Finite Group Databasebeta

← #13149379

Subgroups — #13149379

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×#894C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic, complemented
5#11721051C211yesmaximal, characteristic, complemented
6#11721050C211yesmaximal, characteristic, complemented
7#11721041C211yesmaximal, characteristic, complemented
8#11721040C211yesmaximal, characteristic, complemented
9#11721039C211yesmaximal, characteristic, complemented
10#11721038C211yesmaximal, characteristic, complemented
11#11721034C211yesmaximal, characteristic, complemented
12#11721005C211yesmaximal, characteristic, complemented
13#11720958C211yesmaximal, characteristic, complemented
14#11720957C211yesmaximal, characteristic, complemented
15#11720934C211yesmaximal, characteristic, complemented
16#10594663—31nomaximal
17#10589768—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×C9×D12C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic, complemented
29C2×#6195C2211yescharacteristic, complemented
30C2×#6194C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic
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, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#64104—31no—
54C3×#898—31no—
55C3×#894D311yescharacteristic
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×#123—31no—
69#63502—31no—
70#63499—31no—
71#63492—31no—
72#63492—31no—
73#63460—31no—
74#63460D311yescharacteristic, complemented
75#63457—31no—
76#63457—31no—
77#63457—61no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63445—31no—
82#63444—31no—
83#63444—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
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×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C9×D12—41no—
107C4×D3×C9—41no—
108#6195—41no—
109#6195—41no—
110#6195—41no—
111#6195—41no—
112#6195—41no—
113#6194—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×D12C2×D311yescharacteristic
125C2×C3×C4×D3C2×D311yescharacteristic
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⋊Dic3—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×C4×Dic3—31no—
149#3724—31no—
150Dic3⋊Dic3—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155C2×D4×C9—31no—
156C22×C4×C9—31no—
157C2×#611—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—31no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—61no—
169C2×D36—61no—
170C2×D36—61no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—61no—
174C9×C4⋊C4—21no—
175C9×C4⋊C4—31no—
176C9×C4⋊C4C2×D311yescharacteristic, complemented
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180#3676—31no—
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—61no—
187(C2×D9)⋊C4—61no—
188(C2×D9)⋊C4C2×D311yescharacteristic
189(C2×D9)⋊C4C2×D311yescharacteristic
190(C2×D9)⋊C4C2×D311yescharacteristic
191C4⋊Dic9—31no—
192C4⋊Dic9C2×D311yescharacteristic, complemented
193Dic9⋊C4—31no—
194Dic9⋊C4C2×D311yescharacteristic, complemented
195C4×Dic9C2×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×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×C4×C9—21no—
218C3×C4×C9—21no—
219C3⋊Dic9—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#126—91no—
226C3×#123—31no—
227#940—91no—
228#937—91no—
229#930—91no—
230#930—91no—
231#898—31no—
232#898—91no—
233#895—91no—
234#895—91no—
235#895—91no—
236#895—91no—
237#895—91no—
238#895—181no—
239#894—91no—
240#894—91no—
241#894D911yescharacteristic, complemented
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×D3C22×D311yescharacteristic
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×Dic3—31no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C3×D12—41no—
279C3×C4×D3—41no—
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—
290C23×C9—31no—
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×D9C22×D311yescharacteristic
301D4×C9—121no—
302C2×C4×C9—21no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9—121no—
308C2×C4×C9C22×D311yescharacteristic
309C2×C4×C9C22×D311yescharacteristic
310C2×C4×C9C22×D311yescharacteristic
311#611—121no—
312#611—121no—
313#611—121no—
314#611—121no—
315#611—121no—
316#611—121no—
317C2×Dic9—31no—
318C2×Dic9—61no—
319C2×Dic9C22×D311yescharacteristic
320C2×Dic9C22×D311yescharacteristic
321C2×Dic9C22×D311yescharacteristic
322D36—121no—
323D36—121no—
324D36—121no—
325D36—122no—
326D36—122no—
327D36—122no—
328D36—121no—
329D36—121no—
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—
341D3×C9—41no—
342C3×D9—41no—
343C23×D3—91no—
344C23×D3—91no—
345C2×C3×D4—31no—
346C22×C3×C4—31no—
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—91no—
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—181no—
370C2×D12—181no—
371C2×D12—181no—
372C2×D12C2×D911yescharacteristic
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—181no—
378C2×C4×D3C2×D911yescharacteristic, complemented
379C3×C4⋊C4—21no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—91no—
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—91no—
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, complemented
412C4⋊Dic3—31no—
413C4⋊Dic3—91no—
