Finite Group Databasebeta

← C2×#72219926 #72268786

Subgroups — C2×#72219926 #72268786

Order 5184.

4831 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13047076C211yesmaximal, characteristic, complemented
2C2×#13047075C212yesmaximal, complemented
3C2×#13047081C211yesmaximal, characteristic, complemented
4C2×#13047154C212yesmaximal, complemented
5C2×#13047077C212yesmaximal, complemented
6C2×C9×#3697C212yesmaximal, complemented
7C2×C4×D92C212yesmaximal, complemented
8C22×C4×C9⋊D9C211yesmaximal, characteristic, complemented
9#72219926C2116yesmaximal, direct product factor
10C2×#13047160C212yesmaximal, complemented
11C2×#11722475—32nomaximal
12C23×C9⋊D9C2211yescharacteristic
13C22×D92C2212yes—
14C22×C4×C92C2211yescharacteristic, complemented
15C22×C9⋊Dic9C2211yescharacteristic, complemented
16C2×C4×C9⋊D9C2211yescharacteristic
17C2×C4×C9⋊D9C2211yescharacteristic
18C2×C4×C9⋊D9C2218yescomplemented
19C2×C4×C9⋊D9C2211yescharacteristic, complemented
20C2×C4×C9⋊D9C2211yescharacteristic, complemented
21C2×C9×#611C2214yescomplemented
22C9×#3697C22116yescomplemented
23C2×C9×D36C2212yescomplemented
24C2×C4×C9×D9C2214yescomplemented
25C2×C9×Dic18C2212yescomplemented
26#13047160C22116yescomplemented
27C2×#10619531C2212yescomplemented
28C2×#10619530C2214yescomplemented
29C2×#10619529C2212yescomplemented
30C2×#10619528C2212yes—
31#13047154C22116yescomplemented
32C2×D9×Dic9C2214yescomplemented
33#13047081C2218yescomplemented
34C4×D92C22116yescomplemented
35#13047077C22116yescomplemented
36#13047076C2218yescomplemented
37#13047075C22116yescomplemented
38C22×C4×C3⋊D9—32no—
39C22×C4×C3⋊D9—61no—
40C2×C9×#235—32no—
41C2×C3×#3697D312yes—
42C2×#88668—34no—
43C2×#88663—34no—
44#11722475—332no—
45C2×#88646—32no—
46C2×C4×D3×D9—34no—
47C2×#88640—34no—
48C2×#88639—32no—
49C2×(C3⋊D9)⋊Q8—32no—
50C2×#88634—32no—
51C23×C92C2311yescharacteristic
52C22×C9⋊D9—24no—
53C22×C9⋊D9C2311yescharacteristic
54C22×C9⋊D9C2314yes—
55C22×C9⋊D9C2311yescharacteristic
56C22×C9×D9C2314yes—
57C2×D92—28no—
58C2×D92C2318yes—
59C2×C4×C92C2311yescharacteristic
60C2×C4×C92C2311yescharacteristic
61C2×C4×C92C2314yescomplemented
62C2×C9⋊Dic9C2311yescharacteristic
63C2×C9⋊Dic9C2311yescharacteristic
64C2×C9⋊Dic9C2314yescomplemented
65C4×C9⋊D9C2314yes—
66C4×C9⋊D9C2314yes—
67C4×C9⋊D9C2314yescomplemented
68C4×C9⋊D9C2314yescomplemented
69C9×#611C23116yescomplemented
70C2×C9×Dic9C2314yes—
71C9×D36C2318yescomplemented
72C4×C9×D9C23116yescomplemented
73C9×Dic18C2318yescomplemented
74#10619531C2318yescomplemented
