Finite Group Databasebeta

← #13147927

Subgroups — #13147927

Order 1728.

964 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6189C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3#11721727C211yesmaximal, characteristic, complemented
4C9×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#611⋊C4C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721288C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9#11721044C211yesmaximal, characteristic, complemented
10C4×#6189C211yesmaximal, characteristic, complemented
11#11720956C211yesmaximal, characteristic, complemented
12#11720955C211yesmaximal, characteristic, complemented
13#11720940C211yesmaximal, characteristic, complemented
14#11720939C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10594189—31nomaximal
17#10589654—31nomaximal
18C2×#6233C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×C4×D3×C9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6189—24no—
31C2×#6189C2211yescharacteristic
32C2×#6189C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34C2×#6189C2211yescharacteristic
35#88640—24no—
36C3×C9×C22⋊C4C2211yescharacteristic
37#88536C2211yescharacteristic
38#88534C2211yescharacteristic
39C4×C3⋊Dic9C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C4×C9×Dic3C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×C4×Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic
53#88442C2211yescharacteristic
54Dic9⋊Dic3C2211yescharacteristic
55C22×#627—31no—
56C2×#3798—31no—
57#64090—31no—
58C3×#67⋊C4—31no—
59C3×#67⋊C4D311yescharacteristic
60#63980—31no—
61#63978—31no—
62#63978—31no—
63C4×#627—31no—
64#63915—31no—
65#63865—31no—
66#63852—31no—
67#63852—31no—
68#63851—31no—
69#63851—31no—
70C2×#3697—31no—
71C22×Dic18—31no—
72C4×D4×C9—31no—
73#63501—31no—
74#63501—31no—
75#63492—31no—
76#63486—31no—
77#63458—31no—
78#63458—31no—
79#63447—31no—
80#63447—31no—
81#611⋊C4—31no—
82#611⋊C4—61no—
83#611⋊C4D311yescharacteristic, complemented
84#63437—31no—
85C4×Dic18—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92#6233—22no—
93C2×C3⋊Dic9—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4×C3⋊D9—22no—
98C9×#67—22no—
99C3×#611—22no—
100C2×C9×Dic3—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9—22no—
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C4×D3×C9—22no—
109C3×C4×D9—22no—
110#6195—22no—
111#6194—22no—
112#6192—22no—
113#6189—22no—
114#6189—22no—
115#6189—22no—
116#6189D414yescomplemented
117#5552—91no—
118#5552—91no—
119C2×#638—31no—
120C22×C3⋊Dic3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C3×#67—31no—
123C2×C3×#67C2×D311yescharacteristic
124C22×C3×Dic3—31no—
125C22×C3×Dic3C2×D311yescharacteristic
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3C2×D311yescharacteristic
128C2×#627—31no—
129C2×#627—31no—
130C2×#627—31no—
131C2×#627—31no—
132C2×#627—64no—
133C2×#626—31no—
134C2×#626—31no—
135C2×#625—31no—
136#3798—64no—
137C32×C22⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3750—31no—
140C4×C3⋊Dic3—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4C2×D311yescharacteristic
145C3×C4×Dic3—31no—
146C3×C4×Dic3C2×D311yescharacteristic
147#3724—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151#3722—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156C2×D4×C9—31no—
157C22×C4×C9—31no—
158C22×C4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—61no—
163C2×#611C2×D311yescharacteristic
164C22×Dic9—31no—
165C22×Dic9—61no—
166C22×Dic9C2×D311yescharacteristic
167#3697—64no—
168C2×D36—31no—
169C2×C4×D9—31no—
170C2×C4×D9—61no—
171C2×C4×D9C2×D311yescharacteristic
172C2×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—31no—
176C2×Dic18—64no—
177C9×C4⋊C4—31no—
178C9×C22⋊C4—21no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4C2×D311yescharacteristic
181C42×C9—31no—
182#3676—31no—
183#3676—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—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic
191C4⋊Dic9—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—61no—
196Dic9⋊C4C2×D311yescharacteristic
197C4×Dic9—31no—
198C4×Dic9—61no—
199C4×Dic9C2×D311yescharacteristic
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9#4112yescomplemented
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×#235—91no—
225C2×#235—91no—
226C22×Dic6—91no—
227C22×Dic6—91no—
228C3×C4×D4—31no—
229C3×C4×D4—91no—
230#939—91no—
231#939—91no—
232#939—91no—
233#939—91no—
234#930—91no—
235#930—91no—
236#924—91no—
237#924—91no—
