Finite Group Databasebeta

← C109×#19371 #42137365

Subgroups — C109×#19371 #42137365

Order 27904.

622 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3254C211yesmaximal, characteristic
2C109×#3235C211yesmaximal, characteristic
3C109×#3185C211yesmaximal, characteristic, complemented
4C109×#2935C211yesmaximal, characteristic
5C109×#1703C211yesmaximal, characteristic, complemented
6C109×#1699C211yesmaximal, characteristic, complemented
7C109×#1691C211yesmaximal, characteristic, complemented
8C109×#1689C211yesmaximal, characteristic, complemented
9C109×#1683C211yesmaximal, characteristic, complemented
10C109×#1679C211yesmaximal, characteristic, complemented
11C109×#1671C211yesmaximal, characteristic, complemented
12C109×#1669C211yesmaximal, characteristic, complemented
13C109×#1569C211yesmaximal, characteristic, complemented
14C109×#1552C211yesmaximal, characteristic, complemented
15C109×#1550C211yesmaximal, characteristic, complemented
16C2×#131×C109—21no—
17#533×C109C2211yescharacteristic
18#533×C109C2211yescharacteristic
19#532×C109C2211yescharacteristic
20#501×C109—21no—
21#498×C109C2211yescharacteristic
22#494×C109C2211yescharacteristic
23#490×C109—21no—
24#487×C109C2211yescharacteristic
25#487×C109C2211yescharacteristic
26#482×C109—21no—
27#482×C109—21no—
28#477×C109—21no—
29#476×C109C2211yescharacteristic
30#476×C109C2211yescharacteristic
31#474×C109C2211yescharacteristic
32#474×C109C2211yescharacteristic
33#474×C109C2211yescharacteristic
34#474×C109C2211yescharacteristic
35#470×C109—21no—
36#470×C109—21no—
37#468×C109—21no—
38#468×C109—21no—
39#461×C109C2211yescharacteristic
40#461×C109C2211yescharacteristic
41#460×C109—21no—
42#441×C109—21no—
43#441×C109—21no—
44#436×C109C2211yescharacteristic
45#436×C109C2211yescharacteristic
46#435×C109—21no—
47#435×C109—21no—
48C8×D4×C109C2211yescharacteristic
49C8×D4×C109C2211yescharacteristic
50#432×C109C2211yescharacteristic
51#423×C109C2211yescharacteristic
52C2×C4⋊C8×C109C2211yescharacteristic
53#408×C109—21no—
54C4×M16×C109C2211yescharacteristic
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×C109—21no—
68C2×Q16×C109—21no—
69C2×Q16×C109—21no—
70C2×SD16×C109—21no—
71C2×SD16×C109—21no—
72#131×C109—44no—
73C2×M16×C109—21no—
74C2×M16×C109—21no—
75C2×M16×C109—21no—
76C2×M16×C109D411yescharacteristic
77C2×M16×C109D411yescharacteristic
78C22×C8×C109—21no—
79C22×C8×C109—21no—
80C22×C8×C109—21no—
81C4⋊Q8×C109D411yescharacteristic
82C4⋊Q8×C109C2311yescharacteristic
83C4⋊Q8×C109C2311yescharacteristic
84C4⋊Q8×C109C2311yescharacteristic
85C4⋊Q8×C109C2311yescharacteristic
86#127×C109D411yescharacteristic
87#125×C109—21no—
88#125×C109—21no—
89#124×C109—21no—
90C22⋊Q8×C109—21no—
91C22⋊Q8×C109—21no—
92C22⋊Q8×C109—21no—
93C22⋊Q8×C109—21no—
94#121×C109—21no—
95#121×C109D411yescharacteristic
96#121×C109D411yescharacteristic
97C4×Q8×C109—21no—
98C4×Q8×C109—21no—
99C4×Q8×C109—21no—
100C4×Q8×C109—21no—
101C4×D4×C109—21no—
102C4×D4×C109C2311yescharacteristic
103C4×D4×C109C2311yescharacteristic
104#117×C109—21no—
105#117×C109—21no—
106C2×C42×C109C2311yescharacteristic
107#107×C109—21no—
108#107×C109—21no—
109#107×C109—21no—
110#107×C109—21no—
111#106×C109—21no—
112#106×C109—21no—
113#106×C109—21no—
114#106×C109—21no—
115C4⋊C8×C109—21no—
116C4⋊C8×C109—21no—
117C4⋊C8×C109C2311yescharacteristic
118C4⋊C8×C109C2311yescharacteristic
119C4⋊C8×C109C2311yescharacteristic
