Finite Group Databasebeta

← #13149378

Subgroups — #13149378

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#11721751C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63456C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic, complemented
5#11721051C211yesmaximal, characteristic, complemented
6#11721049C211yesmaximal, characteristic, complemented
7#11721041C211yesmaximal, characteristic, complemented
8#11721039C211yesmaximal, characteristic, complemented
9#11721033C211yesmaximal, characteristic, complemented
10#11721006C211yesmaximal, characteristic, complemented
11#11721005C211yesmaximal, characteristic, complemented
12#11721004C211yesmaximal, characteristic, complemented
13#11720942C211yesmaximal, characteristic, complemented
14#11720941C211yesmaximal, characteristic, complemented
15#11720926C211yesmaximal, characteristic, complemented
16#10594663—31nomaximal
17#10589813—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C3×C9×C4⋊C4C2211yescharacteristic, complemented
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic, complemented
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×C4⋊Dic3C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C4×C9×Dic3C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64104—31no—
54C3×#898D311yescharacteristic
55C3×#894—31no—
56#63923—31no—
57#63923—31no—
58#63922—31no—
59#63912—31no—
60#63911—31no—
61#63910—31no—
62#63910—31no—
63#63909—31no—
64#63906—31no—
65#63868—31no—
66#63854—31no—
67#63853—31no—
68C9×#126—31no—
69#63457—31no—
70#63457—31no—
71#63457—31no—
72#63457—61no—
73#63456—31no—
74#63456—31no—
75#63456D311yescharacteristic, complemented
76#63446—31no—
77#63446—31no—
78#63446—31no—
79#63444—31no—
80#63444—31no—
81#63444—31no—
82#63438—31no—
83#63436—31no—
84C22×C3⋊D9C2311yescharacteristic
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×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4⋊(C3⋊D9)—41no—
98C4⋊(C3⋊D9)—41no—
99C4⋊(C3⋊D9)—41no—
100C4×C3⋊D9—41no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6195—41no—
110#6194—41no—
111#6192—41no—
112#6192—41no—
113#6192—41no—
114#6192—41no—
115#6192—41no—
116(C3⋊D9)⋊C4—41no—
117#5711—91no—
118#5666—91no—
119C22×D32—31no—
120C2×C4⋊(C3⋊D3)—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C4×C3⋊D3—31no—
124C2×C3×D12—31no—
125C2×C3×C4×D3—31no—
126C2×#626—31no—
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—
136C32×C4⋊C4C2×D311yescharacteristic
137#3752—31no—
138#3752—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×C4×Dic3C2×D311yescharacteristic
149#3724—31no—
150Dic3⋊Dic3—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×D36—31no—
159C2×D36—31no—
160C2×D36—31no—
161C2×D36—31no—
162C2×D36—31no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—31no—
166C2×D36—61no—
167C2×D36—61no—
168C2×D36—61no—
169C2×D36C2×D311yescharacteristic
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—61no—
173C2×C4×D9C2×D311yescharacteristic, complemented
174C9×C4⋊C4—21no—
175C9×C4⋊C4—31no—
176C9×C4⋊C4—31no—
177C9×C4⋊C4C2×D311yescharacteristic, complemented
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4—31no—
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—61no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic
191(C2×D9)⋊C4C2×D311yescharacteristic
192(C2×D9)⋊C4C2×D311yescharacteristic, complemented
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4C2×D311yescharacteristic, complemented
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
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×C4×C9—21no—
219C3⋊Dic9—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#126—31no—
226C3×#123—91no—
227#940—91no—
228#937—91no—
229#930—91no—
230#930—91no—
231#898—91no—
232#898D911yescharacteristic, complemented
233#895—91no—
234#895—91no—
235#895—91no—
236#895—91no—
237#895—91no—
238#895—181no—
239#894—31no—
240#894—91no—
241#894—91no—
242#884—91no—
243#884—91no—
244#884—91no—
245#884—91no—
246#884—91no—
247#883—91no—
248#883—91no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—91no—
253#882—91no—
254#876—91no—
255#874—91no—
256C22×C3⋊D3—31no—
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×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C3⋊Dic3—31no—
269C4⋊(C3⋊D3)—121no—
270C4⋊(C3⋊D3)—121no—
271C4⋊(C3⋊D3)—121no—
272C4×C3⋊D3—121no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C3×D12—121no—
