Finite Group Databasebeta

← C107×#18195 #41044159

Subgroups — C107×#18195 #41044159

Order 27392.

1454 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3496C211yesmaximal, characteristic
2C2×#448×C107C212yesmaximal, complemented
3C107×#2409C211yesmaximal, characteristic, complemented
4C107×#1604C214yesmaximal, complemented
5C107×#1601C214yesmaximal, complemented
6C107×#1519C212yesmaximal, complemented
7C107×#1459C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C107—21no—
9C23×Q8×C107C2211yescharacteristic, complemented
10C22×SD16×C107—22no—
11#547×C107—22no—
12#546×C107—24no—
13D42×C107—22no—
14#537×C107C2212yes—
15#534×C107—21no—
16#534×C107C2212yes—
17#532×C107—21no—
18C2×C22⋊Q8×C107—21no—
19C2×#121×C107—21no—
20C2×#121×C107C2212yes—
21C2×C4×D4×C107C2211yescharacteristic
22#448×C107—24no—
23#448×C107C2218yescomplemented
24C2×#103×C107—22no—
25C2×C22⋊C8×C107C2212yescomplemented
26#395×C107C2212yescomplemented
27#393×C107C2212yescomplemented
28#391×C107—21no—
29#386×C107—21no—
30#385×C107—21no—
31#380×C107C2211yescharacteristic, complemented
32#327×C107C2218yescomplemented
33#324×C107C2212yescomplemented
34#323×C107C2212yescomplemented
35H(5,𝔽2)×C107—44no—
36H(5,𝔽2)×C107—44no—
37C2×#41×C107—24no—
38C2×#41×C107—22no—
39C22×Q8×C107—21no—
40C22×Q8×C107—22no—
41C22×Q8×C107—22no—
42C22×Q8×C107—44no—
43C22×Q8×C107C2312yes—
44C22×D4×C107—24no—
45C22×D4×C107—22no—
46C22×D4×C107—22no—
47C22×D4×C107—21no—
48C22×D4×C107D411yescharacteristic
49C22×D4×C107D412yes—
50C23×C4×C107—21no—
51C23×C4×C107D411yescharacteristic
52C23×C4×C107C2311yescharacteristic
53C2×SD16×C107—28no—
54C2×SD16×C107—48no—
55C22×C8×C107—22no—
56C4⋊Q8×C107—21no—
57#127×C107—21no—
58#124×C107—22no—
59#123×C107—24no—
60#123×C107—24no—
61C22⋊Q8×C107—24no—
62C22⋊Q8×C107—44no—
63#121×C107—22no—
64#121×C107—22no—
65#121×C107—24no—
66#121×C107—22no—
67#121×C107—22no—
68#121×C107—22no—
69#121×C107—22no—
70#121×C107D414yes—
71#121×C107C2314yes—
72#120×C107—24no—
73#120×C107—24no—
74C4×D4×C107—22no—
75C4×D4×C107—22no—
76C4×D4×C107—22no—
77C4×D4×C107—22no—
78C2×C4⋊C4×C107—21no—
79C2×C4⋊C4×C107—21no—
80C2×C4⋊C4×C107—22no—
81C2×C4⋊C4×C107D412yes—
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C22⋊C4×C107—22no—
84C2×C22⋊C4×C107—22no—
85C2×C22⋊C4×C107—21no—
86C2×C22⋊C4×C107—22no—
87C2×C22⋊C4×C107D411yescharacteristic
88C2×C22⋊C4×C107C2311yescharacteristic
89C2×C42×C107D411yescharacteristic
90#103×C107—28no—
91C22⋊C8×C107—22no—
92C22⋊C8×C107C2314yes—
93#95×C107—22no—
94#95×C107—22no—
95#95×C107C2312yes—
96C24×C107—22no—
97C24×C107—22no—
98C24×C107C2×D411yescharacteristic
99C24×C107C2×D411yescharacteristic
100#41×C107—44no—
101#41×C107—416no—
102#41×C107—44no—
103C2×Q8×C107—22no—
104C2×Q8×C107—24no—
105C2×Q8×C107—28no—
106C2×Q8×C107—24no—
107C2×Q8×C107—44no—
108C2×Q8×C107—42no—
109C2×Q8×C107—44no—
110C2×Q8×C107—48no—
111C2×Q8×C107—41no—
112C2×Q8×C107—41no—
113C2×D4×C107—22no—
114C2×D4×C107—22no—
115C2×D4×C107—24no—
116C2×D4×C107—22no—
117C2×D4×C107—24no—
118C2×D4×C107—24no—
