Finite Group Databasebeta

← C107×#18223 #41044187

Subgroups — C107×#18223 #41044187

Order 27392.

994 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3506C211yesmaximal, characteristic
2C107×#3104C211yesmaximal, characteristic, complemented
3C107×#3103C211yesmaximal, characteristic, complemented
4C107×#2580C211yesmaximal, characteristic, complemented
5C107×#1618C214yesmaximal, complemented
6C107×#1606C214yesmaximal, complemented
7C107×#1518C211yesmaximal, characteristic, complemented
8C107×#1517C211yesmaximal, characteristic, complemented
9C107×#1460C211yesmaximal, characteristic, complemented
10#559×C107—22no—
11#556×C107—21no—
12#555×C107—21no—
13#553×C107—22no—
14#550×C107—21no—
15#547×C107—21no—
16#538×C107C2214yes—
17#535×C107—21no—
18#533×C107C2211yescharacteristic
19#532×C107C2211yescharacteristic
20#525×C107—22no—
21#520×C107—21no—
22C2×C4×Q8×C107C2211yescharacteristic
23C2×C4×D4×C107C2211yescharacteristic
24#484×C107C2212yes—
25#481×C107C2212yes—
26#477×C107—21no—
27#475×C107—21no—
28#462×C107—21no—
29#460×C107—21no—
30#451×C107C2212yes—
31#448×C107C2212yes—
32C4×Q16×C107—22no—
33C4×SD16×C107—22no—
34#431×C107C2211yescharacteristic
35#431×C107C2211yescharacteristic
36#399×C107C2212yes—
37#393×C107C2212yes—
38#390×C107—21no—
39#389×C107—21no—
40#385×C107—22no—
41#382×C107C2211yescharacteristic
42#328×C107C2214yes—
43#327×C107C2214yes—
44#323×C107C2214yes—
45C2×#41×C107—22no—
46C2×#41×C107—21no—
47C22×Q8×C107C2311yescharacteristic
48C22×D4×C107D411yescharacteristic
49C23×C4×C107D412yes—
50C2×Q16×C107—22no—
51C2×SD16×C107—22no—
52C4⋊Q8×C107D411yescharacteristic
53C4⋊Q8×C107D411yescharacteristic
54C4⋊Q8×C107D411yescharacteristic
55#127×C107—22no—
56#127×C107D411yescharacteristic
57#126×C107—24no—
58#125×C107—21no—
59#124×C107—22no—
60#124×C107—24no—
61#124×C107—21no—
62#123×C107—24no—
63#123×C107—24no—
64C22⋊Q8×C107—22no—
65C22⋊Q8×C107—21no—
66C22⋊Q8×C107C2312yes—
67#121×C107—22no—
68#121×C107—22no—
69#121×C107—22no—
70#121×C107—24no—
71#121×C107—21no—
72#121×C107C2312yes—
73#120×C107—24no—
74C4×Q8×C107—22no—
75C4×Q8×C107—21no—
76C4×Q8×C107—21no—
77C4×Q8×C107—21no—
78C4×Q8×C107—21no—
79C4×Q8×C107—21no—
80C4×Q8×C107D412yes—
81C4×D4×C107—22no—
82C4×D4×C107—24no—
83C4×D4×C107—24no—
84C4×D4×C107—21no—
85C4×D4×C107—21no—
86C4×D4×C107—21no—
87C4×D4×C107—21no—
88C4×D4×C107—21no—
89C4×D4×C107D412yes—
90#117×C107—22no—
91#117×C107—22no—
92#117×C107—21no—
93C2×C4⋊C4×C107—22no—
94C2×C4⋊C4×C107—21no—
95C2×C4⋊C4×C107—21no—
96C2×C4⋊C4×C107—22no—
97C2×C4⋊C4×C107D411yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C22⋊C4×C107—22no—
100C2×C22⋊C4×C107—22no—
101C2×C22⋊C4×C107C2312yes—
102C2×C42×C107—21no—
103C2×C42×C107C2311yescharacteristic
104#107×C107—22no—
105#106×C107—22no—
106C4⋊C8×C107—21no—
107C4⋊C8×C107—21no—
108#103×C107—22no—
109#103×C107—22no—
110#103×C107—22no—
111#102×C107—22no—
112C22⋊C8×C107C2312yes—
