Finite Group Databasebeta

← C109×#18168 #42136162

Subgroups — C109×#18168 #42136162

Order 27904.

1244 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3505C211yesmaximal, characteristic, complemented
2C109×#3007C211yesmaximal, characteristic, complemented
3C109×#3006C211yesmaximal, characteristic, complemented
4C109×#2388C211yesmaximal, characteristic, complemented
5C109×#1606C212yesmaximal, complemented
6C109×#1603C212yesmaximal, complemented
7C109×#1600C212yesmaximal, complemented
8C109×#1597C212yesmaximal, complemented
9C109×#1508C211yesmaximal, characteristic, complemented
10C109×#1507C211yesmaximal, characteristic, complemented
11C109×#1465C211yesmaximal, characteristic, complemented
12C22×#41×C109C2211yescharacteristic
13C2×#137×C109—21no—
14C2×AGL(1,ℤ/8)×C109—21no—
15#553×C109—22no—
16#553×C109—21no—
17#552×C109—21no—
18#551×C109—22no—
19#548×C109—21no—
20#546×C109—21no—
21#539×C109C2212yes—
22#538×C109C2212yes—
23#534×C109—21no—
24#529×C109—21no—
25#525×C109—21no—
26C2×C22⋊Q8×C109C2211yescharacteristic
27C2×#121×C109C2211yescharacteristic
28#518×C109—21no—
29C2×C4×D4×C109—21no—
30C2×C4×D4×C109C2211yescharacteristic
31#452×C109—22no—
32#451×C109C2212yescomplemented
33#450×C109C2212yescomplemented
34#449×C109—22no—
35#448×C109C2212yes—
36#447×C109C2212yes—
37#417×C109—21no—
38#417×C109—21no—
39#407×C109C2211yescharacteristic
40#407×C109C2211yescharacteristic
41#395×C109C2211yescharacteristic, complemented
42#394×C109—21no—
43#394×C109C2211yescharacteristic, complemented
44#393×C109C2211yescharacteristic, complemented
45#392×C109—21no—
46#392×C109C2211yescharacteristic, complemented
47C4×C22⋊C4×C109—21no—
48C4×C22⋊C4×C109C2211yescharacteristic
49#328×C109C2212yescomplemented
50#328×C109C2212yescomplemented
51#327×C109C2212yes—
52#327×C109C2212yes—
53#324×C109C2212yescomplemented
54#323×C109C2212yescomplemented
55C2×#41×C109—21no—
56C2×#41×C109—21no—
57C2×#41×C109—21no—
58C2×#41×C109—21no—
59C2×#41×C109—21no—
60C2×#41×C109—44no—
61C22×Q8×C109D411yescharacteristic, complemented
62C22×Q8×C109C2311yescharacteristic
63C22×D4×C109—21no—
64C22×D4×C109—21no—
65C22×D4×C109—21no—
66C22×D4×C109D411yescharacteristic
67C22×D4×C109D411yescharacteristic, complemented
68C22×D4×C109C2311yescharacteristic
69C23×C4×C109—21no—
70C23×C4×C109D411yescharacteristic
71C23×C4×C109C2311yescharacteristic
72#137×C109—44no—
73AGL(1,ℤ/8)×C109—44no—
74C2×Q16×C109—22no—
75C2×SD16×C109—22no—
76C2×SD16×C109—22no—
77C2×D8×C109—22no—
78C2×M16×C109—21no—
79C2×M16×C109—21no—
80#126×C109—22no—
81#126×C109—22no—
82#126×C109—22no—
83#125×C109—21no—
84#125×C109—22no—
85#124×C109—21no—
86#124×C109—22no—
87#123×C109—22no—
88#123×C109—22no—
89#123×C109—22no—
90#123×C109—22no—
91#123×C109—22no—
92C22⋊Q8×C109—21no—
93C22⋊Q8×C109—22no—
94C22⋊Q8×C109—21no—
95C22⋊Q8×C109—21no—
96C22⋊Q8×C109D412yescomplemented
97C22⋊Q8×C109C2312yes—
98#121×C109—21no—
99#121×C109—22no—
100#121×C109—22no—
101#121×C109—22no—
102#121×C109—21no—
103#121×C109—21no—
104#121×C109D412yescomplemented
105#121×C109C2312yes—
106#120×C109—22no—
107#120×C109—22no—
108C4×Q8×C109—21no—
109C4×D4×C109—22no—
110C4×D4×C109—22no—
111C4×D4×C109—22no—
112C4×D4×C109—21no—
113C4×D4×C109—21no—
114C4×D4×C109—21no—
115C4×D4×C109—21no—
116C4×D4×C109—21no—
117C4×D4×C109—22no—
118C4×D4×C109—22no—
119C4×D4×C109—44no—
