Finite Group Databasebeta

← #13147744

Subgroups — #13147744

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C9×#876C211yesmaximal, characteristic, complemented
3C3×#63437C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic, complemented
5#11721049C211yesmaximal, characteristic, complemented
6#11721048C211yesmaximal, characteristic, complemented
7#11721041C211yesmaximal, characteristic, complemented
8#11721035C211yesmaximal, characteristic, complemented
9#11721005C211yesmaximal, characteristic, complemented
10#11720989C211yesmaximal, characteristic, complemented
11#11720985C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720978C211yesmaximal, characteristic, complemented
14#11720949C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10594019—31nomaximal
17#10589806—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×D36C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic, complemented
24C2×#6195C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic, complemented
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic, complemented
31C3×C42×C9C2211yescharacteristic, complemented
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic, complemented
34C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C4×C4⋊(C3⋊D3)—31no—
54C3×#876D311yescharacteristic
55C3×#875—31no—
56#63923—31no—
57#63922—31no—
58#63921—31no—
59#63912—31no—
60#63910—31no—
61#63907—31no—
62#63891—31no—
63#63888—31no—
64#63886—31no—
65#63881—31no—
66#63861—31no—
67#63853—31no—
68C9×#126—31no—
69#63460—31no—
70#63458—31no—
71#63457—31no—
72#63457—31no—
73#63456—31no—
74#63455—31no—
75#63447—31no—
76#63446—31no—
77#63445—31no—
78#63444—31no—
79#63444—31no—
80C22⋊C4×D9—31no—
81#63437D311yescharacteristic, complemented
82C4×D36—31no—
83C4×D36—61no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4⋊(C3⋊D9)—22no—
98C4×C3⋊D9—41no—
99C4×C3⋊D9—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×D36—41no—
106C3×Dic18—41no—
107#6195—41no—
108#6194—41no—
109#6192—22no—
110#6192—41no—
111#6192—41no—
112(C3⋊D9)⋊C4—41no—
113Dic3×D9—41no—
114#5704—91no—
115#5678—91no—
116C22×D32—31no—
117C2×C4⋊(C3⋊D3)—31no—
118C2×C4×C3⋊D3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C3×D12—31no—
121C2×C3×Dic6—31no—
122C2×#626—31no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#625—31no—
127C2×#624—31no—
128C2×D3×Dic3—31no—
129C23×D9—31no—
130C32×C42C2×D311yescharacteristic
131#3752—31no—
132#3752—31no—
133C4⋊(C3⋊Dic3)—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×Dic3⋊C4C2×D311yescharacteristic
142C3×Dic3⋊C4C2×D311yescharacteristic
143C3×Dic3⋊C4C2×D311yescharacteristic
144#3724—31no—
145Dic3⋊Dic3—31no—
146#3722—31no—
147#3722—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×#611—31no—
153C2×#611—31no—
154C2×D36—31no—
155C2×D36—31no—
156C2×D36—31no—
157C2×D36—31no—
158C2×D36—61no—
159C2×D36C2×D311yescharacteristic
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C2×C4×D9—61no—
165C2×C4×D9—61no—
166C2×Dic18C2×D311yescharacteristic, complemented
167C9×C4⋊C4—31no—
168C9×C4⋊C4—31no—
169C9×C4⋊C4—31no—
170C9×C22⋊C4—31no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C42×C9—21no—
174C42×C9C2×D311yescharacteristic, complemented
175#3676—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—61no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4C2×D311yescharacteristic
185(C2×D9)⋊C4C2×D311yescharacteristic
186(C2×D9)⋊C4C2×D311yescharacteristic, complemented
187(C2×D9)⋊C4C2×D311yescharacteristic, complemented
188C4⋊Dic9—31no—
189C4⋊Dic9—61no—
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192C4×Dic9—31no—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9#4112yes—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209D3×D9—44no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3×C4×C9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—31no—
221C3×#124—91no—
222#947—91no—
223#946—91no—
224#939—91no—
225#937—91no—
226#898—91no—
227#896—91no—
228#895—91no—
229#895—91no—
230#894—91no—
231#893—91no—
232#886—91no—
233#885—91no—
234#884—91no—
235#884—91no—
236#884—91no—
237#883—91no—
238#883—91no—
239#882—91no—
240#882—91no—
241#882—91no—
242#67⋊C4—91no—
243D3×C22⋊C4—91no—
244D3×C22⋊C4—91no—
245#879—91no—
246#876D911yescharacteristic, complemented