113C22⋊C8×C107C2312yes—
114C4×C8×C107—21no—
115C4×C8×C107—21no—
116#95×C107—21no—
117#95×C107—22no—
118#95×C107C2312yes—
119C24×C107C2×D412yes—
120#41×C107—42no—
121#41×C107—42no—
122#41×C107—84no—
123C2×Q8×C107—21no—
124C2×Q8×C107—21no—
125C2×Q8×C107—21no—
126C2×Q8×C107—21no—
127C2×Q8×C107—42no—
128C2×Q8×C107C2×D412yes—
129C2×D4×C107—22no—
130C2×D4×C107—24no—
131C2×D4×C107—24no—
132C2×D4×C107—21no—
133C2×D4×C107—21no—
134C2×D4×C107—21no—
135C2×D4×C107—21no—
136C2×D4×C107—22no—
137C2×D4×C107—22no—
138C2×D4×C107C2×D412yes—
139C22×C4×C107—21no—
140C22×C4×C107—24no—
141C22×C4×C107—22no—
142C22×C4×C107—22no—
143C22×C4×C107—22no—
144C22×C4×C107—22no—
145C22×C4×C107—21no—
146C22×C4×C107—82no—
147C22×C4×C107C2×D412yes—
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2411yescharacteristic
151Q16×C107—44no—
152SD16×C107—44no—
153C2×C8×C107—22no—
154C2×C8×C107—22no—
155C4⋊C4×C107—24no—
156C4⋊C4×C107—21no—
157C4⋊C4×C107—21no—
158C4⋊C4×C107—21no—
159C4⋊C4×C107—21no—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—21no—
162C4⋊C4×C107—22no—
163C4⋊C4×C107—22no—
164C4⋊C4×C107—21no—
165C4⋊C4×C107—21no—
166C4⋊C4×C107—41no—
167C4⋊C4×C107—41no—
168C4⋊C4×C107—42no—
169C4⋊C4×C107—82no—
170C4⋊C4×C107C2×D412yes—
171C4⋊C4×C107C2×D412yes—
172C22⋊C4×C107—24no—
173C22⋊C4×C107—24no—
174C22⋊C4×C107—24no—
175C22⋊C4×C107—22no—
176C22⋊C4×C107—22no—
177C22⋊C4×C107—22no—
178C22⋊C4×C107—22no—
179C22⋊C4×C107—22no—
180C22⋊C4×C107—44no—
181C22⋊C4×C107—82no—
182C42×C107—24no—
183C42×C107—22no—
184C42×C107—41no—
185C42×C107—41no—
186C42×C107C2×D411yescharacteristic
187C42×C107C2×D411yescharacteristic
188C42×C107C2×D411yescharacteristic
189C42×C107C2×D411yescharacteristic
190C23×C107—22no—
191C23×C107—22no—
192C23×C107—22no—
193C23×C107—22no—
194C23×C107—42no—
195C23×C107—42no—
196C23×C107C22×D411yescharacteristic
197Q8×C107—22no—
198Q8×C107—22no—
199Q8×C107—42no—
200Q8×C107—41no—
201Q8×C107—41no—
202Q8×C107—42no—
203Q8×C107—42no—
204D4×C107—42no—
205D4×C107—42no—
206D4×C107—42no—
207D4×C107—42no—
208D4×C107—42no—
209D4×C107—42no—
210D4×C107—42no—
211D4×C107—84no—
212D4×C107—84no—
213C2×C4×C107—22no—
214C2×C4×C107—22no—
215C2×C4×C107—22no—
216C2×C4×C107—22no—
217C2×C4×C107—22no—
218C2×C4×C107—41no—
219C2×C4×C107—41no—
220C2×C4×C107—44no—
221C2×C4×C107—41no—
222C2×C4×C107—41no—
223C2×C4×C107—44no—
224C2×C4×C107—42no—
225C2×C4×C107—42no—
226C2×C4×C107—41no—
227C2×C4×C107—42no—
228C2×C4×C107—41no—
229C2×C4×C107—41no—
230C2×C4×C107—42no—
231C2×C4×C107—82no—
232C2×C4×C107—84no—
233C2×C4×C107#12011yescharacteristic
234C2×C4×C107#12011yescharacteristic
235C2×C4×C107#12011yescharacteristic
236C2×C4×C107#12011yescharacteristic
237C2×C4×C107#13512yes—
238C2×C4×C107#13712yes—
239C2×C4×C107C22×D411yescharacteristic
240C2×C4×C107C22×D411yescharacteristic
241C8×C107—42no—
242C8×C107—42no—
243C22×C107—21no—
244C22×C107—21no—
245C22×C107—44no—
246C22×C107—42no—
247C22×C107—42no—