279C3×C4×D3—121no—
280#626—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—31no—
290C22×D9—31no—
291C22×D9—31no—
292C22×D9—31no—
293C22×D9—61no—
294C22×D9—61no—
295C22×D9—61no—
296C22×D9—121no—
297C22×D9—121no—
298C22×D9—121no—
299C22×D9C22×D311yescharacteristic
300C22×D9C22×D311yescharacteristic
301C2×C4×C9—21no—
302C2×C4×C9—21no—
303C2×C4×C9—21no—
304C2×C4×C9—31no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9C22×D311yescharacteristic
308C2×C4×C9C22×D311yescharacteristic
309C2×C4×C9C22×D311yescharacteristic
310#611—121no—
311#611—121no—
312#611—121no—
313C2×Dic9—31no—
314C2×Dic9—61no—
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317D36—41no—
318D36—121no—
319D36—121no—
320D36—121no—
321D36—122no—
322D36—122no—
323D36—122no—
324D36—121no—
325D36—121no—
326D36—121no—
327D36—121no—
328D36—121no—
329C4×D9—41no—
330C4×D9—121no—
331C4×D9—121no—
332C4×D9—122no—
333#560—271noSylow
334C2×C3×C9H(5,𝔽2)11yescharacteristic
335C2×C3×C9H(5,𝔽2)11yescharacteristic
336C2×C3×C9H(5,𝔽2)11yescharacteristic
337C3⋊D9—41no—
338C3⋊D9—41no—
339C3⋊D9—41no—
340D3×C9—41no—
341C3×D9—41no—
342C3×D9—41no—
343C23×D3—91no—
344C23×D3—91no—
345C2×C3×D4—91no—
346C22×C3×C4—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×D12—31no—
357C2×D12—91no—
358C2×D12—91no—
359C2×D12—91no—
360C2×D12—91no—
361C2×D12—91no—
362C2×D12—91no—
363C2×D12—91no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—181no—
371C2×D12—181no—
372C2×D12—181no—
373C2×C4×D3—31no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—181no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4C2×D911yescharacteristic, complemented
384C3×C4⋊C4D3211yescharacteristic
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C42—31no—
392#217—91no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
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—181no—
408(C2×D3)⋊C4—181no—
409(C2×D3)⋊C4C2×D911yescharacteristic
410(C2×D3)⋊C4C2×D911yescharacteristic
411(C2×D3)⋊C4C2×D911yescharacteristic
412C4⋊Dic3—91no—
413C4⋊Dic3C2×D911yescharacteristic, complemented
414Dic3⋊C4—31no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×D911yescharacteristic, complemented
419C4×Dic3C2×D911yescharacteristic, complemented
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
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—
442C32×C4—21no—
443C3⋊Dic3—61no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C22×C9—21no—
450C22×C9—61no—
451C22×C9—61no—
452C22×C9—61no—
453C22×C9C23×D311yescharacteristic
454C2×D9—21no—
455C2×D9—21no—
456C2×D9—21no—
457C2×D9—21no—
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—62no—
461C2×D9—61no—
462C2×D9—61no—
463C2×D9—61no—
464C2×D9—61no—
465C2×D9—61no—
466C2×D9—61no—
467C2×D9—61no—
468C2×D9—61no—
469C2×D9—61no—
470C2×D9—121no—
471C2×D9—121no—
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—21no—
483C4×C9—41no—
484C4×C9—41no—
485C4×C9—61no—
486C4×C9—61no—
487C4×C9—61no—
488Dic9—21no—
489Dic9—21no—
490Dic9—61no—
491Dic9—121no—
492#127—271no—
493#126—31no—
494#126—271no—
495#123—91no—
496#123—271no—
497#123—271no—
498#121—271no—
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—31no—
509C23×C3—91no—
510C23×C3—91no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—91no—
514C22×D3—91no—
515C22×D3—91no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—181no—
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—361no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—361no—
539C2×C3×C4C22×D911yescharacteristic
540C2×C3×C4C22×D911yescharacteristic
541C2×C3×C4C22×D911yescharacteristic
542C2×C3×C4C2×D3211yescharacteristic
543C2×C3×C4C2×D3211yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545#67—361no—
546#67—361no—
547#67—361no—
548#67—361no—
549#67—361no—
550#67—361no—
551#67—361no—
552#67—361no—
553#67—361no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—181no—
559C2×Dic3C22×D911yescharacteristic
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562D12—121no—
563D12—361no—
564D12—361no—
565D12—361no—
566D12—361no—
567D12—361no—
568D12—361no—
569D12—362no—
570D12—362no—
571D12—362no—
572D12—361no—
573D12—361no—
574D12—361no—
575D12—361no—
576D12—361no—
577D12—361no—
578D12—361no—
579C4×D3—121no—
580C4×D3—361no—
581C4×D3—361no—
582C4×D3—361no—
583C4×D3—361no—
584C4×D3—362no—
585C2×C32#100911yescharacteristic
586C2×C32#100911yescharacteristic
