Finite Group Databasebeta

← C107×#9497 #41035461

Subgroups — C107×#9497 #41035461

Order 27392.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2403C211yesmaximal, characteristic
2C107×#2309C211yesmaximal, characteristic, complemented
3C107×#1781C211yesmaximal, characteristic, complemented
4C107×#1781C212yesmaximal, complemented
5C107×#1304C212yesmaximal, complemented
6C23×D4×C107C2211yescharacteristic
7C23×D4×C107C2211yescharacteristic
8C2×#120×C107—21no—
9C2×#120×C107C412yescomplemented
10C2×#117×C107—21no—
11C2×#99×C107—22no—
12C2×#99×C107—24no—
13#392×C107—22no—
14#390×C107—24no—
15#386×C107—21no—
16#386×C107C412yescomplemented
17#379×C107—21no—
18#379×C107C2212yes—
19#379×C107C2211yescharacteristic
20#379×C107C2212yes—
21C25×C107C2×C411yescharacteristic
22C25×C107D411yescharacteristic
23C25×C107C2311yescharacteristic
24C22×D4×C107—21no—
25C22×D4×C107—22no—
26C22×D4×C107—22no—
27C22×D4×C107—22no—
28C22×D4×C107—21no—
29C22×D4×C107—22no—
30C22×D4×C107—22no—
31C22×D4×C107—44no—
32C22×D4×C107—44no—
33C22×D4×C107C2×C412yes—
34C22×D4×C107D412yes—
35C23×C4×C107C2×C411yescharacteristic
36C23×C4×C107D411yescharacteristic
37#120×C107—44no—
38#120×C107—44no—
39#117×C107—44no—
40C2×C4⋊C4×C107—22no—
41C2×C22⋊C4×C107—22no—
42C2×C22⋊C4×C107—22no—
43C2×C22⋊C4×C107—21no—
44C2×C22⋊C4×C107—22no—
45C2×C22⋊C4×C107—22no—
46C2×C22⋊C4×C107—22no—
47C2×C22⋊C4×C107—22no—
48C2×C22⋊C4×C107—22no—
49C2×C22⋊C4×C107—22no—
50C2×C22⋊C4×C107—21no—
51C2×C22⋊C4×C107—22no—
52C2×C22⋊C4×C107C2×C412yes—
53C2×C22⋊C4×C107D414yescomplemented
54C2×C42×C107—22no—
55#99×C107—48no—
56#99×C107—44no—
57#95×C107—22no—
58C24×C107—21no—
59C24×C107—21no—
60C24×C107—22no—
61C24×C107—21no—
62C24×C107—42no—
63C24×C107—42no—
64C24×C107—42no—
65C24×C107—42no—
66C24×C107—42no—
67C24×C107—42no—
68C24×C107—81no—
69C24×C107—81no—
70C24×C107—81no—
71C24×C107C22⋊C412yes—
72C24×C107C22×C411yescharacteristic
73C24×C107C2×D411yescharacteristic
74C24×C107C2×D411yescharacteristic
75C24×C107C2×D412yes—
76C24×C107#4112yes—
77C2×D4×C107—28no—
78C2×D4×C107—24no—
79C2×D4×C107—24no—
80C2×D4×C107—24no—
81C2×D4×C107—24no—
82C2×D4×C107—24no—
83C2×D4×C107—42no—
84C2×D4×C107—42no—
85C2×D4×C107—44no—
86C2×D4×C107—44no—
87C2×D4×C107—48no—
88C2×D4×C107—42no—
89C2×D4×C107—44no—
90C2×D4×C107—42no—
91C2×D4×C107—44no—
92C2×D4×C107—42no—
93C2×D4×C107—44no—
94C2×D4×C107—41no—
95C2×D4×C107—42no—
96C2×D4×C107—41no—
97C2×D4×C107—44no—
98C2×D4×C107—44no—
99C2×D4×C107—82no—
100C22×C4×C107—21no—
101C22×C4×C107—21no—
102C22×C4×C107—24no—
103C22×C4×C107—21no—
104C22×C4×C107—22no—
105C22×C4×C107—22no—
106C22×C4×C107—24no—
107C22×C4×C107—42no—
108C22×C4×C107—42no—
109C22×C4×C107C22⋊C412yes—
110C4⋊C4×C107—44no—
111C22⋊C4×C107—44no—
112C22⋊C4×C107—44no—
113C22⋊C4×C107—42no—
114C22⋊C4×C107—44no—
115C22⋊C4×C107—44no—
116C22⋊C4×C107—42no—
117C22⋊C4×C107—44no—
118C22⋊C4×C107—44no—
119C22⋊C4×C107—82no—
120C22⋊C4×C107—82no—
121C22⋊C4×C107—81no—
122C22⋊C4×C107—82no—
123C22⋊C4×C107—82no—
124C42×C107—44no—
125C23×C107—22no—
126C23×C107—22no—
127C23×C107—22no—
128C23×C107—22no—
129C23×C107—24no—
130C23×C107—22no—
131C23×C107—24no—
132C23×C107—22no—
133C23×C107—22no—
134C23×C107—22no—
135C23×C107—41no—
136C23×C107—41no—
137C23×C107—41no—
138C23×C107—42no—
139C23×C107—41no—
140C23×C107—42no—
141C23×C107—41no—
142C23×C107—42no—
143C23×C107—42no—
144C23×C107—42no—
145C23×C107—42no—
146C23×C107—42no—
147C23×C107—42no—
148C23×C107—41no—
149C23×C107—42no—
150C23×C107—42no—
151C23×C107—42no—
152C23×C107—42no—
153C23×C107—41no—
154C23×C107—42no—
155C23×C107—42no—
156C23×C107—81no—
157C23×C107—81no—
158C23×C107—82no—
159C23×C107—82no—
160C23×C107—88no—
161C23×C107—88no—
162C23×C107—88no—
163C23×C107C2×C22⋊C411yescharacteristic
164C23×C107C4×D412yes—
165C23×C107#12011yescharacteristic
166C23×C107#12112yes—
167C23×C107#12311yescharacteristic
168D4×C107—48no—
169D4×C107—48no—
170D4×C107—48no—
171D4×C107—44no—
172D4×C107—44no—
173D4×C107—88no—
174C2×C4×C107—22no—
