Finite Group Databasebeta

← #13150583

Subgroups — #13150583

Order 1728.

850 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721819C211yesmaximal, characteristic, complemented
2C9×#929C211yesmaximal, characteristic, complemented
3C3×#63492C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721271C211yesmaximal, characteristic, complemented
7#11721256C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9#11721049C211yesmaximal, characteristic, complemented
10#11721005C211yesmaximal, characteristic, complemented
11#11720989C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720958C211yesmaximal, characteristic, complemented
14#11720949C211yesmaximal, characteristic, complemented
15#11720921C211yesmaximal, characteristic, complemented
16#10595090—31nomaximal
17#10589768—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C3×D36C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34#88536C2211yescharacteristic
35#88536C2211yescharacteristic, complemented
36C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
37C9×#217C2211yescharacteristic, complemented
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64139—31no—
54C3×#930—31no—
55C3×#929D311yescharacteristic
56#63983—31no—
57#63979—31no—
58#63971—31no—
59#63958—31no—
60#63923—31no—
61#63922—31no—
62#63910—31no—
63#63891—31no—
64#63886—31no—
65#63861—31no—
66#63854—31no—
67#63848—31no—
68C9×#123—31no—
69#63502—31no—
70#63499—31no—
71#63492—31no—
72#63492—61no—
73#63492D311yescharacteristic, complemented
74#63460—31no—
75#63460—31no—
76#63457—31no—
77#63457—31no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63445—31no—
82#63444—31no—
83#63444—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×D3×D9—41no—
93C2×C3×C4×C9—41no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96#6233—41no—
97#6233—41no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C4⋊(C3⋊D9)—41no—
101C9×#67—41no—
102C3×#611—41no—
103C3×#611—41no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C3×D36—41no—
110#6195—41no—
111#6194—41no—
112#6192—41no—
113#6192—41no—
114#6192—41no—
115(C3⋊D9)⋊C4—41no—
116Dic3×D9—41no—
117#5666—91no—
118#5620—91no—
119C22×D32—31no—
120C22×C32×C4C2×D311yescharacteristic
121C2×#638—31no—
122C2×#638—31no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×D12—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#625—31no—
133C2×#624—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136#3752—31no—
137#3752—31no—
138C4⋊(C3⋊Dic3)—31no—
139C3×#217C2×D311yescharacteristic
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×C4⋊Dic3—31no—
145C3×Dic3⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4C2×D311yescharacteristic
147#3724—31no—
148Dic3⋊Dic3—31no—
149#3722—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154Dic32—31no—
155C2×D4×C9—31no—
156C22×C4×C9—21no—
157C22×C4×C9C2×D311yescharacteristic, complemented
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—61no—
163C2×#611—61no—
164C2×#611C2×D311yescharacteristic
165C2×#611C2×D311yescharacteristic, complemented
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—61no—
171C2×D36C2×D311yescharacteristic
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C9×C4⋊C4—31no—
175C9×C4⋊C4—31no—
176C9×C22⋊C4—31no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179#3676—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—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—61no—
187(C2×D9)⋊C4—61no—
188(C2×D9)⋊C4C2×D311yescharacteristic
189(C2×D9)⋊C4C2×D311yescharacteristic, complemented
190C4⋊Dic9—31no—
191C4⋊Dic9—61no—
192C4⋊Dic9C2×D311yescharacteristic, complemented
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195C4×Dic9—31no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9C2411yescharacteristic
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215D3×D9—44no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3⋊Dic9—21no—
219C3⋊Dic9—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#123—31no—
226C3×#121—91no—
227#940—91no—
228#940—91no—
229#939—91no—
230#939—91no—
231#938—91no—
232#937—91no—
233#937—91no—
234#937—91no—
235#930—31no—
236#930—91no—
237#930—91no—
238#930—181no—
239#929D911yescharacteristic, complemented
240#898—91no—
241#898—91no—
242#898—91no—
243#895—91no—
244#895—91no—
245#894—91no—
246#886—91no—
247#884—91no—
248#884—91no—
249#884—91no—
250#883—91no—
251#883—91no—
252#882—91no—
253#882—91no—
254#882—91no—
255#879—91no—
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3C22×D311yescharacteristic
262C2×D32—121no—
263C2×D32—121no—
264C2×D32—121no—
265C2×C32×C4—41no—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—121no—
