Finite Group Databasebeta

← C109×#19181 #42137175

Subgroups — C109×#19181 #42137175

Order 27904.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3185C211yesmaximal, characteristic, complemented
2C109×#3107C211yesmaximal, characteristic
3C109×#3076C211yesmaximal, characteristic
4C109×#2970C211yesmaximal, characteristic
5C109×#1704C211yesmaximal, characteristic, complemented
6C109×#1700C211yesmaximal, characteristic, complemented
7C109×#1692C211yesmaximal, characteristic, complemented
8C109×#1690C211yesmaximal, characteristic, complemented
9C109×#1683C211yesmaximal, characteristic, complemented
10C109×#1679C211yesmaximal, characteristic, complemented
11C109×#1671C211yesmaximal, characteristic, complemented
12C109×#1669C211yesmaximal, characteristic, complemented
13C109×#1565C211yesmaximal, characteristic, complemented
14C109×#1554C211yesmaximal, characteristic, complemented
15C109×#1552C211yesmaximal, characteristic, complemented
16#533×C109C2211yescharacteristic
17#533×C109C2211yescharacteristic
18C4×#41×C109C2211yescharacteristic
19#498×C109C2211yescharacteristic
20#494×C109C2211yescharacteristic
21#487×C109C2211yescharacteristic
22#487×C109C2211yescharacteristic
23#485×C109—21no—
24#479×C109—21no—
25#478×C109—21no—
26#477×C109C2211yescharacteristic
27#476×C109C2211yescharacteristic
28#475×C109C2211yescharacteristic
29#475×C109C2211yescharacteristic
30#474×C109C2211yescharacteristic
31#474×C109C2211yescharacteristic
32#470×C109—21no—
33#470×C109—21no—
34#462×C109C2211yescharacteristic
35#461×C109C2211yescharacteristic
36#452×C109—21no—
37#446×C109C2211yescharacteristic
38#446×C109C2211yescharacteristic
39#441×C109—21no—
40#441×C109—21no—
41C4×Q16×C109—21no—
42C4×SD16×C109—21no—
43#435×C109—21no—
44#435×C109—21no—
45C8×D4×C109C2211yescharacteristic
46C8×D4×C109C2211yescharacteristic
47#432×C109—21no—
48#432×C109C2211yescharacteristic
49#431×C109C2211yescharacteristic
50#427×C109—21no—
51C2×C4⋊C8×C109C2211yescharacteristic
52#416×C109—21no—
53C4×M16×C109C2211yescharacteristic
54C2×#97×C109—21no—
55#335×C109C2211yescharacteristic
56#335×C109C2211yescharacteristic
57#334×C109C2211yescharacteristic
58#334×C109C2211yescharacteristic
59#333×C109C2211yescharacteristic
60#333×C109C2211yescharacteristic
61#332×C109C2211yescharacteristic
62#332×C109C2211yescharacteristic
63#332×C109C2211yescharacteristic
64#332×C109C2211yescharacteristic
65#332×C109C2211yescharacteristic
66#332×C109C2211yescharacteristic
67C2×#41×C109D411yescharacteristic
68C2×Q16×C109—21no—
69C2×Q16×C109—21no—
70C2×Q16×C109—21no—
71C2×SD16×C109—21no—
72C2×M16×C109D411yescharacteristic
73C2×M16×C109D411yescharacteristic
74C22×C8×C109—21no—
75C22×C8×C109—21no—
76C22×C8×C109—21no—
77C4⋊Q8×C109C2311yescharacteristic
78C4⋊Q8×C109C2311yescharacteristic
79C4⋊Q8×C109C2311yescharacteristic
80C4⋊Q8×C109C2311yescharacteristic
81#125×C109—21no—
82#125×C109—21no—
83C22⋊Q8×C109—21no—
84C22⋊Q8×C109—21no—
85C22⋊Q8×C109—21no—
86C22⋊Q8×C109—21no—
87C4×Q8×C109—21no—
88C4×Q8×C109—21no—
89C4×Q8×C109—21no—
90C4×Q8×C109—21no—
91C4×Q8×C109D411yescharacteristic
92C4×Q8×C109C2311yescharacteristic
93C4×D4×C109—21no—
94C4×D4×C109—21no—
95C4×D4×C109D411yescharacteristic
96C4×D4×C109C2311yescharacteristic
97#117×C109—21no—
98#117×C109—21no—
99#117×C109—21no—
100#117×C109D411yescharacteristic
101C2×C42×C109—21no—
102C2×C42×C109C2311yescharacteristic
103#107×C109—21no—
104#107×C109—21no—
105#107×C109—21no—
106#106×C109—21no—
