Finite Group Databasebeta

← #13148381

Subgroups — #13148381

Order 1728.

886 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721728C211yesmaximal, characteristic, complemented
2C9×#884C211yesmaximal, characteristic, complemented
3C3×#63441C211yesmaximal, characteristic, complemented
4#11721291C211yesmaximal, characteristic, complemented
5#11721291C211yesmaximal, characteristic, complemented
6#11721282C211yesmaximal, characteristic, complemented
7#11721262C211yesmaximal, characteristic, complemented
8#11721040C211yesmaximal, characteristic, complemented
9#11721039C211yesmaximal, characteristic, complemented
10#11721038C211yesmaximal, characteristic, complemented
11#11721020C211yesmaximal, characteristic, complemented
12#11721017C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720954C211yesmaximal, characteristic, complemented
15#11720934C211yesmaximal, characteristic, complemented
16#10594242—31nomaximal
17#10589722—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic, complemented
25C2×C4×D3×C9C2211yescharacteristic, complemented
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic, complemented
31C2×#6195C2211yescharacteristic, complemented
32C2×D3×Dic9C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C9×Dic3⋊C4C2211yescharacteristic, complemented
41C3×C4⋊Dic9C2211yescharacteristic, complemented
42C3×Dic9⋊C4C2211yescharacteristic, complemented
43C3×Dic9⋊C4C2211yescharacteristic, complemented
44C3×C4×Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#64091—31no—
54C3×#884D311yescharacteristic
55C3×#879—31no—
56#63981—31no—
57#63981—31no—
58#63971—31no—
59#63958—31no—
60#63911—31no—
61#63910—31no—
62#63909—31no—
63#63897—31no—
64#63890—31no—
65#63886—31no—
66#63868—31no—
67#63850—31no—
68C9×#121—31no—
69#63502—31no—
70#63501—31no—
71#63501—31no—
72#63500—31no—
73#63499—31no—
74#63499—31no—
75#63492—31no—
76#63491—31no—
77#63460—31no—
78#63456—31no—
79#63448—31no—
80#63446—31no—
81#63444—31no—
82#63444—61no—
83#63441D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—41no—
86C22×C3⋊D9—41no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95#6233—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C4⋊(C3⋊D9)—41no—
98C4⋊(C3⋊D9)—41no—
99C9×#67—41no—
100C9×#67—41no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×D12—41no—
108C4×D3×C9—41no—
109#6195—41no—
110#6195—41no—
111#6195—41no—
112#6195—41no—
113#6195—41no—
114#6195—41no—
115D3×Dic9—41no—
116(C3⋊D9)⋊C4—41no—
117#5711—91no—
118#5620—91no—
119C23×C3⋊D3—31no—
120C2×#638—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×#67C2×D311yescharacteristic
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×C4×D3C2×D311yescharacteristic
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#624—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136C23×D9—61no—
137C32×C22⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3752—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×C4⋊Dic3—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4C2×D311yescharacteristic
147C3×C4×Dic3—31no—
148#3724—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154#3722—31no—
155(C2×D3)⋊Dic3—31no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C2×D4×C9—31no—
159C22×C4×C9—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—61no—
168C22×Dic9—31no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36—61no—
172C2×D36—61no—
173C2×C4×D9—31no—
174C9×C4⋊C4—31no—
175C9×C22⋊C4—21no—
176C9×C22⋊C4—31no—
177C9×C22⋊C4C2×D311yescharacteristic
178#3676—31no—
179#3676C2×D311yescharacteristic
180#3676C2×D311yescharacteristic
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—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190C4⋊Dic9—31no—
191C4⋊Dic9C2×D311yescharacteristic, complemented
192Dic9⋊C4—31no—
193Dic9⋊C4C2×D311yescharacteristic, complemented
194Dic9⋊C4C2×D311yescharacteristic, complemented
195C4×Dic9C2×D311yescharacteristic, complemented
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×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—44no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3⋊Dic9—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#126—91no—
226C3×#121—31no—
227#940—91no—
228#939—91no—
229#939—91no—
230#938—91no—
231#937—91no—
232#937—91no—
233#930—91no—
234#929—91no—
235#898—91no—
236#895—91no—
237#895—91no—
238#895—91no—
239#894—91no—
240#894—91no—
241#894—91no—
242#894—91no—
243#886—91no—
244#884—91no—
245#884—91no—
246#884—91no—
247#884D911yescharacteristic, complemented
248#882—91no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—181no—
253#879—31no—
254#876—91no—
255#874—91no—
