Finite Group Databasebeta

← #13148816

Subgroups — #13148816

Order 1728.

956 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88641C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3#11721752C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63457C211yesmaximal, characteristic, complemented
6#11721041C211yesmaximal, characteristic, complemented
7#11721034C211yesmaximal, characteristic, complemented
8#11721033C211yesmaximal, characteristic, complemented
9#11720996C211yesmaximal, characteristic, complemented
10#11720984C211yesmaximal, characteristic, complemented
11#11720983C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10594368—31nomaximal
17#10589731—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic
36C2×Dic3×D9C2211yescharacteristic
37#88641—24no—
38#88634—24no—
39C3×C9×C4⋊C4C2211yescharacteristic
40#88536C2211yescharacteristic
41#88536C2211yescharacteristic
42#88534C2211yescharacteristic
43#88534C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C9×(C2×D3)⋊C4C2211yescharacteristic
46C3×(C2×D9)⋊C4C2211yescharacteristic
47C3×(C2×D9)⋊C4C2211yescharacteristic
48C9×Dic3⋊C4C2211yescharacteristic
49C9×Dic3⋊C4C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic
53#88442C2211yescharacteristic
54Dic9⋊Dic3C2211yescharacteristic
55C2×#3796—31no—
56C2×#3795—31no—
57#64105—31no—
58C3×#896D311yescharacteristic
59C3×#895—31no—
60#63912—31no—
61#63906—31no—
62#63906—31no—
63#63896—31no—
64#63887—31no—
65#63886—31no—
66#63886—31no—
67#63885—31no—
68#63885—31no—
69D3×Dic3⋊C4—31no—
70C2×#3701—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63508—31no—
74#63492—31no—
75#63458—31no—
76#63458—31no—
77#63458—61no—
78#63457—31no—
79#63457—31no—
80#63457D311yescharacteristic, complemented
81C4⋊C4×D9—31no—
82#63446—31no—
83#63446—31no—
84#63446—31no—
85#63446—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4×C3⋊D9—22no—
98#6226—22no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C4×D3×C9—22no—
104C3×D36—22no—
105C3×D36—22no—
106C3×D36—41no—
107C3×C4×D9—41no—
108C9×Dic6—22no—
109#6195—41no—
110#6194—22no—
111#6194—22no—
112#6194—41no—
113#6192—22no—
114#6192—22no—
115#6192—41no—
116Dic3×D9—22no—
117Dic3×D9—22no—
118Dic3×D9—41no—
119Dic3×D9D414yescomplemented
120#5629—91no—
121#5597—91no—
122C2×C4×C3⋊D3—31no—
123C2×#634—31no—
124C2×C3×D12—31no—
125C2×C3×D12—31no—
126C2×C3×D12—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×Dic6C2×D311yescharacteristic
130C2×#626—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#625—31no—
135C2×#625—31no—
136C2×#625—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—31no—
141#3796—64no—
142#3795—64no—
143C32×C4⋊C4C2×D311yescharacteristic
144#3752—31no—
145#3752—31no—
146#3750—31no—
147#3750—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×Dic3⋊C4C2×D311yescharacteristic
153C3×Dic3⋊C4C2×D311yescharacteristic
154#3724—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159C2×Q8×C9—31no—
160C22×C4×C9—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165#3701—64no—
166#3697—64no—
167C2×D36—31no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36C2×D311yescharacteristic
171C2×D36C2×D311yescharacteristic
172C2×D36C2×D311yescharacteristic
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—61no—
179C2×C4×D9C2×D311yescharacteristic
180C2×Dic18—31no—
181C2×Dic18—61no—
182C9×C4⋊C4—21no—