269#638—121no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C4⋊(C3⋊D3)—121no—
273C3×#67—41no—
274C3×#67—121no—
275C3×#67—121no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C3×D12—121no—
282#626—121no—
283#626—121no—
284#626—121no—
285#626—121no—
286#625—121no—
287#624—121no—
288D3×Dic3—121no—
289C23×C9—21no—
290C23×C9—31no—
291C23×C9C22×D311yescharacteristic
292C22×D9—31no—
293C22×D9—31no—
294C22×D9—61no—
295C22×D9—61no—
296C22×D9—121no—
297C22×D9—121no—
298C22×D9—121no—
299C22×D9C22×D311yescharacteristic
300C22×D9C22×D311yescharacteristic
301D4×C9—121no—
302C2×C4×C9—21no—
303C2×C4×C9—21no—
304C2×C4×C9—31no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9—41no—
308C2×C4×C9—42no—
309C2×C4×C9C22×D311yescharacteristic
310C2×C4×C9C22×D311yescharacteristic
311#611—41no—
312#611—41no—
313#611—121no—
314#611—121no—
315#611—121no—
316#611—121no—
317#611—122no—
318#611—122no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—61no—
322C2×Dic9—61no—
323C2×Dic9C22×D311yescharacteristic
324C2×Dic9C22×D311yescharacteristic
325D36—41no—
326D36—121no—
327D36—122no—
328D36—121no—
329D36—121no—
330D36—121no—
331C4×D9—121no—
332C4×D9—121no—
333#560—271noSylow
334C2×C3×C9—41no—
335C2×C3×C9H(5,𝔽2)11yescharacteristic
336C2×C3×C9H(5,𝔽2)11yescharacteristic
337C2×C3×C9H(5,𝔽2)11yescharacteristic
338C3⋊D9—41no—
339C3⋊D9—41no—
340D3×C9—41no—
341C3×D9—41no—
342C3×D9—41no—
343C23×D3—91no—
344C23×D3—91no—
345C2×C3×D4—31no—
346C2×C3×D4—91no—
347C2×C3×D4—91no—
348C2×C3×D4—91no—
349C22×C3×C4—21no—
350C22×C3×C4C2×D911yescharacteristic, complemented
351C22×C3×C4D3211yescharacteristic
352C2×#67—31no—
353C2×#67—31no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—181no—
365C2×#67—181no—
366C2×#67C2×D911yescharacteristic
367C22×Dic3—91no—
368C2×D12—31no—
369C2×D12—91no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—91no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—181no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—91no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217C2×D911yescharacteristic, complemented
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—181no—
405(C2×D3)⋊C4—181no—
406(C2×D3)⋊C4C2×D911yescharacteristic
407(C2×D3)⋊C4C2×D911yescharacteristic
408C4⋊Dic3—31no—
409C4⋊Dic3—91no—
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412C4⋊Dic3—181no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4C2×D911yescharacteristic, complemented
417Dic3⋊C4C2×D911yescharacteristic, complemented
418C4×Dic3—91no—
419C4×Dic3—91no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32C23×D311yescharacteristic
424C2×C3⋊D3—61no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439D32—124no—
440C32×C4—21no—
441C32×C4—21no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C22×C9—22no—
450C22×C9—21no—
451C22×C9—21no—
452C22×C9—21no—
453C22×C9—21no—
454C22×C9—41no—
455C22×C9—41no—
456C22×C9—61no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9C23×D311yescharacteristic
460C2×D9—21no—
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—61no—
467C2×D9—61no—
468C2×D9—61no—
469C2×D9—61no—
470C2×D9—61no—
471C2×D9—61no—
472C2×D9—121no—
473C2×D9—121no—
474C2×D9—121no—
475C2×D9—121no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9—124no—
479C4×C9—22no—
480C4×C9—21no—
481C4×C9—21no—
482C4×C9—41no—
483C4×C9—61no—
484C4×C9—61no—
485C4×C9—61no—
486Dic9—21no—
487Dic9—21no—
488Dic9—61no—
489Dic9—61no—
490Dic9—121no—
491Dic9—121no—
492#127—271no—
493#126—271no—
494#126—271no—
495#123—31no—
496#123—271no—
497#123—271no—
498#121—91no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503#121—271no—
504#120—271no—
505#120—271no—
506#120—271no—
507C3×C9#56011yescharacteristic, complemented, Sylow
508C23×C3—21no—
509C23×C3—31no—
510C23×C3—91no—
511C23×C3—91no—
512C23×C3C22×D911yescharacteristic
513C23×C3C2×D3211yescharacteristic
514C22×D3—31no—
515C22×D3—31no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—91no—
520C22×D3—181no—
521C22×D3—181no—
522C22×D3—361no—
523C22×D3—361no—
524C22×D3—361no—
525C22×D3—361no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3C22×D911yescharacteristic
529C3×D4—121no—
530C3×D4—361no—
531C3×D4—361no—
532C3×D4—361no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4C22×D911yescharacteristic
544C2×C3×C4C22×D911yescharacteristic
545C2×C3×C4C2×D3211yescharacteristic
546C2×C3×C4C2×D3211yescharacteristic
547#67—41no—
548#67—121no—
549#67—121no—
550#67—361no—
551#67—361no—
552#67—361no—
553#67—361no—
554#67—361no—
555#67—361no—
556#67—361no—
557#67—361no—
558#67—361no—
559#67—361no—
560#67—362no—
561#67—362no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—361no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573C2×Dic3C22×D911yescharacteristic
