Finite Group Databasebeta

← #13148384

Subgroups — #13148384

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×#883C211yesmaximal, characteristic, complemented
3C3×#63445C211yesmaximal, characteristic, complemented
4#11721291C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8#11721039C211yesmaximal, characteristic, complemented
9#11721038C211yesmaximal, characteristic, complemented
10#11721034C211yesmaximal, characteristic, complemented
11#11721033C211yesmaximal, characteristic, complemented
12#11721005C211yesmaximal, characteristic, complemented
13#11721004C211yesmaximal, characteristic, complemented
14#11720921C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16#10594244—31nomaximal
17#10589768—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic, complemented
29C2×#6194C2211yescharacteristic, complemented
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C9×C4⋊Dic3C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C3×C4⋊Dic9C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64091—31no—
54C3×#883—31no—
55C3×#883D311yescharacteristic
56#63981—31no—
57#63981—31no—
58#63979—31no—
59#63975—31no—
60#63910—31no—
61#63910—31no—
62#63909—31no—
63#63909—31no—
64#63906—31no—
65#63906—31no—
66#63848—31no—
67#63848—31no—
68C9×#123—31no—
69#63502—31no—
70#63499—31no—
71#63492—31no—
72#63492—31no—
73#63460—31no—
74#63460—31no—
75#63457—31no—
76#63457—31no—
77#63446—31no—
78#63446—31no—
79#63445—31no—
80#63445D311yescharacteristic, complemented
81#63444—31no—
82#63444—31no—
83#63444—61no—
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×C3×D9C2311yescharacteristic
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—
100C3×#611—41no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C4×D3×C9—41no—
108C3×C4×D9—41no—
109#6195—41no—
110#6195—41no—
111#6195—41no—
112#6194—41no—
113#6192—41no—
114#6192—41no—
115#6192—41no—
116(C3⋊D9)⋊C4—41no—
117#5666—91no—
118#5666—91no—
119C23×C3⋊D3—31no—
120C2×#638—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C3×#67—31no—
124C2×C3×#67C2×D311yescharacteristic
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3C2×D311yescharacteristic
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#625—31no—
134C2×#624—31no—
135C23×D9—31no—
136C23×D9—61no—
137C32×C22⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3752—31no—
140C3×#217—31no—
141C3×#217C2×D311yescharacteristic
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154#3722—31no—
155Dic32—31no—
156C2×D4×C9—31no—
157C22×C4×C9—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—61no—
164C2×#611C2×D311yescharacteristic
165C2×D36—31no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—61no—
171C2×D36—61no—
172C2×C4×D9—31no—
173C2×C4×D9C2×D311yescharacteristic, complemented
174C9×C4⋊C4—31no—
175C9×C4⋊C4—31no—
176C9×C22⋊C4—21no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4C2×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—
190(C2×D9)⋊C4C2×D311yescharacteristic, complemented
191C4⋊Dic9—31no—
192C4⋊Dic9C2×D311yescharacteristic, complemented
193Dic9⋊C4—31no—
194Dic9⋊C4C2×D311yescharacteristic, complemented
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×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×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—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#123—31no—
226C3×#123—91no—
227#940—91no—
228#940—91no—
229#937—91no—
230#937—91no—
231#930—91no—
232#930—91no—
233#930—91no—
234#930—91no—
235#898—91no—
236#898—91no—
237#898—91no—
238#898—91no—
239#895—91no—
240#895—91no—
241#895—91no—
242#895—91no—
243#884—91no—
244#884—91no—
245#884—91no—
246#884—91no—
247#883—31no—
248#883—91no—
249#883—91no—
250#883D911yescharacteristic, complemented
251#882—91no—
252#882—91no—
253#882—91no—
254#882—91no—
255#882—181no—
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×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—121no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C3×C4×D3—41no—
280C3×C4×D3—121no—
281#626—121no—
282#626—121no—
283#626—121no—
284#626—121no—
285#626—121no—
286#626—121no—
287#625—121no—
288#624—121no—
289C23×C9—21no—
290C23×C9—31no—
291C23×C9C22×D311yescharacteristic
292C22×D9—31no—
293C22×D9—31no—
294C22×D9—31no—
295C22×D9—61no—
296C22×D9—61no—
297C22×D9—61no—
298C22×D9—121no—
299C22×D9—121no—
300C22×D9—121no—
301C22×D9—122no—
302C22×D9—122no—
303C22×D9—122no—
304C22×D9C22×D311yescharacteristic
305D4×C9—121no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—121no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314#611—41no—
315#611—121no—
316#611—121no—
317#611—121no—
318#611—121no—
319#611—121no—
320#611—122no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9C22×D311yescharacteristic
324C2×Dic9C22×D311yescharacteristic
325C2×Dic9C22×D311yescharacteristic
326D36—121no—
327D36—121no—
328D36—122no—
329D36—122no—
330D36—121no—
331D36—121no—
332D36—121no—
333C4×D9—41no—
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—
344C3×D9—41no—
345C23×D3—91no—
346C23×D3—91no—
347C23×D3—181no—
348C2×C3×D4—31no—
349C2×C3×D4—91no—
350C22×C3×C4—31no—
351C22×C3×C4—91no—
352C2×#67—31no—
353C2×#67—91no—
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—181no—
364C2×#67C2×D911yescharacteristic
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×D3C2×D911yescharacteristic, complemented
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4C2×D911yescharacteristic
391C3×C22⋊C4D3211yescharacteristic
