Finite Group Databasebeta

← C109×#19378 #42137372

Subgroups — C109×#19378 #42137372

Order 27904.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3252C211yesmaximal, characteristic
2C109×#3218C211yesmaximal, characteristic
3C109×#3165C211yesmaximal, characteristic, complemented
4C109×#2969C211yesmaximal, characteristic
5C109×#1694C211yesmaximal, characteristic, complemented
6C109×#1693C211yesmaximal, characteristic, complemented
7C109×#1692C211yesmaximal, characteristic, complemented
8C109×#1691C211yesmaximal, characteristic, complemented
9C109×#1674C211yesmaximal, characteristic, complemented
10C109×#1673C211yesmaximal, characteristic, complemented
11C109×#1672C211yesmaximal, characteristic, complemented
12C109×#1671C211yesmaximal, characteristic, complemented
13C109×#1569C211yesmaximal, characteristic, complemented
14C109×#1554C211yesmaximal, characteristic, complemented
15C109×#1546C211yesmaximal, characteristic, complemented
16#533×C109C2211yescharacteristic
17C2×C4⋊Q8×C109C2211yescharacteristic
18#529×C109C2211yescharacteristic
19#501×C109—21no—
20#501×C109—21no—
21#500×C109C2211yescharacteristic
22#500×C109C2211yescharacteristic
23#498×C109C2211yescharacteristic
24#498×C109C2211yescharacteristic
25#497×C109—21no—
26#491×C109—21no—
27#479×C109—21no—
28#477×C109C2211yescharacteristic
29#476×C109C2211yescharacteristic
30#470×C109—21no—
31#468×C109—21no—
32#464×C109—21no—
33#462×C109C2211yescharacteristic
34#462×C109C2211yescharacteristic
35#462×C109C2211yescharacteristic
36#461×C109C2211yescharacteristic
37#461×C109C2211yescharacteristic
38#461×C109C2211yescharacteristic
39#451×C109—21no—
40#448×C109—21no—
41#446×C109C2211yescharacteristic
42C8×Q8×C109C2211yescharacteristic
43#436×C109—21no—
44#436×C109C2211yescharacteristic
45#435×C109—21no—
46C8×D4×C109C2211yescharacteristic
47#433×C109—21no—
48#432×C109C2211yescharacteristic
49#431×C109C2211yescharacteristic
50#428×C109—21no—
51#428×C109—21no—
52#423×C109C2211yescharacteristic
53#405×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
67C22×Q8×C109—21no—
68C2×Q16×C109—21no—
69C2×Q16×C109—21no—
70C2×Q16×C109—21no—
71C2×SD16×C109—21no—
72C2×SD16×C109—21no—
73C2×SD16×C109—21no—
74C2×M16×C109—21no—
75C2×M16×C109—21no—
76C2×M16×C109D411yescharacteristic
77C2×M16×C109D411yescharacteristic
78C22×C8×C109—21no—
79C4⋊Q8×C109—21no—
80C4⋊Q8×C109—21no—
81C4⋊Q8×C109—21no—
82C4⋊Q8×C109C2311yescharacteristic
83C4⋊Q8×C109C2311yescharacteristic
84C4⋊Q8×C109C2311yescharacteristic
85C4⋊Q8×C109C2311yescharacteristic
86#126×C109—21no—
87#125×C109—21no—
88#125×C109D411yescharacteristic
89#124×C109D411yescharacteristic
90#123×C109—21no—
91C22⋊Q8×C109—21no—
92C22⋊Q8×C109—21no—
93C22⋊Q8×C109D411yescharacteristic
94#121×C109D411yescharacteristic
95C4×Q8×C109—21no—
96C4×Q8×C109—21no—
97C4×Q8×C109C2311yescharacteristic
98C4×D4×C109—21no—
99C4×D4×C109C2311yescharacteristic
100#117×C109—21no—
101#117×C109—21no—
102C2×C4⋊C4×C109—21no—
103C2×C4⋊C4×C109—21no—
104C2×C42×C109C2311yescharacteristic
105#107×C109—21no—
106#107×C109—21no—
107#107×C109—21no—
108#107×C109—21no—
109#107×C109—21no—
110#106×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×C109—21no—
118C4⋊C8×C109C2311yescharacteristic
119C4⋊C8×C109C2311yescharacteristic
120C4⋊C8×C109C2311yescharacteristic