120#117×C109—22no—
121#117×C109—21no—
122#117×C109—22no—
123C2×C4⋊C4×C109—21no—
124C2×C4⋊C4×C109—21no—
125C2×C4⋊C4×C109D411yescharacteristic, complemented
126C2×C4⋊C4×C109D411yescharacteristic, complemented
127C2×C4⋊C4×C109C2311yescharacteristic
128C2×C22⋊C4×C109—22no—
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—21no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—21no—
136C2×C22⋊C4×C109D411yescharacteristic
137C2×C22⋊C4×C109C2311yescharacteristic
138C2×C42×C109—21no—
139C2×C42×C109D411yescharacteristic
140#103×C109—22no—
141#103×C109—22no—
142#102×C109—22no—
143#102×C109—22no—
144C22⋊C8×C109—21no—
145C22⋊C8×C109—21no—
146C22⋊C8×C109C2312yes—
147C22⋊C8×C109C2312yes—
148#95×C109—21no—
149#95×C109—21no—
150#95×C109C2311yescharacteristic
151#95×C109C2311yescharacteristic
152C24×C109—21no—
153C24×C109—21no—
154C24×C109C2×D411yescharacteristic
155C24×C109C2×D411yescharacteristic
156#41×C109—24no—
157#41×C109—24no—
158#41×C109—42no—
159#41×C109—42no—
160#41×C109—42no—
161#41×C109—42no—
162#41×C109—42no—
163#41×C109—42no—
164#41×C109—82no—
165C2×Q8×C109—21no—
166C2×Q8×C109—21no—
167C2×Q8×C109—21no—
168C2×Q8×C109—42no—
169C2×Q8×C109—42no—
170C2×Q8×C109C2×D412yes—
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—21no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—41no—
181C2×D4×C109—41no—
182C2×D4×C109—42no—
183C2×D4×C109—42no—
184C2×D4×C109—42no—
185C2×D4×C109—42no—
186C2×D4×C109—42no—
187C2×D4×C109—42no—
188C2×D4×C109—42no—
189C2×D4×C109—42no—
190C2×D4×C109—42no—
191C2×D4×C109—41no—
192C2×D4×C109—41no—
193C2×D4×C109C2×D412yes—
194C22×C4×C109—24no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—22no—
199C22×C4×C109—22no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—42no—
206C22×C4×C109—42no—
207C22×C4×C109—42no—
208C22×C4×C109—41no—
209C22×C4×C109—41no—
210C22×C4×C109C2×D411yescharacteristic
211C22×C4×C109C2×D411yescharacteristic
212C22×C4×C109C2×D411yescharacteristic
213C22×C4×C109C2×D411yescharacteristic
214C22×C4×C109C2×D411yescharacteristic
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2411yescharacteristic
219Q16×C109—44no—
220SD16×C109—44no—
221SD16×C109—44no—
222D8×C109—44no—
223M16×C109—42no—
224M16×C109—42no—
225C2×C8×C109—22no—
226C2×C8×C109—22no—
227C4⋊C4×C109—22no—
228C4⋊C4×C109—22no—
229C4⋊C4×C109—22no—
230C4⋊C4×C109—22no—
231C4⋊C4×C109—22no—
232C4⋊C4×C109—21no—
233C4⋊C4×C109—21no—
234C4⋊C4×C109—22no—
235C4⋊C4×C109—21no—
236C4⋊C4×C109—21no—
237C4⋊C4×C109—42no—
238C4⋊C4×C109C2×D412yes—
239C4⋊C4×C109C2×D412yes—
240C22⋊C4×C109—22no—
241C22⋊C4×C109—22no—
242C22⋊C4×C109—22no—
243C22⋊C4×C109—22no—
244C22⋊C4×C109—22no—
245C22⋊C4×C109—22no—
246C22⋊C4×C109—21no—
247C22⋊C4×C109—22no—
248C22⋊C4×C109—21no—
249C22⋊C4×C109—22no—
250C22⋊C4×C109—22no—
251C22⋊C4×C109—22no—
252C22⋊C4×C109—21no—
253C22⋊C4×C109—21no—
254C22⋊C4×C109—42no—
255C22⋊C4×C109—42no—
256C22⋊C4×C109—42no—
257C22⋊C4×C109—42no—
258C22⋊C4×C109—42no—
259C42×C109—22no—
260C42×C109—22no—
261C42×C109—21no—
262C42×C109—21no—
263C42×C109—42no—
264C23×C109—21no—
265C23×C109—21no—
266C23×C109—22no—
267C23×C109—21no—
268C23×C109—22no—
269C23×C109—21no—
270C23×C109—21no—
271C23×C109—41no—
272C23×C109—41no—
273C23×C109—41no—
274C23×C109—41no—
275C23×C109—41no—
276C23×C109—41no—
277C23×C109—41no—
278C23×C109—42no—
279C23×C109—41no—
