Finite Group Databasebeta

← #13148453

Subgroups — #13148453

Order 1728.

910 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721728C211yesmaximal, characteristic, complemented
2C9×#885C211yesmaximal, characteristic, complemented
3C3×#63447C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721291C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7#11721242C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721035C211yesmaximal, characteristic, complemented
11#11721003C211yesmaximal, characteristic, complemented
12#11720956C211yesmaximal, characteristic, complemented
13#11720953C211yesmaximal, characteristic, complemented
14#11720952C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594311—31nomaximal
17#10589785—31nomaximal
18C23×C3⋊D9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic, complemented
26C2×C3×Dic18C2211yescharacteristic, complemented
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6189C2211yescharacteristic, complemented
32C3×C9×C22⋊C4C2211yescharacteristic, complemented
33#88536C2211yescharacteristic, complemented
34#88536C2211yescharacteristic, complemented
35C9×#217C2211yescharacteristic, complemented
36C3×#3676C2211yescharacteristic, complemented
37C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C4×C9×Dic3C2211yescharacteristic, complemented
42C3×C4×Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic, complemented
44#88445C2211yescharacteristic, complemented
45#88445C2211yescharacteristic, complemented
46#88445C2211yescharacteristic, complemented
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64091—31no—
54C3×#885—31no—
55C3×#885D311yescharacteristic
56#63983—31no—
57#63981—31no—
58#63981—31no—
59#63953—31no—
60#63923—31no—
61#63923—31no—
62#63907—31no—
63#63907—31no—
64#63864—31no—
65#63864—31no—
66#63852—31no—
67#63852—31no—
68C9×#124—31no—
69#63509—31no—
70#63509—31no—
71#63499—31no—
72#63499—31no—
73#63447—31no—
74#63447—31no—
75#63447—31no—
76#63447D311yescharacteristic, complemented
77#63444—31no—
78#63444—31no—
79#63444—31no—
80#63444—31no—
81#63444—61no—
82#63437—31no—
83#63437—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×D3×C9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C2×D3×D9—41no—
94C2×D3×D9—41no—
95C2×D3×D9—41no—
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98#6233—41no—
99C2×C3⋊Dic9C2311yescharacteristic
100C4⋊(C3⋊D9)—41no—
101C4⋊(C3⋊D9)—41no—
102C9×#67—41no—
103C3×#611—41no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C9×Dic6—41no—
111C3×Dic18—41no—
112#6195—41no—
113#6195—41no—
114#6192—41no—
115#6192—41no—
116#6189—41no—
117#5683—91no—
118#5683—91no—
119C23×C3⋊D3—31no—
120C22×D32—31no—
121C2×#638—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C3×#67—31no—
125C2×C3×#67C2×D311yescharacteristic
126C2×C3×Dic6—31no—
127C2×C3×Dic6C2×D311yescharacteristic
128C2×#627—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#626—31no—
133C23×D9—31no—
134C23×D9—31no—
135C23×D9—61no—
136C32×C22⋊C4C2×D311yescharacteristic
137#3752—31no—
138#3752—31no—
139C3×#217—31no—
140C3×#217C2×D311yescharacteristic
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×C4×Dic3—31no—
146C3×C4×Dic3C2×D311yescharacteristic
147#3722—31no—
148#3722—31no—
149#3722—31no—
150#3722—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156Dic32—31no—
157C2×Q8×C9—31no—
158C2×D4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—61no—
163C2×#611C2×D311yescharacteristic
164C2×D36—31no—
165C2×D36—31no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—61no—
169C2×D36—61no—
170C2×Dic18—31no—
171C2×Dic18C2×D311yescharacteristic, complemented
172C9×C22⋊C4—21no—
173C9×C22⋊C4—31no—
174C9×C22⋊C4—31no—
175C9×C22⋊C4—31no—
176C9×C22⋊C4C2×D311yescharacteristic, complemented
