Finite Group Databasebeta

← #13149374

Subgroups — #13149374

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721750C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63457C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic, complemented
5#11721049C211yesmaximal, characteristic, complemented
6#11721049C211yesmaximal, characteristic, complemented
7#11721041C211yesmaximal, characteristic, complemented
8#11721033C211yesmaximal, characteristic, complemented
9#11721007C211yesmaximal, characteristic, complemented
10#11721006C211yesmaximal, characteristic, complemented
11#11720988C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720947C211yesmaximal, characteristic, complemented
15#11720938C211yesmaximal, characteristic, complemented
16#10594661—31nomaximal
17#10589813—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C3×D36C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic, complemented
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34C3×C9×C4⋊C4C2211yescharacteristic, complemented
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88536C2211yescharacteristic, complemented
38#88534C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C9×C4⋊Dic3C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C4×C9×Dic3C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64103—31no—
54C3×#898D311yescharacteristic
55C3×#895—31no—
56#63923—31no—
57#63922—31no—
58#63922—31no—
59#63916—31no—
60#63912—31no—
61#63911—31no—
62#63906—31no—
63#63890—31no—
64#63886—31no—
65#63885—31no—
66#63859—31no—
67#63850—31no—
68C9×#126—31no—
69#63457—31no—
70#63457—31no—
71#63457D311yescharacteristic, complemented
72#63456—31no—
73#63456—31no—
74#63456—31no—
75#63456—61no—
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×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
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
97C2×C3⋊Dic9C2311yescharacteristic
98C4⋊(C3⋊D9)—41no—
99C4×C3⋊D9—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C3×D36—41no—
105C3×D36—41no—
106C3×D36—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6194—41no—
110#6194—41no—
111#6192—41no—
112#6192—41no—
113#6192—41no—
114#6192—41no—
115#6192—41no—
116Dic3×D9—41no—
117#5711—91no—
118#5620—91no—
119C22×D32—31no—
120C2×C4⋊(C3⋊D3)—31no—
121C2×C4×C3⋊D3—31no—
122C2×C3×D12—31no—
123C2×C3×D12—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×#625—31no—
133C2×#625—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136C32×C4⋊C4C2×D311yescharacteristic
137#3752—31no—
138#3752—31no—
139#3752—31no—
140#3750—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×C4×Dic3C2×D311yescharacteristic
149#3724—31no—
150Dic3⋊Dic3—31no—
151#3722—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—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—61no—
165C2×D36C2×D311yescharacteristic
166C2×D36C2×D311yescharacteristic
167C2×D36C2×D311yescharacteristic, complemented
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—61no—
171C2×C4×D9C2×D311yescharacteristic, complemented
172C9×C4⋊C4—21no—
173C9×C4⋊C4—31no—
174C9×C4⋊C4—31no—
175C9×C4⋊C4C2×D311yescharacteristic, complemented
176C9×C22⋊C4—31no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C42×C9—31no—
180(C2×D9)⋊C4—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—31no—
187(C2×D9)⋊C4—61no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic
191(C2×D9)⋊C4C2×D311yescharacteristic, complemented
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—61no—
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×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—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—
220C3⋊Dic9—21no—
221C9×Dic3—21no—
222C9×Dic3—21no—
223C9×Dic3—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#898D911yescharacteristic, complemented
236#895—31no—
237#895—91no—
238#895—91no—
239#894—91no—
240#894—91no—
241#894—91no—
242#894—91no—
243#894—181no—
244#886—91no—
245#884—91no—
246#884—91no—
247#884—91no—
248#884—91no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—91no—
253#879—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—
269C2×C3⋊Dic3—31no—
270C4⋊(C3⋊D3)—121no—
271C4×C3⋊D3—121no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C3×D12—121no—
277C3×D12—121no—
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#625—121no—
287#625—121no—
288D3×Dic3—121no—
289C23×C9—31no—
290C22×D9—31no—
291C22×D9—31no—
292C22×D9—61no—
293C22×D9—61no—
294C22×D9—121no—
