Finite Group Databasebeta

← #13151296

Subgroups — #13151296

Order 1728.

864 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721840C211yesmaximal, characteristic, complemented
2C9×#939C211yesmaximal, characteristic, complemented
3C3×#63501C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721288C211yesmaximal, characteristic, complemented
7#11721277C211yesmaximal, characteristic, complemented
8#11721262C211yesmaximal, characteristic, complemented
9#11721256C211yesmaximal, characteristic, complemented
10#11721255C211yesmaximal, characteristic, complemented
11#11721251C211yesmaximal, characteristic, complemented
12#11721051C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720966C211yesmaximal, characteristic, complemented
15#11720950C211yesmaximal, characteristic, complemented
16#10595312—31nomaximal
17#10589722—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24C2×C4⋊(C3⋊D9)C2211yescharacteristic
25C2×C9×#67C2211yescharacteristic
26C2×C9×#67C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic
29C22×C9×Dic3C2211yescharacteristic, complemented
30C22×C3×Dic9C2211yescharacteristic, complemented
31C2×#6195C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C4×C3⋊Dic9C2211yescharacteristic, complemented
35C9×#217C2211yescharacteristic, complemented
36C3×#3676C2211yescharacteristic, complemented
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C3×Dic9⋊C4C2211yescharacteristic, complemented
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64149—31no—
54C3×#939—31no—
55C3×#939D311yescharacteristic
56#63983—31no—
57#63983—31no—
58#63978—31no—
59#63978—31no—
60#63966—31no—
61#63966—31no—
62#63958—31no—
63#63958—31no—
64#63923—31no—
65#63897—31no—
66#63862—31no—
67#63862—31no—
68C9×#121—31no—
69#63502—31no—
70#63502—61no—
71#63501—31no—
72#63501D311yescharacteristic, complemented
73#63500—31no—
74#63499—31no—
75#63499—31no—
76#63492—31no—
77#63491—31no—
78#63460—31no—
79#63456—31no—
80#63448—31no—
81#63446—31no—
82#63444—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×D3×D9—41no—
93C3×D4×C9—41no—
94C2×C3×C4×C9C2311yescharacteristic
95#6233—41no—
96#6233—41no—
97#6233—41no—
98#6233—41no—
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C4⋊(C3⋊D9)—41no—
102C9×#67—41no—
103C9×#67—41no—
104C3×#611—41no—
105C3×#611—41no—
106C2×C9×Dic3—41no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9—41no—
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114#6195—41no—
115#6192—41no—
116(C3⋊D9)⋊C4—41no—
117#5620—91no—
118#5620—91no—
119C22×D32—31no—
120C2×C32×D4C2×D311yescharacteristic
121C2×#638—31no—
122C2×#638—31no—
123C2×#638—31no—
124C2×#638—31no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67C2×D311yescharacteristic
129C2×C3×#67C2×D311yescharacteristic
130C22×C3×Dic3—31no—
131C22×C3×Dic3C2×D311yescharacteristic
132C2×#626—31no—
133C2×#626—31no—
134C2×#624—31no—
135C23×D9—31no—
136C4×C3⋊Dic3—31no—
137C3×#217—31no—
138C3×#217C2×D311yescharacteristic
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4C2×D311yescharacteristic
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147#3722—31no—
148#3722—31no—
149#3722—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155C2×D4×C9—21no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C2×D4×C9C2×D311yescharacteristic, complemented
159C22×C4×C9—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—61no—
166C2×#611—61no—
167C2×#611—61no—
168C2×#611—61no—
169C2×#611C2×D311yescharacteristic
170C2×#611C2×D311yescharacteristic
171C22×Dic9C2×D311yescharacteristic, complemented
172C2×D36—31no—
173C2×D36—31no—