107#106×C109—21no—
108#106×C109—21no—
109#106×C109—21no—
110#106×C109—21no—
111C4⋊C8×C109—21no—
112C4⋊C8×C109—21no—
113C4⋊C8×C109—21no—
114C4⋊C8×C109C2311yescharacteristic
115C4⋊C8×C109C2311yescharacteristic
116C4⋊C8×C109C2311yescharacteristic
117C4⋊C8×C109C2311yescharacteristic
118C4⋊C8×C109C2311yescharacteristic
119C4⋊C8×C109C2311yescharacteristic
120#103×C109—21no—
121#103×C109—21no—
122#103×C109—21no—
123#103×C109—21no—
124#103×C109—21no—
125#103×C109—21no—
126#103×C109—21no—
127#103×C109—21no—
128#103×C109—21no—
129#102×C109—21no—
130#102×C109—21no—
131#102×C109—21no—
132C22⋊C8×C109—21no—
133C22⋊C8×C109—21no—
134C22⋊C8×C109—21no—
135C22⋊C8×C109—21no—
136#97×C109—21no—
137#97×C109—21no—
138#97×C109—21no—
139#97×C109D411yescharacteristic
140#97×C109D411yescharacteristic
141C4×C8×C109—21no—
142C4×C8×C109C2311yescharacteristic
143C4×C8×C109C2311yescharacteristic
144#41×C109—22no—
145#41×C109—41no—
146C2×Q8×C109—21no—
147C2×Q8×C109—21no—
148C2×Q8×C109—21no—
149C2×Q8×C109—21no—
150C2×Q8×C109C2×D411yescharacteristic
151C2×D4×C109—21no—
152C2×D4×C109C2×D411yescharacteristic
153C22×C4×C109—21no—
154C22×C4×C109—21no—
155C22×C4×C109—21no—
156C22×C4×C109C2×D411yescharacteristic
157C22×C4×C109C2×D411yescharacteristic
158C22×C4×C109#4111yescharacteristic
159Q16×C109—42no—
160Q16×C109—42no—
161Q16×C109—42no—
162SD16×C109—42no—
163M16×C109—22no—
164M16×C109—41no—
165C2×C8×C109—21no—
166C2×C8×C109—21no—
167C2×C8×C109—21no—
168C2×C8×C109—21no—
169C2×C8×C109—21no—
170C2×C8×C109—21no—
171C2×C8×C109—42no—
172C2×C8×C109—42no—
173C2×C8×C109—42no—
174C2×C8×C109C2×D411yescharacteristic
175C2×C8×C109C2×D411yescharacteristic
176C2×C8×C109C2×D411yescharacteristic
177C2×C8×C109C2×D411yescharacteristic
178C4⋊C4×C109—21no—
179C4⋊C4×C109—21no—
180C4⋊C4×C109—21no—
181C4⋊C4×C109—21no—
182C4⋊C4×C109—21no—
183C4⋊C4×C109—21no—
184C4⋊C4×C109—21no—
185C4⋊C4×C109—21no—
186C4⋊C4×C109—21no—
187C4⋊C4×C109—21no—
188C4⋊C4×C109—41no—
189C4⋊C4×C109—41no—
190C4⋊C4×C109—41no—
191C4⋊C4×C109—41no—
192C4⋊C4×C109C2×D411yescharacteristic
193C4⋊C4×C109C2×D411yescharacteristic
194C22⋊C4×C109—21no—
195C22⋊C4×C109—21no—
196C22⋊C4×C109—21no—
197C22⋊C4×C109—41no—
198C22⋊C4×C109—41no—
199C42×C109—21no—
200C42×C109—21no—
201C42×C109—21no—
202C42×C109—41no—
203C42×C109—41no—
204C42×C109C2×D411yescharacteristic
205C42×C109C2×D411yescharacteristic
206C42×C109#4111yescharacteristic
207C42×C109C2411yescharacteristic
208C23×C109—21no—
209C23×C109#12111yescharacteristic
210Q8×C109—21no—
211Q8×C109—21no—
212Q8×C109—41no—
213Q8×C109—41no—
214Q8×C109—41no—
215Q8×C109—41no—
216Q8×C109—41no—
217Q8×C109—41no—
218Q8×C109—81no—
219D4×C109—21no—
220D4×C109—42no—
221D4×C109#13712yes—
222C2×C4×C109—21no—
223C2×C4×C109—21no—
224C2×C4×C109—21no—
225C2×C4×C109—21no—
226C2×C4×C109—21no—
227C2×C4×C109—21no—
228C2×C4×C109—21no—
229C2×C4×C109—41no—
230C2×C4×C109—42no—
231C2×C4×C109—41no—
232C2×C4×C109—41no—
233C2×C4×C109—41no—
234C2×C4×C109—41no—
235C2×C4×C109—41no—
236C2×C4×C109—41no—
237C2×C4×C109—81no—
238C2×C4×C109#12111yescharacteristic
239C2×C4×C109#12111yescharacteristic
240C2×C4×C109#12111yescharacteristic
241C2×C4×C109C22×D411yescharacteristic
242C2×C4×C109C22×D411yescharacteristic
243C2×C4×C109C2×#4111yescharacteristic
244C8×C109—21no—
245C8×C109—21no—
246C8×C109—21no—
247C8×C109—41no—
248C8×C109—41no—
249C8×C109—41no—
250C8×C109—41no—
251C8×C109—41no—
252C8×C109—41no—
253C8×C109#13512yes—
254C22×C109—21no—
