Finite Group Databasebeta

← #13148331

Subgroups — #13148331

Order 1728.

810 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721725C211yesmaximal, characteristic, complemented
2C9×#882C211yesmaximal, characteristic, complemented
3C3×#63447C211yesmaximal, characteristic, complemented
4#11721286C211yesmaximal, characteristic, complemented
5#11721280C211yesmaximal, characteristic, complemented
6D3×#3676C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721028C211yesmaximal, characteristic, complemented
9D12×Dic9C211yesmaximal, characteristic, complemented
10#11721018C211yesmaximal, characteristic, complemented
11#11721016C211yesmaximal, characteristic, complemented
12#11721016C211yesmaximal, characteristic, complemented
13#11720989C211yesmaximal, characteristic, complemented
14#11720967C211yesmaximal, characteristic, complemented
15#11720963C211yesmaximal, characteristic, complemented
16#10594122—31nomaximal
17#10589695—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C2×C9×#67C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C9×D12C2211yescharacteristic
22C2×C9×D12C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic, complemented
24C2×#6194C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×#6194C2211yescharacteristic, complemented
27C2×D3×Dic9C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×D3×Dic9C2211yescharacteristic, complemented
30C2×Dic3×D9C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88551C2211yescharacteristic
33#88551C2211yescharacteristic
34C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
35#88534C2211yescharacteristic, complemented
36#88534C2211yescharacteristic, complemented
37C4×C3⋊Dic9C2211yescharacteristic, complemented
38C3×#3676C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C3×C4×Dic9C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64088—31no—
54C3×#885—31no—
55C3×#882D311yescharacteristic
56#63976—31no—
57#63970—31no—
58#63969—31no—
59D3×#217—31no—
60#63902—31no—
61Dic3×D12—31no—
62#63891—31no—
63#63887—31no—
64#63885—31no—
65#63885—31no—
66#63863—31no—
67#63859—31no—
68C9×#120—31no—
69#63515—31no—
70C2×#3676—31no—
71#63501—31no—
72#63501—31no—
73#63500—31no—
74#63498—31no—
75#63497—31no—
76D4×Dic9—31no—
77#63447D311yescharacteristic, complemented
78#63445—31no—
79#611⋊C4—31no—
80#63441—31no—
81#63441—31no—
82#63441—61no—
83#63440—31no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9—22no—
86C22×D3×C9—41no—
87C22×D3×C9—41no—
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C9×#67—41no—
99C3×#611—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C9×D12—22no—
105C9×D12—41no—
106C3×Dic18—41no—
107#6194—22no—
108#6194—41no—
109#6194—41no—
110D3×Dic9—41no—
111D3×Dic9—41no—
112D3×Dic9—41no—
113Dic3×D9—41no—
114#5678—91no—
115#5593—91no—
116C23×C3×D3C2×D311yescharacteristic
117C2×C3×#67—31no—
118C2×C3×#67C2×D311yescharacteristic
119C2×C3×D12C2×D311yescharacteristic
120C2×C3×D12C2×D311yescharacteristic
121C2×C3×Dic6—31no—
122C2×#625—31no—
123C2×#625—31no—
124C2×#625—31no—
125C2×D3×Dic3—31no—
126C2×D3×Dic3—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129C24×C9—31no—
130C32×C22⋊C4C2×D311yescharacteristic
131#3757—31no—
132#3757—31no—
133C4⋊(C3⋊Dic3)—31no—
134#3750—31no—
135#3750—31no—
136C4×C3⋊Dic3—31no—
137C3×#217—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×(C2×D3)⋊C4C2×D311yescharacteristic
142C3×C4×Dic3—31no—
143#3724—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152C2×D4×C9—31no—
153C2×D4×C9—31no—
154C2×D4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611C2×D311yescharacteristic
159C22×Dic9—31no—
160C22×Dic9—31no—
161C22×Dic9—31no—
162C2×C4×D9—31no—
163C2×Dic18C2×D311yescharacteristic, complemented
164C9×C22⋊C4—21no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4—31no—
167C9×C22⋊C4C2×D311yescharacteristic
168#3676—31no—
169#3676—31no—
170#3676—31no—
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—31no—
176#3676—61no—
177#3676—61no—
178#3676C2×D311yescharacteristic
179(C2×D9)⋊C4C2×D311yescharacteristic, complemented
180(C2×D9)⋊C4C2×D311yescharacteristic, complemented
181C4⋊Dic9—31no—
182C4⋊Dic9—31no—
183C4⋊Dic9—61no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—61no—
189Dic9⋊C4—61no—
190C4×Dic9—31no—
191C4×Dic9—61no—
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C2411yescharacteristic
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—44no—
206C2×D3×C9#4112yes—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#124—91no—
221C3×#120—31no—
222#953—91no—
223C2×#217—91no—
224#947—91no—
225#946—91no—
226#939—91no—
227#939—91no—
228#939—91no—
229#938—91no—
230#937—91no—
231#936—91no—