248C22×C107—42no—
249C22×C107—42no—
250C22×C107—42no—
251C22×C107—42no—
252C22×C107—82no—
253C22×C107C2×#12011yescharacteristic
254C22×C107C2×#13511yescharacteristic
255C22×C107C2×#13711yescharacteristic
256C4×C107—21no—
257C4×C107—21no—
258C4×C107—21no—
259C4×C107—21no—
260C4×C107—42no—
261C4×C107—42no—
262C4×C107—42no—
263C4×C107—42no—
264C4×C107—42no—
265C4×C107—82no—
266C4×C107—81no—
267C4×C107#45212yes—
268C4×C107#45212yes—
269#18223C10711yesmaximal, characteristic, direct product factor, Sylow
270C2×C107—21no—
271C2×C107—21no—
272C2×C107—82no—
273C2×C107—82no—
274C2×C107C2×#45211yescharacteristic
275C2×C107#301911yescharacteristic
276C2×C107#302511yescharacteristic
277#3506C2×C10711yescharacteristic
278#3104C2×C10711yescharacteristic, complemented
279#3103C2×C10711yescharacteristic, complemented
280#2580C2×C10711yescharacteristic, complemented
281#1618C2×C10714yescomplemented
282#1606C2×C10714yescomplemented
283#1518C2×C10711yescharacteristic, complemented
284#1517C2×C10711yescharacteristic, complemented
285#1460C2×C10711yescharacteristic, complemented
286C107#1822311yescharacteristic, direct product factor, Sylow
287#559—22no—
288#556—21no—
289#555—21no—
290#553—22no—
291#550—21no—
292#547—21no—
293#538C22×C10714yes—
294#535—21no—
295#533C22×C10711yescharacteristic
296#532C22×C10711yescharacteristic
297#525—22no—
298#520—21no—
299C2×C4×Q8C22×C10711yescharacteristic
300C2×C4×D4C22×C10711yescharacteristic
301#484C22×C10712yes—
302#481C22×C10712yes—
303#477—21no—
304#475—21no—
305#462—21no—
306#460—21no—
307#451C22×C10712yes—
308#448C22×C10712yes—
309C4×Q16—22no—
310C4×SD16—22no—
311#431C22×C10711yescharacteristic
312#431C22×C10711yescharacteristic
313#399C22×C10712yes—
314#393C22×C10712yes—
315#390—21no—
316#389—21no—
317#385—22no—
318#382C22×C10711yescharacteristic
319#328C22×C10714yes—
320#327C22×C10714yes—
321#323C22×C10714yes—
322C2×#41—22no—
323C2×#41—21no—
324C22×Q8C23×C10711yescharacteristic
325C22×D4D4×C10711yescharacteristic
326C23×C4D4×C10712yes—
327C2×Q16—22no—
328C2×SD16—22no—
329C4⋊Q8D4×C10711yescharacteristic
330C4⋊Q8D4×C10711yescharacteristic
331C4⋊Q8D4×C10711yescharacteristic
332#127—22no—
333#127D4×C10711yescharacteristic
334#126—24no—
335#125—21no—
336#124—22no—
337#124—24no—
338#124—21no—
339#123—24no—
340#123—24no—
341C22⋊Q8—22no—
342C22⋊Q8—21no—
343C22⋊Q8C23×C10712yes—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—24no—
348#121—21no—
349#121C23×C10712yes—
350#120—24no—
351C4×Q8—22no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8D4×C10712yes—
358C4×D4—22no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4D4×C10712yes—
367#117—22no—
368#117—22no—
369#117—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4D4×C10711yescharacteristic
375C2×C4⋊C4C23×C10711yescharacteristic
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4C23×C10712yes—
379C2×C42—21no—
380C2×C42C23×C10711yescharacteristic