177C42×C9—31no—
178#3676—31no—
179#3676C2×D311yescharacteristic, complemented
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—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
193(C2×D9)⋊C4C2×D311yescharacteristic, complemented
194C4×Dic9—31no—
195C4×Dic9C2×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×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216D3×D9—44no—
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×Dic9—21no—
226C3×#124—31no—
227C3×#124—91no—
228#947—91no—
229#947—91no—
230#947—91no—
231#947—91no—
232#937—91no—
233#937—91no—
234#937—91no—
235#937—91no—
236#885—31no—
237#885—91no—
238#885—91no—
239#885—91no—
240#885—91no—
241#885—91no—
242#885—91no—
243#885D911yescharacteristic, complemented
244#882—91no—
245#882—91no—
246#882—91no—
247#882—91no—
248#882—91no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—181no—
253#875—91no—
254#875—91no—
255#875—91no—
256#875—91no—
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—31no—
261C22×C3⋊D3—121no—
262C22×C3⋊D3—121no—
263C22×C3⋊D3—121no—
264C22×C3×D3—31no—
265C22×C3×D3C22×D311yescharacteristic
266C2×D32—121no—
267C2×D32—121no—
268C2×D32—121no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271#638—121no—
272C2×C3⋊Dic3—31no—
273C4⋊(C3⋊D3)—121no—
274C4⋊(C3⋊D3)—121no—
275C3×#67—41no—
276C3×#67—121no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C3×Dic6—41no—
284C3×Dic6—121no—
285#627—121no—
286#626—121no—
287#626—121no—
288#626—121no—
289#626—121no—
290C23×C9—21no—
291C23×C9—31no—
292C23×C9C22×D311yescharacteristic
293C22×D9—31no—
294C22×D9—31no—
295C22×D9—31no—
296C22×D9—61no—
297C22×D9—61no—
298C22×D9—61no—
299C22×D9—121no—
300C22×D9—121no—
301C22×D9—121no—
302C22×D9—121no—
303C22×D9—121no—
304C22×D9—121no—
305C22×D9—122no—
306C22×D9—122no—
307C22×D9—122no—
308C22×D9C22×D311yescharacteristic
309Q8×C9—121no—
310D4×C9—121no—
311C2×C4×C9—21no—
312C2×C4×C9—21no—
313C2×C4×C9—31no—
314C2×C4×C9—31no—
315C2×C4×C9—31no—
316C2×C4×C9C22×D311yescharacteristic
317C2×C4×C9C22×D311yescharacteristic
318#611—41no—
319#611—121no—
320#611—121no—
321#611—121no—
322#611—122no—
323C2×Dic9—31no—
324C2×Dic9—61no—
325C2×Dic9C22×D311yescharacteristic
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328D36—121no—
329D36—121no—
330D36—122no—
331D36—122no—
332D36—121no—
333D36—121no—
334Dic18—41no—
335Dic18—121no—
336H(3,𝔽4)—271noSylow
337C2×C3×C9—41no—
338C2×C3×C9H(5,𝔽2)11yescharacteristic
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C2×C3×C9H(5,𝔽2)11yescharacteristic
341C3⋊D9—41no—
342C3⋊D9—41no—
343C3⋊D9—41no—
344D3×C9—41no—
345C3×D9—41no—
346C23×D3—91no—
347C23×D3—91no—
348C23×D3—91no—
349C23×D3—91no—
350C23×D3—181no—
351C2×C3×Q8—31no—
352C2×C3×Q8—91no—
353C2×C3×D4—31no—
354C2×C3×D4—91no—
355C2×#67—31no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—181no—
363C2×#67C2×D911yescharacteristic
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—181no—
373C2×D12—181no—
374C2×Dic6—31no—
375C2×Dic6—91no—
376C2×Dic6—91no—
377C2×Dic6C2×D911yescharacteristic, complemented
378C3×C22⋊C4—21no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4C2×D911yescharacteristic, complemented
386C3×C22⋊C4D3211yescharacteristic
387C3×C42—31no—
388C3×C42—91no—
389#217—31no—
390#217—91no—
391#217—91no—
392#217C2×D911yescharacteristic, complemented
393(C2×D3)⋊C4—31no—
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—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—181no—
416(C2×D3)⋊C4—181no—
417(C2×D3)⋊C4C2×D911yescharacteristic, complemented
418(C2×D3)⋊C4C2×D911yescharacteristic, complemented
419C4×Dic3—31no—
420C4×Dic3—91no—
421C4×Dic3—91no—
422C4×Dic3C2×D911yescharacteristic, complemented
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32C23×D311yescharacteristic
