Finite Group Databasebeta

← C107×#18172 #41044136

Subgroups — C107×#18172 #41044136

Order 27392.

998 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3492C211yesmaximal, characteristic
2C107×#3092C212yesmaximal, complemented
3C2×#400×C107C211yesmaximal, characteristic, complemented
4C107×#1617C212yesmaximal, complemented
5C107×#1616C212yesmaximal, complemented
6C107×#1615C214yesmaximal, complemented
7C107×#1504C212yesmaximal, complemented
8C107×#1463C211yesmaximal, characteristic, complemented
9#554×C107—22no—
10#553×C107—22no—
11#552×C107—22no—
12#547×C107—22no—
13#544×C107C2211yescharacteristic
14#539×C107—21no—
15#539×C107C2212yes—
16#537×C107C2211yescharacteristic
17#525×C107—21no—
18#525×C107—21no—
19#525×C107C2212yes—
20#520×C107—21no—
21C22×C4⋊C4×C107C2211yescharacteristic
22C22×C4⋊C4×C107C2211yescharacteristic
23#484×C107C2214yes—
24#483×C107—22no—
25#481×C107C2214yes—
26#480×C107—22no—
27#428×C107—22no—
28#417×C107—22no—
29#407×C107C2212yes—
30#400×C107—21no—
31#400×C107—21no—
32#400×C107C2212yes—
33#400×C107C2212yes—
34C2×#95×C107—21no—
35C2×#95×C107—21no—
36C2×#95×C107C2211yescharacteristic
37#328×C107C2214yes—
38#327×C107C2214yes—
39#324×C107C2212yes—
40#324×C107C2212yes—
41C2×#41×C107—21no—
42C2×#41×C107—21no—
43C2×#41×C107D412yes—
44C23×C4×C107—21no—
45C23×C4×C107—21no—
46C23×C4×C107D411yescharacteristic
47C23×C4×C107D411yescharacteristic
48C23×C4×C107C2311yescharacteristic
49C2×M16×C107—22no—
50C4⋊Q8×C107—22no—
51#126×C107—22no—
52#126×C107—22no—
53#125×C107—22no—
54#125×C107—22no—
55#125×C107—22no—
56#123×C107—22no—
57#123×C107—22no—
58#123×C107—22no—
59#123×C107—22no—
60#123×C107—22no—
61C22⋊Q8×C107—21no—
62C22⋊Q8×C107—21no—
63C22⋊Q8×C107—21no—
64C22⋊Q8×C107—22no—
65C22⋊Q8×C107—22no—
66C22⋊Q8×C107—21no—
67C22⋊Q8×C107—22no—
68C22⋊Q8×C107D412yes—
69C22⋊Q8×C107C2312yes—
70#121×C107—21no—
71#121×C107—21no—
72#121×C107—21no—
73#121×C107—22no—
74#121×C107—21no—
75#121×C107D412yes—
76#121×C107C2312yes—
77#120×C107—22no—
78C4×Q8×C107—22no—
79C4×D4×C107—22no—
80C4×D4×C107—22no—
81C4×D4×C107—22no—
82C4×D4×C107—22no—
83C4×D4×C107—22no—
84C4×D4×C107—22no—
85C4×D4×C107—22no—
86#117×C107—22no—
87#117×C107—21no—
88#117×C107—21no—
89#117×C107D412yes—
90C2×C4⋊C4×C107—22no—
91C2×C4⋊C4×C107—22no—
92C2×C4⋊C4×C107—22no—
93C2×C4⋊C4×C107—22no—
94C2×C4⋊C4×C107—22no—
95C2×C4⋊C4×C107—21no—
96C2×C4⋊C4×C107D411yescharacteristic
97C2×C4⋊C4×C107D411yescharacteristic
98C2×C4⋊C4×C107C2312yes—
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101#107×C107—24no—
102#106×C107—24no—
103#103×C107—24no—
104#102×C107—24no—
105C22⋊C8×C107—22no—
106C22⋊C8×C107C2314yes—
107#95×C107—22no—
108#95×C107—22no—
109#95×C107—22no—
110#95×C107—22no—
111#95×C107—21no—
112#95×C107C2312yes—
113C24×C107C2×D411yescharacteristic
114#41×C107—42no—
115#41×C107—44no—
116#41×C107—42no—
117#41×C107—82no—
118C2×Q8×C107—21no—
119C2×Q8×C107—21no—
120C2×Q8×C107C2×D412yes—
121C2×D4×C107—21no—
122C2×D4×C107—22no—
123C2×D4×C107—22no—
124C2×D4×C107—22no—
125C2×D4×C107—21no—
126C2×D4×C107C2×D412yes—
127C22×C4×C107—22no—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—21no—
131C22×C4×C107—22no—
132C22×C4×C107—21no—
133C22×C4×C107—22no—
134C22×C4×C107—22no—
135C22×C4×C107—22no—
136C22×C4×C107—22no—
137C22×C4×C107—41no—
138C22×C4×C107—42no—
139C22×C4×C107—42no—
140C22×C4×C107—42no—
141C22×C4×C107—42no—
142C22×C4×C107—44no—
143C22×C4×C107—42no—
144C22×C4×C107—41no—
145C22×C4×C107—41no—
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D412yes—
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D412yes—
153C22×C4×C107C2411yescharacteristic
154M16×C107—44no—
155C2×C8×C107—24no—
156C4⋊C4×C107—21no—
