Finite Group Databasebeta

← C109×#18198 #42136192

Subgroups — C109×#18198 #42136192

Order 27904.

1396 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3505C211yesmaximal, characteristic, complemented
2C2×#450×C109C211yesmaximal, characteristic, complemented
3C2×#447×C109C211yesmaximal, characteristic, complemented
4C109×#2408C211yesmaximal, characteristic, complemented
5C109×#1600C214yesmaximal, complemented
6C109×#1597C214yesmaximal, complemented
7C109×#1520C211yesmaximal, characteristic, complemented
8C109×#1519C211yesmaximal, characteristic, complemented
9C109×#1459C211yesmaximal, characteristic, complemented
10C23×D4×C109C2211yescharacteristic
11C22×SD16×C109—21no—
12C22×D8×C109—21no—
13#553×C109—22no—
14#553×C109—21no—
15#552×C109—21no—
16#551×C109—22no—
17#548×C109—21no—
18#546×C109—21no—
19#539×C109C2212yescomplemented
20#538×C109C2212yescomplemented
21#534×C109—21no—
22#529×C109—21no—
23#525×C109—21no—
24C2×C22⋊Q8×C109C2211yescharacteristic
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#120×C109—21no—
28#518×C109—21no—
29C2×C4×D4×C109C2211yescharacteristic
30#450×C109—22no—
31#450×C109C2214yescomplemented
32#447×C109—22no—
33#447×C109C2214yes—
34C2×#102×C109—21no—
35C2×#102×C109—21no—
36C2×C22⋊C8×C109C2211yescharacteristic
37C2×C22⋊C8×C109C2211yescharacteristic
38#394×C109C2212yescomplemented
39#392×C109C2212yescomplemented
40#390×C109—21no—
41#380×C109C2211yescharacteristic
42#379×C109—21no—
43#328×C109C2214yescomplemented
44#327×C109C2214yescomplemented
45#324×C109C2212yescomplemented
46#323×C109C2212yescomplemented
47C25×C109—21no—
48C2×#41×C109—21no—
49C22×Q8×C109D411yescharacteristic, complemented
50C22×D4×C109—21no—
51C22×D4×C109—22no—
52C22×D4×C109—21no—
53C22×D4×C109—21no—
54C22×D4×C109—21no—
55C22×D4×C109—21no—
56C22×D4×C109—21no—
57C22×D4×C109—44no—
58C22×D4×C109D411yescharacteristic
59C22×D4×C109D411yescharacteristic, complemented
60C22×D4×C109C2312yes—
61C23×C4×C109D411yescharacteristic
62C23×C4×C109C2311yescharacteristic
63C2×SD16×C109—24no—
64C2×SD16×C109—44no—
65C2×D8×C109—24no—
66C2×D8×C109—44no—
67C22×C8×C109—21no—
68C22×C8×C109—21no—
69#126×C109—22no—
70#126×C109—22no—
71#126×C109—22no—
72#125×C109—21no—
73#125×C109—22no—
74#124×C109—21no—
75#124×C109—22no—
76#123×C109—22no—
77#123×C109—22no—
78#123×C109—22no—
79#123×C109—22no—
80#123×C109—22no—
81C22⋊Q8×C109—21no—
82C22⋊Q8×C109—22no—
83C22⋊Q8×C109—21no—
84C22⋊Q8×C109—21no—
85C22⋊Q8×C109D412yescomplemented
86C22⋊Q8×C109C2312yes—
87#121×C109—21no—
88#121×C109—22no—
89#121×C109—22no—
90#121×C109—22no—
91#121×C109—21no—
92#121×C109—21no—
93#121×C109—44no—
94#121×C109D412yescomplemented
95#121×C109C2312yes—
96#120×C109—22no—
97#120×C109—22no—
98#120×C109—44no—
99C4×Q8×C109—21no—
100C4×D4×C109—22no—
101C4×D4×C109—22no—
102C4×D4×C109—22no—
103C4×D4×C109—21no—
104C4×D4×C109—21no—
105C4×D4×C109—21no—
106C4×D4×C109—21no—
107C4×D4×C109—21no—
108C4×D4×C109—22no—
109C4×D4×C109—22no—
110#117×C109—22no—
111#117×C109—21no—
112#117×C109—22no—
113C2×C4⋊C4×C109—21no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109D411yescharacteristic, complemented
116C2×C4⋊C4×C109D411yescharacteristic, complemented