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—61no—
436C2×C3⋊D3—124no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443D32—124no—
444C32×C4—21no—
445C32×C4—21no—
446C3⋊Dic3—61no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C22×C9—22no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—41no—
459C22×C9—41no—
460C22×C9—61no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9C23×D311yescharacteristic
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—62no—
468C2×D9—62no—
469C2×D9—61no—
470C2×D9—61no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—121no—
482C2×D9—121no—
483C2×D9—121no—
484C2×D9—121no—
485C2×D9—124no—
486C2×D9—128no—
487C2×D9—124no—
488C4×C9—21no—
489C4×C9—21no—
490C4×C9—41no—
491C4×C9—41no—
492C4×C9—61no—
493C4×C9—61no—
494C4×C9—61no—
495Dic9—21no—
496Dic9—21no—
497Dic9—21no—
498Dic9—61no—
499Dic9—121no—
500#124—31no—
501#124—91no—
502#124—271no—
503#124—271no—
504#124—271no—
505#124—271no—
506#124—271no—
507#124—271no—
508#124—271no—
509#120—271no—
510#120—271no—
511#120—271no—
512#120—271no—
513#120—271no—
514#120—271no—
515C3×C9H(3,𝔽4)11yescharacteristic, complemented, Sylow
516C23×C3—21no—
517C23×C3—31no—
518C23×C3—91no—
519C23×C3C22×D911yescharacteristic
520C23×C3C2×D3211yescharacteristic
521C22×D3—31no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—181no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—361no—
535C22×D3—361no—
536C22×D3—361no—
537C22×D3—361no—
538C22×D3—361no—
539C22×D3—361no—
540C22×D3—361no—
541C22×D3—361no—
542C22×D3—361no—
543C22×D3—362no—
544C22×D3—362no—
545C22×D3—362no—
546C22×D3C22×D911yescharacteristic
547C3×Q8—121no—
548C3×Q8—361no—
549C3×D4—121no—
550C3×D4—361no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4C22×D911yescharacteristic
560C2×C3×C4C22×D911yescharacteristic
561C2×C3×C4C2×D3211yescharacteristic
562C2×C3×C4C2×D3211yescharacteristic
563#67—41no—
564#67—121no—
565#67—361no—
566#67—361no—
567#67—361no—
568#67—361no—
569#67—361no—
570#67—361no—
571#67—362no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—91no—
576C2×Dic3—91no—
577C2×Dic3—181no—
578C2×Dic3C22×D911yescharacteristic
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581D12—361no—
582D12—361no—
583D12—361no—
584D12—361no—
585D12—362no—
586D12—362no—
587D12—361no—
588D12—361no—
589D12—361no—
590D12—361no—
591Dic6—41no—
592Dic6—121no—
593Dic6—361no—
594Dic6—361no—
595C2×C32—41no—
596C2×C32#100411yescharacteristic
597C2×C32#100911yescharacteristic
598C2×C32#100911yescharacteristic
599C3⋊D3—121no—
600C3⋊D3—121no—
601C3⋊D3—121no—
602C3×D3—41no—
603C3×D3—121no—
604C2×C9—21no—
605C2×C9—21no—
606C2×C9—21no—
607C2×C9—42no—
608C2×C9—41no—
609C2×C9—121no—
610C2×C9#100411yescharacteristic
611C2×C9#100911yescharacteristic
612C2×C9#100911yescharacteristic
613D9—41no—
614D9—122no—
615D9—122no—
616D9—121no—
617D9—121no—
618D9—121no—
619D9—241no—
620C24—271no—
621C24—271no—
622C2×Q8—31no—
623C2×Q8—91no—
624C2×Q8—271no—
625C2×D4—31no—
626C2×D4—91no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C2×D4—271no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—271no—
641C22⋊C4—271no—
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⋊C4—271no—
651C22⋊C4D3×D911yescharacteristic, complemented
652C42—31no—
653C42—91no—
654C42—271no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3C23×D911yescharacteristic
672C22×C3C22×D3211yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—182no—
680C2×D3—182no—
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—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—361no—
700C2×D3—361no—
701C2×D3—361no—
702C2×D3—361no—
703C2×D3—361no—
704C2×D3—361no—
705C2×D3—361no—
706C2×D3—364no—
707C2×D3—364no—
708C2×D3—364no—
709C2×D3—368no—
