Finite Group Databasebeta

← C109×#18228 #42136222

Subgroups — C109×#18228 #42136222

Order 27904.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3537C211yesmaximal, characteristic, complemented
2C109×#3006C211yesmaximal, characteristic, complemented
3C109×#3002C211yesmaximal, characteristic, complemented
4C109×#2615C211yesmaximal, characteristic, complemented
5C109×#1606C212yesmaximal, complemented
6C109×#1601C212yesmaximal, complemented
7C109×#1600C212yesmaximal, complemented
8C109×#1595C212yesmaximal, complemented
9C109×#1519C211yesmaximal, characteristic, complemented
10C109×#1513C211yesmaximal, characteristic, complemented
11C109×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C109C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C109—21no—
14C2×#135×C109—21no—
15#560×C109—22no—
16#553×C109—21no—
17#553×C109—21no—
18D42×C109—22no—
19D42×C109—21no—
20D42×C109—21no—
21#540×C109—21no—
22#538×C109—21no—
23#538×C109C2212yes—
24#535×C109—21no—
25#534×C109—21no—
26#534×C109C2212yes—
27#525×C109C2211yescharacteristic
28C2×#121×C109—21no—
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic
31#452×C109—21no—
32#451×C109C2211yescharacteristic, complemented
33#450×C109C2211yescharacteristic, complemented
34#449×C109—21no—
35#449×C109—22no—
36#448×C109C2211yescharacteristic, complemented
37#448×C109C2212yescomplemented
38#447×C109C2211yescharacteristic, complemented
39#447×C109C2212yescomplemented
40#417×C109—21no—
41#416×C109—21no—
42#407×C109C2211yescharacteristic, complemented
43C2×C22⋊C8×C109C2211yescharacteristic, complemented
44#393×C109C2212yescomplemented
45#392×C109—22no—
46#392×C109C2212yescomplemented
47#380×C109—21no—
48#380×C109C2211yescharacteristic, complemented
49#328×C109C2212yescomplemented
50#327×C109C2212yescomplemented
51#327×C109C2212yescomplemented
52#327×C109C2212yescomplemented
53#323×C109C2212yescomplemented
54#323×C109C2212yescomplemented
55C2×#41×C109—21no—
56C2×#41×C109—21no—
57C2×#41×C109—21no—
58C2×#41×C109—21no—
59C2×#41×C109—44no—
60C2×#41×C109D411yescharacteristic, complemented
61C22×Q8×C109C2311yescharacteristic
62C22×D4×C109—22no—
63C22×D4×C109—21no—
64C22×D4×C109—21no—
65C22×D4×C109—22no—
66C22×D4×C109—21no—
67C22×D4×C109—22no—
68C22×D4×C109D411yescharacteristic
69C22×D4×C109D412yes—
70C22×D4×C109D411yescharacteristic, complemented
71C22×D4×C109C2311yescharacteristic
72C23×C4×C109—21no—
73C23×C4×C109C2311yescharacteristic
74AGL(1,ℤ/8)×C109—44no—
75#135×C109—44no—
76C2×Q16×C109—21no—
77C2×SD16×C109—21no—
78C2×SD16×C109—21no—
79C2×SD16×C109—22no—
80C2×D8×C109—21no—
81C2×D8×C109—22no—
82C2×M16×C109—21no—
83C22×C8×C109—21no—
84#127×C109—22no—
85#127×C109—21no—
86#126×C109—22no—
87#126×C109—22no—
88#125×C109—21no—
89#124×C109—22no—
90#123×C109—22no—
91#123×C109—21no—
92#123×C109—22no—
93#123×C109—22no—
94#123×C109—22no—
95C22⋊Q8×C109D411yescharacteristic, complemented
96C22⋊Q8×C109C2311yescharacteristic
97#121×C109—22no—
98#121×C109—21no—
99#121×C109—21no—
100#121×C109—22no—
101#121×C109—22no—
102#121×C109—22no—
103#121×C109—22no—
104#121×C109—21no—
105#121×C109—21no—
106#121×C109—21no—
107#121×C109—21no—
108#121×C109—21no—