75#10619530C23116yescomplemented
76#10619529C2318yescomplemented
77#10619528C2318yes—
78D9×Dic9C23116yescomplemented
79C2×#64306—91no—
80C2×#41×D9—92no—
81C23×C3⋊D9—32no—
82C23×C3⋊D9—61no—
83C22×D3×D9—34no—
84C22×C3×C4×C9—21no—
85C22×C3×C4×C9C2×D312yes—
86C22×C3⋊Dic9—32no—
87C22×C3⋊Dic9—61no—
88C2×C4×C3⋊D9—32no—
89C2×C4×C3⋊D9—32no—
90C2×C4×C3⋊D9—32no—
91C2×C4×C3⋊D9—32no—
92C2×C4×C3⋊D9—316no—
93C2×C4×C3⋊D9—61no—
94C2×C4×C3⋊D9—61no—
95C2×C4×C3⋊D9—68no—
96C2×C4×C3⋊D9—61no—
97C2×C4×C3⋊D9—61no—
98C2×C9×#67—34no—
99C2×C3×#611C2×D314yes—
100C9×#235—316no—
101C2×C9×D12—32no—
102C2×C4×D3×C9—34no—
103C3×#3697C2×D3116yes—
104C2×C3×D36C2×D312yes—
105C2×C3×C4×D9C2×D314yes—
106C2×C9×Dic6—32no—
107C2×C3×Dic18C2×D312yes—
108#88668—332no—
109C2×#6195—34no—
110C2×#6194—34no—
111#88663—332no—
112C2×D3×Dic9—34no—
113C2×#6192—34no—
114C2×(C3⋊D9)⋊C4—34no—
115C2×Dic3×D9—34no—
116C2×#6189—34no—
117#88646—316no—
118C4×D3×D9—332no—
119#88640—332no—
120#88639—316no—
121(C3⋊D9)⋊Q8—316no—
122#88634—316no—
123C22×C92—22no—
124C22×C92C2412yes—
125C22×C92C2411yescharacteristic
126C2×C9⋊D9—22no—
127C2×C9⋊D9—28no—
128C2×C9⋊D9#4114yescomplemented
129C2×C9⋊D9C2412yes—
130C2×C9⋊D9C2412yes—
131C2×C9×D9—28no—
132C2×C9×D9C2418yes—
133D92—216no—
134C4×C92C2412yes—
135C4×C92C2412yes—
136C9⋊Dic9C2412yes—
137C9⋊Dic9C2412yes—
138C9×Dic9C2418yes—
139C22×C4×C3⋊D3—91no—
140C2×C3×#235—32no—
141C2×#3811—92no—
142C2×#3805—92no—
143#64306—916no—
144C2×#3802—91no—
145C2×C4×D32—92no—
146C2×#3798—92no—
147C2×#3797—91no—
148C2×#3796—92no—
149C2×C9×#41—92no—
150#41×D9—932no—
151C2×#3701—92no—
152C2×Q8×D9—92no—
153C2×#3699—94no—
154C2×#3699—92no—
155C2×D4×D9—94no—
156C2×D4×D9—92no—
157C2×#3697—94no—
158C2×#3697D912yescomplemented
159C22×C4×D9—92no—
160C22×C4×D9—94no—
161C22×C4×D9—182no—
162C22×C4×D9—183no—
163C23×C3×C9—21no—
164C23×C3×C9C22×D312yes—
165C22×C3⋊D9—32no—
166C22×C3⋊D9—32no—
167C22×C3⋊D9—38no—
168C22×C3⋊D9—68no—
169C22×C3⋊D9—61no—
170C22×C3⋊D9—61no—
171C22×C3⋊D9—64no—
172C22×C3⋊D9—68no—
173C22×D3×C9—34no—
174C22×C3×D9C22×D314yes—
175C2×D3×D9—316no—
176C2×D3×D9—616no—
177C2×C3×C4×C9—21no—
178C2×C3×C4×C9—21no—
179C2×C3×C4×C9—24no—
180C2×C3×C4×C9C22×D312yes—
181C2×C3×C4×C9C22×D312yes—
182C2×C3×C4×C9C22×D318yes—
183C2×C3⋊Dic9—32no—
184C2×C3⋊Dic9—32no—
185C2×C3⋊Dic9—38no—
186C2×C3⋊Dic9—61no—
187C2×C3⋊Dic9—61no—
188C2×C3⋊Dic9—64no—
189C4×C3⋊D9—38no—
190C4×C3⋊D9—38no—
191C4×C3⋊D9—38no—
192C4×C3⋊D9—38no—
193C4×C3⋊D9—64no—
194C4×C3⋊D9—64no—
195C4×C3⋊D9—64no—
196C4×C3⋊D9—64no—
197C9×#67—316no—