157C4⋊C4×C107—22no—
158C4⋊C4×C107—21no—
159C4⋊C4×C107—21no—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—22no—
162C4⋊C4×C107—22no—
163C4⋊C4×C107—22no—
164C4⋊C4×C107—22no—
165C4⋊C4×C107—22no—
166C4⋊C4×C107—22no—
167C4⋊C4×C107—22no—
168C4⋊C4×C107—22no—
169C4⋊C4×C107—22no—
170C4⋊C4×C107—24no—
171C4⋊C4×C107—42no—
172C4⋊C4×C107C2×D412yes—
173C4⋊C4×C107C2×D412yes—
174C22⋊C4×C107—22no—
175C22⋊C4×C107—22no—
176C22⋊C4×C107—22no—
177C22⋊C4×C107—22no—
178C22⋊C4×C107—22no—
179C22⋊C4×C107—22no—
180C22⋊C4×C107—22no—
181C22⋊C4×C107—22no—
182C22⋊C4×C107—22no—
183C42×C107—22no—
184C42×C107—22no—
185C42×C107—22no—
186C23×C107—21no—
187C23×C107—21no—
188C23×C107—22no—
189C23×C107—22no—
190C23×C107—22no—
191C23×C107#12011yescharacteristic
192C23×C107#12011yescharacteristic
193C23×C107C22×D411yescharacteristic
194Q8×C107—42no—
195Q8×C107—42no—
196Q8×C107—81no—
197D4×C107—42no—
198D4×C107—42no—
199D4×C107—42no—
200D4×C107—42no—
201D4×C107—44no—
202D4×C107—44no—
203D4×C107—81no—
204C2×C4×C107—21no—
205C2×C4×C107—21no—
206C2×C4×C107—24no—
207C2×C4×C107—22no—
208C2×C4×C107—22no—
209C2×C4×C107—21no—
210C2×C4×C107—22no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—42no—
216C2×C4×C107—41no—
217C2×C4×C107—41no—
218C2×C4×C107—42no—
219C2×C4×C107—42no—
220C2×C4×C107—44no—
221C2×C4×C107—42no—
222C2×C4×C107—41no—
223C2×C4×C107—41no—
224C2×C4×C107—42no—
225C2×C4×C107—42no—
226C2×C4×C107—44no—
227C2×C4×C107—42no—
228C2×C4×C107—42no—
229C2×C4×C107—82no—
230C2×C4×C107—81no—
231C2×C4×C107—82no—
232C2×C4×C107—84no—
233C2×C4×C107—82no—
234C2×C4×C107—82no—
235C2×C4×C107#12012yes—
236C2×C4×C107#13712yes—
237C2×C4×C107C22×D412yes—
238C8×C107—44no—
239C22×C107—24no—
240C22×C107—24no—
241C22×C107—21no—
242C22×C107—21no—
243C22×C107—21no—
244C22×C107—21no—
245C22×C107—21no—
246C22×C107—21no—
247C22×C107—42no—
248C22×C107—42no—
249C22×C107—42no—
250C22×C107#45412yes—
251C22×C107#45812yes—
252C22×C107C2×#12011yescharacteristic
253C22×C107C2×#13711yescharacteristic
254C22×C107#57511yescharacteristic
255C4×C107—22no—
256C4×C107—22no—
257C4×C107—22no—
258C4×C107—41no—
259C4×C107—42no—
260C4×C107—42no—
261C4×C107—41no—
262C4×C107—41no—
263C4×C107—42no—
264C4×C107—82no—
265C4×C107—82no—
266#18172C10711yesmaximal, characteristic, direct product factor, Sylow
267C2×C107—21no—
268C2×C107—21no—
269C2×C107—22no—
270C2×C107—22no—
271C2×C107—82no—
272C2×C107#300711yescharacteristic
273C2×C107C2×#45411yescharacteristic
274C2×C107C2×#45811yescharacteristic
275#3492C2×C10711yescharacteristic
276#3092C2×C10712yescomplemented
277C2×#400C2×C10711yescharacteristic, complemented
278#1617C2×C10712yescomplemented
279#1616C2×C10712yescomplemented
280#1615C2×C10714yescomplemented
281#1504C2×C10712yescomplemented
282#1463C2×C10711yescharacteristic, complemented
283C107#1817211yescharacteristic, direct product factor, Sylow
284#554—22no—
285#553—22no—
286#552—22no—
287#547—22no—
288#544C22×C10711yescharacteristic
289#539—21no—
290#539C22×C10712yes—
291#537C22×C10711yescharacteristic
292#525—21no—
293#525—21no—
294#525C22×C10712yes—
295#520—21no—
296C22×C4⋊C4C22×C10711yescharacteristic
297C22×C4⋊C4C22×C10711yescharacteristic
298#484C22×C10714yes—
299#483—22no—
300#481C22×C10714yes—
301#480—22no—
302#428—22no—
303#417—22no—
304#407C22×C10712yes—
305#400—21no—
306#400—21no—
307#400C22×C10712yes—
308#400C22×C10712yes—
309C2×#95—21no—
310C2×#95—21no—
311C2×#95C22×C10711yescharacteristic
312#328C22×C10714yes—
313#327C22×C10714yes—
314#324C22×C10712yes—
315#324C22×C10712yes—
316C2×#41—21no—
317C2×#41—21no—
318C2×#41D4×C10712yes—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4D4×C10711yescharacteristic