574D12—121no—
575D12—361no—
576D12—361no—
577D12—362no—
578D12—361no—
579D12—361no—
580D12—361no—
581D12—361no—
582C4×D3—361no—
583C4×D3—361no—
584C4×D3—361no—
585C2×C32—41no—
586C2×C32#100411yescharacteristic
587C2×C32#100911yescharacteristic
588C2×C32#100911yescharacteristic
589C3⋊D3—121no—
590C3⋊D3—121no—
591C3×D3—41no—
592C3×D3—121no—
593C3×D3—121no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—42no—
598C2×C9—41no—
599C2×C9—121no—
600C2×C9#100411yescharacteristic
601C2×C9#100411yescharacteristic
602C2×C9#100911yescharacteristic
603D9—41no—
604D9—41no—
605D9—121no—
606D9—121no—
607D9—241no—
608D9—241no—
609C24—271no—
610C2×D4—31no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C2×D4—271no—
621C2×D4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4D3×D911yescharacteristic, complemented
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—91no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—271no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3C23×D911yescharacteristic
664C22×C3C22×D3211yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—361no—
687C2×D3—361no—
688C2×D3—361no—
689C2×D3—361no—
690C2×D3—361no—
691C2×D3—361no—
692C2×D3—364no—
693C2×D3—364no—
694C3×C4—22no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—181no—
704C3×C4—181no—
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—61no—
709Dic3—61no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—181no—
714Dic3—361no—
715Dic3—361no—
716C32#566611yescharacteristic
717C9—21no—
718C9#562011yescharacteristic, complemented
719C23—31no—
720C23—91no—
721C23—91no—
722C23—271no—
723C23—271no—
724C23—1081no—
725C23—1081no—
726C23—1081no—
727C23C2×D3×D911yescharacteristic
728D4—121no—
729D4—361no—
730D4—361no—
731D4—361no—
732D4—1081no—
733D4—1081no—
734D4—1081no—
735D4—1081no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739D4—1081no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—41no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—271no—
747C2×C4—271no—
748C2×C4—1081no—
749C2×C4—1081no—
750C2×C4C2×D3×D911yescharacteristic
751C2×C4C2×D3×D911yescharacteristic
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—121no—
759C2×C3—361no—
760C2×C3—361no—
761C2×C3#6371011yescharacteristic
762C2×C3#6371511yescharacteristic
763C2×C3#6371511yescharacteristic
764C2×C3#6430711yescharacteristic
765C2×C3#6430811yescharacteristic
766C2×C3#6433011yescharacteristic
767D3—41no—
768D3—121no—
769D3—121no—
770D3—361no—
771D3—361no—
772D3—361no—
773D3—361no—
774D3—721no—
775D3—721no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—181no—
786C22—181no—
787C22—181no—
788C22—541no—
789C22—541no—
790C22—541no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—1084no—
795C22C22×D3×D911yescharacteristic
796C4—21no—
797C4—21no—
798C4—61no—
799C4—61no—
800C4—61no—
801C4—181no—
802C4—181no—
803C4—541no—
804C4—541no—
805C3—21no—
806C3#1058976811yescharacteristic, complemented
807C3#1059509011yescharacteristic
808C2—41no—
809C2—121no—
810C2—361no—
811C2—361no—
812C2—1081no—
813C2—1081no—
814C2#1172247711yescharacteristic
815C2#1172247811yescharacteristic
816C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#560
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. #11721819C2semidirect
2. C9×#929C2semidirect
3. C3×#63492C2semidirect
4. #11721292C2semidirect
5. #11721289C2semidirect
6. #11721271C2semidirect
7. #11721256C2semidirect
8. #11721051C2semidirect
9. #11721049C2semidirect
10. #11721005C2semidirect
11. #11720989C2semidirect
12. #11720983C2semidirect
13. #11720958C2semidirect
14. #11720949C2semidirect
15. #11720921C2semidirect
19. C22×C3×C4×C9C22semidirect
21. C2×#6233C22semidirect
25. C2×C3×#611C22semidirect
31. C2×#6192C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
33. C2×Dic3×D9C22semidirect
35. #88536C22semidirect
36. C4⋊(C3⋊Dic9)C22semidirect
37. C9×#217C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C3×C4⋊Dic9C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
73. #63492D3semidirect
157. C22×C4×C9C2×D3semidirect
165. C2×#611C2×D3semidirect
189. (C2×D9)⋊C4C2×D3semidirect
192. C4⋊Dic9C2×D3semidirect
239. #929D9semidirect
350. C22×C3×C4C2×D9semidirect
390. #217C2×D9semidirect
416. Dic3⋊C4C2×D9semidirect
417. Dic3⋊C4C2×D9semidirect
507. C3×C9#560semidirect
624. C22×C4D3×D9semidirect
718. C9#5620semidirect
806. C3#10589768semidirect

Maximal subgroups

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

subgroupindex
#117218192
C9×#9292
C3×#634922
#117212922
#117212892
#117212712
#117212562
#117210512
#117210492
#117210052
#117209892
#117209832
#117209582
#117209492
#117209212
#105950903
#105897683