295C22×D9—121no—
296C22×D9—121no—
297C22×D9C22×D311yescharacteristic
298C22×D9C22×D311yescharacteristic
299C22×D9C22×D311yescharacteristic
300C2×C4×C9—21no—
301C2×C4×C9—21no—
302C2×C4×C9—21no—
303C2×C4×C9—31no—
304C2×C4×C9—31no—
305C2×C4×C9—31no—
306C2×C4×C9C22×D311yescharacteristic
307C2×C4×C9C22×D311yescharacteristic
308C2×C4×C9C22×D311yescharacteristic
309#611—121no—
310#611—121no—
311#611—121no—
312C2×Dic9—31no—
313C2×Dic9—31no—
314C2×Dic9—61no—
315C2×Dic9—61no—
316C2×Dic9C22×D311yescharacteristic
317D36—41no—
318D36—41no—
319D36—41no—
320D36—121no—
321D36—122no—
322D36—121no—
323D36—121no—
324D36—121no—
325D36—121no—
326D36—121no—
327C4×D9—41no—
328C4×D9—121no—
329C4×D9—121no—
330C4×D9—122no—
331#560—271noSylow
332C2×C3×C9H(5,𝔽2)11yescharacteristic
333C2×C3×C9H(5,𝔽2)11yescharacteristic
334C2×C3×C9H(5,𝔽2)11yescharacteristic
335C3⋊D9—41no—
336C3⋊D9—41no—
337D3×C9—41no—
338C3×D9—41no—
339C3×D9—41no—
340C3×D9—41no—
341C23×D3—91no—
342C23×D3—91no—
343C2×C3×D4—91no—
344C2×C3×D4—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×#67—91no—
357C22×Dic3—91no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
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×C4×D3—31no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—181no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4C2×D911yescharacteristic, complemented
379C3×C4⋊C4D3211yescharacteristic
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C42—31no—
386#217—91no—
387#217—91no—
388#217—91no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—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—181no—
403(C2×D3)⋊C4—181no—
404(C2×D3)⋊C4—181no—
405(C2×D3)⋊C4C2×D911yescharacteristic
406(C2×D3)⋊C4C2×D911yescharacteristic
407(C2×D3)⋊C4C2×D911yescharacteristic
408C4⋊Dic3—91no—
409C4⋊Dic3C2×D911yescharacteristic, complemented
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—181no—
416Dic3⋊C4C2×D911yescharacteristic, complemented
417C4×Dic3C2×D911yescharacteristic, complemented
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—61no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
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—61no—
436C2×C3×D3—61no—
437D32—124no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—21no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—61no—
447C22×C9—21no—
448C22×C9—61no—
449C22×C9—61no—
450C22×C9—61no—
451C22×C9C23×D311yescharacteristic
452C2×D9—21no—
453C2×D9—21no—
454C2×D9—21no—
455C2×D9—21no—
456C2×D9—21no—
457C2×D9—21no—
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—21no—
461C2×D9—62no—
462C2×D9—61no—
463C2×D9—61no—
464C2×D9—61no—
465C2×D9—61no—
466C2×D9—61no—
467C2×D9—61no—
468C2×D9—121no—
469C2×D9—121no—
470C2×D9—121no—
471C2×D9—121no—
472C2×D9—121no—
473C2×D9—124no—
474C4×C9—21no—
475C4×C9—21no—
476C4×C9—21no—
477C4×C9—41no—
478C4×C9—41no—
479C4×C9—41no—
480C4×C9—61no—
481C4×C9—61no—
482C4×C9—61no—
483Dic9—21no—
484Dic9—61no—
485Dic9—61no—
486Dic9—121no—
487Dic9—121no—
488#127—271no—
489#126—31no—
490#126—271no—
491#123—271no—
492#123—271no—
493#123—271no—
494#121—91no—
495#121—271no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502#120—271no—
503C3×C9#56011yescharacteristic, complemented, Sylow
504C23×C3—31no—
505C23×C3—91no—
506C23×C3—91no—
507C23×C3—91no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—91no—
512C22×D3—91no—
513C22×D3—91no—
514C22×D3—91no—
515C22×D3—181no—
516C22×D3—181no—
517C22×D3—361no—
518C22×D3—361no—
519C22×D3—361no—
520C22×D3—361no—
521C22×D3—361no—
522C22×D3—361no—
523C22×D3C22×D911yescharacteristic
524C3×D4—361no—
525C3×D4—361no—
526C3×D4—361no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—91no—
534C2×C3×C4—361no—
535C2×C3×C4C22×D911yescharacteristic
536C2×C3×C4C22×D911yescharacteristic
537C2×C3×C4C22×D911yescharacteristic
538C2×C3×C4C2×D3211yescharacteristic
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541#67—361no—
542#67—361no—
543#67—361no—
544#67—361no—
545#67—361no—
546#67—361no—
547#67—361no—
548#67—361no—
549#67—361no—
550#67—361no—
551C2×Dic3—31no—
552C2×Dic3—91no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—181no—
557C2×Dic3—181no—
558C2×Dic3—361no—
559C2×Dic3C22×D911yescharacteristic
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562D12—121no—
563D12—121no—
564D12—121no—
565D12—361no—
566D12—361no—
567D12—362no—
568D12—361no—
569D12—361no—
570D12—361no—
571D12—361no—
572D12—361no—
573D12—361no—
574C4×D3—121no—
575C4×D3—361no—
