Finite Group Databasebeta

← #36560895

Subgroups — #36560895

Order 22784.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151720C211yesmaximal, characteristic, complemented
2C2×#19151715C211yesmaximal, characteristic, complemented
3#26028970C211yesmaximal, characteristic, complemented
4#26028680C211yesmaximal, characteristic, complemented
5#26021172C211yesmaximal, characteristic, complemented
6#26021028C211yesmaximal, characteristic, complemented
7#26020902C211yesmaximal, characteristic, complemented
8#26020902C211yesmaximal, characteristic, complemented
9#26020581C211yesmaximal, characteristic, complemented
10#26020581C211yesmaximal, characteristic, complemented
11#26020272C211yesmaximal, characteristic, complemented
12#26020129C211yesmaximal, characteristic, complemented
13#26020099C211yesmaximal, characteristic, complemented
14#26020092C211yesmaximal, characteristic, complemented
15C89×#3035C211yesmaximal, characteristic
16C2×#15668019C2211yescharacteristic
17C2×#15668019C2211yescharacteristic
18C2×#15668019C2211yescharacteristic
19C2×#15668019C2211yescharacteristic
20#19151720—24no—
21#19151715—24no—
22#19151670—21no—
23#19151670—21no—
24#19151670—21no—
25#19151670—21no—
26C2×#15667948C2211yescharacteristic
27C2×#15667948C2211yescharacteristic
28#19151622C2211yescharacteristic
29C2×#15667939C2211yescharacteristic
30C2×#15667939C2211yescharacteristic
31C2×#15667939C2211yescharacteristic
32C2×#15667939C2211yescharacteristic
33C2×#15667939C2211yescharacteristic
34C2×#15667939C2211yescharacteristic
35#19151565C2211yescharacteristic
36#19151565C2211yescharacteristic
37#19151554—21no—
38#19151554—21no—
39#19151554C2211yescharacteristic
40#19151554C2211yescharacteristic
41C4×#13083558—21no—
42C4×#13083558C2211yescharacteristic
43C2×#15667923—21no—
44C2×#15667923C2211yescharacteristic
45C2×#15667922C2211yescharacteristic
46C2×C8×Dic89C2211yescharacteristic
47C4×C4⋊Dic89C2211yescharacteristic
48#19151363C2211yescharacteristic
49#19151363C2211yescharacteristic
50#19151357C2211yescharacteristic
51#19151357C2211yescharacteristic
52#19151352C2211yescharacteristic
53#19151352C2211yescharacteristic
54C2×#135×C89C2211yescharacteristic
55C2×#135×C89C2211yescharacteristic
56#532×C89C2211yescharacteristic
57C4×#41×C89C2211yescharacteristic
58#464×C89C411yescharacteristic, complemented
59#464×C89C411yescharacteristic, complemented
60#463×C89C411yescharacteristic, complemented
61#463×C89C411yescharacteristic, complemented
62#462×C89C411yescharacteristic, complemented
63#461×C89C411yescharacteristic, complemented
64#460×C89C411yescharacteristic, complemented
65#459×C89C411yescharacteristic, complemented
66C2×C4⋊C8×C89C2211yescharacteristic
67#416×C89C2211yescharacteristic
68#416×C89C2211yescharacteristic
69#15668019—22no—
70#15668019—22no—
71#15668019—22no—
72#15668019—22no—
73#15668019—22no—
74#15668019—22no—
75#15668019—22no—
76#15668019D414yescomplemented
77C2×#13083558—21no—
78C2×#13083558—21no—
79C2×#13083558—21no—
80C2×#13083558—21no—
81C2×#13083558C2311yescharacteristic