117C2×C4⋊C4×C109C2311yescharacteristic
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—22no—
124C2×C22⋊C4×C109—22no—
125C2×C22⋊C4×C109D411yescharacteristic
126C2×C22⋊C4×C109C2311yescharacteristic
127C2×C42×C109D411yescharacteristic
128#102×C109—24no—
129#102×C109—24no—
130C22⋊C8×C109—21no—
131C22⋊C8×C109—21no—
132C22⋊C8×C109C2312yes—
133C22⋊C8×C109C2312yes—
134#95×C109C2312yes—
135C24×C109—22no—
136C24×C109—21no—
137C24×C109—44no—
138C24×C109—41no—
139C24×C109—41no—
140C24×C109—42no—
141C24×C109—42no—
142C24×C109—82no—
143C24×C109C2×D411yescharacteristic
144C24×C109C2×D411yescharacteristic
145#41×C109—82no—
146C2×Q8×C109—21no—
147C2×Q8×C109—42no—
148C2×Q8×C109C2×D412yes—
149C2×D4×C109—24no—
150C2×D4×C109—24no—
151C2×D4×C109—24no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—22no—
155C2×D4×C109—22no—
156C2×D4×C109—22no—
157C2×D4×C109—22no—
158C2×D4×C109—22no—
159C2×D4×C109—22no—
160C2×D4×C109—21no—
161C2×D4×C109—22no—
162C2×D4×C109—22no—
163C2×D4×C109—42no—
164C2×D4×C109—42no—
165C2×D4×C109—42no—
166C2×D4×C109—42no—
167C2×D4×C109—44no—
168C2×D4×C109—44no—
169C2×D4×C109—44no—
170C2×D4×C109—42no—
171C2×D4×C109—42no—
172C2×D4×C109—44no—
173C2×D4×C109—44no—
174C2×D4×C109—41no—
175C2×D4×C109—41no—
176C2×D4×C109—82no—
177C2×D4×C109C2×D412yes—
178C22×C4×C109—21no—
179C22×C4×C109—22no—
180C22×C4×C109—22no—
181C22×C4×C109—21no—
182C22×C4×C109—21no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—22no—
186C22×C4×C109—42no—
187C22×C4×C109—42no—
188C22×C4×C109C2×D411yescharacteristic
189C22×C4×C109C2×D411yescharacteristic
190C22×C4×C109C2×D411yescharacteristic
191C22×C4×C109C2×D411yescharacteristic
192C22×C4×C109C2×D411yescharacteristic
193C22×C4×C109C2×D411yescharacteristic
194C22×C4×C109C2×D411yescharacteristic
195C22×C4×C109C2×D411yescharacteristic
196C22×C4×C109C2411yescharacteristic
197SD16×C109—48no—
198D8×C109—48no—
199C2×C8×C109—22no—
200C2×C8×C109—22no—
201C2×C8×C109—42no—
202C2×C8×C109—42no—
203C4⋊C4×C109—22no—
204C4⋊C4×C109—22no—
205C4⋊C4×C109—22no—
206C4⋊C4×C109—22no—
207C4⋊C4×C109—22no—
208C4⋊C4×C109—21no—
209C4⋊C4×C109—21no—
210C4⋊C4×C109—22no—
211C4⋊C4×C109—21no—
212C4⋊C4×C109—21no—
213C4⋊C4×C109—42no—
214C4⋊C4×C109C2×D412yes—
215C4⋊C4×C109C2×D412yes—
216C22⋊C4×C109—22no—
217C22⋊C4×C109—22no—
218C22⋊C4×C109—22no—
219C22⋊C4×C109—22no—
220C22⋊C4×C109—22no—
221C22⋊C4×C109—22no—
222C22⋊C4×C109—21no—
223C22⋊C4×C109—22no—
224C22⋊C4×C109—21no—
225C22⋊C4×C109—22no—
226C22⋊C4×C109—22no—
227C22⋊C4×C109—22no—
228C22⋊C4×C109—21no—
229C22⋊C4×C109—21no—
230C22⋊C4×C109—44no—
231C22⋊C4×C109—44no—
232C22⋊C4×C109—42no—
233C22⋊C4×C109—82no—
234C42×C109—22no—
235C42×C109—22no—
236C42×C109—21no—
237C42×C109—21no—
238C23×C109—24no—
239C23×C109—21no—
240C23×C109—22no—
241C23×C109—21no—
242C23×C109—21no—
243C23×C109—41no—
244C23×C109—41no—
245C23×C109—41no—
246C23×C109—41no—
247C23×C109—42no—
248C23×C109—44no—
249C23×C109—44no—
250C23×C109—42no—
251C23×C109—42no—
252C23×C109—42no—
253C23×C109—42no—
254C23×C109—42no—
255C23×C109—42no—
256C23×C109—81no—
257C23×C109—81no—
258C23×C109—82no—
259C23×C109—82no—
260C23×C109—88no—
261C23×C109—88no—
262C23×C109—82no—
263C23×C109—82no—