238#896—91no—
239#896—91no—
240#896—91no—
241#896—91no—
242#885—91no—
243#885—91no—
244#885—91no—
245#885—91no—
246#67⋊C4—31no—
247#67⋊C4—91no—
248#67⋊C4—91no—
249#67⋊C4—181no—
250#67⋊C4D911yescharacteristic, complemented
251#875—91no—
252#875—91no—
253C4×Dic6—91no—
254C4×Dic6—91no—
255C23×C32C22×D311yescharacteristic
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—62no—
266C4×C3⋊D3—62no—
267C3×#67—22no—
268C3×#67—62no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C3×C4×D3—22no—
278C3×C4×D3—62no—
279#627—34no—
280#627—62no—
281#627—62no—
282#627—62no—
283#626—62no—
284#626—62no—
285#625—62no—
286C23×C9—21no—
287C23×C9—31no—
288C23×C9C22×D311yescharacteristic
289C22×D9—31no—
290C22×D9—61no—
291C22×D9C22×D311yescharacteristic
292D4×C9—62no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—62no—
299C2×C4×C9—62no—
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302#611—22no—
303#611—62no—
304#611—64no—
305#611—62no—
306#611—62no—
307C2×Dic9—22no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—31no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9—62no—
315C2×Dic9—122no—
316C2×Dic9C22×D311yescharacteristic
317C2×Dic9C22×D311yescharacteristic
318C2×Dic9C22×D311yescharacteristic
319D36—62no—
320C4×D9—22no—
321C4×D9—62no—
322C4×D9—122no—
323Dic18—34no—
324Dic18—62no—
325Dic18—62no—
326Dic18—62no—
327#548—271noSylow
328C2×C3×C9—22no—
329C2×C3×C9C22×D411yescharacteristic
330C2×C3×C9C2×#4111yescharacteristic
331C2×C3×C92−1+411yescharacteristic
332C3⋊D9—41no—
333D3×C9—41no—
334C3×D9—41no—
335C2×C3×D4—31no—
336C2×C3×D4—91no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C2×#67—31no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—181no—
349C2×#67C2×D911yescharacteristic
350C22×Dic3—31no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—181no—
354C22×Dic3C2×D911yescharacteristic
355#235—184no—
356#235—184no—
357C2×D12—91no—
358C2×D12—91no—
359C2×C4×D3—31no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—181no—
363C2×C4×D3C2×D911yescharacteristic
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—91no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C2×Dic6—184no—
373C2×Dic6—184no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—91no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4C2×D911yescharacteristic
380C3×C22⋊C4D3211yescharacteristic
381C3×C42—31no—
382C3×C42—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
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—181no—
399(C2×D3)⋊C4C2×D911yescharacteristic
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402Dic3⋊C4—31no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—181no—
410Dic3⋊C4C2×D911yescharacteristic
411C4×Dic3—31no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—181no—
415C4×Dic3C2×D911yescharacteristic
416C22×C32—21no—
417C22×C32—21no—
418C22×C32#23512yes—
419C22×C32C23×D311yescharacteristic
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C32×C4—21no—
430C32×C4—21no—
431C3⋊Dic3—32no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3D3×D412yes—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—22no—
444C22×C9—41no—
445C22×C9—41no—
446C22×C9—61no—
447C22×C9—61no—
448C22×C9—61no—
449C22×C9#23512yescomplemented
450C22×C9C23×D311yescharacteristic
451C2×D9—21no—
452C2×D9—21no—
453C2×D9—21no—
454C2×D9—62no—
455C2×D9—61no—
456C2×D9—61no—
457C2×D9—61no—
458C2×D9—121no—
459C2×D9—121no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—32no—
463C4×C9—41no—
464C4×C9—41no—
465C4×C9—61no—
466C4×C9—61no—
467Dic9—21no—
468Dic9—21no—
469Dic9—32no—
470Dic9—62no—
471Dic9—62no—
472Dic9—61no—
473Dic9—61no—
474Dic9—121no—
475Dic9D3×D412yes—
476C2×#41—271no—
477C22×Q8—271no—
478#124—271no—
479#124—271no—
480#124—271no—
481C22⋊Q8—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—271no—
485#121—271no—
486#121—271no—
487C4×Q8—271no—
488C4×D4—31no—
489C4×D4—91no—
490C4×D4—271no—
491C3×C9#54811yescharacteristic, complemented, Sylow
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—91no—
495C23×C3C22×D911yescharacteristic
496C23×C3C2×D3211yescharacteristic
497C22×D3—31no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—181no—
501C22×D3C22×D911yescharacteristic
502C3×D4—62no—
503C3×D4—182no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—182no—
515C2×C3×C4—182no—
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—22no—
521#67—62no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—184no—
526#67—182no—