82C2×#13083558C2311yescharacteristic
83C2×#13083558C2311yescharacteristic
84C2×#13083558C2311yescharacteristic
85C22×#10623494—21no—
86C22×#10623494—21no—
87C22×#10623494—21no—
88C22×#10623494—21no—
89C22×#10623494C2311yescharacteristic
90C22×#10623494C2311yescharacteristic
91C2×C4⋊Dic89—21no—
92C2×C4×Dic89C2311yescharacteristic
93C2×C4×Dic89C2311yescharacteristic
94#15667948—22no—
95#15667948—22no—
96C4⋊#10623494—21no—
97C4⋊#10623494—21no—
98#15667939—22no—
99#15667939—22no—
100#15667939—22no—
101#15667939—22no—
102#15667939—22no—
103#15667939—22no—
104C22⋊#10623494—21no—
105C22⋊#10623494—21no—
106C22⋊#10623494—21no—
107C22⋊#10623494—21no—
108#15667923—21no—
109#15667923—21no—
110#15667923—21no—
111#15667923D411yescharacteristic
112#15667923D411yescharacteristic
113#15667923D411yescharacteristic
114#15667923D411yescharacteristic
115#15667922—22no—
116C4×#10623494—21no—
117C4×#10623494—21no—
118C4×#10623494—21no—
119C8×Dic89—22no—
120#15667919—21no—
121C2×#41×C89C2311yescharacteristic
122C2×#41×C89C2311yescharacteristic
123C2×#41×C89C2311yescharacteristic
124#135×C89—22no—
125#135×C89—22no—
126#135×C89—22no—
127#135×C89—22no—
128C2×Q16×C89C2×C411yescharacteristic
129C2×Q16×C89C2×C411yescharacteristic
130C2×SD16×C89C2×C411yescharacteristic
131C2×SD16×C89C2×C411yescharacteristic
132C2×SD16×C89C2×C411yescharacteristic
133C2×SD16×C89C2×C411yescharacteristic
134C2×D8×C89C2×C411yescharacteristic
135C2×D8×C89C2×C411yescharacteristic
136C22×C8×C89C2311yescharacteristic
137C22×C8×C89C2311yescharacteristic
138C4⋊Q8×C89C2×C411yescharacteristic
139#127×C89C2×C411yescharacteristic
140#124×C89C2×C411yescharacteristic
141#124×C89C2×C411yescharacteristic
142#121×C89—21no—
143#121×C89—21no—
144C4×Q8×C89C2×C411yescharacteristic
145C4×Q8×C89C2×C411yescharacteristic
146C4×D4×C89—21no—
147C4×D4×C89—21no—
148C4×D4×C89—21no—
149C4×D4×C89—21no—
150C4×D4×C89C2×C411yescharacteristic
151C4×D4×C89C2×C411yescharacteristic
152#117×C89—21no—
153#117×C89C2311yescharacteristic
154C2×C42×C89—21no—
155C2×C42×C89C2311yescharacteristic
156C4⋊C8×C89C2×C411yescharacteristic
157C4⋊C8×C89C2×C411yescharacteristic
158C4⋊C8×C89C2×C411yescharacteristic
159C4⋊C8×C89C2×C411yescharacteristic
160#103×C89C2×C411yescharacteristic
161#103×C89C2×C411yescharacteristic
162#103×C89C2×C411yescharacteristic
163#103×C89C2×C411yescharacteristic
164#102×C89C2×C411yescharacteristic
165#102×C89C2×C411yescharacteristic
166#102×C89C2×C411yescharacteristic
167#102×C89C2×C411yescharacteristic
168C22×Dic89—21no—
169C22×Dic89—21no—
170#13083558—24no—
171#13083558—21no—
172#13083558—21no—
173#13083558—24no—
174#13083558—21no—
175#13083558—21no—
176#13083558—21no—
177#13083558—21no—
178#13083558—42no—
179#13083558—42no—
180#13083558C2×D412yes—
181#13083558#4112yes—
182C2×#10623494—24no—
183C2×#10623494—21no—
184C2×#10623494—21no—
185C2×#10623494—21no—
186C2×#10623494—21no—
187C2×#10623494—24no—
188C2×#10623494—21no—
189C2×#10623494—21no—
190C2×#10623494—42no—
191C2×#10623494—42no—
192C2×#10623494C2×D411yescharacteristic