264C23×C109#12011yescharacteristic
265C23×C109#12011yescharacteristic
266C23×C109#13512yes—
267C23×C109AGL(1,ℤ/8)12yes—
268C23×C109C22×D411yescharacteristic
269Q8×C109—42no—
270Q8×C109—42no—
271D4×C109—24no—
272D4×C109—24no—
273D4×C109—42no—
274D4×C109—42no—
275D4×C109—42no—
276D4×C109—44no—
277D4×C109—42no—
278D4×C109—42no—
279D4×C109—42no—
280D4×C109—42no—
281D4×C109—44no—
282D4×C109—44no—
283D4×C109—42no—
284D4×C109—82no—
285D4×C109—82no—
286D4×C109—88no—
287C2×C4×C109—22no—
288C2×C4×C109—22no—
289C2×C4×C109—22no—
290C2×C4×C109—21no—
291C2×C4×C109—21no—
292C2×C4×C109—22no—
293C2×C4×C109—21no—
294C2×C4×C109—22no—
295C2×C4×C109—22no—
296C2×C4×C109—21no—
297C2×C4×C109—21no—
298C2×C4×C109—41no—
299C2×C4×C109—41no—
300C2×C4×C109—41no—
301C2×C4×C109—42no—
302C2×C4×C109—42no—
303C2×C4×C109—41no—
304C2×C4×C109—41no—
305C2×C4×C109—42no—
306C2×C4×C109—42no—
307C2×C4×C109—42no—
308C2×C4×C109—81no—
309C2×C4×C109—81no—
310C2×C4×C109—81no—
311C2×C4×C109—82no—
312C2×C4×C109—82no—
313C2×C4×C109#12011yescharacteristic
314C2×C4×C109#12011yescharacteristic
315C2×C4×C109C22×D411yescharacteristic
316C2×C4×C109C22×D411yescharacteristic
317C8×C109—42no—
318C8×C109—42no—
319C22×C109—21no—
320C22×C109—21no—
321C22×C109—21no—
322C22×C109—21no—
323C22×C109—21no—
324C22×C109—21no—
325C22×C109—42no—
326C22×C109—42no—
327C22×C109—42no—
328C22×C109—44no—
329C22×C109—44no—
330C22×C109—41no—
331C22×C109—42no—
332C22×C109—42no—
333C22×C109—41no—
334C22×C109—41no—
335C22×C109—42no—
336C22×C109—44no—
337C22×C109—81no—
338C22×C109—82no—
339C22×C109—82no—
340C22×C109—88no—
341C22×C109—88no—
342C22×C109—82no—
343C22×C109—82no—
344C22×C109—162no—
345C22×C109#44912yes—
346C22×C109#44912yes—
347C22×C109C2×#12011yescharacteristic
348C22×C109C2×#13511yescharacteristic
349C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
350C4×C109—21no—
351C4×C109—21no—
352C4×C109—21no—
353C4×C109—41no—
354C4×C109—42no—
355C4×C109—41no—
356C4×C109—42no—
357C4×C109—41no—
358C4×C109—42no—
359C4×C109—82no—
360C4×C109B(4,𝔽2)12yes—
361#18198C10911yesmaximal, characteristic, direct product factor, Sylow
362C2×C109—21no—
363C2×C109—21no—
364C2×C109—22no—
365C2×C109—22no—
366C2×C109—81no—
367C2×C109—84no—
368C2×C109—82no—
369C2×C109C2×#44911yescharacteristic
370C2×C109#302111yescharacteristic
371C2×C109C2×B(4,𝔽2)11yescharacteristic
372#3505C2×C10911yescharacteristic, complemented
373C2×#450C2×C10911yescharacteristic, complemented
374C2×#447C2×C10911yescharacteristic, complemented
375#2408C2×C10911yescharacteristic, complemented
376#1600C2×C10914yescomplemented
377#1597C2×C10914yescomplemented
378#1520C2×C10911yescharacteristic, complemented
379#1519C2×C10911yescharacteristic, complemented
380#1459C2×C10911yescharacteristic, complemented
381C109#1819811yescharacteristic, direct product factor, Sylow
382C23×D4C22×C10911yescharacteristic
383C22×SD16—21no—
384C22×D8—21no—
385#553—22no—
386#553—21no—
387#552—21no—
388#551—22no—
389#548—21no—
390#546—21no—
391#539C22×C10912yescomplemented
392#538C22×C10912yescomplemented
393#534—21no—
394#529—21no—
395#525—21no—
396C2×C22⋊Q8C22×C10911yescharacteristic
397C2×#121—21no—
398C2×#121C22×C10911yescharacteristic