121C4⋊C8×C109C2311yescharacteristic
122C4⋊C8×C109C2311yescharacteristic
123C4⋊C8×C109C2311yescharacteristic
124#103×C109—21no—
125#103×C109—21no—
126#103×C109—21no—
127#103×C109—21no—
128#103×C109—21no—
129#103×C109—21no—
130#103×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×C109D411yescharacteristic
139#97×C109D411yescharacteristic
140C4×C8×C109—21no—
141C4×C8×C109—21no—
142C4×C8×C109C2311yescharacteristic
143C4×C8×C109C2311yescharacteristic
144C2×Q8×C109—21no—
145C2×Q8×C109—21no—
146C2×Q8×C109—21no—
147C2×Q8×C109—21no—
148C2×Q8×C109—41no—
149C2×Q8×C109—81no—
150C2×Q8×C109—81no—
151C2×Q8×C109C2×D411yescharacteristic
152C2×D4×C109—21no—
153C2×D4×C109C2×D411yescharacteristic
154C22×C4×C109—21no—
155C22×C4×C109—41no—
156C22×C4×C109C2×D411yescharacteristic
157C22×C4×C109C2×D411yescharacteristic
158C22×C4×C109#4111yescharacteristic
159Q16×C109—81no—
160Q16×C109—81no—
161Q16×C109—81no—
162SD16×C109—81no—
163SD16×C109—81no—
164SD16×C109—81no—
165M16×C109—22no—
166M16×C109—22no—
167M16×C109—42no—
168M16×C109—81no—
169C2×C8×C109—21no—
170C2×C8×C109—21no—
171C2×C8×C109—21no—
172C2×C8×C109—21no—
173C2×C8×C109—21no—
174C2×C8×C109—21no—
175C2×C8×C109—42no—
176C2×C8×C109C2×D411yescharacteristic
177C2×C8×C109C2×D411yescharacteristic
178C2×C8×C109C2×D411yescharacteristic
179C2×C8×C109C2×D411yescharacteristic
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—21no—
189C4⋊C4×C109—21no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—41no—
193C4⋊C4×C109—41no—
194C4⋊C4×C109—41no—
195C4⋊C4×C109—41no—
196C4⋊C4×C109C2×D411yescharacteristic
197C4⋊C4×C109C2×D411yescharacteristic
198C22⋊C4×C109—21no—
199C22⋊C4×C109—21no—
200C22⋊C4×C109—21no—
201C22⋊C4×C109—21no—
202C22⋊C4×C109—21no—
203C22⋊C4×C109—41no—
204C42×C109—21no—
205C42×C109—41no—
206C42×C109C2×D411yescharacteristic
207C42×C109C2×D411yescharacteristic
208C42×C109#4111yescharacteristic
209C42×C109C2411yescharacteristic
210C23×C109—21no—
211C23×C109#12111yescharacteristic
212Q8×C109—21no—
213Q8×C109—21no—
214Q8×C109—41no—
215Q8×C109—41no—
216Q8×C109—41no—
217Q8×C109—41no—
218Q8×C109—41no—
219Q8×C109—41no—
220Q8×C109—81no—
221Q8×C109—82no—
222D4×C109—21no—
223D4×C109—21no—
224D4×C109—81no—
225C2×C4×C109—21no—
226C2×C4×C109—21no—
227C2×C4×C109—21no—
228C2×C4×C109—21no—
229C2×C4×C109—21no—
230C2×C4×C109—21no—
231C2×C4×C109—21no—
232C2×C4×C109—41no—
233C2×C4×C109—41no—
234C2×C4×C109—41no—
235C2×C4×C109—41no—
236C2×C4×C109—41no—
237C2×C4×C109—41no—
238C2×C4×C109—41no—
239C2×C4×C109—82no—
240C2×C4×C109#12111yescharacteristic
241C2×C4×C109#12111yescharacteristic
242C2×C4×C109#12111yescharacteristic
243C2×C4×C109C22×D411yescharacteristic
244C2×C4×C109C22×D411yescharacteristic
245C2×C4×C109C2×#4111yescharacteristic
246C8×C109—21no—
247C8×C109—21no—
248C8×C109—41no—
249C8×C109—41no—
250C8×C109—41no—
251C8×C109—41no—
252C8×C109—41no—
253C8×C109—41no—
254C8×C109#13712yes—
255C8×C109#13712yes—
256C22×C109—21no—
257C22×C109—21no—
258C22×C109—21no—
259C22×C109—41no—
260C22×C109—41no—
261C22×C109—41no—
262C22×C109C2×#12111yescharacteristic
263C4×C109—21no—
264C4×C109—21no—
265C4×C109—21no—
266C4×C109—21no—
267C4×C109—41no—
268C4×C109—41no—
269C4×C109—41no—
270C4×C109—81no—
271C4×C109—81no—
272C4×C109—81no—
273C4×C109—81no—
274C4×C109C2×#13711yescharacteristic
275C4×C109C2×#13711yescharacteristic