193C2×#10623494C2×D411yescharacteristic
194C2×#10623494C2×D411yescharacteristic
195C2×#10623494C2×D411yescharacteristic
196C2×#10623494C2×D412yes—
197C2×#10623494#4112yes—
198C4⋊Dic89—42no—
199C4×Dic89—21no—
200C4×Dic89—21no—
201C4×Dic89—21no—
202C4×Dic89—21no—
203#41×C89—21no—
204#41×C89—21no—
205#41×C89—21no—
206#41×C89—21no—
207#41×C89—21no—
208#41×C89—21no—
209#41×C89—21no—
210#41×C89—21no—
211#41×C89—21no—
212#41×C89—21no—
213#41×C89C2×D412yes—
214#41×C89#4112yes—
215C2×Q8×C89C22×C411yescharacteristic
216C2×Q8×C89C22×C411yescharacteristic
217C2×Q8×C89C22×C411yescharacteristic
218C2×D4×C89—21no—
219C2×D4×C89—21no—
220C2×D4×C89—21no—
221C2×D4×C89—21no—
222C2×D4×C89—21no—
223C2×D4×C89C22×C411yescharacteristic
224C2×D4×C89C22×C411yescharacteristic
225C2×D4×C89C22×C411yescharacteristic
226C22×C4×C89—21no—
227C22×C4×C89—21no—
228C22×C4×C89—21no—
229C22×C4×C89—21no—
230C22×C4×C89—21no—
231C22×C4×C89#4111yescharacteristic
232C22×C4×C89#4111yescharacteristic
233C22×C4×C89C2411yescharacteristic
234Q16×C89—22no—
235Q16×C89—22no—
236SD16×C89—22no—
237SD16×C89—22no—
238SD16×C89—22no—
239SD16×C89—22no—
240D8×C89—22no—
241D8×C89—22no—
242C2×C8×C89—21no—
243C2×C8×C89—21no—
244C2×C8×C89—21no—
245C2×C8×C89—21no—
246C2×C8×C89C22×C411yescharacteristic
247C2×C8×C89C22×C411yescharacteristic
248C2×C8×C89C22×C411yescharacteristic
249C2×C8×C89C22×C411yescharacteristic
250C4⋊C4×C89—21no—
251C4⋊C4×C89—21no—
252C4⋊C4×C89—21no—
253C4⋊C4×C89—21no—
254C4⋊C4×C89C22×C411yescharacteristic
255C4⋊C4×C89C22×C411yescharacteristic
256C22⋊C4×C89—21no—
257C22⋊C4×C89—21no—
258C22⋊C4×C89—21no—
259C22⋊C4×C89—21no—
260C22⋊C4×C89—21no—
261C22⋊C4×C89—21no—
262C22⋊C4×C89—21no—
263C42×C89—21no—
264C42×C89—21no—
265C42×C89—21no—
266C42×C89C22×C411yescharacteristic
267C42×C89C22×C411yescharacteristic
268C42×C89C2×D411yescharacteristic
269C42×C89C2×D411yescharacteristic
270C23×C89—21no—
271C23×C89—21no—
272C23×C89—21no—
273C23×C89C2×#4111yescharacteristic
274Q8×C89—21no—
275Q8×C89—21no—
276Q8×C89—21no—
277Q8×C89—21no—
278Q8×C89—21no—
279Q8×C89C4×D412yes—
280D4×C89—22no—
281D4×C89—22no—
282D4×C89—21no—
283D4×C89—21no—
284D4×C89—21no—
285D4×C89—21no—
286D4×C89—21no—
287D4×C89—41no—
288D4×C89—41no—
289D4×C89—41no—
290D4×C89—41no—
291D4×C89—81no—
292D4×C89—81no—
293D4×C89C4×D412yes—
294C2×C4×C89—21no—
295C2×C4×C89—22no—
296C2×C4×C89—22no—
297C2×C4×C89—21no—
298C2×C4×C89—21no—
299C2×C4×C89—21no—
300C2×C4×C89—21no—
301C2×C4×C89—41no—
302C2×C4×C89—41no—
303C2×C4×C89—41no—
304C2×C4×C89—41no—
305C2×C4×C89—41no—
306C2×C4×C89—41no—
307C2×C4×C89—81no—
308C2×C4×C89—81no—
309C2×C4×C89C4×D411yescharacteristic
310C2×C4×C89C4×D411yescharacteristic
311C2×C4×C89C4×D411yescharacteristic
312C2×C4×C89C4×D411yescharacteristic
313C2×C4×C89C23×C411yescharacteristic
314C2×C4×C89C22×D411yescharacteristic
315C2×C4×C89C22×D411yescharacteristic
316C2×C4×C89C2×#4111yescharacteristic
317C2×C4×C89C2×#4111yescharacteristic
318C2×C4×C89C2×#4111yescharacteristic
319C2×Dic89—22no—
320C2×Dic89—41no—
321C2×Dic89—41no—
322C2×Dic89—41no—
323C2×Dic89—41no—