399C2×#120—21no—
400#518—21no—
401C2×C4×D4C22×C10911yescharacteristic
402#450—22no—
403#450C22×C10914yescomplemented
404#447—22no—
405#447C22×C10914yes—
406C2×#102—21no—
407C2×#102—21no—
408C2×C22⋊C8C22×C10911yescharacteristic
409C2×C22⋊C8C22×C10911yescharacteristic
410#394C22×C10912yescomplemented
411#392C22×C10912yescomplemented
412#390—21no—
413#380C22×C10911yescharacteristic
414#379—21no—
415#328C22×C10914yescomplemented
416#327C22×C10914yescomplemented
417#324C22×C10912yescomplemented
418#323C22×C10912yescomplemented
419C25—21no—
420C2×#41—21no—
421C22×Q8D4×C10911yescharacteristic, complemented
422C22×D4—21no—
423C22×D4—22no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—44no—
430C22×D4D4×C10911yescharacteristic
431C22×D4D4×C10911yescharacteristic, complemented
432C22×D4C23×C10912yes—
433C23×C4D4×C10911yescharacteristic
434C23×C4C23×C10911yescharacteristic
435C2×SD16—24no—
436C2×SD16—44no—
437C2×D8—24no—
438C2×D8—44no—
439C22×C8—21no—
440C22×C8—21no—
441#126—22no—
442#126—22no—
443#126—22no—
444#125—21no—
445#125—22no—
446#124—21no—
447#124—22no—
448#123—22no—
449#123—22no—
450#123—22no—
451#123—22no—
452#123—22no—
453C22⋊Q8—21no—
454C22⋊Q8—22no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8D4×C10912yescomplemented
458C22⋊Q8C23×C10912yes—
459#121—21no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—21no—
464#121—21no—
465#121—44no—
466#121D4×C10912yescomplemented
467#121C23×C10912yes—
468#120—22no—
469#120—22no—
470#120—44no—
471C4×Q8—21no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—22no—
481C4×D4—22no—
482#117—22no—
483#117—21no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4D4×C10911yescharacteristic, complemented
488C2×C4⋊C4D4×C10911yescharacteristic, complemented
489C2×C4⋊C4C23×C10911yescharacteristic
490C2×C22⋊C4—22no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4D4×C10911yescharacteristic
498C2×C22⋊C4C23×C10911yescharacteristic
499C2×C42D4×C10911yescharacteristic
500#102—24no—
501#102—24no—
502C22⋊C8—21no—
503C22⋊C8—21no—
504C22⋊C8C23×C10912yes—
505C22⋊C8C23×C10912yes—
506#95C23×C10912yes—
507C24—22no—
508C24—21no—
509C24—44no—
510C24—41no—
511C24—41no—
512C24—42no—
513C24—42no—
514C24—82no—
515C24C2×D4×C10911yescharacteristic
516C24C2×D4×C10911yescharacteristic
517#41—82no—
518C2×Q8—21no—
519C2×Q8—42no—
520C2×Q8C2×D4×C10912yes—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—82no—
549C2×D4C2×D4×C10912yes—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4C2×D4×C10911yescharacteristic
561C22×C4C2×D4×C10911yescharacteristic
562C22×C4C2×D4×C10911yescharacteristic
563C22×C4C2×D4×C10911yescharacteristic
564C22×C4C2×D4×C10911yescharacteristic
565C22×C4C2×D4×C10911yescharacteristic
566C22×C4C2×D4×C10911yescharacteristic
567C22×C4C2×D4×C10911yescharacteristic
568C22×C4C24×C10911yescharacteristic
569SD16—48no—
570D8—48no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—42no—
574C2×C8—42no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4C2×D4×C10912yes—
587C4⋊C4C2×D4×C10912yes—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—21no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—42no—