232#935—91no—
233D4×Dic3—91no—
234#886—91no—
235#885—31no—
236#884—91no—
237#884—91no—
238#883—91no—
239#883—91no—
240#882D911yescharacteristic, complemented
241#67⋊C4—91no—
242#67⋊C4—91no—
243D3×C22⋊C4—91no—
244#879—91no—
245#879—91no—
246#879—91no—
247#879—181no—
248#878—91no—
249#876—91no—
250C4×D12—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3×D3—22no—
253C22×C3×D3—31no—
254C22×C3×D3—41no—
255C22×C3×D3—41no—
256C22×C3×D3C22×D311yescharacteristic
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C3×#67—41no—
266C3×#67—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3C22×D311yescharacteristic
271C3×D12—22no—
272C3×D12—41no—
273C3×Dic6—121no—
274#625—62no—
275#625—121no—
276#625—121no—
277D3×Dic3—121no—
278D3×Dic3—121no—
279D3×Dic3—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9—31no—
284C23×C9—31no—
285C23×C9—62no—
286C23×C9—121no—
287C23×C9—121no—
288C23×C9C22×D311yescharacteristic
289C22×D9C22×D311yescharacteristic
290D4×C9—62no—
291D4×C9—121no—
292D4×C9—121no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9C22×D311yescharacteristic
297C2×C4×C9C22×D311yescharacteristic
298#611—41no—
299#611—62no—
300#611—121no—
301#611—121no—
302C2×Dic9—31no—
303C2×Dic9—31no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—61no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—121no—
311C2×Dic9—121no—
312C2×Dic9—121no—
313C2×Dic9C22×D311yescharacteristic
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316C4×D9—121no—
317Dic18—41no—
318#538—271noSylow
319C2×C3×C9—41no—
320C2×C3×C9C2×#4111yescharacteristic
321C2×C3×C9H(5,𝔽2)11yescharacteristic
322C2×C3×C9H(5,𝔽2)11yescharacteristic
323D3×C9—22no—
324D3×C9—41no—
325D3×C9—41no—
326C3×D9—41no—
327C24×C3—31no—
328C23×D3C2×D911yescharacteristic
329C2×C3×Q8—91no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—91no—
334C2×#67—31no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67C2×D911yescharacteristic
342C22×Dic3—91no—
343C22×Dic3—91no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346C2×D12C2×D911yescharacteristic
347C2×D12C2×D911yescharacteristic
348C2×C4×D3—91no—
349C2×C4×D3—91no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×Dic6—31no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—91no—
357C3×C22⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4C2×D911yescharacteristic
360C3×C22⋊C4D3211yescharacteristic
361C3×C42—91no—
362#217—31no—
363#217—91no—
364#217—91no—
365#217—91no—
366#217—91no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—181no—
374#217—181no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4C2×D911yescharacteristic
384(C2×D3)⋊C4C2×D911yescharacteristic
385C4⋊Dic3—91no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—91no—
389C4⋊Dic3—181no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—181no—
399Dic3⋊C4—181no—
400C4×Dic3—31no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—181no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32C23×D311yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—44no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3#23712yes—
421C32×C4—21no—
422C32×C4—21no—
423C3⋊Dic3—61no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3×Dic3—21no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C22×C9—21no—
432C22×C9—21no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—32no—
436C22×C9—41no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—61no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9—61no—
445C22×C9—61no—
446C22×C9—61no—
447C22×C9—124no—
448C22×C9C23×D311yescharacteristic
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C4×C9—21no—
453C4×C9—21no—
454C4×C9—41no—
455C4×C9—41no—
456C4×C9—61no—
457Dic9—21no—
458Dic9—21no—
459Dic9—21no—
460Dic9—61no—
461Dic9—61no—
462Dic9—61no—
463Dic9—61no—
464Dic9—121no—
465Dic9—121no—
466Dic9—121no—
467Dic9—121no—
468#126—271no—
469#126—271no—
470#124—91no—
471#124—271no—
472#123—271no—
473#123—271no—
474C22⋊Q8—271no—
475#121—271no—
476#121—271no—
477#121—271no—
478#120—31no—
479#120—271no—
480C4×D4—271no—
481C4×D4—271no—
482C2×C22⋊C4—271no—
483C3×C9#53811yescharacteristic, complemented, Sylow
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—62no—
489C23×C3—91no—
490C23×C3—121no—
491C23×C3—121no—
492C23×C3C22×D911yescharacteristic
493C23×C3C2×D3211yescharacteristic
494C22×D3—22no—
495C22×D3—31no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3C22×D911yescharacteristic
499C22×D3C22×D911yescharacteristic
500C22×D3C22×D911yescharacteristic
501C3×Q8—361no—
502C3×D4—62no—
503C3×D4—121no—
504C3×D4—121no—
505C3×D4—361no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516#67—41no—