255C22×C109—21no—
256C22×C109—22no—
257C22×C109—21no—
258C22×C109—41no—
259C22×C109—41no—
260C22×C109C2×#12111yescharacteristic
261C4×C109—21no—
262C4×C109—21no—
263C4×C109—21no—
264C4×C109—21no—
265C4×C109—41no—
266C4×C109—41no—
267C4×C109—41no—
268C4×C109—81no—
269C4×C109—81no—
270C4×C109—81no—
271C4×C109—81no—
272C4×C109C2×#13511yescharacteristic
273C4×C109C2×#13711yescharacteristic
274C4×C109#57511yescharacteristic
275C4×C109#57511yescharacteristic
276#19181C10911yesmaximal, characteristic, direct product factor, Sylow
277C2×C109—41no—
278C2×C109—42no—
279C2×C109#303511yescharacteristic
280C2×C109#305611yescharacteristic
281C2×C109#306911yescharacteristic
282#3185C2×C10911yescharacteristic, complemented
283#3107C2×C10911yescharacteristic
284#3076C2×C10911yescharacteristic
285#2970C2×C10911yescharacteristic
286#1704C2×C10911yescharacteristic, complemented
287#1700C2×C10911yescharacteristic, complemented
288#1692C2×C10911yescharacteristic, complemented
289#1690C2×C10911yescharacteristic, complemented
290#1683C2×C10911yescharacteristic, complemented
291#1679C2×C10911yescharacteristic, complemented
292#1671C2×C10911yescharacteristic, complemented
293#1669C2×C10911yescharacteristic, complemented
294#1565C2×C10911yescharacteristic, complemented
295#1554C2×C10911yescharacteristic, complemented
296#1552C2×C10911yescharacteristic, complemented
297C109#1918111yescharacteristic, direct product factor, Sylow
298#533C22×C10911yescharacteristic
299#533C22×C10911yescharacteristic
300C4×#41C22×C10911yescharacteristic
301#498C22×C10911yescharacteristic
302#494C22×C10911yescharacteristic
303#487C22×C10911yescharacteristic
304#487C22×C10911yescharacteristic
305#485—21no—
306#479—21no—
307#478—21no—
308#477C22×C10911yescharacteristic
309#476C22×C10911yescharacteristic
310#475C22×C10911yescharacteristic
311#475C22×C10911yescharacteristic
312#474C22×C10911yescharacteristic
313#474C22×C10911yescharacteristic
314#470—21no—
315#470—21no—
316#462C22×C10911yescharacteristic
317#461C22×C10911yescharacteristic
318#452—21no—
319#446C22×C10911yescharacteristic
320#446C22×C10911yescharacteristic
321#441—21no—
322#441—21no—
323C4×Q16—21no—
324C4×SD16—21no—
325#435—21no—
326#435—21no—
327C8×D4C22×C10911yescharacteristic
328C8×D4C22×C10911yescharacteristic
329#432—21no—
330#432C22×C10911yescharacteristic
331#431C22×C10911yescharacteristic
332#427—21no—
333C2×C4⋊C8C22×C10911yescharacteristic
334#416—21no—
335C4×M16C22×C10911yescharacteristic
336C2×#97—21no—
337#335C22×C10911yescharacteristic
338#335C22×C10911yescharacteristic
339#334C22×C10911yescharacteristic
340#334C22×C10911yescharacteristic
341#333C22×C10911yescharacteristic
342#333C22×C10911yescharacteristic
343#332C22×C10911yescharacteristic
344#332C22×C10911yescharacteristic
345#332C22×C10911yescharacteristic
346#332C22×C10911yescharacteristic
347#332C22×C10911yescharacteristic
348#332C22×C10911yescharacteristic
349C2×#41D4×C10911yescharacteristic
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×SD16—21no—
354C2×M16D4×C10911yescharacteristic
355C2×M16D4×C10911yescharacteristic
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C4⋊Q8C23×C10911yescharacteristic
360C4⋊Q8C23×C10911yescharacteristic
361C4⋊Q8C23×C10911yescharacteristic
362C4⋊Q8C23×C10911yescharacteristic
363#125—21no—
364#125—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8D4×C10911yescharacteristic
374C4×Q8C23×C10911yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4D4×C10911yescharacteristic