576C4×D3—361no—
577C4×D3—361no—
578C4×D3—362no—
579C2×C32#100911yescharacteristic
580C2×C32#100911yescharacteristic
581C2×C32#100911yescharacteristic
582C3⋊D3—121no—
583C3⋊D3—121no—
584C3×D3—41no—
585C3×D3—121no—
586C3×D3—121no—
587C3×D3—121no—
588C2×C9—21no—
589C2×C9—21no—
590C2×C9—21no—
591C2×C9—121no—
592C2×C9#100411yescharacteristic
593C2×C9#100411yescharacteristic
594C2×C9#100911yescharacteristic
595D9—41no—
596D9—41no—
597D9—41no—
598D9—122no—
599D9—121no—
600D9—121no—
601D9—241no—
602C24—271no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—91no—
606C2×D4—271no—
607C2×D4—271no—
608C2×D4—271no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—91no—
616C22×C4—271no—
617C22×C4—271no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4D3×D911yescharacteristic, complemented
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C42—31no—
637C22×C3—21no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3C23×D911yescharacteristic
651C22×C3C22×D3211yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—182no—
665C2×D3—181no—
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—361no—
678C2×D3—361no—
679C2×D3—361no—
680C2×D3—361no—
681C2×D3—361no—
682C2×D3—364no—
683C2×D3—364no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—181no—
697Dic3—21no—
698Dic3—21no—
699Dic3—21no—
700Dic3—61no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—361no—
706Dic3—361no—
707C32#571111yescharacteristic
708C9—21no—
709C9#562011yescharacteristic, complemented
710C23—31no—
711C23—91no—
712C23—91no—
713C23—91no—
714C23—271no—
715C23—271no—
716C23—1081no—
717C23—1081no—
718C23—1081no—
719D4—361no—
720D4—361no—
721D4—361no—
722D4—1081no—
723D4—1081no—
724D4—1081no—
725D4—1081no—
726D4—1081no—
727D4—1081no—
728D4—1081no—
729D4—1081no—
730D4—1081no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—91no—
735C2×C4—271no—
736C2×C4—271no—
737C2×C4—361no—
738C2×C4—1081no—
739C2×C4—1081no—
740C2×C4C2×D3×D911yescharacteristic
741C2×C4C2×D3×D911yescharacteristic
742C2×C4C2×D3×D911yescharacteristic
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—121no—
747C2×C3—361no—
748C2×C3—361no—
749C2×C3—361no—
750C2×C3#6371511yescharacteristic
751C2×C3#6371511yescharacteristic
752C2×C3#6371511yescharacteristic
753C2×C3#6430711yescharacteristic
754C2×C3#6431411yescharacteristic
755C2×C3#6432011yescharacteristic
756D3—41no—
757D3—121no—
758D3—121no—
759D3—121no—
760D3—362no—
761D3—361no—
762D3—361no—
763D3—361no—
764D3—361no—
765D3—721no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—541no—
779C22—541no—
780C22—541no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—1084no—
785C22C22×D3×D911yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—181no—
793C4—541no—
794C4—541no—
795C3—21no—
796C3#1058981311yescharacteristic, complemented
797C3#1059466111yescharacteristic
798C2—121no—
799C2—361no—
800C2—361no—
801C2—361no—
802C2—1081no—
803C2—1081no—
804C2#1172247711yescharacteristic
805C2#1172250111yescharacteristic
806C2#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. #11721750C2semidirect
2. C9×#898C2semidirect
3. C3×#63457C2semidirect
4. #11721051C2semidirect
5. #11721049C2semidirect
6. #11721049C2semidirect
7. #11721041C2semidirect
8. #11721033C2semidirect
9. #11721007C2semidirect
10. #11721006C2semidirect
11. #11720988C2semidirect
12. #11720983C2semidirect
13. #11720982C2semidirect
14. #11720947C2semidirect
15. #11720938C2semidirect
20. C2×C4×C3⋊D9C22semidirect
23. C2×C3×D36C22semidirect
24. C2×C3×C4×D9C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×Dic3×D9C22semidirect
34. C3×C9×C4⋊C4C22semidirect
37. #88536C22semidirect
38. #88534C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C9×C4⋊Dic3C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C4×C9×Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
71. #63457D3semidirect
167. C2×D36C2×D3semidirect
171. C2×C4×D9C2×D3semidirect
175. C9×C4⋊C4C2×D3semidirect
191. (C2×D9)⋊C4C2×D3semidirect
235. #898D9semidirect
378. C3×C4⋊C4C2×D9semidirect
409. C4⋊Dic3C2×D9semidirect
416. Dic3⋊C4C2×D9semidirect
417. C4×Dic3C2×D9semidirect
503. C3×C9#560semidirect
623. C4⋊C4D3×D9semidirect
709. C9#5620semidirect
796. C3#10589813semidirect

Maximal subgroups

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

subgroupindex
#117217502
C9×#8982
C3×#634572
#117210512
#117210492
#117210412
#117210332
#117210072
#117210062
#117209882
#117209832
#117209822
#117209472
#117209382
#105946613
#105898133