183C9×C4⋊C4—31no—
184C9×C4⋊C4—31no—
185C9×C4⋊C4C2×D311yescharacteristic
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4—61no—
194(C2×D9)⋊C4C2×D311yescharacteristic
195(C2×D9)⋊C4C2×D311yescharacteristic
196C4⋊Dic9—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—61no—
202Dic9⋊C4—61no—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9C2×D412yes—
219C3×C4×C9—21no—
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9C2×D412yes—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3C2×D412yes—
228C3×Dic9—21no—
229C2×#239—91no—
230C2×#237—91no—
231C2×#237—91no—
232C2×#235—91no—
233C3×C22⋊Q8—31no—
234C3×#121—91no—
235#946—91no—
236#939—91no—
237#939—91no—
238#939—91no—
239#939—91no—
240#930—91no—
241#930—91no—
242C2×Dic3⋊C4—91no—
243#896—91no—
244#896—91no—
245#896—91no—
246#896—181no—
247#896D911yescharacteristic, complemented
248#895—31no—
249#895—91no—
250#895—91no—
251D3×C4⋊C4—91no—
252#884—91no—
253#884—91no—
254#884—91no—
255#884—91no—
256#884—91no—
257#884—91no—
258#878—91no—
259#878—91no—
260C22×C3⋊D3—31no—
261C22×C3×D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C4×C3⋊D3—62no—
272#634—62no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C3×D12—62no—
278C3×D12—62no—
279C3×D12—121no—
280C3×C4×D3—22no—
281C3×C4×D3—121no—
282C3×Dic6—22no—
283#626—62no—
284#626—62no—
285#626—121no—
286#626—121no—
287#625—62no—
288#625—62no—
289#625—121no—
290D3×Dic3—34no—
291D3×Dic3—62no—
292D3×Dic3—62no—
293D3×Dic3—121no—
294C23×C9—31no—
295C22×D9—31no—
296C22×D9—61no—
297C22×D9C22×D311yescharacteristic
298C22×D9C22×D311yescharacteristic
299C22×D9C22×D311yescharacteristic
300Q8×C9—62no—
301C2×C4×C9—21no—
302C2×C4×C9—21no—
303C2×C4×C9—21no—
304C2×C4×C9—31no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9—62no—
308C2×C4×C9C22×D311yescharacteristic
309C2×C4×C9C22×D311yescharacteristic
310C2×C4×C9C22×D311yescharacteristic
311#611—62no—
312#611—62no—
313#611—121no—
314#611—121no—
315C2×Dic9—31no—
316C2×Dic9—31no—
317C2×Dic9—31no—
318C2×Dic9—61no—
319C2×Dic9—61no—
320C2×Dic9—61no—
321C2×Dic9C22×D311yescharacteristic
322D36—22no—
323D36—22no—
324D36—41no—
325D36—62no—
326D36—62no—
327D36—121no—
328C4×D9—34no—
329C4×D9—41no—
330C4×D9—62no—
331C4×D9—62no—
332C4×D9—62no—
333C4×D9—122no—
334C4×D9—121no—
335Dic18—62no—
336Dic18—122no—
337#537—271noSylow
338C2×C3×C9C22×D411yescharacteristic
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C2×C3×C92−1+411yescharacteristic
341C3⋊D9—41no—
342D3×C9—41no—
343C3×D9—22no—
344C3×D9—41no—
345C3×D9—41no—
346C2×C3×Q8—31no—
347C2×C3×D4—91no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C22×C3×C4—31no—
351C22×C3×C4—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C22×Dic3—91no—
363C22×Dic3—91no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366#239—184no—
367#237—184no—
368#237—184no—
369#235—184no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—91no—
376C2×D12—91no—
377C2×C4×D3—31no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—181no—
385C2×C4×D3C2×D911yescharacteristic
386C2×Dic6—91no—
387C2×Dic6—91no—
388C2×Dic6—181no—
389C2×Dic6C2×D911yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4C2×D911yescharacteristic
394C3×C4⋊C4D3211yescharacteristic
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399#217—91no—
400#217—91no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—181no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4C2×D911yescharacteristic