324C2×Dic89—41no—
325C8×C89—21no—
326C8×C89—21no—
327C8×C89—21no—
328C8×C89—21no—
329#10623494—22no—
330#10623494—21no—
331#10623494—22no—
332#10623494—21no—
333#10623494—41no—
334#10623494—41no—
335#10623494#12112yes—
336#10623494#12112yes—
337C22×C89—21no—
338C22×C89—21no—
339C22×C89—22no—
340C22×C89—41no—
341C22×C89—41no—
342C22×C89—41no—
343C22×C89—41no—
344C22×C89—41no—
345C22×C89—41no—
346C22×C89—41no—
347C22×C89—41no—
348C22×C89C2×C4×D411yescharacteristic
349C22×C89#52911yescharacteristic
350C22×C89#53211yescharacteristic
351C4×C89—21no—
352C4×C89—21no—
353C4×C89—21no—
354C4×C89—21no—
355C4×C89—22no—
356C4×C89—41no—
357C4×C89—41no—
358C4×C89—41no—
359C4×C89—41no—
360C4×C89C2×C4×D411yescharacteristic
361C4×C89C4×#4111yescharacteristic
362C4×C89C2×#12111yescharacteristic
363C4×C89#52511yescharacteristic
364Dic89—42no—
365Dic89—81no—
366#21519—891nomaximal, Sylow
367C2×C89—21no—
368C2×C89—21no—
369C2×C89—42no—
370C2×C89—81no—
371C2×C89—81no—
372C2×C89C4×#12111yescharacteristic
373C2×C89#295611yescharacteristic
374C2×C89#295711yescharacteristic
375#3035D8911yescharacteristic
376C2×#444—891no—
377C2×#443—891no—
378#2932—891no—
379#2875—891no—
380#1980—891no—
381#1950—891no—
382#1929—891no—
383#1929—891no—
384#1876—891no—
385#1876—891no—
386#1806—891no—
387#1771—891no—
388#1765—891no—
389#1764—891no—
390C89#2151911yescharacteristic, complemented, Sylow
391C2×#135C2×D8911yescharacteristic
392C2×#135C2×D8911yescharacteristic
393C2×#131—891no—
394C2×#131—891no—
395C2×#131—891no—
396C2×#131—891no—
397#532C2×D8911yescharacteristic
398C4×#41C2×D8911yescharacteristic
399#464Dic8911yescharacteristic, complemented
400#464Dic8911yescharacteristic, complemented
401#463Dic8911yescharacteristic, complemented
402#463Dic8911yescharacteristic, complemented
403#462Dic8911yescharacteristic, complemented
404#461Dic8911yescharacteristic, complemented
405#460Dic8911yescharacteristic, complemented
406#459Dic8911yescharacteristic, complemented
407#444—1784no—
408#443—1784no—
409#435—1781no—
410#435—1781no—
411#435—1781no—
412#435—1781no—
413C2×#108—891no—
414C2×#108—891no—
415#423—891no—
416C2×C4⋊C8C2×D8911yescharacteristic
417C2×#104—891no—
418C2×#104—891no—
419C2×#104—891no—
420C2×#104—891no—
421C2×#104—891no—
422C2×#104—891no—
423#416C2×D8911yescharacteristic
424#416C2×D8911yescharacteristic
425#408—891no—
426#408—891no—
427#405—891no—
428#405—891no—
429#405—1781no—
430#405—1781no—
431C4×M16—891no—
432C4×M16—1781no—
433C2×#97—891no—
434C2×#97—891no—
435C2×#97—1781no—
436C2×C4×C8—891no—
437C4×C4⋊C4—891no—
438#341—891no—
439#341—891no—
440#339—891no—
441#339—891no—
442#336—891no—
443#336—891no—
444C2×#41C22×D8911yescharacteristic
445C2×#41C22×D8911yescharacteristic
446C2×#41C22×D8911yescharacteristic
447#135—22no—
448#135—22no—
449#135—22no—
450#135—22no—
451C2×Q16C2×Dic8911yescharacteristic
452C2×Q16C2×Dic8911yescharacteristic
453C2×SD16C2×Dic8911yescharacteristic
454C2×SD16C2×Dic8911yescharacteristic
455C2×SD16C2×Dic8911yescharacteristic
456C2×SD16C2×Dic8911yescharacteristic