247#875—31no—
248C4×D12—91no—
249C4×D12—91no—
250C4×D12—181no—
251C22×C3⋊D3—31no—
252C22×C3⋊D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3C22×D311yescharacteristic
256C2×D32—62no—
257C2×D32—121no—
258C2×D32—121no—
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—121no—
266C4×C3⋊D3—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×D12—121no—
273C3×Dic6—121no—
274#626—62no—
275#626—121no—
276#626—121no—
277#626—121no—
278#625—121no—
279#624—121no—
280D3×Dic3—121no—
281C23×C9—31no—
282C22×D9—31no—
283C22×D9—31no—
284C22×D9—61no—
285C22×D9—61no—
286C22×D9—62no—
287C22×D9—121no—
288C22×D9—121no—
289C22×D9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—31no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9C22×D311yescharacteristic
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300#611—121no—
301#611—121no—
302C2×Dic9—31no—
303C2×Dic9—31no—
304C2×Dic9—61no—
305C2×Dic9—61no—
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308D36—41no—
309D36—62no—
310D36—64no—
311D36—62no—
312D36—121no—
313D36—121no—
314C4×D9—121no—
315C4×D9—121no—
316C4×D9—121no—
317C4×D9—121no—
318C4×D9—122no—
319C4×D9—122no—
320Dic18—41no—
321#538—271noSylow
322C2×C3×C9C2×#4111yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C3⋊D9—22no—
326C3⋊D9—41no—
327D3×C9—41no—
328C3×D9—41no—
329C3×D9—41no—
330C23×D3—91no—
331C23×D3—91no—
332C2×C3×Q8—91no—
333C2×C3×D4—91no—
334C2×#67—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C22×Dic3—91no—
341C2×D12—31no—
342C2×D12—91no—
343C2×D12—91no—
344C2×D12—91no—
345C2×D12—91no—
346C2×D12—91no—
347C2×D12—91no—
348C2×D12—181no—
349C2×C4×D3—91no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—181no—
357C2×C4×D3—181no—
358C2×Dic6—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C42—21no—
370C3×C42C2×D911yescharacteristic, complemented
371C3×C42D3211yescharacteristic
372#217—91no—
373#217—91no—
374#217—91no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—181no—
391(C2×D3)⋊C4—181no—
392(C2×D3)⋊C4C2×D911yescharacteristic
393(C2×D3)⋊C4C2×D911yescharacteristic
394(C2×D3)⋊C4C2×D911yescharacteristic
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398C4⋊Dic3—181no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4C2×D911yescharacteristic, complemented
403Dic3⋊C4C2×D911yescharacteristic, complemented
404Dic3⋊C4C2×D911yescharacteristic, complemented
405C4×Dic3—91no—
406C4×Dic3—91no—
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—32no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—61no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423D32—124no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C22×C9—21no—
435C22×C9—61no—
436C22×C9—61no—
437C22×C9—61no—
438C22×C9C23×D311yescharacteristic
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—32no—
446C2×D9—62no—
447C2×D9—61no—
448C2×D9—61no—
449C2×D9—62no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—124no—
458C4×C9—22no—
459C4×C9—22no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—21no—
463C4×C9—41no—
464C4×C9—61no—
465C4×C9—61no—
466C4×C9—61no—
467Dic9—21no—
468Dic9—21no—
469Dic9—61no—
470Dic9—61no—
471Dic9—121no—
472Dic9—121no—
473#126—31no—
474#126—271no—
475#124—91no—
476#124—271no—
477#123—271no—
478#123—271no—
479C22⋊Q8—271no—
480#121—271no—
481#121—271no—
482#121—271no—
483#120—271no—
484#120—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C22⋊C4—271no—
488C3×C9#53811yescharacteristic, 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—91no—
497C22×D3—91no—
498C22×D3—181no—
499C22×D3—181no—
500C22×D3—182no—
501C22×D3—182no—
502C22×D3—361no—
503C22×D3—361no—
504C22×D3—361no—
505C22×D3—361no—
506C22×D3C22×D911yescharacteristic
507C3×Q8—361no—
508C3×D4—361no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C22×D911yescharacteristic
519C2×C3×C4C22×D911yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523#67—182no—
524#67—361no—
525#67—361no—
526#67—361no—
527#67—361no—
528#67—361no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—361no—
538C2×Dic3C22×D911yescharacteristic
539C2×Dic3C22×D911yescharacteristic
540C2×Dic3C22×D911yescharacteristic
541D12—121no—
542D12—182no—
543D12—182no—
544D12—184no—
545D12—182no—
546D12—361no—
547D12—361no—
548D12—361no—