378C4×D4C23×C10911yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382#117D4×C10911yescharacteristic
383C2×C42—21no—
384C2×C42C23×C10911yescharacteristic
385#107—21no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C10911yescharacteristic
397C4⋊C8C23×C10911yescharacteristic
398C4⋊C8C23×C10911yescharacteristic
399C4⋊C8C23×C10911yescharacteristic
400C4⋊C8C23×C10911yescharacteristic
401C4⋊C8C23×C10911yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418#97—21no—
419#97—21no—
420#97—21no—
421#97D4×C10911yescharacteristic
422#97D4×C10911yescharacteristic
423C4×C8—21no—
424C4×C8C23×C10911yescharacteristic
425C4×C8C23×C10911yescharacteristic
426#41—22no—
427#41—41no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8C2×D4×C10911yescharacteristic
433C2×D4—21no—
434C2×D4C2×D4×C10911yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×D4×C10911yescharacteristic
439C22×C4C2×D4×C10911yescharacteristic
440C22×C4#41×C10911yescharacteristic
441Q16—42no—
442Q16—42no—
443Q16—42no—
444SD16—42no—
445M16—22no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8C2×D4×C10911yescharacteristic
457C2×C8C2×D4×C10911yescharacteristic
458C2×C8C2×D4×C10911yescharacteristic
459C2×C8C2×D4×C10911yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4C2×D4×C10911yescharacteristic
475C4⋊C4C2×D4×C10911yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42C2×D4×C10911yescharacteristic
487C42C2×D4×C10911yescharacteristic
488C42#41×C10911yescharacteristic
489C42C24×C10911yescharacteristic
490C23—21no—
491C23#121×C10911yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501D4—21no—
502D4—42no—
503D4#137×C10912yes—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4#121×C10911yescharacteristic
521C2×C4#121×C10911yescharacteristic
522C2×C4#121×C10911yescharacteristic
523C2×C4C22×D4×C10911yescharacteristic
524C2×C4C22×D4×C10911yescharacteristic
525C2×C4C2×#41×C10911yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8#135×C10912yes—
536C22—21no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22C2×#121×C10911yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4C2×#135×C10911yescharacteristic
555C4C2×#137×C10911yescharacteristic
556C4#575×C10911yescharacteristic
557C4#575×C10911yescharacteristic
558C2—41no—
559C2—42no—
560C2C109×#303511yescharacteristic
561C2C109×#305611yescharacteristic
562C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radicalC2×#41×C109D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3185C2semidirect
5. C109×#1704C2semidirect
6. C109×#1700C2semidirect
7. C109×#1692C2semidirect
8. C109×#1690C2semidirect
9. C109×#1683C2semidirect
10. C109×#1679C2semidirect
11. C109×#1671C2semidirect
12. C109×#1669C2semidirect
13. C109×#1565C2semidirect
14. C109×#1554C2semidirect
15. C109×#1552C2semidirect
276. #19181C109direct (N × H)
282. #3185C2×C109semidirect
286. #1704C2×C109semidirect
287. #1700C2×C109semidirect
288. #1692C2×C109semidirect
289. #1690C2×C109semidirect
290. #1683C2×C109semidirect
291. #1679C2×C109semidirect
292. #1671C2×C109semidirect
293. #1669C2×C109semidirect
294. #1565C2×C109semidirect
295. #1554C2×C109semidirect
296. #1552C2×C109semidirect
297. C109#19181direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#31852
C109×#31072
C109×#30762
C109×#29702
C109×#17042
C109×#17002
C109×#16922
C109×#16902
C109×#16832
C109×#16792
C109×#16712
C109×#16692
C109×#15652
C109×#15542
C109×#15522
#19181109