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—121no—
261C22×C3⋊D3—121no—
262C22×C3⋊D3—121no—
263C22×C3×D3C22×D311yescharacteristic
264C22×C3×D3C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267#638—121no—
268C2×C3⋊Dic3—31no—
269C4⋊(C3⋊D3)—121no—
270C4⋊(C3⋊D3)—121no—
271C3×#67—41no—
272C3×#67—41no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C3×D12—41no—
280C3×C4×D3—41no—
281#626—121no—
282#626—121no—
283#626—121no—
284#626—121no—
285#626—121no—
286#626—121no—
287#624—121no—
288D3×Dic3—121no—
289C23×C9—21no—
290C23×C9—31no—
291C23×C9—31no—
292C23×C9C22×D311yescharacteristic
293C22×D9—31no—
294C22×D9—31no—
295C22×D9—31no—
296C22×D9—61no—
297C22×D9—61no—
298C22×D9—61no—
299C22×D9—121no—
300C22×D9—121no—
301C22×D9—121no—
302C22×D9—122no—
303C22×D9—122no—
304C22×D9—122no—
305D4×C9—121no—
306D4×C9—121no—
307D4×C9—121no—
308C2×C4×C9—21no—
309C2×C4×C9—21no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—121no—
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315#611—121no—
316#611—121no—
317#611—121no—
318#611—121no—
319#611—121no—
320#611—121no—
321#611—121no—
322#611—122no—
323C2×Dic9—31no—
324C2×Dic9—61no—
325C2×Dic9—121no—
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330D36—121no—
331D36—121no—
332D36—122no—
333D36—122no—
334C4×D9—121no—
335#560—271noSylow
336C2×C3×C9—41no—
337C2×C3×C9H(5,𝔽2)11yescharacteristic
338C2×C3×C9H(5,𝔽2)11yescharacteristic
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C3⋊D9—41no—
341C3⋊D9—41no—
342C3⋊D9—41no—
343D3×C9—41no—
344D3×C9—41no—
345C23×D3—91no—
346C23×D3—91no—
347C23×D3—181no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C22×C3×C4—31no—
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—181no—
361C2×#67C2×D911yescharacteristic
362C2×#67C2×D911yescharacteristic
363C22×Dic3—91no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—91no—
373C2×D12—91no—
374C2×D12—181no—
375C2×D12—181no—
376C2×D12C2×D911yescharacteristic, complemented
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3C2×D911yescharacteristic, complemented
381C3×C4⋊C4—31no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—91no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4C2×D911yescharacteristic
390C3×C22⋊C4D3211yescharacteristic
391C3×C42—91no—
392#217—31no—
393#217—31no—
394#217—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—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—91no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4C2×D911yescharacteristic, complemented
413C4⋊Dic3—31no—
414C4⋊Dic3—91no—
415Dic3⋊C4—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4C2×D911yescharacteristic, complemented
421C4×Dic3—31no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C23×D311yescharacteristic
426C2×C3⋊D3—61no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
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—124no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C32×C4—21no—
443C32×C4—21no—
444C3⋊Dic3—61no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C22×C9—22no—
452C22×C9—21no—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—41no—
457C22×C9—41no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9—61no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9C23×D311yescharacteristic
465C2×D9—62no—
466C2×D9—62no—
467C2×D9—61no—
468C2×D9—61no—
469C2×D9—61no—
470C2×D9—61no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—121no—
482C2×D9—121no—
483C2×D9—128no—
484C2×D9—124no—
485C4×C9—21no—
486C4×C9—21no—
487C4×C9—41no—
488C4×C9—41no—
489C4×C9—61no—
490C4×C9—61no—
491Dic9—21no—
492Dic9—21no—
493Dic9—21no—
494Dic9—21no—
495Dic9—61no—
496Dic9—121no—
497#127—271no—
498#126—91no—
499#126—271no—
500#123—271no—
501#123—271no—
502#123—271no—
503#121—31no—
504#121—271no—
505#121—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509#120—271no—
510#120—271no—
511#120—271no—
512C3×C9#56011yescharacteristic, complemented, Sylow
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—31no—
516C23×C3C22×D911yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C22×D3—91no—
519C22×D3—91no—
520C22×D3—91no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—181no—
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×D3—362no—
534C22×D3—362no—
535C22×D3—362no—
536C22×D3C22×D911yescharacteristic
537C22×D3C22×D911yescharacteristic
538C3×D4—121no—
539C3×D4—121no—
540C3×D4—121no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—121no—
550C2×C3×C4C22×D911yescharacteristic
551C2×C3×C4C22×D911yescharacteristic
552C2×C3×C4C2×D3211yescharacteristic
553C2×C3×C4C2×D3211yescharacteristic
554#67—41no—
555#67—41no—