412(C2×D3)⋊C4C2×D911yescharacteristic
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—181no—
424Dic3⋊C4—181no—
425Dic3⋊C4C2×D911yescharacteristic
426Dic3⋊C4C2×D911yescharacteristic
427C22×C32C23×D311yescharacteristic
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—32no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C3⋊Dic3—32no—
447C3⋊Dic3—61no—
448C3⋊Dic3—61no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—61no—
452C3×Dic3D3×D412yes—
453C22×C9—21no—
454C22×C9—61no—
455C22×C9—61no—
456C22×C9—61no—
457C22×C9C23×D311yescharacteristic
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—21no—
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—62no—
467C2×D9—61no—
468C2×D9—61no—
469C2×D9—61no—
470C2×D9—121no—
471C2×D9—121no—
472C2×D9D3×D412yes—
473C4×C9—21no—
474C4×C9—21no—
475C4×C9—21no—
476C4×C9—32no—
477C4×C9—41no—
478C4×C9—41no—
479C4×C9—41no—
480C4×C9—61no—
481C4×C9—61no—
482Dic9—21no—
483Dic9—32no—
484Dic9—62no—
485Dic9—61no—
486Dic9—61no—
487Dic9—121no—
488Dic9—121no—
489C2×#41—271no—
490C2×#41—271no—
491C22⋊Q8—31no—
492C22⋊Q8—271no—
493C22⋊Q8—271no—
494C22⋊Q8—271no—
495#121—91no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503C2×C4⋊C4—271no—
504C3×C9#53711yescharacteristic, complemented, Sylow
505C23×C3—31no—
506C23×C3—91no—
507C23×C3—91no—
508C23×C3—91no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—31no—
512C22×D3—91no—
513C22×D3—91no—
514C22×D3—181no—
515C22×D3C22×D911yescharacteristic
516C3×Q8—62no—
517C3×D4—182no—
518C3×D4—182no—
519C3×D4—361no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—62no—
527C2×C3×C4—91no—
528C2×C3×C4—361no—
529C2×C3×C4C22×D911yescharacteristic
530C2×C3×C4C22×D911yescharacteristic
531C2×C3×C4C22×D911yescharacteristic
532C2×C3×C4C2×D3211yescharacteristic
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535#67—182no—
536#67—182no—
537#67—182no—
538#67—182no—
539#67—182no—
540#67—182no—
541#67—361no—
542#67—361no—
543#67—361no—
544#67—361no—
545C2×Dic3—31no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—94no—
549C2×Dic3—91no—
550C2×Dic3—91no—
551C2×Dic3—91no—
552C2×Dic3—91no—
553C2×Dic3—181no—
554C2×Dic3—181no—
555C2×Dic3—181no—
556C2×Dic3—182no—
557C2×Dic3—182no—
558C2×Dic3—361no—
559C2×Dic3C22×D911yescharacteristic
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562D12—62no—
563D12—62no—
564D12—121no—
565D12—182no—
566D12—182no—
567D12—361no—
568D12—361no—
569C4×D3—22no—
570C4×D3—94no—
571C4×D3—121no—
572C4×D3—182no—
573C4×D3—182no—
574C4×D3—182no—
575C4×D3—182no—
576C4×D3—362no—
577C4×D3—361no—
578Dic6—22no—
579Dic6—182no—
580Dic6—182no—
581Dic6—362no—
582C2×C32C2×D3×D411yescharacteristic
583C2×C32#100711yescharacteristic
584C2×C32#100911yescharacteristic
585C3⋊D3—121no—
586C3×D3—41no—
587C3×D3—62no—
588C3×D3—121no—
589C3×D3—121no—
590C2×C9—21no—
591C2×C9—21no—
592C2×C9—21no—
593C2×C9—121no—
594C2×C9C2×D3×D411yescharacteristic
595C2×C9#100411yescharacteristic
596C2×C9#101011yescharacteristic
597D9—22no—
598D9—41no—
599D9—41no—
600D9—122no—
601D9—121no—
602#41—544no—
603#41—544no—
604C2×Q8—31no—
605C2×Q8—271no—
606C2×D4—91no—
607C2×D4—91no—
608C2×D4—91no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C2×D4—271no—
616C22×C4—31no—
617C22×C4—91no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4D3×D911yescharacteristic