280C23×C109—41no—
281C23×C109—41no—
282C23×C109—81no—
283C23×C109—81no—
284C23×C109#12011yescharacteristic
285C23×C109#12011yescharacteristic
286C23×C109C22×D411yescharacteristic
287Q8×C109—22no—
288Q8×C109—22no—
289Q8×C109—42no—
290Q8×C109—41no—
291Q8×C109—41no—
292Q8×C109—42no—
293D4×C109—22no—
294D4×C109—22no—
295D4×C109—42no—
296D4×C109—41no—
297D4×C109—41no—
298D4×C109—42no—
299D4×C109—42no—
300D4×C109—44no—
301D4×C109—44no—
302D4×C109—44no—
303D4×C109—48no—
304D4×C109—42no—
305D4×C109—42no—
306D4×C109—42no—
307D4×C109—82no—
308D4×C109—82no—
309C2×C4×C109—22no—
310C2×C4×C109—22no—
311C2×C4×C109—22no—
312C2×C4×C109—22no—
313C2×C4×C109—22no—
314C2×C4×C109—21no—
315C2×C4×C109—21no—
316C2×C4×C109—22no—
317C2×C4×C109—21no—
318C2×C4×C109—22no—
319C2×C4×C109—22no—
320C2×C4×C109—21no—
321C2×C4×C109—21no—
322C2×C4×C109—41no—
323C2×C4×C109—41no—
324C2×C4×C109—41no—
325C2×C4×C109—44no—
326C2×C4×C109—41no—
327C2×C4×C109—41no—
328C2×C4×C109—42no—
329C2×C4×C109—41no—
330C2×C4×C109—41no—
331C2×C4×C109—44no—
332C2×C4×C109—42no—
333C2×C4×C109—41no—
334C2×C4×C109—41no—
335C2×C4×C109—41no—
336C2×C4×C109—41no—
337C2×C4×C109—41no—
338C2×C4×C109—81no—
339C2×C4×C109—81no—
340C2×C4×C109—81no—
341C2×C4×C109—82no—
342C2×C4×C109—82no—
343C2×C4×C109#12011yescharacteristic
344C2×C4×C109#12011yescharacteristic
345C2×C4×C109C22×D411yescharacteristic
346C2×C4×C109C22×D411yescharacteristic
347C8×C109—42no—
348C8×C109—42no—
349C22×C109—21no—
350C22×C109—21no—
351C22×C109—21no—
352C22×C109—21no—
353C22×C109—21no—
354C22×C109—21no—
355C22×C109—21no—
356C22×C109—21no—
357C22×C109—42no—
358C22×C109—42no—
359C22×C109—42no—
360C22×C109—41no—
361C22×C109—42no—
362C22×C109—42no—
363C22×C109—41no—
364C22×C109—42no—
365C22×C109—41no—
366C22×C109—42no—
367C22×C109—81no—
368C22×C109—81no—
369C22×C109—81no—
370C22×C109—81no—
371C22×C109—81no—
372C22×C109—81no—
373C22×C109—81no—
374C22×C109—162no—
375C22×C109C2×#12011yescharacteristic
376C22×C109#57511yescharacteristic
377C22×C109#57511yescharacteristic
378C4×C109—21no—
379C4×C109—21no—
380C4×C109—21no—
381C4×C109—42no—
382C4×C109—41no—
383C4×C109—42no—
384C4×C109—41no—
385C4×C109—42no—
386C4×C109—42no—
387C4×C109—41no—
388C4×C109—42no—
389C4×C109—81no—
390C4×C109B(4,𝔽2)12yes—
391#18168C10911yesmaximal, characteristic, direct product factor, Sylow
392C2×C109—21no—
393C2×C109—21no—
394C2×C109—41no—
395C2×C109—41no—
396C2×C109—81no—
397C2×C109—82no—
398C2×C109—82no—
399C2×C109#300511yescharacteristic
400C2×C109#301811yescharacteristic
401C2×C109C2×B(4,𝔽2)11yescharacteristic
402#3505C2×C10911yescharacteristic, complemented
403#3007C2×C10911yescharacteristic, complemented
404#3006C2×C10911yescharacteristic, complemented
405#2388C2×C10911yescharacteristic, complemented
406#1606C2×C10912yescomplemented
407#1603C2×C10912yescomplemented
408#1600C2×C10912yescomplemented
409#1597C2×C10912yescomplemented
410#1508C2×C10911yescharacteristic, complemented
411#1507C2×C10911yescharacteristic, complemented
412#1465C2×C10911yescharacteristic, complemented
413C109#1816811yescharacteristic, direct product factor, Sylow
414C22×#41C22×C10911yescharacteristic
415C2×#137—21no—
416C2×AGL(1,ℤ/8)—21no—
417#553—22no—
418#553—21no—
419#552—21no—
420#551—22no—
421#548—21no—
422#546—21no—
423#539C22×C10912yes—
424#538C22×C10912yes—
425#534—21no—