119C2×D4×C107—22no—
120C2×D4×C107—22no—
121C2×D4×C107—22no—
122C2×D4×C107—44no—
123C2×D4×C107—416no—
124C2×D4×C107—44no—
125C2×D4×C107—44no—
126C2×D4×C107—44no—
127C2×D4×C107—44no—
128C2×D4×C107—82no—
129C2×D4×C107SD1614yescomplemented
130C2×D4×C107C2×D414yes—
131C22×C4×C107—22no—
132C22×C4×C107—24no—
133C22×C4×C107—22no—
134C22×C4×C107—22no—
135C22×C4×C107—21no—
136C22×C4×C107—21no—
137C22×C4×C107—22no—
138C22×C4×C107—42no—
139C22×C4×C107—44no—
140C22×C4×C107—42no—
141C22×C4×C107—42no—
142C22×C4×C107C2×D411yescharacteristic
143C22×C4×C107C2×D412yes—
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D412yes—
148C22×C4×C107C2411yescharacteristic
149SD16×C107—416no—
150C2×C8×C107—24no—
151C2×C8×C107—44no—
152C4⋊C4×C107—22no—
153C4⋊C4×C107—22no—
154C4⋊C4×C107—22no—
155C4⋊C4×C107—22no—
156C4⋊C4×C107—42no—
157C4⋊C4×C107—44no—
158C4⋊C4×C107C2×D414yes—
159C22⋊C4×C107—24no—
160C22⋊C4×C107—24no—
161C22⋊C4×C107—22no—
162C22⋊C4×C107—24no—
163C22⋊C4×C107—24no—
164C22⋊C4×C107—22no—
165C22⋊C4×C107—44no—
166C22⋊C4×C107—42no—
167C42×C107—21no—
168C42×C107—21no—
169C23×C107—21no—
170C23×C107—21no—
171C23×C107—24no—
172C23×C107—41no—
173C23×C107—41no—
174C23×C107—41no—
175C23×C107—41no—
176C23×C107—44no—
177C23×C107—44no—
178C23×C107—82no—
179C23×C107—82no—
180C23×C107—82no—
181C23×C107—82no—
182C23×C107#12012yes—
183C23×C107C2×SD1612yes—
184C23×C107C2×SD1612yescomplemented
185C23×C107AGL(1,ℤ/8)12yes—
186C23×C107C22×D411yescharacteristic
187Q8×C107—28no—
188Q8×C107—44no—
189Q8×C107—44no—
190Q8×C107—44no—
191Q8×C107—44no—
192D4×C107—28no—
193D4×C107—44no—
194D4×C107—44no—
195D4×C107—48no—
196D4×C107—44no—
197D4×C107—44no—
198D4×C107—48no—
199D4×C107—44no—
200D4×C107—82no—
201D4×C107—82no—
202C2×C4×C107—21no—
203C2×C4×C107—21no—
204C2×C4×C107—22no—
205C2×C4×C107—24no—
206C2×C4×C107—24no—
207C2×C4×C107—21no—
208C2×C4×C107—21no—
209C2×C4×C107—24no—
210C2×C4×C107—42no—
211C2×C4×C107—41no—
212C2×C4×C107—48no—
213C2×C4×C107—42no—
214C2×C4×C107—44no—
215C2×C4×C107—48no—
216C2×C4×C107—42no—
217C2×C4×C107—44no—
218C2×C4×C107—42no—
219C2×C4×C107—41no—
220C2×C4×C107—41no—
221C2×C4×C107—42no—
222C2×C4×C107—42no—
223C2×C4×C107—42no—
224C2×C4×C107—81no—
225C2×C4×C107#12011yescharacteristic
226C2×C4×C107#12011yescharacteristic
227C2×C4×C107C2×SD1612yescomplemented
228C2×C4×C107C22×D412yes—
229C8×C107—44no—
230C22×C107—21no—
231C22×C107—22no—
232C22×C107—21no—
233C22×C107—22no—
234C22×C107—22no—
235C22×C107—42no—
236C22×C107—42no—
237C22×C107—42no—
238C22×C107—41no—
239C22×C107—41no—
240C22×C107—44no—
241C22×C107—44no—
242C22×C107—44no—
243C22×C107—81no—
244C22×C107—164no—
245C22×C107—164no—
246C22×C107#45014yes—
247C22×C107C2×#12011yescharacteristic
248C22×C107C22×SD1611yescharacteristic
249C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
250C4×C107—22no—
251C4×C107—22no—
252C4×C107—21no—
253C4×C107—44no—
254C4×C107—41no—
255C4×C107—44no—
256C4×C107—41no—
257C4×C107—82no—
258C4×C107B(4,𝔽2)12yes—
259#18195C10711yesmaximal, characteristic, direct product factor, Sylow
