Finite Group Databasebeta

← C107×#9950 #41035914

Subgroups — C107×#9950 #41035914

Order 27392.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3186C211yesmaximal, characteristic
2C2×#481×C107C211yesmaximal, characteristic, complemented
3C107×#2504C211yesmaximal, characteristic, complemented
4C107×#1964C211yesmaximal, characteristic, complemented
5C107×#1824C211yesmaximal, characteristic, complemented
6C107×#1519C211yesmaximal, characteristic, complemented
7C107×#1282C211yesmaximal, characteristic, complemented
8C2×#121×C107C2211yescharacteristic
9C2×#121×C107C2211yescharacteristic
10C22×C4⋊C4×C107C2211yescharacteristic
11#481×C107—22no—
12#481×C107—22no—
13#480×C107—21no—
14#480×C107—21no—
15#466×C107—22no—
16#447×C107—21no—
17#447×C107—21no—
18C2×#106×C107—21no—
19C2×#102×C107—21no—
20C2×#99×C107—22no—
21C2×C22⋊C8×C107C2211yescharacteristic
22C2×C22⋊C8×C107C2211yescharacteristic
23#397×C107—22no—
24#390×C107—21no—
25#386×C107—22no—
26#382×C107—21no—
27#380×C107C2211yescharacteristic
28C4×C22⋊C4×C107C2211yescharacteristic
29#340×C107—22no—
30#327×C107—22no—
31C22×D4×C107—21no—
32C22×D4×C107—21no—
33C22×D4×C107D411yescharacteristic
34C22×D4×C107D411yescharacteristic
35C23×C4×C107—21no—
36C23×C4×C107C2311yescharacteristic
37C2×D8×C107—22no—
38C22×C8×C107—21no—
39C22×C8×C107D412yes—
40#121×C107—21no—
41#121×C107—21no—
42#121×C107—21no—
43#121×C107—21no—
44#121×C107—21no—
45#121×C107—21no—
46#121×C107—21no—
47#121×C107—21no—
48C2×C4⋊C4×C107—21no—
49C2×C4⋊C4×C107—21no—
50C2×C4⋊C4×C107—21no—
51C2×C4⋊C4×C107—21no—
52C2×C4⋊C4×C107—21no—
53C2×C4⋊C4×C107—21no—
54C2×C4⋊C4×C107D411yescharacteristic
55C2×C4⋊C4×C107D412yes—
56C2×C4⋊C4×C107D411yescharacteristic
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—21no—
59C2×C22⋊C4×C107—21no—
60C2×C22⋊C4×C107—24no—
61C2×C22⋊C4×C107D412yes—
62C2×C42×C107—21no—
63#107×C107—22no—
64#106×C107—24no—
65#102×C107—24no—
66#102×C107—22no—
67#102×C107—22no—
68#99×C107—44no—
69C22⋊C8×C107—21no—
70C22⋊C8×C107—21no—
71C22⋊C8×C107—21no—
72C22⋊C8×C107D412yes—
73#95×C107—24no—
74#95×C107—21no—
75#95×C107—21no—
76C24×C107—21no—
77C24×C107—21no—
78C24×C107C2×D411yescharacteristic
79C2×D4×C107—21no—
80C2×D4×C107—21no—
81C2×D4×C107—21no—
82C2×D4×C107—21no—
83C2×D4×C107—42no—
84C2×D4×C107—42no—
85C2×D4×C107—41no—
86C2×D4×C107—41no—
87C2×D4×C107—41no—
88C2×D4×C107—41no—
89C2×D4×C107—42no—
90C2×D4×C107—42no—
91C2×D4×C107—42no—
92C2×D4×C107—42no—
93C22×C4×C107—21no—
94C22×C4×C107—22no—
95C22×C4×C107—22no—
96C22×C4×C107—21no—
97C22×C4×C107—42no—
98C22×C4×C107—41no—
99C22×C4×C107—41no—
100C22×C4×C107—41no—
101C22×C4×C107—82no—
102C22×C4×C107C2×D411yescharacteristic
103C22×C4×C107C2×D411yescharacteristic
104C22×C4×C107C2×D411yescharacteristic
105C22×C4×C107C2×D411yescharacteristic
106C22×C4×C107C2×D411yescharacteristic
107C22×C4×C107#4111yescharacteristic
108D8×C107—82no—
109C2×C8×C107—22no—
110C2×C8×C107—22no—
111C2×C8×C107—42no—
112C2×C8×C107—42no—
113C4⋊C4×C107—22no—
114C4⋊C4×C107—21no—