322C23×C4D4×C10711yescharacteristic
323C23×C4C23×C10711yescharacteristic
324C2×M16—22no—
325C4⋊Q8—22no—
326#126—22no—
327#126—22no—
328#125—22no—
329#125—22no—
330#125—22no—
331#123—22no—
332#123—22no—
333#123—22no—
334#123—22no—
335#123—22no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—21no—
342C22⋊Q8—22no—
343C22⋊Q8D4×C10712yes—
344C22⋊Q8C23×C10712yes—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—22no—
349#121—21no—
350#121D4×C10712yes—
351#121C23×C10712yes—
352#120—22no—
353C4×Q8—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361#117—22no—
362#117—21no—
363#117—21no—
364#117D4×C10712yes—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C10711yescharacteristic
372C2×C4⋊C4D4×C10711yescharacteristic
373C2×C4⋊C4C23×C10712yes—
374C2×C4⋊C4C23×C10711yescharacteristic
375C2×C4⋊C4C23×C10711yescharacteristic
376#107—24no—
377#106—24no—
378#103—24no—
379#102—24no—
380C22⋊C8—22no—
381C22⋊C8C23×C10714yes—
382#95—22no—
383#95—22no—
384#95—22no—
385#95—22no—
386#95—21no—
387#95C23×C10712yes—
388C24C2×D4×C10711yescharacteristic
389#41—42no—
390#41—44no—
391#41—42no—
392#41—82no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8C2×D4×C10712yes—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4C2×D4×C10712yes—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—41no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—44no—
418C22×C4—42no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4C2×D4×C10711yescharacteristic
422C22×C4C2×D4×C10712yes—
423C22×C4C2×D4×C10711yescharacteristic
424C22×C4C2×D4×C10711yescharacteristic
425C22×C4C2×D4×C10711yescharacteristic
426C22×C4C2×D4×C10711yescharacteristic
427C22×C4C2×D4×C10712yes—
428C22×C4C24×C10711yescharacteristic
429M16—44no—
430C2×C8—24no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—42no—
447C4⋊C4C2×D4×C10712yes—
448C4⋊C4C2×D4×C10712yes—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C42—22no—
459C42—22no—
460C42—22no—
461C23—22no—
462C23—22no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23#120×C10711yescharacteristic
467C23#120×C10711yescharacteristic
468C23C22×D4×C10711yescharacteristic
469Q8—42no—
470Q8—42no—
471Q8—81no—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478D4—81no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—82no—
505C2×C4—81no—
506C2×C4—82no—
507C2×C4—84no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4#120×C10712yes—
511C2×C4#137×C10712yes—
512C2×C4C22×D4×C10712yes—
513C8—44no—
514C22—24no—
515C22—24no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22#454×C10712yes—
526C22#458×C10712yes—
527C22C2×#120×C10711yescharacteristic
528C22C2×#137×C10711yescharacteristic
529C22#575×C10711yescharacteristic
530C4—22no—
531C4—22no—
532C4—22no—
533C4—41no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—82no—
540C4—82no—
541C2—21no—
542C2—22no—
543C2—22no—
544C2—21no—
545C2—82no—
546C2C107×#300711yescharacteristic
547C2C2×#454×C10711yescharacteristic
548C2C2×#458×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3492C2
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. C107×#3092C2semidirect
3. C2×#400×C107C2semidirect
4. C107×#1617C2semidirect
5. C107×#1616C2semidirect
6. C107×#1615C2semidirect
7. C107×#1504C2semidirect
8. C107×#1463C2semidirect
266. #18172C107direct (N × H)
276. #3092C2×C107semidirect
277. C2×#400C2×C107semidirect
278. #1617C2×C107semidirect
279. #1616C2×C107semidirect
280. #1615C2×C107semidirect
281. #1504C2×C107semidirect
282. #1463C2×C107semidirect
283. C107#18172direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#34922
C107×#30922
C2×#400×C1072
C107×#16172
C107×#16162
C107×#16152
C107×#15042
C107×#14632
#18172107