109#121×C109—21no—
110#121×C109—22no—
111#121×C109—44no—
112#121×C109D412yescomplemented
113#121×C109D411yescharacteristic, complemented
114#121×C109C2312yes—
115#121×C109C2311yescharacteristic
116#120×C109—22no—
117#120×C109—22no—
118#120×C109—22no—
119#120×C109—21no—
120#120×C109—22no—
121#120×C109—22no—
122#120×C109—22no—
123C4×D4×C109—22no—
124C4×D4×C109—21no—
125C4×D4×C109—21no—
126C4×D4×C109—21no—
127C4×D4×C109—21no—
128C4×D4×C109—22no—
129#117×C109—21no—
130#117×C109D411yescharacteristic, complemented
131C2×C4⋊C4×C109—21no—
132C2×C4⋊C4×C109D411yescharacteristic
133C2×C4⋊C4×C109D411yescharacteristic, complemented
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—22no—
136C2×C22⋊C4×C109—21no—
137C2×C22⋊C4×C109—22no—
138C2×C22⋊C4×C109C2312yes—
139#103×C109—21no—
140#103×C109—21no—
141#103×C109—22no—
142#102×C109—21no—
143#102×C109—21no—
144#102×C109—22no—
145C22⋊C8×C109—21no—
146C22⋊C8×C109—21no—
147C22⋊C8×C109C2311yescharacteristic
148C22⋊C8×C109C2311yescharacteristic
149C22⋊C8×C109C2312yes—
150#95×C109—22no—
151#95×C109C2312yes—
152C24×C109—22no—
153C24×C109—21no—
154C24×C109—21no—
155C24×C109C2×D412yes—
156C24×C109C2×D411yescharacteristic
157#41×C109—24no—
158#41×C109—24no—
159#41×C109—42no—
160#41×C109—42no—
161#41×C109—42no—
162#41×C109—42no—
163#41×C109—42no—
164#41×C109—42no—
165#41×C109—42no—
166C2×Q8×C109—21no—
167C2×Q8×C109—21no—
168C2×Q8×C109—42no—
169C2×Q8×C109C2×D411yescharacteristic
170C2×D4×C109—22no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—22no—
174C2×D4×C109—22no—
175C2×D4×C109—22no—
176C2×D4×C109—22no—
177C2×D4×C109—22no—
178C2×D4×C109—22no—
179C2×D4×C109—21no—
180C2×D4×C109—22no—
181C2×D4×C109—22no—
182C2×D4×C109—21no—
183C2×D4×C109—21no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—42no—
188C2×D4×C109—42no—
189C2×D4×C109—42no—
190C2×D4×C109—42no—
191C2×D4×C109—42no—
192C2×D4×C109—41no—
193C2×D4×C109—41no—
194C2×D4×C109—44no—
195C2×D4×C109—82no—
196C2×D4×C109—82no—
197C2×D4×C109—82no—
198C2×D4×C109—82no—
199C2×D4×C109—81no—
200C2×D4×C109—81no—
201C2×D4×C109—82no—
202C2×D4×C109—82no—
203C2×D4×C109—84no—
204C2×D4×C109C2×D411yescharacteristic
205C2×D4×C109C2×D412yes—
206C22×C4×C109—24no—
207C22×C4×C109—21no—
208C22×C4×C109—22no—
209C22×C4×C109—22no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—22no—
213C22×C4×C109—42no—
214C22×C4×C109—42no—
215C22×C4×C109—41no—
216C22×C4×C109—41no—
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2×D411yescharacteristic
219C22×C4×C109C2×D411yescharacteristic
220C22×C4×C109C2×D412yes—
221C22×C4×C109C2×D411yescharacteristic
222C22×C4×C109C2×D411yescharacteristic
223C22×C4×C109C2411yescharacteristic
224Q16×C109—42no—
225SD16×C109—42no—
226SD16×C109—42no—
227SD16×C109—44no—
228D8×C109—42no—
229D8×C109—44no—
230M16×C109—42no—
231C2×C8×C109—21no—
232C2×C8×C109—21no—
233C2×C8×C109—22no—
234C2×C8×C109—42no—
235C4⋊C4×C109—22no—
236C4⋊C4×C109—22no—
237C4⋊C4×C109—21no—
238C4⋊C4×C109—21no—
239C4⋊C4×C109—21no—
240C4⋊C4×C109—21no—
241C4⋊C4×C109—21no—
242C4⋊C4×C109—42no—
243C4⋊C4×C109C2×D412yes—
244C4⋊C4×C109C2×D411yescharacteristic
245C4⋊C4×C109C2×D411yescharacteristic
246C22⋊C4×C109—22no—