426#529—21no—
427#525—21no—
428C2×C22⋊Q8C22×C10911yescharacteristic
429C2×#121C22×C10911yescharacteristic
430#518—21no—
431C2×C4×D4—21no—
432C2×C4×D4C22×C10911yescharacteristic
433#452—22no—
434#451C22×C10912yescomplemented
435#450C22×C10912yescomplemented
436#449—22no—
437#448C22×C10912yes—
438#447C22×C10912yes—
439#417—21no—
440#417—21no—
441#407C22×C10911yescharacteristic
442#407C22×C10911yescharacteristic
443#395C22×C10911yescharacteristic, complemented
444#394—21no—
445#394C22×C10911yescharacteristic, complemented
446#393C22×C10911yescharacteristic, complemented
447#392—21no—
448#392C22×C10911yescharacteristic, complemented
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C10911yescharacteristic
451#328C22×C10912yescomplemented
452#328C22×C10912yescomplemented
453#327C22×C10912yes—
454#327C22×C10912yes—
455#324C22×C10912yescomplemented
456#323C22×C10912yescomplemented
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—44no—
463C22×Q8D4×C10911yescharacteristic, complemented
464C22×Q8C23×C10911yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4D4×C10911yescharacteristic
469C22×D4D4×C10911yescharacteristic, complemented
470C22×D4C23×C10911yescharacteristic
471C23×C4—21no—
472C23×C4D4×C10911yescharacteristic
473C23×C4C23×C10911yescharacteristic
474#137—44no—
475AGL(1,ℤ/8)—44no—
476C2×Q16—22no—
477C2×SD16—22no—
478C2×SD16—22no—
479C2×D8—22no—
480C2×M16—21no—
481C2×M16—21no—
482#126—22no—
483#126—22no—
484#126—22no—
485#125—21no—
486#125—22no—
487#124—21no—
488#124—22no—
489#123—22no—
490#123—22no—
491#123—22no—
492#123—22no—
493#123—22no—
494C22⋊Q8—21no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C10912yescomplemented
499C22⋊Q8C23×C10912yes—
500#121—21no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121D4×C10912yescomplemented
507#121C23×C10912yes—
508#120—22no—
509#120—22no—
510C4×Q8—21no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—44no—
522#117—22no—
523#117—21no—
524#117—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4D4×C10911yescharacteristic, complemented
528C2×C4⋊C4D4×C10911yescharacteristic, complemented
529C2×C4⋊C4C23×C10911yescharacteristic
530C2×C22⋊C4—22no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4D4×C10911yescharacteristic
539C2×C22⋊C4C23×C10911yescharacteristic
540C2×C42—21no—
541C2×C42D4×C10911yescharacteristic
542#103—22no—
543#103—22no—
544#102—22no—
545#102—22no—
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8C23×C10912yes—
549C22⋊C8C23×C10912yes—
550#95—21no—
551#95—21no—
552#95C23×C10911yescharacteristic
553#95C23×C10911yescharacteristic
554C24—21no—
555C24—21no—
556C24C2×D4×C10911yescharacteristic
557C24C2×D4×C10911yescharacteristic
558#41—24no—
559#41—24no—
560#41—42no—
561#41—42no—
562#41—42no—
563#41—42no—
564#41—42no—
565#41—42no—
566#41—82no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8C2×D4×C10912yes—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C2×D4×C10912yes—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4C2×D4×C10911yescharacteristic
613C22×C4C2×D4×C10911yescharacteristic
614C22×C4C2×D4×C10911yescharacteristic
615C22×C4C2×D4×C10911yescharacteristic
616C22×C4C2×D4×C10911yescharacteristic
617C22×C4C2×D4×C10911yescharacteristic
618C22×C4C2×D4×C10911yescharacteristic
619C22×C4C2×D4×C10911yescharacteristic