605C22⋊C4—82no—
606C42—22no—
607C42—22no—
608C42—21no—
609C42—21no—
610C23—24no—
611C23—21no—
612C23—22no—
613C23—21no—
614C23—21no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—81no—
629C23—81no—
630C23—82no—
631C23—82no—
632C23—88no—
633C23—88no—
634C23—82no—
635C23—82no—
636C23#120×C10911yescharacteristic
637C23#120×C10911yescharacteristic
638C23#135×C10912yes—
639C23AGL(1,ℤ/8)×C10912yes—
640C23C22×D4×C10911yescharacteristic
641Q8—42no—
642Q8—42no—
643D4—24no—
644D4—24no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—44no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—44no—
654D4—44no—
655D4—42no—
656D4—82no—
657D4—82no—
658D4—88no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4#120×C10911yescharacteristic
686C2×C4#120×C10911yescharacteristic
687C2×C4C22×D4×C10911yescharacteristic
688C2×C4C22×D4×C10911yescharacteristic
689C8—42no—
690C8—42no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—44no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—44no—
709C22—81no—
710C22—82no—
711C22—82no—
712C22—88no—
713C22—88no—
714C22—82no—
715C22—82no—
716C22—162no—
717C22#449×C10912yes—
718C22#449×C10912yes—
719C22C2×#120×C10911yescharacteristic
720C22C2×#135×C10911yescharacteristic
721C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
722C4—21no—
723C4—21no—
724C4—21no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—82no—
732C4B(4,𝔽2)×C10912yes—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—22no—
737C2—81no—
738C2—84no—
739C2—82no—
740C2C2×#449×C10911yescharacteristic
741C2C109×#302111yescharacteristic
742C2C2×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. C2×#450×C109C2semidirect
3. C2×#447×C109C2semidirect
4. C109×#2408C2semidirect
5. C109×#1600C2semidirect
6. C109×#1597C2semidirect
7. C109×#1520C2semidirect
8. C109×#1519C2semidirect
9. C109×#1459C2semidirect
19. #539×C109C22semidirect
20. #538×C109C22semidirect
31. #450×C109C22semidirect
38. #394×C109C22semidirect
39. #392×C109C22semidirect
43. #328×C109C22semidirect
44. #327×C109C22semidirect
45. #324×C109C22semidirect
46. #323×C109C22semidirect
49. C22×Q8×C109D4semidirect
59. C22×D4×C109D4semidirect
85. C22⋊Q8×C109D4semidirect
94. #121×C109D4semidirect
115. C2×C4⋊C4×C109D4semidirect
116. C2×C4⋊C4×C109D4semidirect
361. #18198C109direct (N × H)
372. #3505C2×C109semidirect
373. C2×#450C2×C109semidirect
374. C2×#447C2×C109semidirect
375. #2408C2×C109semidirect
376. #1600C2×C109semidirect
377. #1597C2×C109semidirect
378. #1520C2×C109semidirect
379. #1519C2×C109semidirect
380. #1459C2×C109semidirect
381. C109#18198direct (N × H)
391. #539C22×C109semidirect
392. #538C22×C109semidirect
403. #450C22×C109semidirect
410. #394C22×C109semidirect
411. #392C22×C109semidirect
415. #328C22×C109semidirect
416. #327C22×C109semidirect
417. #324C22×C109semidirect
418. #323C22×C109semidirect
421. C22×Q8D4×C109semidirect
431. C22×D4D4×C109semidirect
457. C22⋊Q8D4×C109semidirect
466. #121D4×C109semidirect
487. C2×C4⋊C4D4×C109semidirect
488. 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
C2×#450×C1092
C2×#447×C1092
C109×#24082
C109×#16002
C109×#15972
C109×#15202
C109×#15192
C109×#14592
#18198109