Finite Group Databasebeta

← C107×#18183 #41044147

Subgroups — C107×#18183 #41044147

Order 27392.

926 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3507C211yesmaximal, characteristic
2C107×#3113C211yesmaximal, characteristic, complemented
3C107×#3112C211yesmaximal, characteristic
4C107×#2399C211yesmaximal, characteristic, complemented
5C107×#1609C214yesmaximal, complemented
6C107×#1603C214yesmaximal, complemented
7C107×#1506C211yesmaximal, characteristic, complemented
8C107×#1505C211yesmaximal, characteristic
9C107×#1467C211yesmaximal, characteristic, complemented
10#559×C107—21no—
11#557×C107—21no—
12#556×C107—21no—
13#556×C107—22no—
14#554×C107—21no—
15#552×C107—22no—
16#539×C107C2214yes—
17#536×C107—21no—
18#533×C107C2211yescharacteristic
19#532×C107C2211yescharacteristic
20#529×C107—22no—
21#520×C107—21no—
22C2×C4×Q8×C107C2211yescharacteristic
23C2×C4×Q8×C107C2211yescharacteristic
24#483×C107C2212yes—
25#480×C107C2212yes—
26#477×C107—21no—
27#475×C107—21no—
28#462×C107—21no—
29#460×C107—21no—
30#451×C107C2212yes—
31#448×C107C2212yes—
32#441×C107—22no—
33#440×C107—22no—
34#432×C107C2211yescharacteristic
35#432×C107C2211yescharacteristic
36#398×C107—21no—
37#398×C107C2212yes—
38#395×C107—21no—
39#395×C107C2212yes—
40C4×C4⋊C4×C107—22no—
41#376×C107C2211yescharacteristic
42#328×C107C2214yes—
43#327×C107C2214yes—
44#324×C107C2214yes—
45C2×#41×C107—21no—
46C22×Q8×C107D411yescharacteristic
47C22×Q8×C107C2311yescharacteristic
48C2×Q16×C107—22no—
49C2×SD16×C107—22no—
50C4⋊Q8×C107—22no—
51C4⋊Q8×C107D411yescharacteristic
52C4⋊Q8×C107D411yescharacteristic
53C4⋊Q8×C107D411yescharacteristic
54#127×C107D411yescharacteristic
55#126×C107—24no—
56#126×C107—24no—
57#125×C107—22no—
58#125×C107—24no—
59#125×C107—21no—
60#124×C107—22no—
61#124×C107—22no—
62#124×C107—21no—
63#123×C107—24no—
64#123×C107—24no—
65C22⋊Q8×C107—22no—
66C22⋊Q8×C107—22no—
67C22⋊Q8×C107—24no—
68C22⋊Q8×C107—21no—
69C22⋊Q8×C107C2312yes—
70#121×C107—21no—
71#121×C107C2312yes—
72C4×Q8×C107—22no—
73C4×Q8×C107—22no—
74C4×Q8×C107—21no—
75C4×Q8×C107—21no—
76C4×Q8×C107—21no—
77C4×Q8×C107—21no—
78C4×Q8×C107—21no—
79C4×Q8×C107—21no—
80C4×Q8×C107—21no—
81C4×Q8×C107—21no—
82C4×Q8×C107—21no—
83C4×Q8×C107D412yes—
84C4×D4×C107—22no—
85C4×D4×C107—22no—
86C4×D4×C107—24no—
87C4×D4×C107—21no—
88C4×D4×C107D412yes—
89#117×C107—22no—
90#117×C107—24no—
91#117×C107—21no—
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×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2312yes—
99C2×C42×C107—21no—
100C2×C42×C107—21no—
101C2×C42×C107D412yes—
102C2×C42×C107C2311yescharacteristic
103#107×C107—22no—
104#106×C107—22no—
105C4⋊C8×C107—21no—
106C4⋊C8×C107—21no—
107#103×C107—22no—
108#103×C107—22no—
109#103×C107—22no—
110#102×C107—22no—
111C22⋊C8×C107C2312yes—
112C22⋊C8×C107C2312yes—
113#97×C107—21no—
114#97×C107—21no—
115#95×C107—21no—
116#95×C107—22no—
117#95×C107—22no—
118#95×C107C2312yes—
119#41×C107—44no—
120C2×Q8×C107—21no—
121C2×Q8×C107—21no—
122C2×Q8×C107—21no—
123C2×Q8×C107—21no—
124C2×Q8×C107—21no—
125C2×Q8×C107—21no—
126C2×Q8×C107—42no—
127C2×Q8×C107—42no—
128C2×Q8×C107C2×D412yes—
129C2×D4×C107—22no—
130C2×D4×C107—21no—
131C2×D4×C107—21no—
132C2×D4×C107C2×D412yes—
133C22×C4×C107—22no—
134C22×C4×C107—21no—
135C22×C4×C107—24no—
136C22×C4×C107—22no—
137C22×C4×C107—21no—
138C22×C4×C107C2×D412yes—
139C22×C4×C107C2×D411yescharacteristic
140C22×C4×C107C2×D411yescharacteristic
141C22×C4×C107C2×D412yes—
142C22×C4×C107C2411yescharacteristic
143Q16×C107—44no—
144SD16×C107—44no—
145C2×C8×C107—22no—
146C2×C8×C107—22no—
147C4⋊C4×C107—24no—
148C4⋊C4×C107—24no—