247C22⋊C4×C109—22no—
248C22⋊C4×C109—22no—
249C22⋊C4×C109—22no—
250C22⋊C4×C109—22no—
251C22⋊C4×C109—21no—
252C22⋊C4×C109—21no—
253C22⋊C4×C109—21no—
254C22⋊C4×C109—22no—
255C22⋊C4×C109—21no—
256C22⋊C4×C109—22no—
257C22⋊C4×C109—22no—
258C22⋊C4×C109—22no—
259C22⋊C4×C109—21no—
260C22⋊C4×C109—44no—
261C22⋊C4×C109—81no—
262C22⋊C4×C109—82no—
263C42×C109—22no—
264C42×C109—21no—
265C23×C109—21no—
266C23×C109—21no—
267C23×C109—22no—
268C23×C109—22no—
269C23×C109—22no—
270C23×C109—21no—
271C23×C109—22no—
272C23×C109—22no—
273C23×C109—41no—
274C23×C109—41no—
275C23×C109—41no—
276C23×C109—41no—
277C23×C109—41no—
278C23×C109—42no—
279C23×C109—42no—
280C23×C109—42no—
281C23×C109—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—81no—
285C23×C109—81no—
286C23×C109—82no—
287C23×C109—82no—
288C23×C109—82no—
289C23×C109#12011yescharacteristic
290C23×C109#12011yescharacteristic
291C23×C109C22×D411yescharacteristic
292Q8×C109—22no—
293Q8×C109—22no—
294Q8×C109—41no—
295Q8×C109—41no—
296Q8×C109—41no—
297D4×C109—22no—
298D4×C109—22no—
299D4×C109—42no—
300D4×C109—41no—
301D4×C109—41no—
302D4×C109—41no—
303D4×C109—44no—
304D4×C109—42no—
305D4×C109—44no—
306D4×C109—44no—
307D4×C109—42no—
308D4×C109—41no—
309D4×C109—42no—
310D4×C109—41no—
311D4×C109—42no—
312D4×C109—42no—
313D4×C109—81no—
314D4×C109—82no—
315D4×C109—82no—
316D4×C109—81no—
317D4×C109—82no—
318D4×C109—82no—
319D4×C109—82no—
320D4×C109—82no—
321D4×C109—82no—
322D4×C109—88no—
323C2×C4×C109—22no—
324C2×C4×C109—22no—
325C2×C4×C109—22no—
326C2×C4×C109—22no—
327C2×C4×C109—21no—
328C2×C4×C109—22no—
329C2×C4×C109—22no—
330C2×C4×C109—21no—
331C2×C4×C109—21no—
332C2×C4×C109—41no—
333C2×C4×C109—41no—
334C2×C4×C109—41no—
335C2×C4×C109—44no—
336C2×C4×C109—41no—
337C2×C4×C109—41no—
338C2×C4×C109—44no—
339C2×C4×C109—42no—
340C2×C4×C109—42no—
341C2×C4×C109—42no—
342C2×C4×C109—42no—
343C2×C4×C109—42no—
344C2×C4×C109—81no—
345C2×C4×C109—82no—
346C2×C4×C109—82no—
347C2×C4×C109#12011yescharacteristic
348C2×C4×C109#12011yescharacteristic
349C2×C4×C109C22×D411yescharacteristic
350C2×C4×C109C22×D411yescharacteristic
351C8×C109—41no—
352C8×C109—41no—
353C8×C109—42no—
354C22×C109—21no—
355C22×C109—21no—
356C22×C109—21no—
357C22×C109—21no—
358C22×C109—21no—
359C22×C109—21no—
360C22×C109—21no—
361C22×C109—21no—
362C22×C109—42no—
363C22×C109—42no—
364C22×C109—42no—
365C22×C109—42no—
366C22×C109—41no—
367C22×C109—42no—
368C22×C109—42no—
369C22×C109—41no—
370C22×C109—42no—
371C22×C109—41no—
372C22×C109—42no—
373C22×C109—42no—
374C22×C109—81no—
375C22×C109—81no—
376C22×C109—82no—
377C22×C109—82no—
378C22×C109—81no—
379C22×C109—81no—
380C22×C109—81no—
381C22×C109—81no—
382C22×C109—162no—
383C22×C109—164no—
384C22×C109C2×#12011yescharacteristic
385C22×C109#57611yescharacteristic
386C22×C109#57711yescharacteristic
387C4×C109—21no—
388C4×C109—21no—
389C4×C109—21no—
390C4×C109—42no—
391C4×C109—41no—
392C4×C109—42no—
393C4×C109—41no—
394C4×C109—42no—
395C4×C109—41no—
396C4×C109—82no—
397C4×C109B(4,𝔽2)12yes—
398#18228C10911yesmaximal, characteristic, direct product factor, Sylow
399C2×C109—21no—
400C2×C109—21no—
401C2×C109—41no—
402C2×C109—41no—
403C2×C109—82no—