710C2×D3—364no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723Dic3—21no—
724Dic3—21no—
725Dic3—21no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—181no—
730Dic3—181no—
731Dic3—361no—
732C32#568311yescharacteristic
733C9—21no—
734C9#568311yescharacteristic, complemented
735C23—31no—
736C23—91no—
737C23—271no—
738C23—271no—
739C23—271no—
740C23—1081no—
741C23—1081no—
742C23—1081no—
743C23—1081no—
744C23—1081no—
745C23—1081no—
746C23C2×D3×D911yescharacteristic
747Q8—121no—
748Q8—361no—
749Q8—1081no—
750D4—121no—
751D4—361no—
752D4—1081no—
753D4—1081no—
754D4—1081no—
755D4—1081no—
756D4—1081no—
757D4—1081no—
758D4—1081no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—271no—
766C2×C4C2×D3×D911yescharacteristic
767C2×C4C2×D3×D911yescharacteristic
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—42no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—121no—
775C2×C3—361no—
776C2×C3#6371011yescharacteristic
777C2×C3#6371511yescharacteristic
778C2×C3#6371511yescharacteristic
779C2×C3#6430811yescharacteristic
780C2×C3#6431411yescharacteristic
781C2×C3#6431411yescharacteristic
782D3—41no—
783D3—121no—
784D3—362no—
785D3—362no—
786D3—361no—
787D3—361no—
788D3—361no—
789D3—361no—
790D3—361no—
791D3—361no—
792D3—721no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—181no—
800C22—181no—
801C22—181no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22—541no—
807C22—541no—
808C22—541no—
809C22—541no—
810C22—541no—
811C22—1084no—
812C22—1084no—
813C22C22×D3×D911yescharacteristic
814C4—21no—
815C4—21no—
816C4—61no—
817C4—61no—
818C4—61no—
819C4—181no—
820C4—181no—
821C4—181no—
822C4—541no—
823C3—21no—
824C3#1058978511yescharacteristic, complemented
825C3#1059431111yescharacteristic
826C2—41no—
827C2—121no—
828C2—361no—
829C2—1081no—
830C2—1081no—
831C2—1081no—
832C2#1172247811yescharacteristic
833C2#1172250011yescharacteristic
834C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9H(3,𝔽4)
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×#885C2semidirect
3. C3×#63447C2semidirect
4. #11721292C2semidirect
5. #11721291C2semidirect
6. #11721278C2semidirect
7. #11721242C2semidirect
8. #11721051C2semidirect
9. #11721051C2semidirect
10. #11721035C2semidirect
11. #11721003C2semidirect
12. #11720956C2semidirect
13. #11720953C2semidirect
14. #11720952C2semidirect
15. #11720940C2semidirect
18. C23×C3⋊D9C22semidirect
19. C22×D3×D9C22semidirect
25. C2×C9×Dic6C22semidirect
26. C2×C3×Dic18C22semidirect
31. C2×#6189C22semidirect
32. C3×C9×C22⋊C4C22semidirect
33. #88536C22semidirect
34. #88536C22semidirect
35. C9×#217C22semidirect
36. C3×#3676C22semidirect
37. C9×(C2×D3)⋊C4C22semidirect
38. C9×(C2×D3)⋊C4C22semidirect
39. C3×(C2×D9)⋊C4C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C4×C9×Dic3C22semidirect
42. C3×C4×Dic9C22semidirect
43. (C2×D3)⋊Dic9C22semidirect
44. #88445C22semidirect
45. #88445C22semidirect
46. #88445C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
76. #63447D3semidirect
171. C2×Dic18C2×D3semidirect
176. C9×C22⋊C4C2×D3semidirect
179. #3676C2×D3semidirect
192. (C2×D9)⋊C4C2×D3semidirect
193. (C2×D9)⋊C4C2×D3semidirect
195. C4×Dic9C2×D3semidirect
243. #885D9semidirect
377. C2×Dic6C2×D9semidirect
385. C3×C22⋊C4C2×D9semidirect
392. #217C2×D9semidirect
417. (C2×D3)⋊C4C2×D9semidirect
418. (C2×D3)⋊C4C2×D9semidirect
422. C4×Dic3C2×D9semidirect
515. C3×C9H(3,𝔽4)semidirect
651. C22⋊C4D3×D9semidirect
734. C9#5683semidirect
824. C3#10589785semidirect

Maximal subgroups

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

subgroupindex
#117217282
C9×#8852
C3×#634472
#117212922
#117212912
#117212782
#117212422
#117210512
#117210352
#117210032
#117209562
#117209532
#117209522
#117209402
#105943113
#105897853