211yesmaximal, characteristic, complemented
13#11720977C211yesmaximal, characteristic, complemented
14D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#11720942C211yesmaximal, characteristic, complemented
16#10594372—31nomaximal
17#10589828—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C3×D36C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C9×Dic6C2211yescharacteristic
23C2×C9×Dic6C2211yescharacteristic
24C2×#6192C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34#88635—24no—
35#88634—24no—
36C3×C9×C4⋊C4C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40#88534C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C9×C4⋊Dic3C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46C9×Dic3⋊C4C2211yescharacteristic
47C4×C9×Dic3C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic
53#88442C2211yescharacteristic
54Dic9⋊Dic3C2211yescharacteristic
55C2×#3799—31no—
56C2×#3796—31no—
57#64103—31no—
58C3×#894—31no—
59C3×#888D311yescharacteristic
60#63910—31no—
61#63890—31no—
62#63888—31no—
63#63887—31no—
64#63886—31no—
65#63883—31no—
66#63880—31no—
67#63880—31no—
68D3×Dic3⋊C4—31no—
69#63854—31no—
70C2×#3701—31no—
71C2×#3701—31no—
72C9×C4⋊Q8—31no—
73#63508—31no—
74#63508—31no—
75#63457—31no—
76#63457—31no—
77#63456—31no—
78#63456—31no—
79#63456—31no—
80#63456—61no—
81#63456D311yescharacteristic, complemented
82C4⋊C4×D9—31no—
83C4⋊C4×D9—31no—
84C4×D36—31no—
85C4×D36—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
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—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—22no—
104C3×C4×D9—22no—
105C9×Dic6—22no—
106C9×Dic6—22no—
107#6192—22no—
108#6192—22no—
109#6192—22no—
110#6192D414yescomplemented
111(C3⋊D9)⋊C4—22no—
112(C3⋊D9)⋊C4—22no—
113(C3⋊D9)⋊C4—22no—
114Dic3×D9—22no—
115Dic3×D9—22no—
116Dic3×D9—22no—
117#5726—91no—
118#5655—91no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4×C3⋊D3—31no—
121C2×C3×D12—31no—
122C2×C3×C4×D3—31no—
123C2×C3×Dic6C2×D311yescharacteristic
124C2×C3×Dic6C2×D311yescharacteristic
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#624—31no—
130C2×#624—31no—
131C2×#624—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135#3799—64no—
136#3796—64no—
137C32×C4⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3752—31no—
140#3752—31no—
141#3750—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×Dic3⋊C4C2×D311yescharacteristic
149C3×C4×Dic3C2×D311yescharacteristic
150#3724—31no—
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154#3722—31no—
155(C2×D3)⋊Dic3—31no—
156C2×Q8×C9—31no—
157C2×Q8×C9—31no—
158#3701—64no—
159#3701—64no—
160C2×D36—31no—
161C2×D36—31no—
162C2×D36—31no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—61no—
166C2×D36C2×D311yescharacteristic
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—61no—
175C2×C4×D9C2×D311yescharacteristic
176C9×C4⋊C4—21no—
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180C9×C4⋊C4C2×D311yescharacteristic
181C42×C9—31no—
182(C2×D9)⋊C4—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—61no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic
191(C2×D9)⋊C4C2×D311yescharacteristic
192(C2×D9)⋊C4C2×D311yescharacteristic
193C4⋊Dic9—31no—
194C4⋊Dic9—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—61no—
199Dic9⋊C4C2×D311yescharacteristic
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⋊D9C2×D412yes—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9C2×D412yes—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C9×Dic3#4112yescomplemented
222C3×Dic9—21no—
223C3×Dic9—21no—
224C2×#239—91no—
225C2×#239—91no—
226C2×#237—91no—
227C2×#235—91no—
228C3×C4⋊Q8—31no—
229C3×#123—91no—
230#946—91no—
231#946—91no—
232#939—91no—
233C2×Dic3⋊C4—91no—
234#896—91no—
235#895—91no—
236#895—91no—
237#894—31no—
238#894—91no—
239#894—91no—
240#894—91no—
241#894—91no—
242#894—181no—
243D3×C4⋊C4—91no—
244D3×C4⋊C4—91no—
245D3×C4⋊C4—91no—
246#888D911yescharacteristic, complemented
247#886—91no—
248#884—91no—
249#883—91no—
250#67⋊C4—91no—
251#67⋊C4—91no—