549C4×D3—361no—
550C4×D3—361no—
551C4×D3—361no—
552C4×D3—361no—
553C4×D3—361no—
554C4×D3—361no—
555C4×D3—361no—
556C4×D3—362no—
557C4×D3—362no—
558Dic6—121no—
559C2×C32D3×#4111yescharacteristic
560C2×C32#100911yescharacteristic
561C2×C32#100911yescharacteristic
562C3⋊D3—62no—
563C3⋊D3—121no—
564C3×D3—41no—
565C3×D3—121no—
566C3×D3—121no—
567C2×C9—21no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—121no—
571C2×C9#100411yescharacteristic
572C2×C9D3×#4111yescharacteristic
573C2×C9#100911yescharacteristic
574D9—41no—
575D9—41no—
576D9—62no—
577D9—122no—
578D9—122no—
579D9—121no—
580C24—271no—
581C2×Q8—91no—
582C2×D4—91no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4—271no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—91no—
603C22⋊C4—91no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C42—271no—
614C42D3×D911yescharacteristic, complemented
615C22×C3—21no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—181no—
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—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—92no—
637C2×D3—92no—
638C2×D3—182no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—182no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—361no—
651C2×D3—361no—
652C2×D3—361no—
653C2×D3—361no—
654C2×D3—364no—
655C2×D3—364no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—181no—
669C3×C4—181no—
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—61no—
674Dic3—61no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—361no—
680Dic3—361no—
681C32#570411yescharacteristic
682C9—21no—
683C9#567811yescharacteristic, complemented
684C23—31no—
685C23—91no—
686C23—91no—
687C23—271no—
688C23—271no—
689C23—542no—
690C23—1081no—
691C23—1081no—
692Q8—361no—
693D4—361no—
694D4—542no—
695D4—542no—
696D4—1081no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—1081no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4—1081no—
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×C3—361no—
720C2×C3#41×D911yescharacteristic
721C2×C3#6371511yescharacteristic
722C2×C3#6371511yescharacteristic
723C2×C3#6430611yescharacteristic
724C2×C3#6430711yescharacteristic
725C2×C3#6430811yescharacteristic
726D3—41no—
727D3—121no—
728D3—121no—
729D3—182no—
730D3—182no—
731D3—362no—
732D3—362no—
733D3—361no—
734D3—361no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—272no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22—1084no—
751C22C22×D3×D911yescharacteristic
752C4—21no—
753C4—21no—
754C4—21no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—181no—
759C4—181no—
760C4—541no—
761C4—541no—
762C3—21no—
763C3#1058980611yescharacteristic, complemented
764C3#1059401911yescharacteristic
765C2—121no—
766C2—361no—
767C2—361no—
768C2—542no—
769C2—1081no—
770C2#1172247511yescharacteristic
771C2#1172247711yescharacteristic
772C2#1172247811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
hypercenterC42D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C3⋊D9)C2semidirect
2. C9×#876C2semidirect
3. C3×#63437C2semidirect
4. #11721051C2semidirect
5. #11721049C2semidirect
6. #11721048C2semidirect
7. #11721041C2semidirect
8. #11721035C2semidirect
9. #11721005C2semidirect
10. #11720989C2semidirect
11. #11720985C2semidirect
12. #11720983C2semidirect
13. #11720978C2semidirect
14. #11720949C2semidirect
15. #11720941C2semidirect
21. C2×C4×C3⋊D9C22semidirect
23. C2×C3×Dic18C22semidirect
28. C2×#6192C22semidirect
30. C2×Dic3×D9C22semidirect
31. C3×C42×C9C22semidirect
33. #88536C22semidirect
34. C4⋊(C3⋊Dic9)C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
47. #88445C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
81. #63437D3semidirect
166. C2×Dic18C2×D3semidirect
174. C42×C9C2×D3semidirect
186. (C2×D9)⋊C4C2×D3semidirect
187. (C2×D9)⋊C4C2×D3semidirect
246. #876D9semidirect
370. C3×C42C2×D9semidirect
402. Dic3⋊C4C2×D9semidirect
403. Dic3⋊C4C2×D9semidirect
404. Dic3⋊C4C2×D9semidirect
488. C3×C9#538semidirect
614. C42D3×D9semidirect
683. C9#5678semidirect
763. C3#10589806semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C3⋊D9)2
C9×#8762
C3×#634372
#117210512
#117210492
#117210482
#117210412
#117210352
#117210052
#117209892
#117209852
#117209832
#117209782
#117209492
#117209412
#105940193
#105898063