175C2×C4×C107—22no—
176C2×C4×C107—24no—
177C2×C4×C107—22no—
178C2×C4×C107—22no—
179C2×C4×C107—22no—
180C2×C4×C107—24no—
181C2×C4×C107—41no—
182C2×C4×C107—42no—
183C2×C4×C107—41no—
184C2×C4×C107—44no—
185C2×C4×C107—42no—
186C2×C4×C107—44no—
187C2×C4×C107—42no—
188C2×C4×C107—42no—
189C2×C4×C107—44no—
190C2×C4×C107—82no—
191C2×C4×C107—82no—
192C2×C4×C107—82no—
193C2×C4×C107#9914yescomplemented
194C22×C107—21no—
195C22×C107—21no—
196C22×C107—21no—
197C22×C107—21no—
198C22×C107—22no—
199C22×C107—22no—
200C22×C107—21no—
201C22×C107—21no—
202C22×C107—22no—
203C22×C107—22no—
204C22×C107—22no—
205C22×C107—22no—
206C22×C107—21no—
207C22×C107—44no—
208C22×C107—44no—
209C22×C107—44no—
210C22×C107—44no—
211C22×C107—42no—
212C22×C107—42no—
213C22×C107—42no—
214C22×C107—42no—
215C22×C107—84no—
216C22×C107—82no—
217C22×C107—82no—
218C22×C107—84no—
219C22×C107—82no—
220C22×C107—84no—
221C22×C107—84no—
222C22×C107—84no—
223C22×C107—84no—
224C22×C107—81no—
225C22×C107—81no—
226C22×C107#38611yescharacteristic
227C22×C107C2×#9912yes—
228C22×C107B(4,𝔽2)12yes—
229C4×C107—24no—
230C4×C107—42no—
231C4×C107—84no—
232C4×C107—82no—
233C4×C107—162no—
234#9497C10711yesmaximal, characteristic, direct product factor, Sylow
235C2×C107—22no—
236C2×C107—22no—
237C2×C107—42no—
238C2×C107—42no—
239C2×C107—41no—
240C2×C107—82no—
241C2×C107—82no—
242C2×C107#188911yescharacteristic
243C2×C107#189811yescharacteristic
244C2×C107#191311yescharacteristic
245#2403C2×C10711yescharacteristic
246#2309C2×C10711yescharacteristic, complemented
247#1781C2×C10712yescomplemented
248#1781C2×C10711yescharacteristic, complemented
249#1304C2×C10712yescomplemented
250C107#949711yescharacteristic, direct product factor, Sylow
251C23×D4C22×C10711yescharacteristic
252C23×D4C22×C10711yescharacteristic
253C2×#120—21no—
254C2×#120C4×C10712yescomplemented
255C2×#117—21no—
256C2×#99—22no—
257C2×#99—24no—
258#392—22no—
259#390—24no—
260#386—21no—
261#386C4×C10712yescomplemented
262#379—21no—
263#379C22×C10712yes—
264#379C22×C10711yescharacteristic
265#379C22×C10712yes—
266C25C2×C4×C10711yescharacteristic
267C25D4×C10711yescharacteristic
268C25C23×C10711yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C10712yes—
279C22×D4D4×C10712yes—
280C23×C4C2×C4×C10711yescharacteristic
281C23×C4D4×C10711yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C10712yes—
298C2×C22⋊C4D4×C10714yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C10712yes—
317C24C22×C4×C10711yescharacteristic
318C24C2×D4×C10711yescharacteristic
319C24C2×D4×C10711yescharacteristic
320C24C2×D4×C10712yes—
321C24#41×C10712yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C10712yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C10711yescharacteristic
409C23C4×D4×C10712yes—
410C23#120×C10711yescharacteristic
411C23#121×C10712yes—
412C23#123×C10711yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C10714yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#386×C10711yescharacteristic
472C22C2×#99×C10712yes—
473C22B(4,𝔽2)×C10712yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C107×#188911yescharacteristic
487C2C107×#189811yescharacteristic
488C2C107×#191311yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC24C22×C4×C107
Frattini, cosocleC25C23×C107
prime radicalC107×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C25×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2309C2semidirect
3. C107×#1781C2semidirect
4. C107×#1781C2semidirect
5. C107×#1304C2semidirect
9. C2×#120×C107C4semidirect
16. #386×C107C4semidirect
53. C2×C22⋊C4×C107D4semidirect
193. C2×C4×C107#99semidirect
234. #9497C107direct (N × H)
246. #2309C2×C107semidirect
247. #1781C2×C107semidirect
248. #1781C2×C107semidirect
249. #1304C2×C107semidirect
250. C107#9497direct (N × H)
254. C2×#120C4×C107semidirect
261. #386C4×C107semidirect
298. C2×C22⋊C4D4×C107semidirect
438. C2×C4#99×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#24032
C107×#23092
C107×#17812
C107×#13042
#9497107