120C4⋊C8×C109C2311yescharacteristic
121C4⋊C8×C109C2311yescharacteristic
122C4⋊C8×C109C2311yescharacteristic
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—
132#102×C109—21no—
133#102×C109—21no—
134#102×C109—21no—
135C22⋊C8×C109—21no—
136C22⋊C8×C109—21no—
137C22⋊C8×C109—21no—
138C22⋊C8×C109—21no—
139C22⋊C8×C109—21no—
140#97×C109—21no—
141#97×C109D411yescharacteristic
142#97×C109D411yescharacteristic
143C4×C8×C109C2311yescharacteristic
144C4×C8×C109C2311yescharacteristic
145#41×C109—42no—
146#41×C109—42no—
147C2×Q8×C109—21no—
148C2×Q8×C109—21no—
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—21no—
156C2×D4×C109C2×D411yescharacteristic
157C2×D4×C109C2×D411yescharacteristic
158C22×C4×C109—21no—
159C22×C4×C109—21no—
160C22×C4×C109C2×D411yescharacteristic
161C22×C4×C109C2×D411yescharacteristic
162C22×C4×C109#4111yescharacteristic
163Q16×C109—42no—
164Q16×C109—42no—
165SD16×C109—81no—
166SD16×C109—81no—
167M16×C109—22no—
168M16×C109—41no—
169M16×C109—42no—
170M16×C109—42no—
171M16×C109—81no—
172C2×C8×C109—21no—
173C2×C8×C109—21no—
174C2×C8×C109—21no—
175C2×C8×C109—21no—
176C2×C8×C109—21no—
177C2×C8×C109—21no—
178C2×C8×C109—42no—
179C2×C8×C109—42no—
180C2×C8×C109—42no—
181C2×C8×C109C2×D411yescharacteristic
182C2×C8×C109C2×D411yescharacteristic
183C2×C8×C109C2×D411yescharacteristic
184C2×C8×C109C2×D411yescharacteristic
185C4⋊C4×C109—21no—
186C4⋊C4×C109—21no—
187C4⋊C4×C109—21no—
188C4⋊C4×C109—21no—
189C4⋊C4×C109—21no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—41no—
195C4⋊C4×C109—41no—
196C4⋊C4×C109—41no—
197C4⋊C4×C109—41no—
198C4⋊C4×C109C2×D411yescharacteristic
199C4⋊C4×C109C2×D411yescharacteristic
200C22⋊C4×C109—21no—
201C22⋊C4×C109—21no—
202C22⋊C4×C109—21no—
203C22⋊C4×C109—21no—
204C22⋊C4×C109—41no—
205C22⋊C4×C109—41no—
206C42×C109—41no—
207C42×C109—41no—
208C42×C109C2×D411yescharacteristic
209C42×C109C2×D411yescharacteristic
210C42×C109#4111yescharacteristic
211C42×C109C2411yescharacteristic
212C23×C109—21no—
213C23×C109—21no—
214C23×C109#12111yescharacteristic
215Q8×C109—42no—
216Q8×C109—41no—
217Q8×C109—41no—
218Q8×C109—41no—
219Q8×C109—41no—
220Q8×C109—41no—
221Q8×C109—41no—
222Q8×C109—81no—
223D4×C109—21no—
224D4×C109—21no—
225D4×C109—21no—
226D4×C109—21no—
227D4×C109—42no—
228D4×C109—42no—
229D4×C109—42no—
230D4×C109—81no—
231C2×C4×C109—21no—
232C2×C4×C109—21no—
233C2×C4×C109—21no—
234C2×C4×C109—21no—
235C2×C4×C109—21no—
236C2×C4×C109—21no—
237C2×C4×C109—41no—
238C2×C4×C109—41no—
239C2×C4×C109—41no—
240C2×C4×C109—41no—
241C2×C4×C109—41no—
242C2×C4×C109—41no—
243C2×C4×C109—41no—
244C2×C4×C109—41no—
245C2×C4×C109—41no—
246C2×C4×C109#12111yescharacteristic
247C2×C4×C109#12111yescharacteristic
248C2×C4×C109#12111yescharacteristic
249C2×C4×C109C22×D411yescharacteristic
250C2×C4×C109C22×D411yescharacteristic
251C2×C4×C109C2×#4111yescharacteristic
252C8×C109—21no—
253C8×C109—21no—
254C8×C109—21no—
255C8×C109—41no—
256C8×C109—41no—
257C8×C109—41no—
258C8×C109—41no—
259C8×C109—41no—
260C8×C109—41no—
261C8×C109AGL(1,ℤ/8)12yes—
262C22×C109—21no—
263C22×C109—21no—
264C22×C109—21no—
265C22×C109—41no—
266C22×C109—41no—
267C22×C109—41no—
268C22×C109—41no—
269C22×C109—41no—
270C22×C109—41no—
271C22×C109C2×#12111yescharacteristic
272C4×C109—21no—
273C4×C109—21no—
274C4×C109—21no—
275C4×C109—21no—
276C4×C109—41no—
277C4×C109—41no—
278C4×C109—81no—
279C4×C109—81no—
280C4×C109—81no—