115C4⋊C4×C107—21no—
116C4⋊C4×C107—21no—
117C4⋊C4×C107—22no—
118C4⋊C4×C107—21no—
119C4⋊C4×C107—42no—
120C4⋊C4×C107—41no—
121C4⋊C4×C107—41no—
122C22⋊C4×C107—22no—
123C22⋊C4×C107—22no—
124C22⋊C4×C107—41no—
125C22⋊C4×C107—41no—
126C22⋊C4×C107—41no—
127C22⋊C4×C107—41no—
128C22⋊C4×C107—42no—
129C22⋊C4×C107—84no—
130C42×C107—42no—
131C23×C107—41no—
132C23×C107—41no—
133C23×C107—42no—
134C23×C107—42no—
135C23×C107—41no—
136C23×C107—41no—
137C23×C107—42no—
138C23×C107—42no—
139C23×C107—81no—
140C23×C107—81no—
141C23×C107#12011yescharacteristic
142C23×C107#12111yescharacteristic
143C23×C107#12711yescharacteristic
144C23×C107#13512yes—
145C23×C107AGL(1,ℤ/8)12yes—
146D4×C107—42no—
147D4×C107—42no—
148D4×C107—42no—
149D4×C107—81no—
150D4×C107—82no—
151D4×C107—82no—
152D4×C107—81no—
153D4×C107—81no—
154D4×C107—81no—
155D4×C107—81no—
156C2×C4×C107—22no—
157C2×C4×C107—22no—
158C2×C4×C107—22no—
159C2×C4×C107—41no—
160C2×C4×C107—41no—
161C2×C4×C107—41no—
162C2×C4×C107—42no—
163C2×C4×C107—42no—
164C2×C4×C107—44no—
165C2×C4×C107—41no—
166C2×C4×C107—41no—
167C2×C4×C107—42no—
168C2×C4×C107—42no—
169C2×C4×C107—42no—
170C2×C4×C107—42no—
171C2×C4×C107—82no—
172C2×C4×C107—82no—
173C2×C4×C107—81no—
174C2×C4×C107—81no—
175C2×C4×C107—81no—
176C2×C4×C107#12011yescharacteristic
177C2×C4×C107#12011yescharacteristic
178C2×C4×C107#12111yescharacteristic
179C2×C4×C107#12111yescharacteristic
180C8×C107—42no—
181C8×C107—42no—
182C22×C107—21no—
183C22×C107—21no—
184C22×C107—21no—
185C22×C107—21no—
186C22×C107—21no—
187C22×C107—21no—
188C22×C107—42no—
189C22×C107—42no—
190C22×C107—84no—
191C22×C107—81no—
192C22×C107—81no—
193C22×C107—81no—
194C22×C107—81no—
195C22×C107—81no—
196C22×C107—81no—
197C22×C107—162no—
198C22×C107#39211yescharacteristic
199C22×C107#44912yes—
200C22×C107#46312yes—
201C22×C107#49511yescharacteristic
202C22×C107#49611yescharacteristic
203C4×C107—21no—
204C4×C107—21no—
205C4×C107—21no—
206C4×C107—82no—
207C4×C107—82no—
208C4×C107—81no—
209C4×C107—81no—
210C4×C107—161no—
211C4×C107#45812yes—
212#9950C10711yesmaximal, characteristic, direct product factor, Sylow
213C2×C107—22no—
214C2×C107—21no—
215C2×C107—22no—
216C2×C107—21no—
217C2×C107—161no—
218C2×C107—161no—
219C2×C107#200811yescharacteristic
220C2×C107#201211yescharacteristic
221C2×C107#202211yescharacteristic
222#3186C2×C10711yescharacteristic
223C2×#481C2×C10711yescharacteristic, complemented
224#2504C2×C10711yescharacteristic, complemented
225#1964C2×C10711yescharacteristic, complemented
226#1824C2×C10711yescharacteristic, complemented
227#1519C2×C10711yescharacteristic, complemented
228#1282C2×C10711yescharacteristic, complemented
229C107#995011yescharacteristic, direct product factor, Sylow
230C2×#121C22×C10711yescharacteristic
231C2×#121C22×C10711yescharacteristic
232C22×C4⋊C4C22×C10711yescharacteristic
233#481—22no—
234#481—22no—
235#480—21no—
236#480—21no—
237#466—22no—
238#447—21no—
239#447—21no—
240C2×#106—21no—
241C2×#102—21no—
242C2×#99—22no—
243C2×C22⋊C8C22×C10711yescharacteristic