404C2×C109—82no—
405C2×C109—82no—
406C2×C109—81no—
407C2×C109#301211yescharacteristic
408C2×C109#301911yescharacteristic
409C2×C109C2×B(4,𝔽2)11yescharacteristic
410#3537C2×C10911yescharacteristic, complemented
411#3006C2×C10911yescharacteristic, complemented
412#3002C2×C10911yescharacteristic, complemented
413#2615C2×C10911yescharacteristic, complemented
414#1606C2×C10912yescomplemented
415#1601C2×C10912yescomplemented
416#1600C2×C10912yescomplemented
417#1595C2×C10912yescomplemented
418#1519C2×C10911yescharacteristic, complemented
419#1513C2×C10911yescharacteristic, complemented
420#1471C2×C10911yescharacteristic, complemented
421C109#1822811yescharacteristic, direct product factor, Sylow
422C22×#41C22×C10911yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C10912yes—
434#535—21no—
435#534—21no—
436#534C22×C10912yes—
437#525C22×C10911yescharacteristic
438C2×#121—21no—
439C2×#121C22×C10911yescharacteristic
440C2×#121C22×C10911yescharacteristic
441#452—21no—
442#451C22×C10911yescharacteristic, complemented
443#450C22×C10911yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C10911yescharacteristic, complemented
447#448C22×C10912yescomplemented
448#447C22×C10911yescharacteristic, complemented
449#447C22×C10912yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C10911yescharacteristic, complemented
453C2×C22⋊C8C22×C10911yescharacteristic, complemented
454#393C22×C10912yescomplemented
455#392—22no—
456#392C22×C10912yescomplemented
457#380—21no—
458#380C22×C10911yescharacteristic, complemented
459#328C22×C10912yescomplemented
460#327C22×C10912yescomplemented
461#327C22×C10912yescomplemented
462#327C22×C10912yescomplemented
463#323C22×C10912yescomplemented
464#323C22×C10912yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C10911yescharacteristic, complemented
471C22×Q8C23×C10911yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C10911yescharacteristic
479C22×D4D4×C10912yes—
480C22×D4D4×C10911yescharacteristic, complemented
481C22×D4C23×C10911yescharacteristic
482C23×C4—21no—
483C23×C4C23×C10911yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C10911yescharacteristic, complemented
506C22⋊Q8C23×C10911yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C10912yescomplemented
523#121D4×C10911yescharacteristic, complemented
524#121C23×C10912yes—
525#121C23×C10911yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C10911yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C10911yescharacteristic
543C2×C4⋊C4D4×C10911yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C10912yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C10911yescharacteristic
558C22⋊C8C23×C10911yescharacteristic
559C22⋊C8C23×C10912yes—
560#95—22no—
561#95C23×C10912yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C10912yes—
566C24C2×D4×C10911yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C10911yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C10911yescharacteristic
615C2×D4C2×D4×C10912yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C10911yescharacteristic
628C22×C4C2×D4×C10911yescharacteristic
629C22×C4C2×D4×C10911yescharacteristic
630C22×C4C2×D4×C10912yes—