260C2×C107—21no—
261C2×C107—21no—
262C2×C107—24no—
263C2×C107—42no—
264C2×C107—84no—
265C2×C107C2×#45011yescharacteristic
266C2×C107#302211yescharacteristic
267C2×C107C2×B(4,𝔽2)11yescharacteristic
268#3496C2×C10711yescharacteristic
269C2×#448C2×C10712yescomplemented
270#2409C2×C10711yescharacteristic, complemented
271#1604C2×C10714yescomplemented
272#1601C2×C10714yescomplemented
273#1519C2×C10712yescomplemented
274#1459C2×C10711yescharacteristic, complemented
275C107#1819511yescharacteristic, direct product factor, Sylow
276C2×H(5,𝔽2)—21no—
277C23×Q8C22×C10711yescharacteristic, complemented
278C22×SD16—22no—
279#547—22no—
280#546—24no—
281D42—22no—
282#537C22×C10712yes—
283#534—21no—
284#534C22×C10712yes—
285#532—21no—
286C2×C22⋊Q8—21no—
287C2×#121—21no—
288C2×#121C22×C10712yes—
289C2×C4×D4C22×C10711yescharacteristic
290#448—24no—
291#448C22×C10718yescomplemented
292C2×#103—22no—
293C2×C22⋊C8C22×C10712yescomplemented
294#395C22×C10712yescomplemented
295#393C22×C10712yescomplemented
296#391—21no—
297#386—21no—
298#385—21no—
299#380C22×C10711yescharacteristic, complemented
300#327C22×C10718yescomplemented
301#324C22×C10712yescomplemented
302#323C22×C10712yescomplemented
303H(5,𝔽2)—44no—
304H(5,𝔽2)—44no—
305C2×#41—24no—
306C2×#41—22no—
307C22×Q8—21no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—44no—
311C22×Q8C23×C10712yes—
312C22×D4—24no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4D4×C10711yescharacteristic
317C22×D4D4×C10712yes—
318C23×C4—21no—
319C23×C4D4×C10711yescharacteristic
320C23×C4C23×C10711yescharacteristic
321C2×SD16—28no—
322C2×SD16—48no—
323C22×C8—22no—
324C4⋊Q8—21no—
325#127—21no—
326#124—22no—
327#123—24no—
328#123—24no—
329C22⋊Q8—24no—
330C22⋊Q8—44no—
331#121—22no—
332#121—22no—
333#121—24no—
334#121—22no—
335#121—22no—
336#121—22no—
337#121—22no—
338#121D4×C10714yes—
339#121C23×C10714yes—
340#120—24no—
341#120—24no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4D4×C10712yes—
350C2×C4⋊C4C23×C10711yescharacteristic
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4D4×C10711yescharacteristic
356C2×C22⋊C4C23×C10711yescharacteristic
357C2×C42D4×C10711yescharacteristic
358#103—28no—
359C22⋊C8—22no—
360C22⋊C8C23×C10714yes—
361#95—22no—
362#95—22no—
363#95C23×C10712yes—
364C24—22no—
365C24—22no—
366C24C2×D4×C10711yescharacteristic
367C24C2×D4×C10711yescharacteristic
368#41—44no—
369#41—416no—
370#41—44no—
371C2×Q8—22no—
372C2×Q8—24no—
373C2×Q8—28no—
374C2×Q8—24no—
375C2×Q8—44no—
376C2×Q8—42no—
377C2×Q8—44no—
378C2×Q8—48no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—44no—
391C2×D4—416no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—82no—
397C2×D4SD16×C10714yescomplemented
398C2×D4C2×D4×C10714yes—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—44no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4C2×D4×C10711yescharacteristic
411C22×C4C2×D4×C10712yes—
412C22×C4C2×D4×C10711yescharacteristic
413C22×C4C2×D4×C10711yescharacteristic
414C22×C4C2×D4×C10711yescharacteristic
415C22×C4C2×D4×C10712yes—