281C4×C109—81no—
282C4×C109C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C109#57511yescharacteristic
284C4×C109#57711yescharacteristic
285C4×C109#57811yescharacteristic
286#19371C10911yesmaximal, characteristic, direct product factor, Sylow
287C2×C109—41no—
288C2×C109—81no—
289C2×C109—81no—
290C2×C109#303611yescharacteristic
291C2×C109#306311yescharacteristic
292C2×C109#306911yescharacteristic
293#3254C2×C10911yescharacteristic
294#3235C2×C10911yescharacteristic
295#3185C2×C10911yescharacteristic, complemented
296#2935C2×C10911yescharacteristic
297#1703C2×C10911yescharacteristic, complemented
298#1699C2×C10911yescharacteristic, complemented
299#1691C2×C10911yescharacteristic, complemented
300#1689C2×C10911yescharacteristic, complemented
301#1683C2×C10911yescharacteristic, complemented
302#1679C2×C10911yescharacteristic, complemented
303#1671C2×C10911yescharacteristic, complemented
304#1669C2×C10911yescharacteristic, complemented
305#1569C2×C10911yescharacteristic, complemented
306#1552C2×C10911yescharacteristic, complemented
307#1550C2×C10911yescharacteristic, complemented
308C109#1937111yescharacteristic, direct product factor, Sylow
309C2×#131—21no—
310#533C22×C10911yescharacteristic
311#533C22×C10911yescharacteristic
312#532C22×C10911yescharacteristic
313#501—21no—
314#498C22×C10911yescharacteristic
315#494C22×C10911yescharacteristic
316#490—21no—
317#487C22×C10911yescharacteristic
318#487C22×C10911yescharacteristic
319#482—21no—
320#482—21no—
321#477—21no—
322#476C22×C10911yescharacteristic
323#476C22×C10911yescharacteristic
324#474C22×C10911yescharacteristic
325#474C22×C10911yescharacteristic
326#474C22×C10911yescharacteristic
327#474C22×C10911yescharacteristic
328#470—21no—
329#470—21no—
330#468—21no—
331#468—21no—
332#461C22×C10911yescharacteristic
333#461C22×C10911yescharacteristic
334#460—21no—
335#441—21no—
336#441—21no—
337#436C22×C10911yescharacteristic
338#436C22×C10911yescharacteristic
339#435—21no—
340#435—21no—
341C8×D4C22×C10911yescharacteristic
342C8×D4C22×C10911yescharacteristic
343#432C22×C10911yescharacteristic
344#423C22×C10911yescharacteristic
345C2×C4⋊C8C22×C10911yescharacteristic
346#408—21no—
347C4×M16C22×C10911yescharacteristic
348#335C22×C10911yescharacteristic
349#335C22×C10911yescharacteristic
350#334C22×C10911yescharacteristic
351#334C22×C10911yescharacteristic
352#333C22×C10911yescharacteristic
353#333C22×C10911yescharacteristic
354#332C22×C10911yescharacteristic
355#332C22×C10911yescharacteristic
356#332C22×C10911yescharacteristic
357#332C22×C10911yescharacteristic
358#332C22×C10911yescharacteristic
359#332C22×C10911yescharacteristic
360C2×#41—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365#131—44no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16D4×C10911yescharacteristic
370C2×M16D4×C10911yescharacteristic
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8D4×C10911yescharacteristic
375C4⋊Q8C23×C10911yescharacteristic
376C4⋊Q8C23×C10911yescharacteristic
377C4⋊Q8C23×C10911yescharacteristic
378C4⋊Q8C23×C10911yescharacteristic
379#127D4×C10911yescharacteristic
380#125—21no—
381#125—21no—
382#124—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387#121—21no—
388#121D4×C10911yescharacteristic
389#121D4×C10911yescharacteristic
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×D4—21no—
395C4×D4C23×C10911yescharacteristic
396C4×D4C23×C10911yescharacteristic