244C2×C22⋊C8C22×C10711yescharacteristic
245#397—22no—
246#390—21no—
247#386—22no—
248#382—21no—
249#380C22×C10711yescharacteristic
250C4×C22⋊C4C22×C10711yescharacteristic
251#340—22no—
252#327—22no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4D4×C10711yescharacteristic
256C22×D4D4×C10711yescharacteristic
257C23×C4—21no—
258C23×C4C23×C10711yescharacteristic
259C2×D8—22no—
260C22×C8—21no—
261C22×C8D4×C10712yes—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C10712yes—
277C2×C4⋊C4D4×C10711yescharacteristic
278C2×C4⋊C4D4×C10711yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4D4×C10712yes—
284C2×C42—21no—
285#107—22no—
286#106—24no—
287#102—24no—
288#102—22no—
289#102—22no—
290#99—44no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8D4×C10712yes—
295#95—24no—
296#95—21no—
297#95—21no—
298C24—21no—
299C24—21no—
300C24C2×D4×C10711yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—82no—
324C22×C4C2×D4×C10711yescharacteristic
325C22×C4C2×D4×C10711yescharacteristic
326C22×C4C2×D4×C10711yescharacteristic
327C22×C4C2×D4×C10711yescharacteristic
328C22×C4C2×D4×C10711yescharacteristic
329C22×C4#41×C10711yescharacteristic
330D8—82no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—42no—
351C22⋊C4—84no—
352C42—42no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—42no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23#120×C10711yescharacteristic
364C23#121×C10711yescharacteristic
365C23#127×C10711yescharacteristic
366C23#135×C10712yes—
367C23AGL(1,ℤ/8)×C10712yes—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—82no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4#120×C10711yescharacteristic
399C2×C4#120×C10711yescharacteristic
400C2×C4#121×C10711yescharacteristic
401C2×C4#121×C10711yescharacteristic
402C8—42no—
403C8—42no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—162no—
420C22#392×C10711yescharacteristic
421C22#449×C10712yes—
422C22#463×C10712yes—
423C22#495×C10711yescharacteristic
424C22#496×C10711yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—82no—
429C4—82no—
430C4—81no—
431C4—81no—
432C4—161no—
433C4#458×C10712yes—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—21no—
438C2—161no—
439C2—161no—
440C2C107×#200811yescharacteristic
441C2C107×#201211yescharacteristic
442C2C107×#202211yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC23×C4C23×C107
prime radicalC107×#3186C2
LCSG ▷ C23×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×#481×C107C2semidirect
3. C107×#2504C2semidirect
4. C107×#1964C2semidirect
5. C107×#1824C2semidirect
6. C107×#1519C2semidirect
7. C107×#1282C2semidirect
212. #9950C107direct (N × H)
223. C2×#481C2×C107semidirect
224. #2504C2×C107semidirect
225. #1964C2×C107semidirect
226. #1824C2×C107semidirect
227. #1519C2×C107semidirect
228. #1282C2×C107semidirect
229. C107#9950direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#31862
C2×#481×C1072
C107×#25042
C107×#19642
C107×#18242
C107×#15192
C107×#12822
#9950107