392#217—31no—
393#217C2×D911yescharacteristic
394(C2×D3)⋊C4—31no—
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—181no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4C2×D911yescharacteristic, complemented
412C4⋊Dic3—31no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3C2×D911yescharacteristic, complemented
416Dic3⋊C4—31no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4C2×D911yescharacteristic, complemented
420C4×Dic3—91no—
421C4×Dic3—91no—
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—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—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×C9C23×D311yescharacteristic
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—
492Dic9—21no—
493Dic9—21no—
494Dic9—21no—
495Dic9—61no—
496Dic9—121no—
497#127—271no—
498#126—271no—
499#126—271no—
500#123—31no—
501#123—91no—
502#123—271no—
503#121—271no—
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—91no—
516C23×C3C22×D911yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C22×D3—31no—
519C22×D3—91no—
520C22×D3—91no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—181no—
526C22×D3—181no—
527C22×D3—181no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3—361no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—362no—
535C22×D3—362no—
536C22×D3—362no—
537C22×D3C22×D911yescharacteristic
538C3×D4—121no—
539C3×D4—361no—
540C2×C3×C4—21no—
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×C4C22×D911yescharacteristic
552C2×C3×C4C2×D3211yescharacteristic
553C2×C3×C4C2×D3211yescharacteristic
554#67—41no—
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—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—181no—
573C2×Dic3C22×D911yescharacteristic
574C2×Dic3C22×D911yescharacteristic
575C2×Dic3C22×D911yescharacteristic
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—121no—
590C4×D3—361no—
591C4×D3—361no—
592C2×C32—41no—
593C2×C32#100411yescharacteristic
594C2×C32#100911yescharacteristic
595C2×C32#100911yescharacteristic
596C3⋊D3—121no—
597C3⋊D3—121no—
598C3⋊D3—121no—
599C3×D3—41no—
600C3×D3—121no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—42no—
605C2×C9—41no—
606C2×C9—121no—
607C2×C9#100411yescharacteristic
608C2×C9#100911yescharacteristic
609C2×C9#100911yescharacteristic
610D9—41no—
611D9—122no—
612D9—122no—
613D9—121no—
614D9—121no—
615D9—121no—
616D9—241no—
617C24—271no—
618C2×D4—31no—
619C2×D4—91no—
620C2×D4—271no—
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—91no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—91no—
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—271no—
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—181no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
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—181no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—21no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—181no—
725Dic3—181no—
726Dic3—361no—
727C32#566611yescharacteristic
728C9—21no—
729C9#566611yescharacteristic, complemented
730C23—31no—
731C23—91no—
732C23—271no—
733C23—271no—
734C23—271no—
735C23—1081no—
736C23—1081no—
737C23—1081no—
738C23C2×D3×D911yescharacteristic
739D4—121no—
740D4—361no—
741D4—1081no—
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—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—121no—
758C2×C4—271no—
759C2×C4—361no—
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—361no—
771C2×C3#6371011yescharacteristic
772C2×C3#6371511yescharacteristic
773C2×C3#6371511yescharacteristic
774C2×C3#6430811yescharacteristic
775C2×C3#6431411yescharacteristic
776C2×C3#6431411yescharacteristic
777D3—41no—
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—61no—
792C22—61no—
793C22—61no—
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—181no—
814C4—181no—
815C4—181no—
816C4—541no—
817C3—21no—
818C3#1058976811yescharacteristic, complemented
819C3#1059424411yescharacteristic
820C2—41no—
821C2—121no—
822C2—361no—
823C2—1081no—
824C2—1081no—
825C2—1081no—
826C2#1172247811yescharacteristic
827C2#1172250011yescharacteristic
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. C9×#883C2semidirect
3. C3×#63445C2semidirect
4. #11721291C2semidirect
5. #11721289C2semidirect
6. #11721278C2semidirect
7. #11721275C2semidirect
8. #11721039C2semidirect
9. #11721038C2semidirect
10. #11721034C2semidirect
11. #11721033C2semidirect
12. #11721005C2semidirect
13. #11721004C2semidirect
14. #11720921C2semidirect
15. #11720920C2semidirect
24. C2×C4×D3×C9C22semidirect
25. C2×C3×C4×D9C22semidirect
28. C2×#6195C22semidirect
29. C2×#6194C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C9×C4⋊Dic3C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C3×C4⋊Dic9C22semidirect
44. C3×Dic9⋊C4C22semidirect
49. #88445C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
80. #63445D3semidirect
173. C2×C4×D9C2×D3semidirect
190. (C2×D9)⋊C4C2×D3semidirect
192. C4⋊Dic9C2×D3semidirect
194. Dic9⋊C4C2×D3semidirect
250. #883D9semidirect
380. C2×C4×D3C2×D9semidirect
411. (C2×D3)⋊C4C2×D9semidirect
415. C4⋊Dic3C2×D9semidirect
419. Dic3⋊C4C2×D9semidirect
512. C3×C9#560semidirect
729. C9#5666semidirect
818. C3#10589768semidirect

Maximal subgroups

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

subgroupindex
#117217282
C9×#8832
C3×#634452
#117212912
#117212892
#117212782
#117212752
#117210392
#117210382
#117210342
#117210332
#117210052
#117210042
#117209212
#117209202
#105942443
#105897683