397#117—21no—
398#117—21no—
399C2×C42C23×C10911yescharacteristic
400#107—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C10911yescharacteristic
411C4⋊C8C23×C10911yescharacteristic
412C4⋊C8C23×C10911yescharacteristic
413C4⋊C8C23×C10911yescharacteristic
414C4⋊C8C23×C10911yescharacteristic
415C4⋊C8C23×C10911yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434#97D4×C10911yescharacteristic
435#97D4×C10911yescharacteristic
436C4×C8C23×C10911yescharacteristic
437C4×C8C23×C10911yescharacteristic
438#41—42no—
439#41—42no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×D4×C10911yescharacteristic
450C2×D4C2×D4×C10911yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4C2×D4×C10911yescharacteristic
454C22×C4C2×D4×C10911yescharacteristic
455C22×C4#41×C10911yescharacteristic
456Q16—42no—
457Q16—42no—
458SD16—81no—
459SD16—81no—
460M16—22no—
461M16—41no—
462M16—42no—
463M16—42no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8C2×D4×C10911yescharacteristic
475C2×C8C2×D4×C10911yescharacteristic
476C2×C8C2×D4×C10911yescharacteristic
477C2×C8C2×D4×C10911yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C10911yescharacteristic
492C4⋊C4C2×D4×C10911yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—41no—
500C42—41no—
501C42C2×D4×C10911yescharacteristic
502C42C2×D4×C10911yescharacteristic
503C42#41×C10911yescharacteristic
504C42C24×C10911yescharacteristic
505C23—21no—
506C23—21no—
507C23#121×C10911yescharacteristic
508Q8—42no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—81no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—81no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4#121×C10911yescharacteristic
540C2×C4#121×C10911yescharacteristic
541C2×C4#121×C10911yescharacteristic
542C2×C4C22×D4×C10911yescharacteristic
543C2×C4C22×D4×C10911yescharacteristic
544C2×C4C2×#41×C10911yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8AGL(1,ℤ/8)×C10912yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22C2×#121×C10911yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×AGL(1,ℤ/8)×C10911yescharacteristic
576C4#575×C10911yescharacteristic
577C4#577×C10911yescharacteristic
578C4#578×C10911yescharacteristic
579C2—41no—
580C2—81no—
581C2—81no—
582C2C109×#303611yescharacteristic
583C2C109×#306311yescharacteristic
584C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radical#532×C109C22
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
3. C109×#3185C2semidirect
5. C109×#1703C2semidirect
6. C109×#1699C2semidirect
7. C109×#1691C2semidirect
8. C109×#1689C2semidirect
9. C109×#1683C2semidirect
10. C109×#1679C2semidirect
11. C109×#1671C2semidirect
12. C109×#1669C2semidirect
13. C109×#1569C2semidirect
14. C109×#1552C2semidirect
15. C109×#1550C2semidirect
286. #19371C109direct (N × H)
295. #3185C2×C109semidirect
297. #1703C2×C109semidirect
298. #1699C2×C109semidirect
299. #1691C2×C109semidirect
300. #1689C2×C109semidirect
301. #1683C2×C109semidirect
302. #1679C2×C109semidirect
303. #1671C2×C109semidirect
304. #1669C2×C109semidirect
305. #1569C2×C109semidirect
306. #1552C2×C109semidirect
307. #1550C2×C109semidirect
308. C109#19371direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#32542
C109×#32352
C109×#31852
C109×#29352
C109×#17032
C109×#16992
C109×#16912
C109×#16892
C109×#16832
C109×#16792
C109×#16712
C109×#16692
C109×#15692
C109×#15522
C109×#15502
#19371109