149C4⋊C4×C107—24no—
150C4⋊C4×C107—21no—
151C4⋊C4×C107—21no—
152C4⋊C4×C107—21no—
153C4⋊C4×C107—21no—
154C4⋊C4×C107—22no—
155C4⋊C4×C107—21no—
156C4⋊C4×C107—21no—
157C4⋊C4×C107—22no—
158C4⋊C4×C107—22no—
159C4⋊C4×C107—22no—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—21no—
162C4⋊C4×C107—44no—
163C4⋊C4×C107—44no—
164C4⋊C4×C107—41no—
165C4⋊C4×C107—41no—
166C4⋊C4×C107C2×D412yes—
167C4⋊C4×C107C2×D412yes—
168C22⋊C4×C107—24no—
169C22⋊C4×C107—24no—
170C22⋊C4×C107—24no—
171C22⋊C4×C107—22no—
172C22⋊C4×C107—22no—
173C22⋊C4×C107—22no—
174C42×C107—24no—
175C42×C107—24no—
176C42×C107—22no—
177C42×C107—22no—
178C42×C107—22no—
179C42×C107—41no—
180C42×C107—41no—
181C42×C107C2×D411yescharacteristic
182C42×C107C2×D411yescharacteristic
183C42×C107C2×D411yescharacteristic
184C42×C107C2×D411yescharacteristic
185C23×C107—22no—
186C23×C107C22×D411yescharacteristic
187Q8×C107—22no—
188Q8×C107—22no—
189Q8×C107—42no—
190Q8×C107—42no—
191Q8×C107—42no—
192Q8×C107—41no—
193Q8×C107—41no—
194Q8×C107—42no—
195Q8×C107—42no—
196D4×C107—42no—
197D4×C107—42no—
198D4×C107—44no—
199D4×C107—42no—
200C2×C4×C107—22no—
201C2×C4×C107—22no—
202C2×C4×C107—24no—
203C2×C4×C107—22no—
204C2×C4×C107—22no—
205C2×C4×C107—22no—
206C2×C4×C107—22no—
207C2×C4×C107—22no—
208C2×C4×C107—22no—
209C2×C4×C107—22no—
210C2×C4×C107—22no—
211C2×C4×C107—41no—
212C2×C4×C107—44no—
213C2×C4×C107—42no—
214C2×C4×C107—41no—
215C2×C4×C107—41no—
216C2×C4×C107—42no—
217C2×C4×C107—42no—
218C2×C4×C107—41no—
219C2×C4×C107—42no—
220C2×C4×C107—84no—
221C2×C4×C107#12011yescharacteristic
222C2×C4×C107#12011yescharacteristic
223C2×C4×C107#12011yescharacteristic
224C2×C4×C107#12011yescharacteristic
225C2×C4×C107C22×D411yescharacteristic
226C2×C4×C107C22×D411yescharacteristic
227C8×C107—42no—
228C8×C107—42no—
229C22×C107—21no—
230C22×C107—21no—
231C22×C107—42no—
232C22×C107—42no—
233C22×C107—42no—
234C22×C107C2×#12011yescharacteristic
235C22×C107#57512yes—
236C4×C107—21no—
237C4×C107—21no—
238C4×C107—21no—
239C4×C107—21no—
240C4×C107—21no—
241C4×C107—44no—
242C4×C107—42no—
243C4×C107—42no—
244C4×C107—42no—
245C4×C107—42no—
246C4×C107—42no—
247C4×C107—42no—
248C4×C107—81no—
249C4×C107#45612yes—
250#18183C10711yesmaximal, characteristic, direct product factor, Sylow
251C2×C107—22no—
252C2×C107—82no—
253C2×C107#300511yescharacteristic
254C2×C107C2×#45611yescharacteristic
255C2×C107#302511yescharacteristic
256#3507C2×C10711yescharacteristic
257#3113C2×C10711yescharacteristic, complemented
258#3112C2×C10711yescharacteristic
259#2399C2×C10711yescharacteristic, complemented
260#1609C2×C10714yescomplemented
261#1603C2×C10714yescomplemented
262#1506C2×C10711yescharacteristic, complemented
263#1505C2×C10711yescharacteristic
264#1467C2×C10711yescharacteristic, complemented
265C107#1818311yescharacteristic, direct product factor, Sylow
266#559—21no—
267#557—21no—
268#556—21no—
269#556—22no—
270#554—21no—
271#552—22no—
272#539C22×C10714yes—
273#536—21no—
274#533C22×C10711yescharacteristic
275#532C22×C10711yescharacteristic
276#529—22no—
277#520—21no—
278C2×C4×Q8C22×C10711yescharacteristic
279C2×C4×Q8C22×C10711yescharacteristic
280#483C22×C10712yes—
281#480C22×C10712yes—
282#477—21no—
283#475—21no—
284#462—21no—
285#460—21no—
286#451C22×C10712yes—
287#448C22×C10712yes—
288#441—22no—
289#440—22no—
290#432C22×C10711yescharacteristic
291#432C22×C10711yescharacteristic
292#398—21no—
293#398C22×C10712yes—
294#395—21no—
295#395C22×C10712yes—
296C4×C4⋊C4—22no—
297#376C22×C10711yescharacteristic
298#328C22×C10714yes—
299#327C22×C10714yes—
300#324C22×C10714yes—
301C2×#41—21no—
302C22×Q8D4×C10711yescharacteristic
