Finite Group Databasebeta

← C139×#35845 #48030441

Subgroups — C139×#35845 #48030441

Order 35584.

2174 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C211yesmaximal, characteristic, complemented
2C2×#519×C139C211yesmaximal, characteristic
3#2628×C139C213yesmaximal
4#2581×C139C213yesmaximal, complemented
5#2567×C139C213yesmaximal, complemented
6#2453×C139C216yesmaximal, complemented
7#2441×C139C216yesmaximal
8#2396×C139C213yesmaximal
9#2351×C139C211yesmaximal, characteristic, complemented
10Q8×C4⋊C4×C139C212yesmaximal, complemented
11Q8×C22⋊C4×C139C212yesmaximal
12C23×Q8×C139C2211yescharacteristic
13#557×C139—28no—
14C2×C4⋊Q8×C139C2213yes—
15C2×#125×C139C2216yes—
16#519×C139—28no—
17C2×C4×Q8×C139C2213yes—
18C2×C4×Q8×C139C2213yes—
19C2×C4×Q8×C139C2212yes—
20C2×C4×Q8×C139C2212yes—
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2213yes—
23C2×C4×Q8×C139C2211yescharacteristic
24C2×#117×C139C2213yes—
25C2×#117×C139C2213yes—
26#400×C139C2213yes—
27#400×C139C2216yes—
28#399×C139C2216yes—
29#399×C139C2211yescharacteristic
30#398×C139C2216yes—
31#396×C139C2216yes—
32#395×C139C2213yes—
33#395×C139C2216yes—
34#393×C139C2213yes—
35#391×C139C2216yes—
36#391×C139C2216yes—
37#389×C139C22112yes—
38#389×C139C2216yes—
39#389×C139C2216yes—
40#389×C139C2216yes—
41#387×C139C22112yes—
42#384×C139C2216yes—
43#382×C139C2213yes—
44#380×C139C2216yes—
45C4×C4⋊C4×C139C2213yes—
46C4×C4⋊C4×C139C2216yes—
47C4×C22⋊C4×C139C2216yes—
48C22×Q8×C139—24no—
49C22×Q8×C139—24no—
50C22×Q8×C139Q818yescomplemented
51C22×Q8×C139C2313yes—
52C22×Q8×C139C2313yes—
53C22×Q8×C139C2311yescharacteristic
54C23×C4×C139C2313yes—
55C4⋊Q8×C139—212no—
56#125×C139—224no—
57C4×Q8×C139—24no—
58C4×Q8×C139—28no—
59C4×Q8×C139—28no—
60C4×Q8×C139—212no—
61C4×Q8×C139—212no—
62C4×Q8×C139—212no—
63C4×Q8×C139D418yes—
64#117×C139—212no—
65#117×C139—212no—
66C2×C4⋊C4×C139C2313yes—
67C2×C4⋊C4×C139C2316yes—
68C2×C4⋊C4×C139C2316yes—
69C2×C4⋊C4×C139C2312yes—
70C2×C4⋊C4×C139C2313yes—
71C2×C4⋊C4×C139C2311yescharacteristic
72C2×C4⋊C4×C139C2316yes—
73C2×C4⋊C4×C139C2313yes—
74C2×C4⋊C4×C139C2316yes—
75C2×C4⋊C4×C139C2316yes—
76C2×C4⋊C4×C139C2316yes—
77C2×C4⋊C4×C139C23112yes—
78C2×C4⋊C4×C139C2313yes—
79C2×C22⋊C4×C139C2312yes—
80C2×C22⋊C4×C139C2313yes—
81C2×C22⋊C4×C139C2311yescharacteristic
82C2×C22⋊C4×C139C2316yes—
83C2×C42×C139C2313yes—
84C2×C42×C139C2316yes—
85C2×C42×C139C2316yes—
86C2×C42×C139C2316yes—
87C2×C42×C139C2313yes—
88#95×C139C2311yescharacteristic
89#95×C139C2313yes—
90#95×C139C2316yes—
91#95×C139C23112yes—
92#95×C139C2316yes—
93#95×C139C2316yes—
94#95×C139C2316yes—
95#95×C139C2316yes—
96C24×C139C2411yescharacteristic
97C2×Q8×C139—232no—