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—362no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—181no—
572C2×Dic3—361no—
573C2×Dic3C22×D911yescharacteristic
574C2×Dic3C22×D911yescharacteristic
575D12—41no—
576D12—361no—
577D12—361no—
578D12—361no—
579D12—361no—
580D12—362no—
581D12—362no—
582D12—361no—
583D12—361no—
584D12—361no—
585D12—361no—
586D12—361no—
587D12—361no—
588C4×D3—41no—
589C4×D3—361no—
590C4×D3—361no—
591C4×D3—361no—
592C2×C32—41no—
593C2×C32#100411yescharacteristic
594C2×C32#100411yescharacteristic
595C2×C32#100911yescharacteristic
596C3⋊D3—121no—
597C3⋊D3—121no—
598C3⋊D3—121no—
599C3×D3—41no—
600C3×D3—41no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—42no—
605C2×C9—41no—
606C2×C9—121no—
607C2×C9—121no—
608C2×C9#100911yescharacteristic
609C2×C9#100911yescharacteristic
610C2×C9#100911yescharacteristic
611D9—122no—
612D9—122no—
613D9—121no—
614D9—121no—
615D9—121no—
616D9—241no—
617C24—271no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C22×C4—31no—
631C22×C4—271no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—271no—
638C4⋊C4—271no—
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—
650C22⋊C4D3×D911yescharacteristic
651C42—91no—
652C22×C3—22no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—182no—
677C2×D3—182no—
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—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—361no—
703C2×D3—364no—
704C2×D3—368no—
705C2×D3—364no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—181no—
715C3×C4—181no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—181no—
725Dic3—181no—
726Dic3—361no—
727C32#562011yescharacteristic
728C9—21no—
729C9#571111yescharacteristic, complemented
730C23—31no—
731C23—31no—
732C23—271no—
733C23—271no—
734C23—271no—
735C23—1081no—
736C23—1081no—
737C23—1081no—
738C23C2×D3×D911yescharacteristic
739D4—121no—
740D4—121no—
741D4—121no—
742D4—1081no—
743D4—1081no—
744D4—1081no—
745D4—1081no—
746D4—1081no—
747D4—1081no—
748D4—1081no—
749D4—1081no—
750D4—1081no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—121no—
758C2×C4—271no—
759C2×C4—1081no—
760C2×C4—1081no—
761C2×C4C2×D3×D911yescharacteristic
762C2×C4C2×D3×D911yescharacteristic
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—41no—
768C2×C3—41no—
769C2×C3—121no—
770C2×C3—121no—
771C2×C3#6371011yescharacteristic
772C2×C3#6371011yescharacteristic
773C2×C3#6371511yescharacteristic
774C2×C3#6430811yescharacteristic
775C2×C3#6431411yescharacteristic
776C2×C3#6431411yescharacteristic
777D3—41no—
778D3—41no—
779D3—362no—
780D3—362no—
781D3—361no—
782D3—361no—
783D3—361no—
784D3—361no—
785D3—361no—
786D3—361no—
787D3—721no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—541no—
798C22—541no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22—1084no—
807C22C22×D3×D911yescharacteristic
808C4—21no—
809C4—21no—
810C4—61no—
811C4—61no—
812C4—181no—
813C4—181no—
814C4—181no—
815C4—181no—
816C4—541no—
817C3—21no—
818C3#1058972211yescharacteristic, complemented
819C3#1059424211yescharacteristic
820C2—41no—
821C2—121no—
822C2—121no—
823C2—1081no—
824C2—1081no—
825C2—1081no—
826C2#1172247811yescharacteristic
827C2#1172250011yescharacteristic
828C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
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. #11721728C2semidirect
2. C9×#884C2semidirect
3. C3×#63441C2semidirect
4. #11721291C2semidirect
5. #11721291C2semidirect
6. #11721282C2semidirect
7. #11721262C2semidirect
8. #11721040C2semidirect
9. #11721039C2semidirect
10. #11721038C2semidirect
11. #11721020C2semidirect
12. #11721017C2semidirect
13. #11720997C2semidirect
14. #11720954C2semidirect
15. #11720934C2semidirect
24. C2×C9×D12C22semidirect
25. C2×C4×D3×C9C22semidirect
30. C2×#6195C22semidirect
31. C2×#6195C22semidirect
32. C2×D3×Dic9C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
40. C9×Dic3⋊C4C22semidirect
41. C3×C4⋊Dic9C22semidirect
42. C3×Dic9⋊C4C22semidirect
43. C3×Dic9⋊C4C22semidirect
44. C3×C4×Dic9C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
83. #63441D3semidirect
191. C4⋊Dic9C2×D3semidirect
193. Dic9⋊C4C2×D3semidirect
194. Dic9⋊C4C2×D3semidirect
195. C4×Dic9C2×D3semidirect
247. #884D9semidirect
376. C2×D12C2×D9semidirect
380. C2×C4×D3C2×D9semidirect
412. (C2×D3)⋊C4C2×D9semidirect
420. Dic3⋊C4C2×D9semidirect
512. C3×C9#560semidirect
729. C9#5711semidirect
818. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117217282
C9×#8842
C3×#634412
#117212912
#117212822
#117212622
#117210402
#117210392
#117210382
#117210202
#117210172
#117209972
#117209542
#117209342
#105942423
#105897223