174C2×D36—61no—
175C2×C4×D9—31no—
176C9×C4⋊C4—31no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179#3676—31no—
180#3676—31no—
181#3676C2×D311yescharacteristic, complemented
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—31no—
188(C2×D9)⋊C4C2×D311yescharacteristic
189C4⋊Dic9—31no—
190C4⋊Dic9—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4C2×D311yescharacteristic, complemented
194C4×Dic9—31no—
195C4×Dic9—61no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C2411yescharacteristic
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215D3×D9—44no—
216C3×C4×C9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#121—31no—
226C3×#121—91no—
227#940—91no—
228#940—91no—
229#940—181no—
230#939—31no—
231#939—91no—
232#939—91no—
233#939D911yescharacteristic, complemented
234#938—91no—
235#938—91no—
236#937—91no—
237#937—91no—
238#937—91no—
239#937—91no—
240#930—91no—
241#930—91no—
242#929—91no—
243#929—91no—
244#898—91no—
245#898—91no—
246#894—91no—
247#894—91no—
248#886—91no—
249#886—91no—
250#884—91no—
251#884—91no—
252#882—91no—
253#882—91no—
254#879—91no—
255#879—91no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
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—
265C32×D4—41no—
266C2×C32×C4C22×D311yescharacteristic
267#638—121no—
268#638—121no—
269#638—121no—
270#638—121no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C4⋊(C3⋊D3)—121no—
274C3×#67—41no—
275C3×#67—41no—
276C3×#67—121no—
277C3×#67—121no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—41no—
282C2×C3×Dic3—121no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286#626—121no—
287#626—121no—
288#624—121no—
289C23×C9—21no—
290C23×C9—21no—
291C23×C9—31no—
292C23×C9C22×D311yescharacteristic
293C23×C9C22×D311yescharacteristic
294C22×D9—31no—
295C22×D9—31no—
296C22×D9—61no—
297C22×D9—61no—
298C22×D9—121no—
299C22×D9—121no—
300C22×D9—121no—
301C22×D9C22×D311yescharacteristic
302D4×C9—41no—
303D4×C9—42no—
304D4×C9—121no—
305D4×C9—121no—
306C2×C4×C9—21no—
307C2×C4×C9—31no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—121no—
311C2×C4×C9C22×D311yescharacteristic
312#611—41no—
313#611—41no—
314#611—121no—
315#611—121no—
316#611—121no—
317#611—121no—
318#611—121no—
319#611—122no—
320#611—122no—
321#611—122no—
322#611—122no—
323C2×Dic9—31no—
324C2×Dic9—31no—
325C2×Dic9—41no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331D36—121no—
332D36—122no—
333D36—121no—
334C4×D9—121no—
335#560—271noSylow
336C2×C3×C9—41no—
337C2×C3×C9—41no—
338C2×C3×C9H(5,𝔽2)11yescharacteristic
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C2×C3×C9H(5,𝔽2)11yescharacteristic
341C3⋊D9—41no—
342C3⋊D9—41no—
343D3×C9—41no—
344C3×D9—41no—
345C23×D3—91no—
346C23×D3—91no—
347C2×C3×D4—21no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4C2×D911yescharacteristic, complemented
353C2×C3×D4D3211yescharacteristic
354C22×C3×C4—31no—
355C22×C3×C4—91no—
356C2×#67—31no—
357C2×#67—31no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—181no—
369C2×#67—181no—
370C2×#67—181no—
371C2×#67—181no—
372C2×#67C2×D911yescharacteristic
373C2×#67C2×D911yescharacteristic
374C22×Dic3—31no—
375C22×Dic3C2×D911yescharacteristic, complemented
376C2×D12—91no—
377C2×D12—91no—
378C2×D12—91no—
379C2×D12—91no—
380C2×D12—181no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—91no—
388C3×C22⋊C4—91no—
389#217—31no—
390#217—91no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217C2×D911yescharacteristic, complemented
395(C2×D3)⋊C4—31no—
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—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4C2×D911yescharacteristic