198C3×#611C22×D3116yes—
199C2×C9×Dic3—34no—
200C2×C3×Dic9C22×D314yes—
201C9×D12—38no—
202C4×D3×C9—316no—
203C3×D36C22×D318yes—
204C3×C4×D9C22×D3116yes—
205C9×Dic6—38no—
206C3×Dic18C22×D318yes—
207#6195—316no—
208#6194—316no—
209D3×Dic9—316no—
210#6192—316no—
211(C3⋊D9)⋊C4—316no—
212Dic3×D9—316no—
213#6189—316no—
214C2×D3×#41—272no—
215C2×C92—22no—
216C2×C92C2×#4112yescomplemented
217C2×C92C2511yescharacteristic
218C9⋊D9—22no—
219C9⋊D9C2×#4114yescomplemented
220C9×D9—28no—
221C23×C3⋊D3—91no—
222C22×D32—92no—
223C22×C32×C4D3211yescharacteristic
224C22×C3⋊Dic3—91no—
225C2×C4×C3⋊D3—91no—
226C2×C4×C3⋊D3—91no—
227C2×C4×C3⋊D3—91no—
228C2×C4×C3⋊D3—91no—
229C2×C4×C3⋊D3—98no—
230C2×C3×#67—34no—
231C3×#235—316no—
232C2×C3×D12—32no—
233C2×C3×C4×D3—34no—
234C2×C3×Dic6—32no—
235#3811—916no—
236C2×#627—92no—
237C2×#626—94no—
238C2×#625—92no—
239C2×#624—92no—
240#3805—916no—
241C2×D3×Dic3—94no—
242#3802—98no—
243C4×D32—916no—
244#3798—916no—
245#3797—98no—
246#3796—916no—
247C23×D9—92no—
248C23×D9—94no—
249C23×D9—182no—
250C23×D9—183no—
251C9×#41—916no—
252C2×Q8×C9—92no—
253C2×D4×C9—94no—
254C2×D4×C9—92no—
255C22×C4×C9—23no—
256C22×C4×C9—22no—
257C22×C4×C9—94no—
258C22×C4×C9C2×D912yescomplemented
259C2×#611—94no—
260C2×#611—94no—
261C2×#611C2×D914yescomplemented
262C22×Dic9—92no—
263C22×Dic9—94no—
264C22×Dic9—182no—
265C22×Dic9—183no—
266#3701—916no—
267Q8×D9—916no—
268#3699—932no—
269#3699—916no—
270D4×D9—932no—
271D4×D9—916no—
272#3697—932no—
273#3697C2×D9116yescomplemented
274C2×D36—94no—
275C2×D36C2×D912yescomplemented
276C2×C4×D9—94no—
277C2×C4×D9—92no—
278C2×C4×D9—92no—
279C2×C4×D9—92no—
280C2×C4×D9—92no—
281C2×C4×D9—916no—
282C2×C4×D9—94no—
283C2×C4×D9—932no—
284C2×C4×D9—182no—
285C2×C4×D9—182no—
286C2×C4×D9—182no—
287C2×C4×D9—182no—
288C2×C4×D9—1816no—
289C2×C4×D9—183no—
290C2×C4×D9—183no—
291C2×C4×D9—1824no—
292C2×C4×D9—183no—
293C2×C4×D9—183no—
294C2×C4×D9C2×D914yescomplemented
295C2×Dic18—94no—
296C2×Dic18C2×D912yescomplemented
297C22×C3×C9—24no—
298C22×C3×C9—22no—
299C22×C3×C9—21no—
300C22×C3×C9—24no—
301C22×C3×C9C23×D314yes—
302C22×C3×C9C23×D312yes—
303C2×C3⋊D9—38no—
304C2×C3⋊D9—34no—
305C2×C3⋊D9—34no—
306C2×C3⋊D9—616no—
307C2×C3⋊D9—64no—
308C2×C3⋊D9—62no—
309C2×C3⋊D9—62no—
310C2×C3⋊D9—616no—
311C2×C3⋊D9—64no—
312C2×C3⋊D9—64no—
313C2×D3×C9—38no—
314C2×D3×C9—68no—
315C2×C3×D9—28no—
316C2×C3×D9C23×D318yes—
317D3×D9—632no—
318C3×C4×C9—22no—
319C3×C4×C9—22no—
320C3×C4×C9C23×D314yes—
321C3×C4×C9C23×D314yes—
322C3⋊Dic9—34no—
323C3⋊Dic9—34no—
324C3⋊Dic9—62no—