276C4×C109#57611yescharacteristic
277C4×C109#57711yescharacteristic
278#19378C10911yesmaximal, characteristic, direct product factor, Sylow
279C2×C109—41no—
280C2×C109—81no—
281C2×C109#303911yescharacteristic
282C2×C109#306211yescharacteristic
283C2×C109#306911yescharacteristic
284#3252C2×C10911yescharacteristic
285#3218C2×C10911yescharacteristic
286#3165C2×C10911yescharacteristic, complemented
287#2969C2×C10911yescharacteristic
288#1694C2×C10911yescharacteristic, complemented
289#1693C2×C10911yescharacteristic, complemented
290#1692C2×C10911yescharacteristic, complemented
291#1691C2×C10911yescharacteristic, complemented
292#1674C2×C10911yescharacteristic, complemented
293#1673C2×C10911yescharacteristic, complemented
294#1672C2×C10911yescharacteristic, complemented
295#1671C2×C10911yescharacteristic, complemented
296#1569C2×C10911yescharacteristic, complemented
297#1554C2×C10911yescharacteristic, complemented
298#1546C2×C10911yescharacteristic, complemented
299C109#1937811yescharacteristic, direct product factor, Sylow
300#533C22×C10911yescharacteristic
301C2×C4⋊Q8C22×C10911yescharacteristic
302#529C22×C10911yescharacteristic
303#501—21no—
304#501—21no—
305#500C22×C10911yescharacteristic
306#500C22×C10911yescharacteristic
307#498C22×C10911yescharacteristic
308#498C22×C10911yescharacteristic
309#497—21no—
310#491—21no—
311#479—21no—
312#477C22×C10911yescharacteristic
313#476C22×C10911yescharacteristic
314#470—21no—
315#468—21no—
316#464—21no—
317#462C22×C10911yescharacteristic
318#462C22×C10911yescharacteristic
319#462C22×C10911yescharacteristic
320#461C22×C10911yescharacteristic
321#461C22×C10911yescharacteristic
322#461C22×C10911yescharacteristic
323#451—21no—
324#448—21no—
325#446C22×C10911yescharacteristic
326C8×Q8C22×C10911yescharacteristic
327#436—21no—
328#436C22×C10911yescharacteristic
329#435—21no—
330C8×D4C22×C10911yescharacteristic
331#433—21no—
332#432C22×C10911yescharacteristic
333#431C22×C10911yescharacteristic
334#428—21no—
335#428—21no—
336#423C22×C10911yescharacteristic
337#405—21no—
338C4×M16C22×C10911yescharacteristic
339#335C22×C10911yescharacteristic
340#335C22×C10911yescharacteristic
341#334C22×C10911yescharacteristic
342#334C22×C10911yescharacteristic
343#333C22×C10911yescharacteristic
344#333C22×C10911yescharacteristic
345#332C22×C10911yescharacteristic
346#332C22×C10911yescharacteristic
347#332C22×C10911yescharacteristic
348#332C22×C10911yescharacteristic
349#332C22×C10911yescharacteristic
350#332C22×C10911yescharacteristic
351C22×Q8—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16D4×C10911yescharacteristic
361C2×M16D4×C10911yescharacteristic
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C10911yescharacteristic
367C4⋊Q8C23×C10911yescharacteristic
368C4⋊Q8C23×C10911yescharacteristic
369C4⋊Q8C23×C10911yescharacteristic
370#126—21no—
371#125—21no—
372#125D4×C10911yescharacteristic
373#124D4×C10911yescharacteristic
374#123—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8D4×C10911yescharacteristic
378#121D4×C10911yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C10911yescharacteristic
382C4×D4—21no—
383C4×D4C23×C10911yescharacteristic
384#117—21no—
385#117—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C23×C10911yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8C23×C10911yescharacteristic