409C4⋊Dic3—91no—
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412C4⋊Dic3—91no—
413Dic3⋊C4—31no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×D911yescharacteristic, complemented
419C4×Dic3—91no—
420C4×Dic3—91no—
421C4×Dic3—181no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441D32—124no—
442C32×C4—21no—
443C3⋊Dic3—61no—
444C3⋊Dic3—61no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C22×C9—21no—
452C22×C9—21no—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—41no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—41no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—61no—
465C22×C9—61no—
466C22×C9—61no—
467C22×C9C23×D311yescharacteristic
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—121no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—121no—
482C2×D9—121no—
483C2×D9—124no—
484C4×C9—22no—
485C4×C9—21no—
486C4×C9—61no—
487C4×C9—61no—
488C4×C9—61no—
489Dic9—21no—
490Dic9—21no—
491Dic9—21no—
492Dic9—62no—
493Dic9—62no—
494Dic9—61no—
495Dic9—61no—
496#127—271no—
497#126—271no—
498#126—271no—
499#123—271no—
500#123—271no—
501#123—271no—
502#121—31no—
503#121—91no—
504#121—271no—
505#121—271no—
506#121—271no—
507#121—271no—
508#120—271no—
509#120—271no—
510#120—271no—
511C3×C9#56011yescharacteristic, complemented, Sylow
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—91no—
516C23×C3C22×D911yescharacteristic
517C23×C3C22×D911yescharacteristic
518C23×C3C2×D3211yescharacteristic
519C23×C3C2×D3211yescharacteristic
520C22×D3—31no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—181no—
526C22×D3—181no—
527C22×D3—361no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3—361no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3C22×D911yescharacteristic
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—42no—
537C3×D4—121no—
538C3×D4—121no—
539C3×D4—361no—
540C3×D4—361no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—121no—
549C2×C3×C4—361no—
550C2×C3×C4C22×D911yescharacteristic
551C2×C3×C4C2×D3211yescharacteristic
552#67—41no—
553#67—41no—
554#67—121no—
555#67—121no—
556#67—361no—
557#67—361no—
558#67—361no—
559#67—361no—
560#67—361no—
561#67—361no—
562#67—361no—
563#67—361no—
564#67—361no—
565#67—361no—
566#67—362no—
567#67—362no—
568#67—362no—
569#67—362no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—41no—
574C2×Dic3—91no—
575C2×Dic3—91no—
576C2×Dic3—91no—
577C2×Dic3—91no—
578C2×Dic3—121no—
579C2×Dic3—181no—
580C2×Dic3—181no—
581C2×Dic3C22×D911yescharacteristic
582C2×Dic3C22×D911yescharacteristic
583C2×Dic3C22×D911yescharacteristic
584D12—361no—
585D12—361no—
586D12—362no—
587D12—361no—
588D12—361no—
589C4×D3—361no—
590C4×D3—361no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32#100411yescharacteristic
594C2×C32#100411yescharacteristic
595C2×C32#100911yescharacteristic
596C3⋊D3—121no—
597C3⋊D3—121no—
598C3×D3—41no—
599C3×D3—121no—
600C2×C9—21no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—41no—
604C2×C9—41no—
605C2×C9—81no—
606C2×C9—81no—
607C2×C9—121no—
608C2×C9#100411yescharacteristic
609C2×C9#100411yescharacteristic
610C2×C9#100911yescharacteristic
611D9—41no—
612D9—121no—
613D9—121no—
614D9—241no—
615D9—241no—
616C24—271no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—91no—
620C2×D4—91no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4D3×D911yescharacteristic, complemented
629C22×C4—31no—
630C22×C4—91no—
631C22×C4—271no—
632C4⋊C4—31no—
633C4⋊C4—91no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—91no—