587C2×C32#100911yescharacteristic
588C3⋊D3—121no—
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—121no—
598C2×C9#100411yescharacteristic
599C2×C9#100911yescharacteristic
600C2×C9#100911yescharacteristic
601D9—41no—
602D9—41no—
603D9—122no—
604D9—121no—
605D9—121no—
606D9—121no—
607D9—241no—
608D9—241no—
609C24—271no—
610C2×D4—91no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
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—91no—
623C22×C4—271no—
624C22×C4—271no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—91no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4D3×D911yescharacteristic, complemented
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—31no—
644C22×C3—21no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3C23×D911yescharacteristic
655C22×C3C22×D3211yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—182no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—181no—
670C2×D3—181no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
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—361no—
685C2×D3—361no—
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—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—181no—
707C3×C4—181no—
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—61no—
712Dic3—61no—
713Dic3—181no—
714Dic3—181no—
715Dic3—361no—
716C32#571111yescharacteristic
717C9—21no—
718C9#566611yescharacteristic, complemented
719C23—31no—
720C23—91no—
721C23—91no—
722C23—271no—
723C23—271no—
724C23—271no—
725C23—1081no—
726C23—1081no—
727C23—1081no—
728D4—361no—
729D4—1081no—
730D4—1081no—
731D4—1081no—
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—91no—
744C2×C4—91no—
745C2×C4—271no—
746C2×C4—361no—
747C2×C4—1081no—
748C2×C4—1081no—
749C2×C4C2×D3×D911yescharacteristic
750C2×C4C2×D3×D911yescharacteristic
751C2×C4C2×D3×D911yescharacteristic
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—121no—
756C2×C3—361no—
757C2×C3—361no—
758C2×C3#6371511yescharacteristic
759C2×C3#6371511yescharacteristic
760C2×C3#6371511yescharacteristic
761C2×C3#6430811yescharacteristic
762C2×C3#6431411yescharacteristic
763C2×C3#6432011yescharacteristic
764D3—41no—
765D3—121no—
766D3—121no—
767D3—362no—
768D3—361no—
769D3—361no—
770D3—361no—
771D3—361no—
772D3—361no—
773D3—361no—
774D3—721no—
775D3—721no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—541no—
786C22—541no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—541no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—1084no—
795C22C22×D3×D911yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—61no—
800C4—61no—
801C4—61no—
802C4—181no—
803C4—181no—
804C4—541no—
805C3—21no—
806C3#1058981311yescharacteristic, complemented
807C3#1059466311yescharacteristic
808C2—121no—
809C2—361no—
810C2—361no—
811C2—1081no—
812C2—1081no—
813C2—1081no—
814C2#1172247811yescharacteristic
815C2#1172250111yescharacteristic
816C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721751C2semidirect
2. C9×#898C2semidirect
3. C3×#63456C2semidirect
4. #11721051C2semidirect
5. #11721051C2semidirect
6. #11721049C2semidirect
7. #11721041C2semidirect
8. #11721039C2semidirect
9. #11721033C2semidirect
10. #11721006C2semidirect
11. #11721005C2semidirect
12. #11721004C2semidirect
13. #11720942C2semidirect
14. #11720941C2semidirect
15. #11720926C2semidirect
21. C2×C4⋊(C3⋊D9)C22semidirect
22. C2×C4×C3⋊D9C22semidirect
24. C2×C3×C4×D9C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C3×C9×C4⋊C4C22semidirect
36. #88536C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×C4⋊Dic3C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C4×C9×Dic3C22semidirect
46. C3×Dic9⋊C4C22semidirect
49. #88445C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
75. #63456D3semidirect
173. C2×C4×D9C2×D3semidirect
177. C9×C4⋊C4C2×D3semidirect
192. (C2×D9)⋊C4C2×D3semidirect
195. Dic9⋊C4C2×D3semidirect
232. #898D9semidirect
383. C3×C4⋊C4C2×D9semidirect
413. C4⋊Dic3C2×D9semidirect
418. Dic3⋊C4C2×D9semidirect
419. C4×Dic3C2×D9semidirect
507. C3×C9#560semidirect
630. C4⋊C4D3×D9semidirect
718. C9#5666semidirect
806. C3#10589813semidirect

Maximal subgroups

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

subgroupindex
#117217512
C9×#8982
C3×#634562
#117210512
#117210492
#117210412
#117210392
#117210332
#117210062
#117210052
#117210042
#117209422
#117209412
#117209262
#105946633
#105898133