416C22×C4C24×C10711yescharacteristic
417SD16—416no—
418C2×C8—24no—
419C2×C8—44no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—42no—
425C4⋊C4—44no—
426C4⋊C4C2×D4×C10714yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—44no—
434C22⋊C4—42no—
435C42—21no—
436C42—21no—
437C23—21no—
438C23—21no—
439C23—24no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—44no—
445C23—44no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23#120×C10712yes—
451C23C2×SD16×C10712yes—
452C23C2×SD16×C10712yescomplemented
453C23AGL(1,ℤ/8)×C10712yes—
454C23C22×D4×C10711yescharacteristic
455Q8—28no—
456Q8—44no—
457Q8—44no—
458Q8—44no—
459Q8—44no—
460D4—28no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—48no—
465D4—44no—
466D4—44no—
467D4—44no—
468D4—82no—
469D4—82no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—48no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—48no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—81no—
493C2×C4#120×C10711yescharacteristic
494C2×C4#120×C10711yescharacteristic
495C2×C4C2×SD16×C10712yescomplemented
496C2×C4C22×D4×C10712yes—
497C8—44no—
498C22—21no—
499C22—22no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—44no—
509C22—44no—
510C22—44no—
511C22—81no—
512C22—164no—
513C22—164no—
514C22#450×C10714yes—
515C22C2×#120×C10711yescharacteristic
516C22C22×SD16×C10711yescharacteristic
517C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
518C4—22no—
519C4—22no—
520C4—21no—
521C4—44no—
522C4—41no—
523C4—44no—
524C4—41no—
525C4—82no—
526C4B(4,𝔽2)×C10712yes—
527C2—21no—
528C2—21no—
529C2—24no—
530C2—42no—
531C2—84no—
532C2C2×#450×C10711yescharacteristic
533C2C107×#302211yescharacteristic
534C2C2×B(4,𝔽2)×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3496C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#448×C107C2semidirect
3. C107×#2409C2semidirect
4. C107×#1604C2semidirect
5. C107×#1601C2semidirect
6. C107×#1519C2semidirect
7. C107×#1459C2semidirect
9. C23×Q8×C107C22semidirect
23. #448×C107C22semidirect
25. C2×C22⋊C8×C107C22semidirect
26. #395×C107C22semidirect
27. #393×C107C22semidirect
31. #380×C107C22semidirect
32. #327×C107C22semidirect
33. #324×C107C22semidirect
34. #323×C107C22semidirect
129. C2×D4×C107SD16semidirect
184. C23×C107C2×SD16semidirect
227. C2×C4×C107C2×SD16semidirect
259. #18195C107direct (N × H)
269. C2×#448C2×C107semidirect
270. #2409C2×C107semidirect
271. #1604C2×C107semidirect
272. #1601C2×C107semidirect
273. #1519C2×C107semidirect
274. #1459C2×C107semidirect
275. C107#18195direct (N × H)
277. C23×Q8C22×C107semidirect
291. #448C22×C107semidirect
293. C2×C22⋊C8C22×C107semidirect
294. #395C22×C107semidirect
295. #393C22×C107semidirect
299. #380C22×C107semidirect
300. #327C22×C107semidirect
301. #324C22×C107semidirect
302. #323C22×C107semidirect
397. C2×D4SD16×C107semidirect
452. C23C2×SD16×C107semidirect
495. C2×C4C2×SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34962
C2×#448×C1072
C107×#24092
C107×#16042
C107×#16012
C107×#15192
C107×#14592
#18195107