517#67—121no—
518#67—182no—
519#67—182no—
520#67—361no—
521#67—361no—
522#67—361no—
523#67—361no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—181no—
538C2×Dic3—181no—
539C2×Dic3—361no—
540C2×Dic3—361no—
541C2×Dic3—361no—
542C2×Dic3—361no—
543C2×Dic3C22×D911yescharacteristic
544D12—22no—
545D12—41no—
546C4×D3—361no—
547C4×D3—361no—
548C4×D3—361no—
549C4×D3—361no—
550Dic6—121no—
551C2×C32—41no—
552C2×C32C2×#23711yescharacteristic
553C2×C32#100411yescharacteristic
554C2×C32#100411yescharacteristic
555C3×D3—22no—
556C3×D3—41no—
557C3×D3—41no—
558C3×D3—121no—
559C2×C9—21no—
560C2×C9—21no—
561C2×C9—21no—
562C2×C9—41no—
563C2×C9—62no—
564C2×C9—81no—
565C2×C9—121no—
566C2×C9—121no—
567C2×C9#100411yescharacteristic
568C2×C9D3×#4111yescharacteristic
569C2×C9#100911yescharacteristic
570D9—41no—
571C24—31no—
572C2×Q8—91no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—31no—
576C2×D4—91no—
577C2×D4—271no—
578C2×D4—271no—
579C2×D4—271no—
580C22×C4—271no—
581C22×C4—271no—
582C22×C4—271no—
583C22×C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4—271no—
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4D3×D911yescharacteristic
604C42—91no—
605C42—271no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—32no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—124no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3C23×D911yescharacteristic
630C22×C3C22×D3211yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—44no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3#369912yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—61no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654Dic3—21no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—181no—
659Dic3—181no—
660Dic3—181no—
661Dic3—181no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—361no—
667Dic3—361no—
668Dic3—361no—
669Dic3—361no—
670C32#559311yescharacteristic
671C9—21no—
672C9#567811yescharacteristic, complemented
673C23—31no—
674C23—31no—
675C23—31no—
676C23—62no—
677C23—91no—
678C23—121no—
679C23—121no—
680C23C2×D3×D911yescharacteristic
681Q8—361no—
682D4—62no—
683D4—121no—
684D4—121no—
685D4—361no—
686D4—542no—
687D4—1081no—
688D4—1081no—
689C2×C4—31no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—271no—
694C2×C4—271no—
695C2×C4—271no—
696C2×C4—271no—
697C2×C4—1081no—
698C2×C4—1081no—
699C2×C4—1081no—
700C2×C4—1081no—
701C2×C4C2×D3×D911yescharacteristic
702C2×C4C2×D3×D911yescharacteristic
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—62no—
709C2×C3—81no—
710C2×C3—121no—
711C2×C3—121no—
712C2×C3—361no—
713C2×C3C2×#369911yescharacteristic
714C2×C3#6371011yescharacteristic
715C2×C3#6371011yescharacteristic
716C2×C3#6430711yescharacteristic
717C2×C3D3×#23711yescharacteristic
718C2×C3#6431311yescharacteristic
719D3—22no—
720D3—41no—
721D3—41no—
722D3—121no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—32no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—124no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22C22×D3×D911yescharacteristic
740C4—21no—
741C4—21no—
742C4—61no—
743C4—181no—
744C4—181no—
745C4—181no—
746C4—541no—
747C4—541no—
748C4—541no—
749C4—541no—
750C3—21no—
751C3#1058969511yescharacteristic, complemented
752C3#1059412211yescharacteristic
753C2—41no—
754C2—62no—
755C2—121no—
756C2—121no—
757C2—361no—
758C2#1172247611yescharacteristic
759C2D3×#369911yescharacteristic
760C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721725C2semidirect
2. C9×#882C2semidirect
3. C3×#63447C2semidirect
4. #11721286C2semidirect
5. #11721280C2semidirect
6. D3×#3676C2semidirect
7. #11721270C2semidirect
8. #11721028C2semidirect
9. D12×Dic9C2semidirect
10. #11721018C2semidirect
11. #11721016C2semidirect
12. #11721016C2semidirect
13. #11720989C2semidirect
14. #11720967C2semidirect
15. #11720963C2semidirect
23. C2×C3×Dic18C22semidirect
26. C2×#6194C22semidirect
29. C2×D3×Dic9C22semidirect
30. C2×Dic3×D9C22semidirect
34. C4⋊(C3⋊Dic9)C22semidirect
35. #88534C22semidirect
36. #88534C22semidirect
37. C4×C3⋊Dic9C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C3×C4×Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
77. #63447D3semidirect
163. C2×Dic18C2×D3semidirect
179. (C2×D9)⋊C4C2×D3semidirect
180. (C2×D9)⋊C4C2×D3semidirect
192. C4×Dic9C2×D3semidirect
240. #882D9semidirect
483. C3×C9#538semidirect
672. C9#5678semidirect
751. C3#10589695semidirect

Maximal subgroups

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

subgroupindex
#117217252
C9×#8822
C3×#634472
#117212862
#117212802
D3×#36762
#117212702
#117210282
D12×Dic92
#117210182
#117210162
#117209892
#117209672
#117209632
#105941223
#105896953