641C22⋊C4—91no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C42—271no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—181no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3C23×D911yescharacteristic
677C22×C3C22×D3211yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—361no—
697C2×D3—361no—
698C2×D3—361no—
699C2×D3—361no—
700C2×D3—361no—
701C2×D3—361no—
702C2×D3—364no—
703C2×D3—364no—
704C3×C4—22no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—181no—
711C3×C4—181no—
712C3×C4—181no—
713Dic3—21no—
714Dic3—21no—
715Dic3—21no—
716Dic3—61no—
717Dic3—61no—
718Dic3—61no—
719Dic3—182no—
720Dic3—182no—
721Dic3—181no—
722Dic3—181no—
723Dic3—181no—
724Dic3—181no—
725C32#562011yescharacteristic
726C9—21no—
727C9#562011yescharacteristic, complemented
728C23—31no—
729C23—91no—
730C23—271no—
731C23—271no—
732C23—1081no—
733C23—1081no—
734C23—1081no—
735C23C2×D3×D911yescharacteristic
736C23C2×D3×D911yescharacteristic
737D4—41no—
738D4—121no—
739D4—121no—
740D4—361no—
741D4—361no—
742D4—1081no—
743D4—1081no—
744D4—1081no—
745D4—1081no—
746D4—1081no—
747D4—1081no—
748D4—1081no—
749C2×C4—31no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—121no—
756C2×C4—271no—
757C2×C4—271no—
758C2×C4—361no—
759C2×C4—1081no—
760C2×C4C2×D3×D911yescharacteristic
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—81no—
769C2×C3—81no—
770C2×C3—121no—
771C2×C3—361no—
772C2×C3#6371011yescharacteristic
773C2×C3#6371011yescharacteristic
774C2×C3#6371511yescharacteristic
775C2×C3#6431411yescharacteristic
776C2×C3#6431411yescharacteristic
777C2×C3#6433011yescharacteristic
778D3—41no—
779D3—121no—
780D3—361no—
781D3—361no—
782D3—361no—
783D3—361no—
784D3—721no—
785D3—721no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—181no—
796C22—181no—
797C22—181no—
798C22—541no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—1084no—
805C22C22×D3×D911yescharacteristic
806C4—21no—
807C4—61no—
808C4—61no—
809C4—61no—
810C4—181no—
811C4—181no—
812C4—181no—
813C4—541no—
814C4—541no—
815C3—21no—
816C3#1058972211yescharacteristic, complemented
817C3#1059531211yescharacteristic
818C2—41no—
819C2—41no—
820C2—121no—
821C2—361no—
822C2—1081no—
823C2—1081no—
824C2#1172250011yescharacteristic
825C2#1172250111yescharacteristic
826C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11721840C2semidirect
2. C9×#939C2semidirect
3. C3×#63501C2semidirect
4. #11721292C2semidirect
5. #11721292C2semidirect
6. #11721288C2semidirect
7. #11721277C2semidirect
8. #11721262C2semidirect
9. #11721256C2semidirect
10. #11721255C2semidirect
11. #11721251C2semidirect
12. #11721051C2semidirect
13. #11720997C2semidirect
14. #11720966C2semidirect
15. #11720950C2semidirect
19. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
29. C22×C9×Dic3C22semidirect
30. C22×C3×Dic9C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C4×C3⋊Dic9C22semidirect
35. C9×#217C22semidirect
36. C3×#3676C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C3×Dic9⋊C4C22semidirect
46. #88445C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic9⋊Dic3C22semidirect
72. #63501D3semidirect
158. C2×D4×C9C2×D3semidirect
171. C22×Dic9C2×D3semidirect
181. #3676C2×D3semidirect
193. Dic9⋊C4C2×D3semidirect
233. #939D9semidirect
352. C2×C3×D4C2×D9semidirect
375. C22×Dic3C2×D9semidirect
394. #217C2×D9semidirect
418. Dic3⋊C4C2×D9semidirect
511. C3×C9#560semidirect
628. C2×D4D3×D9semidirect
727. C9#5620semidirect
816. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117218402
C9×#9392
C3×#635012
#117212922
#117212882
#117212772
#117212622
#117212562
#117212552
#117212512
#117210512
#117209972
#117209662
#117209502
#105953123
#105897223