620C22×C4C24×C10911yescharacteristic
621Q16—44no—
622SD16—44no—
623SD16—44no—
624D8—44no—
625M16—42no—
626M16—42no—
627C2×C8—22no—
628C2×C8—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—42no—
640C4⋊C4C2×D4×C10912yes—
641C4⋊C4C2×D4×C10912yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C42—22no—
662C42—22no—
663C42—21no—
664C42—21no—
665C42—42no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—81no—
686C23#120×C10911yescharacteristic
687C23#120×C10911yescharacteristic
688C23C22×D4×C10911yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—42no—
692Q8—41no—
693Q8—41no—
694Q8—42no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—41no—
699D4—41no—
700D4—42no—
701D4—42no—
702D4—44no—
703D4—44no—
704D4—44no—
705D4—48no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—82no—
710D4—82no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4#120×C10911yescharacteristic
746C2×C4#120×C10911yescharacteristic
747C2×C4C22×D4×C10911yescharacteristic
748C2×C4C22×D4×C10911yescharacteristic
749C8—42no—
750C8—42no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—162no—
777C22C2×#120×C10911yescharacteristic
778C22#575×C10911yescharacteristic
779C22#575×C10911yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—42no—
784C4—41no—
785C4—42no—
786C4—41no—
787C4—42no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4B(4,𝔽2)×C10912yes—
793C2—21no—
794C2—21no—
795C2—41no—
796C2—41no—
797C2—81no—
798C2—82no—
799C2—82no—
800C2C109×#300511yescharacteristic
801C2C109×#301811yescharacteristic
802C2C2×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×#3505C2semidirect
2. C109×#3007C2semidirect
3. C109×#3006C2semidirect
4. C109×#2388C2semidirect
5. C109×#1606C2semidirect
6. C109×#1603C2semidirect
7. C109×#1600C2semidirect
8. C109×#1597C2semidirect
9. C109×#1508C2semidirect
10. C109×#1507C2semidirect
11. C109×#1465C2semidirect
32. #451×C109C22semidirect
33. #450×C109C22semidirect
41. #395×C109C22semidirect
43. #394×C109C22semidirect
44. #393×C109C22semidirect
46. #392×C109C22semidirect
49. #328×C109C22semidirect
50. #328×C109C22semidirect
53. #324×C109C22semidirect
54. #323×C109C22semidirect
61. C22×Q8×C109D4semidirect
67. C22×D4×C109D4semidirect
96. C22⋊Q8×C109D4semidirect
104. #121×C109D4semidirect
125. C2×C4⋊C4×C109D4semidirect
126. C2×C4⋊C4×C109D4semidirect
391. #18168C109direct (N × H)
402. #3505C2×C109semidirect
403. #3007C2×C109semidirect
404. #3006C2×C109semidirect
405. #2388C2×C109semidirect
406. #1606C2×C109semidirect
407. #1603C2×C109semidirect
408. #1600C2×C109semidirect
409. #1597C2×C109semidirect
410. #1508C2×C109semidirect
411. #1507C2×C109semidirect
412. #1465C2×C109semidirect
413. C109#18168direct (N × H)
434. #451C22×C109semidirect
435. #450C22×C109semidirect
443. #395C22×C109semidirect
445. #394C22×C109semidirect
446. #393C22×C109semidirect
448. #392C22×C109semidirect
451. #328C22×C109semidirect
452. #328C22×C109semidirect
455. #324C22×C109semidirect
456. #323C22×C109semidirect
463. C22×Q8D4×C109semidirect
469. C22×D4D4×C109semidirect
498. C22⋊Q8D4×C109semidirect
506. #121D4×C109semidirect
527. C2×C4⋊C4D4×C109semidirect
528. 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×#35052
C109×#30072
C109×#30062
C109×#23882
C109×#16062
C109×#16032
C109×#16002
C109×#15972
C109×#15082
C109×#15072
C109×#14652
#18168109