Finite Group Databasebeta

← #13148186

Subgroups — #13148186

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
2C3×#63446C211yesmaximal, characteristic, complemented
3C9×#879C211yesmaximal, characteristic, complemented
4#11721278C211yesmaximal, characteristic, complemented
5#11721278C211yesmaximal, characteristic, complemented
6#11721271C211yesmaximal, characteristic, complemented
7#11721256C211yesmaximal, characteristic, complemented
8#11721006C211yesmaximal, characteristic, complemented
9#11721005C211yesmaximal, characteristic, complemented
10#11721004C211yesmaximal, characteristic, complemented
11#11720997C211yesmaximal, characteristic, complemented
12#11720988C211yesmaximal, characteristic, complemented
13#11720983C211yesmaximal, characteristic, complemented
14#11720938C211yesmaximal, characteristic, complemented
15#11720926C211yesmaximal, characteristic, complemented
16#10594242—31nomaximal
17#10589813—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic, complemented
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C9×#217C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C4×C9×Dic3C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64091—31no—
54C3×#884—31no—
55C3×#879D311yescharacteristic
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×#126—31no—
69#63457—31no—
70#63457—31no—
71#63457—31no—
72#63456—31no—
73#63456—31no—
74#63456—31no—
75#63446—31no—
76#63446—31no—
77#63446D311yescharacteristic, complemented
78#63444—31no—
79#63444—31no—
80#63444—31no—
81#63444—61no—
82#63438—31no—
83#63436—31no—
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×C3×D9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95#6233—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C4⋊(C3⋊D9)—41no—
98C4⋊(C3⋊D9)—41no—
99C3×#611—41no—
100C3×#611—41no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×D36—41no—
108C3×C4×D9—41no—
109#6192—41no—
110#6192—41no—
111#6192—41no—
112#6192—41no—
113#6192—41no—
114#6192—41no—
115(C3⋊D9)⋊C4—41no—
116Dic3×D9—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×#67—31no—
124C2×C3×#67—31no—
125C2×C3×D12—31no—
126C2×C3×C4×D3—31no—
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×#217C2×D311yescharacteristic
141C3×#217C2×D311yescharacteristic
142C3×(C2×D3)⋊C4—31no—
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4C2×D311yescharacteristic
147C3×C4×Dic3C2×D311yescharacteristic
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×#611—31no—
157C2×#611—61no—
158C2×#611C2×D311yescharacteristic
159C2×#611C2×D311yescharacteristic
160C2×D36—31no—
161C2×D36—31no—
162C2×D36—31no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—31no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—61no—
169C2×D36—61no—
170C2×D36C2×D311yescharacteristic, complemented
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9C2×D311yescharacteristic, complemented
174C9×C4⋊C4—31no—
175C9×C4⋊C4—31no—
176C9×C4⋊C4—31no—
177C9×C22⋊C4—21no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4C2×D311yescharacteristic
181C42×C9—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—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4C2×D311yescharacteristic, complemented
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4C2×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×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3⋊Dic9—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#126—31no—
226C3×#121—91no—
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—31no—
245#884—91no—
246#884—91no—
247#884—91no—
248#882—91no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—181no—
253#879D911yescharacteristic, complemented
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×D3—31no—
264C22×C3×D3—31no—
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—121no—
272C3×#67—121no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C3×D12—121no—
280C3×C4×D3—121no—
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×C9C22×D311yescharacteristic
291C22×D9—31no—
292C22×D9—31no—
293C22×D9—31no—
294C22×D9—61no—
295C22×D9—61no—
296C22×D9—61no—
297C22×D9—121no—
298C22×D9—121no—
299C22×D9—121no—
300C22×D9—122no—
301C22×D9—122no—
302C22×D9—122no—
303C22×D9C22×D311yescharacteristic
304C22×D9C22×D311yescharacteristic
305C2×C4×C9—21no—
306C2×C4×C9—21no—
307C2×C4×C9—31no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9C22×D311yescharacteristic
312C2×C4×C9C22×D311yescharacteristic
313#611—41no—
314#611—41no—
315#611—121no—
316#611—122no—
317C2×Dic9—31no—
318C2×Dic9—61no—
319C2×Dic9C22×D311yescharacteristic
320C2×Dic9C22×D311yescharacteristic
321D36—41no—
322D36—121no—
323D36—121no—
324D36—122no—
325D36—122no—
326D36—121no—
327D36—121no—
328D36—121no—
329D36—121no—
330D36—121no—
331D36—121no—
332C4×D9—41no—
333C4×D9—121no—
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—
343C3×D9—41no—
344C3×D9—41no—
345C23×D3—91no—
346C23×D3—91no—
347C23×D3—181no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C22×C3×C4—91no—
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—181no—
363C22×Dic3—91no—
364C2×D12—31no—
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—91no—
375C2×D12—181no—
376C2×D12—181no—
377C2×C4×D3—31no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4C2×D911yescharacteristic
390C3×C22⋊C4D3211yescharacteristic
391C3×C42—31no—
392#217—91no—
393#217C2×D911yescharacteristic
394#217C2×D911yescharacteristic
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)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4—181no—
413C4⋊Dic3—91no—
414C4⋊Dic3C2×D911yescharacteristic, complemented