381#107—22no—
382#106—22no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389C22⋊C8C23×C10712yes—
390C22⋊C8C23×C10712yes—
391C4×C8—21no—
392C4×C8—21no—
393#95—21no—
394#95—22no—
395#95C23×C10712yes—
396C24C2×D4×C10712yes—
397#41—42no—
398#41—42no—
399#41—84no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—42no—
405C2×Q8C2×D4×C10712yes—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4C2×D4×C10712yes—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—82no—
424C22×C4C2×D4×C10712yes—
425C22×C4C2×D4×C10711yescharacteristic
426C22×C4C2×D4×C10711yescharacteristic
427C22×C4C24×C10711yescharacteristic
428Q16—44no—
429SD16—44no—
430C2×C8—22no—
431C2×C8—22no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—42no—
446C4⋊C4—82no—
447C4⋊C4C2×D4×C10712yes—
448C4⋊C4C2×D4×C10712yes—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—44no—
458C22⋊C4—82no—
459C42—24no—
460C42—22no—
461C42—41no—
462C42—41no—
463C42C2×D4×C10711yescharacteristic
464C42C2×D4×C10711yescharacteristic
465C42C2×D4×C10711yescharacteristic
466C42C2×D4×C10711yescharacteristic
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—42no—
472C23—42no—
473C23C22×D4×C10711yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—42no—
477Q8—41no—
478Q8—41no—
479Q8—42no—
480Q8—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—84no—
489D4—84no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4—84no—
510C2×C4#120×C10711yescharacteristic
511C2×C4#120×C10711yescharacteristic
512C2×C4#120×C10711yescharacteristic
513C2×C4#120×C10711yescharacteristic
514C2×C4#135×C10712yes—
515C2×C4#137×C10712yes—
516C2×C4C22×D4×C10711yescharacteristic
517C2×C4C22×D4×C10711yescharacteristic
518C8—42no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—44no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22C2×#120×C10711yescharacteristic
531C22C2×#135×C10711yescharacteristic
532C22C2×#137×C10711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—81no—
544C4#452×C10712yes—
545C4#452×C10712yes—
546C2—21no—
547C2—21no—
548C2—82no—
549C2—82no—
550C2C2×#452×C10711yescharacteristic
551C2C107×#301911yescharacteristic
552C2C107×#302511yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3506C2
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×#3104C2semidirect
3. C107×#3103C2semidirect
4. C107×#2580C2semidirect
5. C107×#1618C2semidirect
6. C107×#1606C2semidirect
7. C107×#1518C2semidirect
8. C107×#1517C2semidirect
9. C107×#1460C2semidirect
269. #18223C107direct (N × H)
278. #3104C2×C107semidirect
279. #3103C2×C107semidirect
280. #2580C2×C107semidirect
281. #1618C2×C107semidirect
282. #1606C2×C107semidirect
283. #1518C2×C107semidirect
284. #1517C2×C107semidirect
285. #1460C2×C107semidirect
286. C107#18223direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35062
C107×#31042
C107×#31032
C107×#25802
C107×#16182
C107×#16062
C107×#15182
C107×#15172
C107×#14602
#18223107