303C22×Q8C23×C10711yescharacteristic
304C2×Q16—22no—
305C2×SD16—22no—
306C4⋊Q8—22no—
307C4⋊Q8D4×C10711yescharacteristic
308C4⋊Q8D4×C10711yescharacteristic
309C4⋊Q8D4×C10711yescharacteristic
310#127D4×C10711yescharacteristic
311#126—24no—
312#126—24no—
313#125—22no—
314#125—24no—
315#125—21no—
316#124—22no—
317#124—22no—
318#124—21no—
319#123—24no—
320#123—24no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—24no—
324C22⋊Q8—21no—
325C22⋊Q8C23×C10712yes—
326#121—21no—
327#121C23×C10712yes—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8D4×C10712yes—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—24no—
343C4×D4—21no—
344C4×D4D4×C10712yes—
345#117—22no—
346#117—24no—
347#117—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4D4×C10711yescharacteristic
353C2×C4⋊C4C23×C10711yescharacteristic
354C2×C4⋊C4C23×C10712yes—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42D4×C10712yes—
358C2×C42C23×C10711yescharacteristic
359#107—22no—
360#106—22no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363#103—22no—
364#103—22no—
365#103—22no—
366#102—22no—
367C22⋊C8C23×C10712yes—
368C22⋊C8C23×C10712yes—
369#97—21no—
370#97—21no—
371#95—21no—
372#95—22no—
373#95—22no—
374#95C23×C10712yes—
375#41—44no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8C2×D4×C10712yes—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4C2×D4×C10712yes—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4C2×D4×C10712yes—
395C22×C4C2×D4×C10711yescharacteristic
396C22×C4C2×D4×C10711yescharacteristic
397C22×C4C2×D4×C10712yes—
398C22×C4C24×C10711yescharacteristic
399Q16—44no—
400SD16—44no—
401C2×C8—22no—
402C2×C8—22no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—44no—
419C4⋊C4—44no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4C2×D4×C10712yes—
423C4⋊C4C2×D4×C10712yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C42—24no—
431C42—24no—
432C42—22no—
433C42—22no—
434C42—22no—
435C42—41no—
436C42—41no—
437C42C2×D4×C10711yescharacteristic
438C42C2×D4×C10711yescharacteristic
439C42C2×D4×C10711yescharacteristic
440C42C2×D4×C10711yescharacteristic
441C23—22no—
442C23C22×D4×C10711yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—41no—
449Q8—41no—
450Q8—42no—
451Q8—42no—
452D4—42no—
453D4—42no—
454D4—44no—
455D4—42no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—84no—
477C2×C4#120×C10711yescharacteristic
478C2×C4#120×C10711yescharacteristic
479C2×C4#120×C10711yescharacteristic
480C2×C4#120×C10711yescharacteristic
481C2×C4C22×D4×C10711yescharacteristic
482C2×C4C22×D4×C10711yescharacteristic
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22C2×#120×C10711yescharacteristic
491C22#575×C10712yes—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—44no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C4#456×C10712yes—
506C2—22no—
507C2—82no—
508C2C107×#300511yescharacteristic
509C2C2×#456×C10711yescharacteristic
510C2C107×#302511yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radical#532×C107C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3113C2semidirect
4. C107×#2399C2semidirect
5. C107×#1609C2semidirect
6. C107×#1603C2semidirect
7. C107×#1506C2semidirect
9. C107×#1467C2semidirect
250. #18183C107direct (N × H)
257. #3113C2×C107semidirect
259. #2399C2×C107semidirect
260. #1609C2×C107semidirect
261. #1603C2×C107semidirect
262. #1506C2×C107semidirect
264. #1467C2×C107semidirect
265. C107#18183direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35072
C107×#31132
C107×#31122
C107×#23992
C107×#16092
C107×#16032
C107×#15062
C107×#15052
C107×#14672
#18183107