415Dic3⋊C4—31no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4C2×D911yescharacteristic, complemented
420Dic3⋊C4C2×D911yescharacteristic, complemented
421C4×Dic3C2×D911yescharacteristic, complemented
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—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C32×C4—21no—
443C32×C4—21no—
444C3⋊Dic3—61no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—21no—
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×C9C23×D311yescharacteristic
459C2×D9—21no—
460C2×D9—21no—
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—21no—
464C2×D9—21no—
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—
491C4×C9—61no—
492C4×C9—61no—
493Dic9—21no—
494Dic9—21no—
495Dic9—61no—
496Dic9—121no—
497#127—271no—
498#126—31no—
499#126—271no—
500#123—271no—
501#123—271no—
502#123—271no—
503#121—91no—
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—91no—
515C23×C3—91no—
516C23×C3C22×D911yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C22×D3—31no—
519C22×D3—31no—
520C22×D3—91no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—181no—
527C22×D3—181no—
528C22×D3—181no—
529C22×D3—361no—
530C22×D3—361no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—361no—
535C22×D3—362no—
536C22×D3—362no—
537C22×D3—362no—
538C3×D4—361no—
539C3×D4—361no—
540C3×D4—361no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—361no—
550C2×C3×C4C22×D911yescharacteristic
551C2×C3×C4C22×D911yescharacteristic
552C2×C3×C4C2×D3211yescharacteristic
553C2×C3×C4C2×D3211yescharacteristic
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—362no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—181no—
570C2×Dic3—361no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573C2×Dic3C22×D911yescharacteristic
574C2×Dic3C22×D911yescharacteristic
575D12—121no—
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—121no—
589C4×D3—361no—
590C4×D3—361no—
591C4×D3—361no—
592C2×C32—41no—
593C2×C32#100911yescharacteristic
594C2×C32#100911yescharacteristic
595C2×C32#100911yescharacteristic
596C3⋊D3—121no—
597C3⋊D3—121no—
598C3⋊D3—121no—
599C3×D3—121no—
600C3×D3—121no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—42no—
605C2×C9—41no—
606C2×C9#100411yescharacteristic
607C2×C9#100411yescharacteristic
608C2×C9#100911yescharacteristic
609D9—41no—
610D9—41no—
611D9—122no—
612D9—122no—
613D9—121no—
614D9—121no—
615D9—121no—
616D9—241no—
617C24—271no—
618C2×D4—91no—
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×D4—271no—
629C2×D4—271no—
630C22×C4—91no—
631C22×C4—271no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—91no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
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—31no—
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—181no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
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—61no—
715C3×C4—61no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—21no—
721Dic3—21no—
722Dic3—61no—
723Dic3—61no—
724Dic3—181no—
725Dic3—181no—
726Dic3—361no—
727C32#571111yescharacteristic
728C9—21no—
729C9#562011yescharacteristic, complemented
730C23—91no—
731C23—91no—
732C23—271no—
733C23—271no—
734C23—271no—
735C23—1081no—
736C23—1081no—
737C23—1081no—
738C23C2×D3×D911yescharacteristic
739D4—361no—
740D4—361no—
741D4—361no—
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—31no—
754C2×C4—31no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—271no—
758C2×C4—361no—
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—361no—
770C2×C3—361no—
771C2×C3#6371511yescharacteristic
772C2×C3#6371511yescharacteristic
773C2×C3#6371511yescharacteristic
774C2×C3#6430811yescharacteristic
775C2×C3#6431411yescharacteristic
776C2×C3#6431411yescharacteristic
777D3—121no—
778D3—121no—
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—181no—
792C22—181no—
793C22—181no—
794C22—181no—
795C22—181no—
796C22—181no—
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—61no—
813C4—61no—
814C4—181no—
815C4—181no—
816C4—541no—
817C3—21no—
818C3#1058981311yescharacteristic, complemented
819C3#1059424211yescharacteristic
820C2—41no—
821C2—361no—
822C2—361no—
823C2—1081no—
824C2—1081no—
825C2—1081no—
826C2#1172247811yescharacteristic
827C2#1172250111yescharacteristic
828C2#1172250111yescharacteristic
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. C3×#63446C2semidirect
3. C9×#879C2semidirect
4. #11721278C2semidirect
5. #11721278C2semidirect
6. #11721271C2semidirect
7. #11721256C2semidirect
8. #11721006C2semidirect
9. #11721005C2semidirect
10. #11721004C2semidirect
11. #11720997C2semidirect
12. #11720988C2semidirect
13. #11720983C2semidirect
14. #11720938C2semidirect
15. #11720926C2semidirect
24. C2×C3×D36C22semidirect
25. C2×C3×C4×D9C22semidirect
30. C2×#6192C22semidirect
31. C2×#6192C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
33. C2×Dic3×D9C22semidirect
39. C3×(C2×D9)⋊C4C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C4×C9×Dic3C22semidirect
44. C3×Dic9⋊C4C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
77. #63446D3semidirect
170. C2×D36C2×D3semidirect
173. C2×C4×D9C2×D3semidirect
192. (C2×D9)⋊C4C2×D3semidirect
195. Dic9⋊C4C2×D3semidirect
253. #879D9semidirect
414. C4⋊Dic3C2×D9semidirect
419. Dic3⋊C4C2×D9semidirect
420. Dic3⋊C4C2×D9semidirect
421. C4×Dic3C2×D9semidirect
512. C3×C9#560semidirect
729. C9#5620semidirect
818. C3#10589813semidirect

Maximal subgroups

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

subgroupindex
#117217282
C3×#634462
C9×#8792
#117212782
#117212712
#117212562
#117210062
#117210052
#117210042
#117209972
#117209882
#117209832
#117209382
#117209262
#105942423
#105898133