325C3⋊Dic9—62no—
326C9×Dic3—38no—
327C3×Dic9C23×D318yes—
328C2×C3×#41—92no—
329D3×#41—2732no—
330C2×#239—272no—
331C2×D3×Q8—272no—
332C2×#237—272no—
333C2×#237—274no—
334C2×D3×D4—272no—
335C2×D3×D4—274no—
336C2×#235—32no—
337C2×#235—274no—
338C22×C4×D3—274no—
339C22×C4×D3—272no—
340C22×C4×D3—541no—
341C92C22×#4111yescharacteristic, complemented, Sylow
342C23×C32C2×D3211yescharacteristic
343C22×C3⋊D3—91no—
344C22×C3⋊D3—91no—
345C22×C3⋊D3—94no—
346C22×C3⋊D3—184no—
347C22×C3×D3—34no—
348C2×D32—98no—
349C2×D32—188no—
350C2×C32×C4C2×D3211yescharacteristic
351C2×C32×C4C2×D3211yescharacteristic
352C2×C32×C4C2×D3214yes—
353C2×C3⋊Dic3—91no—
354C2×C3⋊Dic3—94no—
355C2×C3⋊Dic3—91no—
356C4×C3⋊D3—94no—
357C4×C3⋊D3—94no—
358C4×C3⋊D3—94no—
359C4×C3⋊D3—94no—
360C3×#67—316no—
361C2×C3×Dic3—34no—
362C3×D12—38no—
363C3×C4×D3—316no—
364C3×Dic6—38no—
365#627—98no—
366#626—916no—
367#625—98no—
368#624—98no—
369D3×Dic3—916no—
370C23×C9—23no—
371C23×C9—22no—
372C23×C9—94no—
373C23×C9C22×D912yes—
374C22×D9—92no—
375C22×D9—92no—
376C22×D9—98no—
377C22×D9—916no—
378C22×D9—182no—
379C22×D9—182no—
380C22×D9—188no—
381C22×D9—1816no—
382C22×D9—188no—
383C22×D9—183no—
384C22×D9—183no—
385C22×D9—1812no—
386C22×D9—1816no—
387C22×D9—1824no—
388C22×D9C22×D914yes—
389Q8×C9—98no—
390D4×C9—916no—
391D4×C9—98no—
392C2×C4×C9—23no—
393C2×C4×C9—23no—
394C2×C4×C9—212no—
395C2×C4×C9—22no—
396C2×C4×C9—22no—
397C2×C4×C9—28no—
398C2×C4×C9—94no—
399C2×C4×C9—916no—
400C2×C4×C9C22×D912yes—
401C2×C4×C9C22×D912yes—
402C2×C4×C9C22×D918yescomplemented
403#611—916no—
404#611—916no—
405#611C22×D9116yescomplemented
406C2×Dic9—92no—
407C2×Dic9—92no—
408C2×Dic9—98no—
409C2×Dic9—916no—
410C2×Dic9—182no—
411C2×Dic9—182no—
412C2×Dic9—188no—
413C2×Dic9—183no—
414C2×Dic9—183no—
415C2×Dic9—1812no—
416C2×Dic9C22×D914yes—
417D36—916no—
418D36C22×D918yescomplemented
419C4×D9—916no—
420C4×D9—98no—
421C4×D9—98no—
422C4×D9—98no—
423C4×D9—98no—
424C4×D9—916no—
425C4×D9—188no—
426C4×D9—188no—
427C4×D9—188no—
428C4×D9—188no—
429C4×D9—1812no—
430C4×D9—1812no—
431C4×D9—1812no—
432C4×D9—1812no—
433C4×D9C22×D9116yescomplemented
434Dic18—916no—
435Dic18C22×D918yescomplemented
436C22×#41—811noSylow
437C2×C3×C9—24no—
438C2×C3×C9—24no—
439C2×C3×C9—22no—
440C2×C3×C9—21no—
441C2×C3×C9D3×#4114yes—
442C2×C3×C9C24×D312yes—
443C3⋊D9—38no—
444C3⋊D9—64no—
445C3⋊D9—64no—
446C3⋊D9—64no—
447D3×C9—68no—
448C3×D9—28no—
449C23×D3—274no—
450C23×D3—272no—
451C23×D3—541no—
452C3×#41—916no—
453C2×C3×Q8—92no—
454C2×C3×D4—94no—
455C2×C3×D4—92no—