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22×C3—21no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—92no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3C23×D911yescharacteristic
653C22×C3C22×D3211yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—32no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—182no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—181no—
670C2×D3—181no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—361no—
674C2×D3—361no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—32no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—181no—
688Dic3—21no—
689Dic3—21no—
690Dic3—61no—
691Dic3—92no—
692Dic3—92no—
693Dic3—182no—
694Dic3—181no—
695Dic3—181no—
696Dic3—181no—
697Dic3—181no—
698Dic3—361no—
699Dic3—361no—
700Dic3D4×D912yes—
701C32#562911yescharacteristic
702C9—21no—
703C9#559711yescharacteristic, complemented
704C23—31no—
705C23—91no—
706C23—91no—
707C23—91no—
708C23—271no—
709Q8—62no—
710Q8—542no—
711D4—182no—
712D4—182no—
713D4—361no—
714D4—542no—
715D4—542no—
716D4—542no—
717D4—542no—
718D4—1081no—
719D4—1081no—
720D4—1081no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—62no—
725C2×C4—91no—
726C2×C4—274no—
727C2×C4—271no—
728C2×C4—271no—
729C2×C4—271no—
730C2×C4—361no—
731C2×C4—542no—
732C2×C4—542no—
733C2×C4—542no—
734C2×C4—1081no—
735C2×C4C2×D3×D911yescharacteristic
736C2×C4C2×D3×D911yescharacteristic
737C2×C4C2×D3×D911yescharacteristic
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—121no—
742C2×C3—182no—
743C2×C3—361no—
744C2×C3—361no—
745C2×C3C2×D4×D911yescharacteristic
746C2×C3#6371311yescharacteristic
747C2×C3#6371511yescharacteristic
748C2×C3#6430711yescharacteristic
749C2×C3D32×D411yescharacteristic
750C2×C3#6431511yescharacteristic
751D3—41no—
752D3—62no—
753D3—121no—
754D3—121no—
755D3—362no—
756D3—361no—
757D3—361no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—92no—
762C22—181no—
763C22—181no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22—541no—
771C22—541no—
772C22—541no—
773C22C22×D3×D911yescharacteristic
774C4—21no—
775C4—21no—
776C4—21no—
777C4—32no—
778C4—61no—
779C4—61no—
780C4—181no—
781C4—272no—
782C4—541no—
783C4—541no—
784C3—21no—
785C3#1058973111yescharacteristic, complemented
786C3#1059436811yescharacteristic
787C2—121no—
788C2—182no—
789C2—361no—
790C2—361no—
791C2—1081no—
792C2#1172247711yescharacteristic
793C2D3×D4×D911yescharacteristic
794C2#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#537
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×#88641C2semidirect
2. C2×#88634C2semidirect
3. #11721752C2semidirect
4. C9×#896C2semidirect
5. C3×#63457C2semidirect
6. #11721041C2semidirect
7. #11721034C2semidirect
8. #11721033C2semidirect
9. #11720996C2semidirect
10. #11720984C2semidirect
11. #11720983C2semidirect
12. #11720983C2semidirect
13. #11720982C2semidirect
14. #11720982C2semidirect
15. D9×Dic3⋊C4C2semidirect
80. #63457D3semidirect
119. Dic3×D9D4semidirect
247. #896D9semidirect
504. C3×C9#537semidirect
703. C9#5597semidirect
785. C3#10589731semidirect

Maximal subgroups

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

subgroupindex
C2×#886412
C2×#886342
#117217522
C9×#8962
C3×#634572
#117210412
#117210342
#117210332
#117209962
#117209842
#117209832
#117209822
D9×Dic3⋊C42
#105943683
#105897313