457C2×D8C2×Dic8911yescharacteristic
458C2×D8C2×Dic8911yescharacteristic
459#131—894no—
460#131—1782no—
461#131—1782no—
462#131—1782no—
463#131—1782no—
464#131—1782no—
465#131—1782no—
466#131—1782no—
467C2×M16—891no—
468C2×M16—891no—
469C2×M16—891no—
470C2×M16—891no—
471C2×M16—1781no—
472C2×M16—1781no—
473C2×M16—1781no—
474C2×M16—1781no—
475C22×C8—891no—
476C22×C8—891no—
477C22×C8—1781no—
478C22×C8—1781no—
479C22×C8—1781no—
480C22×C8—1781no—
481C22×C8C22×D8911yescharacteristic
482C22×C8C22×D8911yescharacteristic
483C4⋊Q8C2×Dic8911yescharacteristic
484#127C2×Dic8911yescharacteristic
485#124C2×Dic8911yescharacteristic
486#124C2×Dic8911yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8C2×Dic8911yescharacteristic
490C4×Q8C2×Dic8911yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4C2×Dic8911yescharacteristic
496C4×D4C2×Dic8911yescharacteristic
497#117—21no—
498#117C22×D8911yescharacteristic
499C2×C4⋊C4—1781no—
500C2×C42—21no—
501C2×C42—891no—
502C2×C42—891no—
503C2×C42C22×D8911yescharacteristic
504#108—1782no—
505#108—1782no—
506C4⋊C8—1781no—
507C4⋊C8—1781no—
508C4⋊C8C2×Dic8911yescharacteristic
509C4⋊C8C2×Dic8911yescharacteristic
510C4⋊C8C2×Dic8911yescharacteristic
511C4⋊C8C2×Dic8911yescharacteristic
512#104—1782no—
513#104—1782no—
514#104—1782no—
515#104—1782no—
516#104—1782no—
517#104—1782no—
518#103C2×Dic8911yescharacteristic
519#103C2×Dic8911yescharacteristic
520#103C2×Dic8911yescharacteristic
521#103C2×Dic8911yescharacteristic
522#102C2×Dic8911yescharacteristic
523#102C2×Dic8911yescharacteristic
524#102C2×Dic8911yescharacteristic
525#102C2×Dic8911yescharacteristic
526C22⋊C8—1781no—
527C22⋊C8—1781no—
528C22⋊C8—1781no—
529C22⋊C8—1781no—
530#97—891no—
531#97—891no—
532#97—891no—
533#97—891no—
534#97—1781no—
535#97—1781no—
536#97—1782no—
537#97—1781no—
538C4×C8—1781no—
539C4×C8—1781no—
540C4×C8—1782no—
541C4×C8—1781no—
542#95—1781no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41D4×D8912yes—
554#41#1308357312yes—
555C2×Q8C22×Dic8911yescharacteristic
556C2×Q8C22×Dic8911yescharacteristic
557C2×Q8C22×Dic8911yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×Dic8911yescharacteristic
564C2×D4C22×Dic8911yescharacteristic
565C2×D4C22×Dic8911yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—1781no—
572C22×C4—1781no—
573C22×C4#1308357311yescharacteristic
574C22×C4#1308357311yescharacteristic
575C22×C4C23×D8911yescharacteristic
576Q16—22no—
577Q16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582D8—22no—
583D8—22no—
584M16—892no—
585M16—892no—
586M16—3562no—
587M16—3562no—
588M16—1784no—
589M16—1781no—
590M16—1781no—
591M16—1781no—
592M16—1781no—
593M16—1784no—
594M16—1781no—
595M16—1781no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—892no—
601C2×C8—891no—
602C2×C8—891no—
603C2×C8—892no—
604C2×C8—891no—
605C2×C8—891no—
606C2×C8—3562no—
607C2×C8—3562no—
608C2×C8—1784no—
609C2×C8—1781no—
610C2×C8—1781no—
611C2×C8—1784no—
612C2×C8—1781no—
613C2×C8—1781no—
614C2×C8—1781no—
615C2×C8—1781no—
616C2×C8C22×Dic8911yescharacteristic
617C2×C8C22×Dic8911yescharacteristic