456C22×C3×C4—21no—
457C22×C3×C4—94no—
458C22×C3×C4D3×D912yes—
459C2×#67—34no—
460C2×#67—274no—
461C2×#67—274no—
462C22×Dic3—274no—
463C22×Dic3—272no—
464C22×Dic3—541no—
465#239—2716no—
466D3×Q8—2716no—
467#237—2716no—
468#237—2732no—
469D3×D4—2716no—
470D3×D4—2732no—
471#235—316no—
472#235—2732no—
473C2×D12—32no—
474C2×D12—274no—
475C2×C4×D3—34no—
476C2×C4×D3—2732no—
477C2×C4×D3—274no—
478C2×C4×D3—274no—
479C2×C4×D3—272no—
480C2×C4×D3—272no—
481C2×C4×D3—272no—
482C2×C4×D3—272no—
483C2×C4×D3—2716no—
484C2×C4×D3—541no—
485C2×C4×D3—541no—
486C2×C4×D3—541no—
487C2×C4×D3—541no—
488C2×C4×D3—548no—
489C2×Dic6—32no—
490C2×Dic6—274no—
491C22×C32—22no—
492C22×C32C22×D3212yes—
493C22×C32C22×D3211yescharacteristic
494C2×C3⋊D3—94no—
495C2×C3⋊D3—92no—
496C2×C3⋊D3—92no—
497C2×C3⋊D3—188no—
498C2×C3⋊D3—182no—
499C2×C3×D3—38no—
500C2×C3×D3—68no—
501D32—1816no—
502C32×C4C22×D3212yes—
503C32×C4C22×D3212yes—
504C3⋊Dic3—92no—
505C3⋊Dic3—92no—
506C3×Dic3—38no—
507C22×C9—26no—
508C22×C9—23no—
509C22×C9—212no—
510C22×C9—28no—
511C22×C9—24no—
512C22×C9—24no—
513C22×C9—22no—
514C22×C9—98no—
515C22×C9—188no—
516C22×C9C23×D914yes—
517C22×C9C23×D912yes—
518C2×D9—28no—
519C2×D9—94no—
520C2×D9—98no—
521C2×D9—94no—
522C2×D9—184no—
523C2×D9—184no—
524C2×D9—188no—
525C2×D9—1832no—
526C2×D9—1816no—
527C2×D9—186no—
528C2×D9—186no—
529C2×D9—1812no—
530C2×D9—1832no—
531C2×D9—1848no—
532C2×D9—1812no—
533C2×D9—188no—
534C2×D9—184no—
535C2×D9C23×D918yes—
536C4×C9—26no—
537C4×C9—26no—
538C4×C9—24no—
539C4×C9—24no—
540C4×C9—98no—
541C4×C9C23×D914yes—
542C4×C9C23×D914yes—
543Dic9—94no—
544Dic9—94no—
545Dic9—184no—
546Dic9—184no—
547Dic9—186no—
548Dic9—186no—
549Dic9C23×D918yes—
550C2×#41—92no—
551C2×#41—812no—
552C2×#41—812no—
553C2×#41—812no—
554C2×#41—8116no—
555C22×Q8—811no—
556C22×D4—812no—
557C22×D4—811no—
558C23×C4—812no—
559C23×C4—811no—
560C3×C9—21no—
561C3×C9C2×D3×#4112yes—
562C23×C3—21no—
563C23×C3—94no—
564C23×C3C2×D3×D912yes—
565C22×D3—34no—
566C22×D3—2716no—
567C22×D3—272no—
568C22×D3—272no—
569C22×D3—278no—
570C22×D3—541no—
571C22×D3—541no—
572C22×D3—544no—
573C22×D3—5416no—
574C22×D3—548no—
575C22×D3—548no—
576C3×Q8—98no—
577C3×D4—916no—
578C3×D4—98no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—24no—
582C2×C3×C4—94no—
583C2×C3×C4—916no—
584C2×C3×C4C2×D3×D912yes—
585C2×C3×C4C2×D3×D912yes—
586C2×C3×C4C2×D3×D918yes—
587#67—316no—
588#67—2716no—
589#67—2716no—
590C2×Dic3—34no—
591C2×Dic3—2716no—
592C2×Dic3—272no—
593C2×Dic3—272no—
594C2×Dic3—278no—
595C2×Dic3—541no—