631C22×C4C2×D4×C10911yescharacteristic
632C22×C4C2×D4×C10911yescharacteristic
633C22×C4C24×C10911yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C10912yes—
654C4⋊C4C2×D4×C10911yescharacteristic
655C4⋊C4C2×D4×C10911yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C10911yescharacteristic
700C23#120×C10911yescharacteristic
701C23C22×D4×C10911yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C10911yescharacteristic
758C2×C4#120×C10911yescharacteristic
759C2×C4C22×D4×C10911yescharacteristic
760C2×C4C22×D4×C10911yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C10911yescharacteristic
795C22#576×C10911yescharacteristic
796C22#577×C10911yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C10912yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C109×#301211yescharacteristic
817C2C109×#301911yescharacteristic
818C2C2×B(4,𝔽2)×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3537C2semidirect
2. C109×#3006C2semidirect
3. C109×#3002C2semidirect
4. C109×#2615C2semidirect
5. C109×#1606C2semidirect
6. C109×#1601C2semidirect
7. C109×#1600C2semidirect
8. C109×#1595C2semidirect
9. C109×#1519C2semidirect
10. C109×#1513C2semidirect
11. C109×#1471C2semidirect
12. C22×#41×C109C22semidirect
32. #451×C109C22semidirect
33. #450×C109C22semidirect
36. #448×C109C22semidirect
37. #448×C109C22semidirect
38. #447×C109C22semidirect
39. #447×C109C22semidirect
42. #407×C109C22semidirect
43. C2×C22⋊C8×C109C22semidirect
44. #393×C109C22semidirect
46. #392×C109C22semidirect
48. #380×C109C22semidirect
49. #328×C109C22semidirect
50. #327×C109C22semidirect
51. #327×C109C22semidirect
52. #327×C109C22semidirect
53. #323×C109C22semidirect
54. #323×C109C22semidirect
60. C2×#41×C109D4semidirect
70. C22×D4×C109D4semidirect
95. C22⋊Q8×C109D4semidirect
112. #121×C109D4semidirect
113. #121×C109D4semidirect
130. #117×C109D4semidirect
133. C2×C4⋊C4×C109D4semidirect
398. #18228C109direct (N × H)
410. #3537C2×C109semidirect
411. #3006C2×C109semidirect
412. #3002C2×C109semidirect
413. #2615C2×C109semidirect
414. #1606C2×C109semidirect
415. #1601C2×C109semidirect
416. #1600C2×C109semidirect
417. #1595C2×C109semidirect
418. #1519C2×C109semidirect
419. #1513C2×C109semidirect
420. #1471C2×C109semidirect
421. C109#18228direct (N × H)
422. C22×#41C22×C109semidirect
442. #451C22×C109semidirect
443. #450C22×C109semidirect
446. #448C22×C109semidirect
447. #448C22×C109semidirect
448. #447C22×C109semidirect
449. #447C22×C109semidirect
452. #407C22×C109semidirect
453. C2×C22⋊C8C22×C109semidirect
454. #393C22×C109semidirect
456. #392C22×C109semidirect
458. #380C22×C109semidirect
459. #328C22×C109semidirect
460. #327C22×C109semidirect
461. #327C22×C109semidirect
462. #327C22×C109semidirect
463. #323C22×C109semidirect
464. #323C22×C109semidirect
470. C2×#41D4×C109semidirect
480. C22×D4D4×C109semidirect
505. C22⋊Q8D4×C109semidirect
522. #121D4×C109semidirect
523. #121D4×C109semidirect
540. #117D4×C109semidirect
543. C2×C4⋊C4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35372
C109×#30062
C109×#30022
C109×#26152
C109×#16062
C109×#16012
C109×#16002
C109×#15952
C109×#15192
C109×#15132
C109×#14712
#18228109