98C2×Q8×C139—26no—
99C2×Q8×C139—26no—
100C2×Q8×C139—26no—
101C2×Q8×C139—46no—
102C2×Q8×C139C2×D414yes—
103C2×Q8×C139C2×Q8112yes—
104C2×Q8×C139C2×Q814yes—
105C2×Q8×C139#4114yes—
106C22×C4×C139—26no—
107C22×C4×C139—26no—
108C22×C4×C139C2×Q8112yes—
109C22×C4×C139C2416yes—
110C22×C4×C139C2411yescharacteristic
111C22×C4×C139C2412yes—
112C22×C4×C139C2416yes—
113C22×C4×C139C2413yes—
114C22×C4×C139C2411yescharacteristic
115C22×C4×C139C2413yes—
116C22×C4×C139C2413yes—
117C22×C4×C139C2412yes—
118C22×C4×C139C2413yes—
119C4⋊C4×C139—26no—
120C4⋊C4×C139—26no—
121C4⋊C4×C139—26no—
122C4⋊C4×C139—22no—
123C4⋊C4×C139—212no—
124C4⋊C4×C139—212no—
125C4⋊C4×C139—212no—
126C4⋊C4×C139—212no—
127C4⋊C4×C139—212no—
128C4⋊C4×C139—24no—
129C4⋊C4×C139—46no—
130C4⋊C4×C139—412no—
131C4⋊C4×C139C2×D4112yes—
132C22⋊C4×C139—26no—
133C22⋊C4×C139—22no—
134C22⋊C4×C139—24no—
135C22⋊C4×C139—46no—
136C42×C139—212no—
137C42×C139—26no—
138C42×C139—212no—
139C42×C139—212no—
140C42×C139C2×D4112yes—
141C23×C139—21no—
142C23×C139—21no—
143C23×C139—22no—
144C23×C139—22no—
145C23×C139C22×Q812yes—
146C23×C139C2511yescharacteristic
147Q8×C139—224no—
148Q8×C139—412no—
149Q8×C139C22⋊Q8116yes—
150C2×C4×C139—23no—
151C2×C4×C139—22no—
152C2×C4×C139—23no—
153C2×C4×C139—26no—
154C2×C4×C139—22no—
155C2×C4×C139—22no—
156C2×C4×C139—224no—
157C2×C4×C139—23no—
158C2×C4×C139—21no—
159C2×C4×C139—22no—
160C2×C4×C139—26no—
161C2×C4×C139—26no—
162C2×C4×C139—22no—
163C2×C4×C139—22no—
164C2×C4×C139—22no—
165C2×C4×C139—26no—
166C2×C4×C139—26no—
167C2×C4×C139—26no—
168C2×C4×C139—26no—
169C2×C4×C139—26no—
170C2×C4×C139C22×D416yes—
171C2×C4×C139C22×D412yes—
172C2×C4×C139C22×D416yes—
173C2×C4×C139C22×Q816yes—
174C2×C4×C139C22×Q816yes—
175C2×C4×C139C2×#4116yes—
176C2×C4×C1392−1+414yes—
177C22×C139—22no—
178C22×C139—24no—
179C22×C139—41no—
180C22×C139—41no—
181C22×C139—42no—
182C22×C139C23×D411yescharacteristic
183C22×C139C23×Q811yescharacteristic
184C22×C139C22×#4111yescharacteristic
185C22×C139C2×2−1+412yes—
186C22×C139#58512yes—
187C4×C139—26no—
188C4×C139—22no—
189C4×C139—26no—
190C4×C139—24no—
191C4×C139—43no—
192C4×C139—46no—
193C4×C139—41no—
194C4×C139—42no—
195C4×C139—46no—
196C4×C139C2×C22⋊Q8112yes—
197C2×C139—42no—
198C2×C139C22×C22⋊Q811yescharacteristic
199C2×C139#348711yescharacteristic
200C2×C139#349911yescharacteristic
201C2×C139#350212yes—
202C2×C139#351612yes—
203#35845C13911yesmaximal, characteristic, direct product factor, Sylow
204C139#3584511yescharacteristic, direct product factor, Sylow
205C2×#557C2×C13911yescharacteristic, complemented
206C2×#519C2×C13911yescharacteristic
207#2628C2×C13913yes—
208#2581C2×C13913yescomplemented