618C2×C8C22×Dic8911yescharacteristic
619C2×C8C22×Dic8911yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—3562no—
625C4⋊C4C22×Dic8911yescharacteristic
626C4⋊C4C22×Dic8911yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—1781no—
638C42—1781no—
639C42—1781no—
640C42—1781no—
641C42C22×Dic8911yescharacteristic
642C42C22×Dic8911yescharacteristic
643C42D4×D8911yescharacteristic
644C42D4×D8911yescharacteristic
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#1308357311yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8D4×Dic8912yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4D4×Dic8912yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—3561no—
685C2×C4—3561no—
686C2×C4—3561no—
687C2×C4—3561no—
688C2×C4—3561no—
689C2×C4—1782no—
690C2×C4D4×Dic8911yescharacteristic
691C2×C4D4×Dic8911yescharacteristic
692C2×C4D4×Dic8911yescharacteristic
693C2×C4D4×Dic8911yescharacteristic
694C2×C4C23×Dic8911yescharacteristic
695C2×C4C2×D4×D8911yescharacteristic
696C2×C4C2×D4×D8911yescharacteristic
697C2×C4#41×D8911yescharacteristic
698C2×C4#41×D8911yescharacteristic
699C2×C4C2×#1308357311yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—892no—
705C8—892no—
706C8—3561no—
707C8—3561no—
708C8—1782no—
709C8—1781no—
710C8—1781no—
711C8—1782no—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×D4×Dic8911yescharacteristic
724C22#1915212911yescharacteristic
725C22#1915214311yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—3562no—
736C4—7121no—
737C4C2×D4×Dic8911yescharacteristic
738C4#41×Dic8911yescharacteristic
739C4#121×D8911yescharacteristic
740C4#1915210811yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2#121×Dic8911yescharacteristic
747C2#2602916211yescharacteristic
748C2#2602916911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
Fitting, prime radicalC89×#3035C2
socleC22×C89C2×C4×D4
cosocleC22×C4×C89C24
hypercenter#3035D89
hypocenterC89#21519
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#19151720C2semidirect
2. C2×#19151715C2semidirect
3. #26028970C2semidirect
4. #26028680C2semidirect
5. #26021172C2semidirect
6. #26021028C2semidirect
7. #26020902C2semidirect
8. #26020902C2semidirect
9. #26020581C2semidirect
10. #26020581C2semidirect
11. #26020272C2semidirect
12. #26020129C2semidirect
13. #26020099C2semidirect
14. #26020092C2semidirect
58. #464×C89C4semidirect
59. #464×C89C4semidirect
60. #463×C89C4semidirect
61. #463×C89C4semidirect
62. #462×C89C4semidirect
63. #461×C89C4semidirect
64. #460×C89C4semidirect
65. #459×C89C4semidirect
76. #15668019D4semidirect
390. C89#21519semidirect
399. #464Dic89semidirect
400. #464Dic89semidirect
401. #463Dic89semidirect
402. #463Dic89semidirect
403. #462Dic89semidirect
404. #461Dic89semidirect
405. #460Dic89semidirect
406. #459Dic89semidirect

Maximal subgroups

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

subgroupindex
C2×#191517202
C2×#191517152
#260289702
#260286802
#260211722
#260210282
#260209022
#260205812
#260202722
#260201292
#260200992
#260200922
C89×#30352
#2151989