252#878—91no—
253C4×D12—91no—
254C4×D12—91no—
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
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—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×D12—62no—
273C3×C4×D3—62no—
274C3×Dic6—22no—
275C3×Dic6—22no—
276#626—34no—
277#626—62no—
278#626—62no—
279#626—62no—
280#624—62no—
281#624—62no—
282#624—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C22×D9—31no—
287C22×D9—31no—
288C22×D9—61no—
289C22×D9—61no—
290C22×D9C22×D311yescharacteristic
291C22×D9C22×D311yescharacteristic
292Q8×C9—62no—
293Q8×C9—62no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—21no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9C22×D311yescharacteristic
302C2×C4×C9C22×D311yescharacteristic
303C2×C4×C9C22×D311yescharacteristic
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—61no—
307C2×Dic9—61no—
308C2×Dic9C22×D311yescharacteristic
309C2×Dic9C22×D311yescharacteristic
310D36—22no—
311D36—34no—
312D36—62no—
313D36—62no—
314D36—62no—
315D36—62no—
316D36—122no—
317C4×D9—22no—
318C4×D9—62no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—62no—
322C4×D9—62no—
323C4×D9—62no—
324C4×D9—62no—
325C4×D9—122no—
326#547—271noSylow
327C2×C3×C9C22×D411yescharacteristic
328C2×C3×C9C2×#4111yescharacteristic
329C2×C3×C92−1+411yescharacteristic
330C3⋊D9—22no—
331C3⋊D9—41no—
332C3×D9—22no—
333C3×D9—41no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×D4—91no—
337C22×C3×C4—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C22×Dic3—91no—
343C22×Dic3—91no—
344C22×Dic3—91no—
345#239—184no—
346#239—184no—
347#237—184no—
348#235—184no—
349C2×D12—31no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×D12—181no—
357C2×C4×D3—31no—
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—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3—181no—
370C2×Dic6C2×D911yescharacteristic
371C2×Dic6C2×D911yescharacteristic
372C3×C4⋊C4—21no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4C2×D911yescharacteristic
378C3×C4⋊C4D3211yescharacteristic
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C42—31no—
383#217—91no—
384(C2×D3)⋊C4—31no—
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)⋊C4—181no—
399C4⋊Dic3—91no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3C2×D911yescharacteristic
403Dic3⋊C4—31no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—181no—
412Dic3⋊C4C2×D911yescharacteristic
413Dic3⋊C4C2×D911yescharacteristic
414C4×Dic3C2×D911yescharacteristic
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—32no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
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—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C3×Dic3D3×D412yes—
438C3×Dic3#23912yes—
439C22×C9—21no—
440C22×C9C23×D311yescharacteristic
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—32no—
447C2×D9—62no—
448C2×D9—61no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9D3×D412yes—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—32no—
463C4×C9—32no—
464C4×C9—41no—
465C4×C9—41no—
466C4×C9—41no—
467C4×C9—61no—
468C4×C9—61no—
469Dic9—21no—
470Dic9—21no—
471Dic9—61no—
472Dic9—61no—
473Dic9—121no—
474Dic9—121no—
475C2×#41—271no—
476C2×#41—271no—
477C4⋊Q8—31no—
478#123—91no—
479#123—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—271no—
485#121—271no—
486C4×D4—271no—
487C4×D4—271no—
488C2×C4⋊C4—271no—
489C2×C4⋊C4—271no—
490C3×C9#54711yescharacteristic, complemented, Sylow
491C23×C3—91no—
492C23×C3—91no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—91no—
498C22×D3—91no—
499C22×D3—181no—
500C22×D3—181no—
501C3×Q8—62no—
502C3×Q8—62no—
503C3×D4—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—31no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—182no—
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—94no—
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—181no—
531C2×Dic3—181no—
532C2×Dic3—182no—
533C2×Dic3—182no—
534C2×Dic3—182no—
535C2×Dic3C22×D911yescharacteristic
536C2×Dic3C22×D911yescharacteristic