403C4⋊C8C23×C10911yescharacteristic
404C4⋊C8C23×C10911yescharacteristic
405C4⋊C8C23×C10911yescharacteristic
406C4⋊C8C23×C10911yescharacteristic
407C4⋊C8C23×C10911yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#102—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421#97—21no—
422#97D4×C10911yescharacteristic
423#97D4×C10911yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C10911yescharacteristic
427C4×C8C23×C10911yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×Q8C2×D4×C10911yescharacteristic
436C2×D4—21no—
437C2×D4C2×D4×C10911yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4C2×D4×C10911yescharacteristic
441C22×C4C2×D4×C10911yescharacteristic
442C22×C4#41×C10911yescharacteristic
443Q16—81no—
444Q16—81no—
445Q16—81no—
446SD16—81no—
447SD16—81no—
448SD16—81no—
449M16—22no—
450M16—22no—
451M16—42no—
452M16—81no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8C2×D4×C10911yescharacteristic
461C2×C8C2×D4×C10911yescharacteristic
462C2×C8C2×D4×C10911yescharacteristic
463C2×C8C2×D4×C10911yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C10911yescharacteristic
481C4⋊C4C2×D4×C10911yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C42—21no—
489C42—41no—
490C42C2×D4×C10911yescharacteristic
491C42C2×D4×C10911yescharacteristic
492C42#41×C10911yescharacteristic
493C42C24×C10911yescharacteristic
494C23—21no—
495C23#121×C10911yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—82no—
506D4—21no—
507D4—21no—
508D4—81no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4#121×C10911yescharacteristic
525C2×C4#121×C10911yescharacteristic
526C2×C4#121×C10911yescharacteristic
527C2×C4C22×D4×C10911yescharacteristic
528C2×C4C22×D4×C10911yescharacteristic
529C2×C4C2×#41×C10911yescharacteristic
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8#137×C10912yes—
539C8#137×C10912yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×#121×C10911yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×#137×C10911yescharacteristic
559C4C2×#137×C10911yescharacteristic
560C4#576×C10911yescharacteristic
561C4#577×C10911yescharacteristic
562C2—41no—
563C2—81no—
564C2C109×#303911yescharacteristic
565C2C109×#306211yescharacteristic
566C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radical#121×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
3. C109×#3165C2semidirect
5. C109×#1694C2semidirect
6. C109×#1693C2semidirect
7. C109×#1692C2semidirect
8. C109×#1691C2semidirect
9. C109×#1674C2semidirect
10. C109×#1673C2semidirect
11. C109×#1672C2semidirect
12. C109×#1671C2semidirect
13. C109×#1569C2semidirect
14. C109×#1554C2semidirect
15. C109×#1546C2semidirect
278. #19378C109direct (N × H)
286. #3165C2×C109semidirect
288. #1694C2×C109semidirect
289. #1693C2×C109semidirect
290. #1692C2×C109semidirect
291. #1691C2×C109semidirect
292. #1674C2×C109semidirect
293. #1673C2×C109semidirect
294. #1672C2×C109semidirect
295. #1671C2×C109semidirect
296. #1569C2×C109semidirect
297. #1554C2×C109semidirect
298. #1546C2×C109semidirect
299. C109#19378direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#32522
C109×#32182
C109×#31652
C109×#29692
C109×#16942
C109×#16932
C109×#16922
C109×#16912
C109×#16742
C109×#16732
C109×#16722
C109×#16712
C109×#15692
C109×#15542
C109×#15462
#19378109