414Dic3⋊C4—31no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×D911yescharacteristic, complemented
419C4×Dic3—31no—
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—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
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—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C22×C9—21no—
450C22×C9—61no—
451C22×C9—61no—
452C22×C9—61no—
453C22×C9—61no—
454C22×C9—61no—
455C22×C9—61no—
456C22×C9C23×D311yescharacteristic
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—
487Dic9—21no—
488Dic9—21no—
489Dic9—21no—
490Dic9—61no—
491Dic9—121no—
492#127—271no—
493#126—91no—
494#126—271no—
495#123—31no—
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—31no—
510C23×C3—91no—
511C22×D3—31no—
512C22×D3—91no—
513C22×D3—91no—
514C22×D3—91no—
515C22×D3—91no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—181no—
519C22×D3—181no—
520C22×D3—181no—
521C22×D3—361no—
522C22×D3—361no—
523C22×D3—361no—
524C22×D3—361no—
525C22×D3—361no—
526C22×D3—361no—
527C22×D3C22×D911yescharacteristic
528C22×D3C22×D911yescharacteristic
529C3×D4—121no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—91no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—121no—
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—31no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—181no—
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562D12—41no—
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—41no—
580C4×D3—361no—
581C4×D3—361no—
582C4×D3—361no—
583C4×D3—361no—
584C4×D3—362no—
585C2×C32#100411yescharacteristic
586C2×C32#100911yescharacteristic
587C2×C32#100911yescharacteristic
588C3⋊D3—121no—
589C3⋊D3—121no—
590C3⋊D3—121no—
591C3×D3—41no—
592C3×D3—41no—
593C3×D3—121no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—121no—
598C2×C9—121no—
599C2×C9#100911yescharacteristic
600C2×C9#100911yescharacteristic
601C2×C9#100911yescharacteristic
602D9—41no—
603D9—122no—
604D9—121no—
605D9—121no—
606D9—121no—
607D9—241no—
608D9—241no—
609C24—271no—
610C2×D4—31no—
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—31no—
623C22×C4—271no—
624C22×C4—271no—
625C4⋊C4—31no—
626C4⋊C4—91no—
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—91no—
644C22×C3—21no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
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—21no—
660C2×D3—21no—
661C2×D3—21no—
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—181no—
706C3×C4—181no—
707C3×C4—181no—
708Dic3—21no—
709Dic3—21no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—181no—
714Dic3—181no—
715Dic3—361no—
716C32#566611yescharacteristic
717C9—21no—
718C9#571111yescharacteristic, complemented
719C23—31no—
720C23—31no—
721C23—91no—
722C23—271no—
723C23—271no—
724C23—271no—
725C23—1081no—
726C23—1081no—
727C23—1081no—
728D4—121no—
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—91no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—121no—
746C2×C4—271no—
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—121no—
757C2×C3—361no—
758C2×C3#6371011yescharacteristic
759C2×C3#6371511yescharacteristic
760C2×C3#6371511yescharacteristic
761C2×C3#6430811yescharacteristic
762C2×C3#6431411yescharacteristic
763C2×C3#6432011yescharacteristic
764D3—41no—
765D3—41no—
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—61no—
780C22—61no—
781C22—61no—
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—181no—
802C4—181no—
803C4—181no—
804C4—541no—
805C3—21no—
806C3#1058976811yescharacteristic, complemented
807C3#1059466311yescharacteristic
808C2—121no—
809C2—121no—
810C2—361no—
811C2—1081no—
812C2—1081no—
813C2—1081no—
814C2#1172247811yescharacteristic
815C2#1172250011yescharacteristic
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×#894C2semidirect
3. C3×#63460C2semidirect
4. #11721051C2semidirect
5. #11721051C2semidirect
6. #11721050C2semidirect
7. #11721041C2semidirect
8. #11721040C2semidirect
9. #11721039C2semidirect
10. #11721038C2semidirect
11. #11721034C2semidirect
12. #11721005C2semidirect
13. #11720958C2semidirect
14. #11720957C2semidirect
15. #11720934C2semidirect
21. C2×C4⋊(C3⋊D9)C22semidirect
22. C2×C4×C3⋊D9C22semidirect
24. C2×C4×D3×C9C22semidirect
28. C2×#6195C22semidirect
29. C2×#6195C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C3×C9×C4⋊C4C22semidirect
36. #88536C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×C4×Dic9C22semidirect
50. #88445C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
74. #63460D3semidirect
176. C9×C4⋊C4C2×D3semidirect
192. C4⋊Dic9C2×D3semidirect
194. Dic9⋊C4C2×D3semidirect
195. C4×Dic9C2×D3semidirect
241. #894D9semidirect
378. C2×C4×D3C2×D9semidirect
383. C3×C4⋊C4C2×D9semidirect
411. (C2×D3)⋊C4C2×D9semidirect
418. Dic3⋊C4C2×D9semidirect
507. C3×C9#560semidirect
630. C4⋊C4D3×D9semidirect
718. C9#5711semidirect
806. C3#10589768semidirect

Maximal subgroups

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

subgroupindex
#117217512
C9×#8942
C3×#634602
#117210512
#117210502
#117210412
#117210402
#117210392
#117210382
#117210342
#117210052
#117209582
#117209572
#117209342
#105946633
#105897683