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539D12—62no—
540D12—94no—
541D12—182no—
542D12—182no—
543D12—182no—
544D12—182no—
545D12—182no—
546D12—362no—
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—182no—
557C4×D3—182no—
558C4×D3—182no—
559C4×D3—362no—
560Dic6—22no—
561Dic6—22no—
562C2×C32C2×D3×D411yescharacteristic
563C2×C32C2×#23911yescharacteristic
564C2×C32#100711yescharacteristic
565C3⋊D3—62no—
566C3⋊D3—121no—
567C3×D3—62no—
568C3×D3—121no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—21no—
572C2×C9C2×D3×D411yescharacteristic
573C2×C9D3×#4111yescharacteristic
574C2×C9#101011yescharacteristic
575D9—22no—
576D9—41no—
577D9—62no—
578D9—122no—
579D9—121no—
580D9—241no—
581#41—544no—
582#41—544no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×D4—91no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C22×C4—91no—
592C22×C4—271no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4D3×D911yescharacteristic
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—31no—
618C22×C3—21no—
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—32no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—92no—
634C2×D3—92no—
635C2×D3—182no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—361no—
647C2×D3—361no—
648C2×D3—361no—
649C2×D3—361no—
650C2×D3—361no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—32no—
658C3×C4—32no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—181no—
665C3×C4—181no—
666Dic3—21no—
667Dic3—21no—
668Dic3—61no—
669Dic3—61no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—361no—
675Dic3—361no—
676Dic3D4×D912yes—
677Dic3#370112yescomplemented
678C32#572611yescharacteristic
679C9—21no—
680C9#565511yescharacteristic, complemented
681C23—91no—
682C23—91no—
683C23—271no—
684C23—271no—
685Q8—62no—
686Q8—62no—
687D4—182no—
688D4—274no—
689D4—542no—
690D4—542no—
691D4—542no—
692D4—542no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—182no—
700C2×C4—271no—
701C2×C4—271no—
702C2×C4—542no—
703C2×C4—542no—
704C2×C4—542no—
705C2×C4—542no—
706C2×C4—542no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4C2×D3×D911yescharacteristic
710C2×C4C2×D3×D911yescharacteristic
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—182no—
716C2×C3—361no—
717C2×C3C2×D4×D911yescharacteristic
718C2×C3C2×#370111yescharacteristic
719C2×C3#6371311yescharacteristic
720C2×C3#6429711yescharacteristic
721C2×C3D32×D411yescharacteristic
722C2×C3D3×#23911yescharacteristic
723D3—62no—
724D3—121no—
725D3—182no—
726D3—182no—
727D3—362no—
728D3—361no—
729D3—361no—
730D3—721no—
731C22—92no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—272no—
738C22—541no—
739C22—541no—
740C22—541no—
741C22—541no—
742C22—541no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—32no—
748C4—32no—
749C4—61no—
750C4—61no—
751C4—181no—
752C4—181no—
753C4—541no—
754C4—541no—
755C3—21no—
756C3#1058982811yescharacteristic, complemented
757C3#1059437211yescharacteristic
758C2—182no—
759C2—361no—
760C2—542no—
761C2—1081no—
762C2#1172245811yescharacteristic
763C2D3×D4×D911yescharacteristic
764C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#547
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×#88635C2semidirect
2. C2×#88634C2semidirect
3. #11721750C2semidirect
4. C3×#63456C2semidirect
5. C9×#888C2semidirect
6. #11721005C2semidirect
7. #11720988C2semidirect
8. #11720986C2semidirect
9. #11720984C2semidirect
10. #11720983C2semidirect
11. #11720980C2semidirect
12. #11720977C2semidirect
13. #11720977C2semidirect
14. D9×Dic3⋊C4C2semidirect
15. #11720942C2semidirect
81. #63456D3semidirect
110. #6192D4semidirect
221. C9×Dic3#41semidirect
246. #888D9semidirect
490. C3×C9#547semidirect
677. Dic3#3701semidirect
680. C9#5655semidirect
756. C3#10589828semidirect

Maximal subgroups

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

subgroupindex
C2×#886352
C2×#886342
#117217502
C3×#634562
C9×#8882
#117210052
#117209882
#117209862
#117209842
#117209832
#117209802
#117209772
D9×Dic3⋊C42
#117209422
#105943723
#105898283