596C2×Dic3—541no—
597C2×Dic3—544no—
598D12—38no—
599D12—2716no—
600C4×D3—316no—
601C4×D3—2716no—
602C4×D3—2716no—
603C4×D3—278no—
604C4×D3—278no—
605C4×D3—278no—
606C4×D3—278no—
607C4×D3—544no—
608C4×D3—544no—
609C4×D3—544no—
610C4×D3—544no—
611Dic6—38no—
612Dic6—2716no—
613C2×C32—22no—
614C2×C32#6430612yes—
615C2×C32C23×D3211yescharacteristic
616C3⋊D3—94no—
617C3⋊D3—182no—
618C3×D3—68no—
619C2×C9—23no—
620C2×C9—212no—
621C2×C9—28no—
622C2×C9—26no—
623C2×C9—24no—
624C2×C9—22no—
625C2×C9—24no—
626C2×C9—188no—
627C2×C9#41×D914yescomplemented
628C2×C9C24×D912yes—
629D9—28no—
630D9—98no—
631D9—188no—
632D9—1812no—
633D9—1812no—
634D9—188no—
635D9—184no—
636C24—812no—
637C24—811no—
638#41—916no—
639#41—8116no—
640#41—8116no—
641#41—8116no—
642C2×Q8—92no—
643C2×Q8—812no—
644C2×Q8—818no—
645C2×D4—94no—
646C2×D4—92no—
647C2×D4—814no—
648C2×D4—8116no—
649C2×D4—818no—
650C2×D4—812no—
651C22×C4—94no—
652C22×C4—812no—
653C22×C4—8116no—
654C22×C4—814no—
655C22×C4—811no—
656C22×C4—811no—
657C22×C4—811no—
658C22×C4—811no—
659C22×C4—811no—
660C22×C4—818no—
661C22×C4D9211yescharacteristic, complemented
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—22no—
665C22×C3—21no—
666C22×C3—98no—
667C22×C3—188no—
668C22×C3C22×D3×D914yes—
669C22×C3C22×D3×D912yes—
670C2×D3—38no—
671C2×D3—68no—
672C2×D3—274no—
673C2×D3—278no—
674C2×D3—274no—
675C2×D3—542no—
676C2×D3—542no—
677C2×D3—544no—
678C2×D3—5432no—
679C2×D3—5416no—
680C2×D3—5416no—
681C2×D3—544no—
682C2×D3—544no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—98no—
686C3×C4C22×D3×D914yes—
687C3×C4C22×D3×D914yes—
688Dic3—38no—
689Dic3—274no—
690Dic3—274no—
691Dic3—542no—
692Dic3—542no—
693C32C2×#6430611yescharacteristic
694C9—23no—
695C9—22no—
696C9C2×#41×D912yescomplemented
697C23—94no—
698C23—818no—
699C23—811no—
700C23—814no—
701C23—811no—
702C23—1624no—
703C23—1628no—
704C23C2×D9211yescharacteristic
705Q8—98no—
706Q8—818no—
707D4—916no—
708D4—98no—
709D4—8116no—
710D4—818no—
711C2×C4—94no—
712C2×C4—916no—
713C2×C4—818no—
714C2×C4—8116no—
715C2×C4—811no—
716C2×C4—811no—
717C2×C4—814no—
718C2×C4—814no—
719C2×C4—814no—
720C2×C4—814no—
721C2×C4—814no—
722C2×C4C2×D9211yescharacteristic
723C2×C4C2×D9211yescharacteristic
724C2×C4C2×D9214yescomplemented
725C2×C3—24no—
726C2×C3—24no—
727C2×C3—22no—
728C2×C3—21no—
729C2×C3—188no—
730C2×C3#1172247514yes—
731C2×C3C23×D3×D912yes—
732D3—68no—
733D3—278no—
734D3—544no—
735D3—544no—
736D3—544no—
737C22—22no—
738C22—98no—
739C22—188no—
740C22—814no—
741C22—812no—
742C22—812no—