527#67—182no—
528#67—182no—
529C2×Dic3—22no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—62no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—182no—
544C2×Dic3—182no—
545C2×Dic3—362no—
546C2×Dic3C22×D911yescharacteristic
547C2×Dic3C22×D911yescharacteristic
548C2×Dic3C22×D911yescharacteristic
549D12—182no—
550D12—182no—
551C4×D3—22no—
552C4×D3—62no—
553C4×D3—182no—
554C4×D3—182no—
555C4×D3—362no—
556Dic6—94no—
557Dic6—94no—
558Dic6—182no—
559Dic6—182no—
560Dic6—182no—
561Dic6—182no—
562Dic6—182no—
563Dic6—182no—
564C2×C32—22no—
565C2×C32C2×#23511yescharacteristic
566C2×C32C2×D3×D411yescharacteristic
567C2×C32#101011yescharacteristic
568C3⋊D3—121no—
569C3×D3—41no—
570C3×D3—121no—
571C2×C9—22no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—21no—
575C2×C9—42no—
576C2×C9—121no—
577C2×C9C2×#23511yescharacteristic
578C2×C9C2×D3×D411yescharacteristic
579C2×C9#101011yescharacteristic
580D9—41no—
581D9—122no—
582D9—121no—
583#41—544no—
584C2×Q8—271no—
585C2×Q8—271no—
586C2×Q8—271no—
587C2×Q8—271no—
588C2×Q8—544no—
589C2×D4—31no—
590C2×D4—91no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4—271no—
594C2×D4—271no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—91no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4D3×D911yescharacteristic
617C42—31no—
618C42—91no—
619C42—271no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3#369712yescomplemented
635C22×C3C23×D911yescharacteristic
636C22×C3#379812yes—
637C22×C3C22×D3211yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—182no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—361no—
652C2×D3—361no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—32no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—92no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—32no—
668Dic3—61no—
669Dic3—61no—
670Dic3—92no—
671Dic3—92no—
672Dic3—182no—
673Dic3—182no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—361no—
679Dic3D4×D912yes—
680C32#555211yescharacteristic
681C9—21no—
682C9#555211yescharacteristic, complemented
683C23—31no—
684C23—91no—
685C23—271no—
686C23C2×D3×D911yescharacteristic
687Q8—274no—
688Q8—542no—
689Q8—542no—
690Q8—542no—
691D4—62no—
692D4—182no—
693D4—542no—
694D4—542no—
695D4—542no—
696D4—542no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—182no—
706C2×C4—182no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—271no—
710C2×C4—542no—
711C2×C4—542no—
712C2×C4C2×D3×D911yescharacteristic
713C2×C4C2×D3×D911yescharacteristic
714C2×C3—22no—
715C2×C3—22no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—121no—
721C2×C3—361no—
722C2×C3C2×#369711yescharacteristic
723C2×C3C2×D4×D911yescharacteristic
724C2×C3#6371611yescharacteristic
725C2×C3C2×#379811yescharacteristic
726C2×C3#6430911yescharacteristic
727C2×C3D32×D411yescharacteristic
728D3—41no—
729D3—121no—
730D3—362no—
731D3—361no—
732D3—361no—
733C22—21no—
734C22—21no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—541no—
742C22—541no—
743C22—541no—
744C22#8864012yescomplemented
745C22C22×D3×D911yescharacteristic
746C4—21no—
747C4—21no—
748C4—32no—
749C4—61no—
750C4—61no—
751C4—92no—
752C4—181no—
753C4—181no—
754C4—272no—
755C4—541no—
756C4—541no—
757C3—21no—
758C3#1058965411yescharacteristic, complemented
759C3#1059418911yescharacteristic
760C2—22no—
761C2—121no—
762C2—361no—
763C2—1081no—
764C2C2×#8864011yescharacteristic
765C2#1172249411yescharacteristic
766C2D3×D4×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#548
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. C22×#6189C2semidirect
2. C2×#88640C2semidirect
3. #11721727C2semidirect
4. C9×#67⋊C4C2semidirect
5. C3×#611⋊C4C2semidirect
6. #11721290C2semidirect
7. #11721288C2semidirect
8. #11721277C2semidirect
9. #11721044C2semidirect
10. C4×#6189C2semidirect
11. #11720956C2semidirect
12. #11720955C2semidirect
13. #11720940C2semidirect
14. #11720939C2semidirect
15. #11720923C2semidirect
83. #611⋊C4D3semidirect
116. #6189D4semidirect
202. C22×C3×C9#41semidirect
250. #67⋊C4D9semidirect
449. C22×C9#235semidirect
491. C3×C9#548semidirect
634. C22×C3#3697semidirect
682. C9#5552semidirect
744. C22#88640semidirect
758. C3#10589654semidirect

Maximal subgroups

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

subgroupindex
C22×#61892
C2×#886402
#117217272
C9×#67⋊C42
C3×#611⋊C42
#117212902
#117212882
#117212772
#117210442
C4×#61892
#117209562
#117209552
#117209402
#117209392
#117209232
#105941893
#105896543