743C22—1628no—
744C22—16216no—
745C22—1622no—
746C22C22×D9212yes—
747C22C22×D9211yescharacteristic
748C4—98no—
749C4—812no—
750C4—812no—
751C4C22×D9212yes—
752C4C22×D9212yes—
753C3—21no—
754C3C2×#1172247512yes—
755C2—22no—
756C2—188no—
757C2—814no—
758C2—1622no—
759C2#7221992612yesdirect product factor
760C2C23×D9211yescharacteristic
subgroupG/H
centerC2×C4C2×D92
commutator, cosocleC2×C92C25
FrattiniC2×C32C23×D32
FittingC22×C4×C92C22
socleC22×C32C22×D32
hypercenterC22×C4D92
hypocenterC92C22×#41
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#13047076C2semidirect
2. C2×#13047075C2semidirect
3. C2×#13047081C2semidirect
4. C2×#13047154C2semidirect
5. C2×#13047077C2semidirect
6. C2×C9×#3697C2semidirect
7. C2×C4×D92C2semidirect
8. C22×C4×C9⋊D9C2semidirect
9. #72219926C2direct (N × H)
10. C2×#13047160C2semidirect
14. C22×C4×C92C22semidirect
15. C22×C9⋊Dic9C22semidirect
18. C2×C4×C9⋊D9C22semidirect
19. C2×C4×C9⋊D9C22semidirect
20. C2×C4×C9⋊D9C22semidirect
21. C2×C9×#611C22semidirect
22. C9×#3697C22semidirect
23. C2×C9×D36C22semidirect
24. C2×C4×C9×D9C22semidirect
25. C2×C9×Dic18C22semidirect
26. #13047160C22semidirect
27. C2×#10619531C22semidirect
28. C2×#10619530C22semidirect
29. C2×#10619529C22semidirect
31. #13047154C22semidirect
32. C2×D9×Dic9C22semidirect
33. #13047081C22semidirect
34. C4×D92C22semidirect
35. #13047077C22semidirect
36. #13047076C22semidirect
37. #13047075C22semidirect
61. C2×C4×C92C23semidirect
64. C2×C9⋊Dic9C23semidirect
67. C4×C9⋊D9C23semidirect
68. C4×C9⋊D9C23semidirect
69. C9×#611C23semidirect
71. C9×D36C23semidirect
72. C4×C9×D9C23semidirect
73. C9×Dic18C23semidirect
74. #10619531C23semidirect
75. #10619530C23semidirect
76. #10619529C23semidirect
78. D9×Dic9C23semidirect
128. C2×C9⋊D9#41semidirect
158. C2×#3697D9semidirect
216. C2×C92C2×#41semidirect
219. C9⋊D9C2×#41semidirect
258. C22×C4×C9C2×D9semidirect
261. C2×#611C2×D9semidirect
273. #3697C2×D9semidirect
275. C2×D36C2×D9semidirect
294. C2×C4×D9C2×D9semidirect
296. C2×Dic18C2×D9semidirect
341. C92C22×#41semidirect
402. C2×C4×C9C22×D9semidirect
405. #611C22×D9semidirect
418. D36C22×D9semidirect
433. C4×D9C22×D9semidirect
435. Dic18C22×D9semidirect
627. C2×C9#41×D9semidirect
661. C22×C4D92semidirect
696. C9C2×#41×D9semidirect
724. C2×C4C2×D92semidirect
759. C2#72219926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#130470762
C2×#130470752
C2×#130470812
C2×#130471542
C2×#130470772
C2×C9×#36972
C2×C4×D922
C22×C4×C9⋊D92
#722199262
C2×#130471602
C2×#117224753