209#2567C2×C13913yescomplemented
210#2453C2×C13916yescomplemented
211#2441C2×C13916yes—
212#2396C2×C13913yes—
213#2351C2×C13911yescharacteristic, complemented
214Q8×C4⋊C4C2×C13912yescomplemented
215Q8×C22⋊C4C2×C13912yes—
216C23×Q8C22×C13911yescharacteristic
217#557—28no—
218C2×C4⋊Q8C22×C13913yes—
219C2×#125C22×C13916yes—
220#519—28no—
221C2×C4×Q8C22×C13913yes—
222C2×C4×Q8C22×C13913yes—
223C2×C4×Q8C22×C13912yes—
224C2×C4×Q8C22×C13912yes—
225C2×C4×Q8C22×C13911yescharacteristic
226C2×C4×Q8C22×C13913yes—
227C2×C4×Q8C22×C13911yescharacteristic
228C2×#117C22×C13913yes—
229C2×#117C22×C13913yes—
230#400C22×C13913yes—
231#400C22×C13916yes—
232#399C22×C13916yes—
233#399C22×C13911yescharacteristic
234#398C22×C13916yes—
235#396C22×C13916yes—
236#395C22×C13913yes—
237#395C22×C13916yes—
238#393C22×C13913yes—
239#391C22×C13916yes—
240#391C22×C13916yes—
241#389C22×C139112yes—
242#389C22×C13916yes—
243#389C22×C13916yes—
244#389C22×C13916yes—
245#387C22×C139112yes—
246#384C22×C13916yes—
247#382C22×C13913yes—
248#380C22×C13916yes—
249C4×C4⋊C4C22×C13913yes—
250C4×C4⋊C4C22×C13916yes—
251C4×C22⋊C4C22×C13916yes—
252C22×Q8—24no—
253C22×Q8—24no—
254C22×Q8Q8×C13918yescomplemented
255C22×Q8C23×C13913yes—
256C22×Q8C23×C13913yes—
257C22×Q8C23×C13911yescharacteristic
258C23×C4C23×C13913yes—
259C4⋊Q8—212no—
260#125—224no—
261C4×Q8—24no—
262C4×Q8—28no—
263C4×Q8—28no—
264C4×Q8—212no—
265C4×Q8—212no—
266C4×Q8—212no—
267C4×Q8D4×C13918yes—
268#117—212no—
269#117—212no—
270C2×C4⋊C4C23×C13913yes—
271C2×C4⋊C4C23×C13913yes—
272C2×C4⋊C4C23×C13913yes—
273C2×C4⋊C4C23×C13911yescharacteristic
274C2×C4⋊C4C23×C13916yes—
275C2×C4⋊C4C23×C13916yes—
276C2×C4⋊C4C23×C13916yes—
277C2×C4⋊C4C23×C13916yes—
278C2×C4⋊C4C23×C13912yes—
279C2×C4⋊C4C23×C13916yes—
280C2×C4⋊C4C23×C13916yes—
281C2×C4⋊C4C23×C139112yes—
282C2×C4⋊C4C23×C13913yes—
283C2×C22⋊C4C23×C13911yescharacteristic
284C2×C22⋊C4C23×C13913yes—
285C2×C22⋊C4C23×C13912yes—
286C2×C22⋊C4C23×C13916yes—
287C2×C42C23×C13913yes—
288C2×C42C23×C13916yes—
289C2×C42C23×C13916yes—
290C2×C42C23×C13916yes—
291C2×C42C23×C13913yes—
292#95C23×C13916yes—
293#95C23×C13916yes—
294#95C23×C13911yescharacteristic
295#95C23×C13913yes—
296#95C23×C13916yes—
297#95C23×C13916yes—
298#95C23×C139112yes—
299#95C23×C13916yes—
300C24C24×C13911yescharacteristic
301C2×Q8—232no—
302C2×Q8—26no—
303C2×Q8—26no—
304C2×Q8—26no—
305C2×Q8—46no—
306C2×Q8C2×D4×C13914yes—
307C2×Q8C2×Q8×C139112yes—
308C2×Q8C2×Q8×C13914yes—
309C2×Q8#41×C13914yes—
310C22×C4—26no—
311C22×C4—26no—
312C22×C4C2×Q8×C139112yes—
313C22×C4C24×C13916yes—
314C22×C4C24×C13911yescharacteristic
315C22×C4C24×C13912yes—
316C22×C4C24×C13916yes—
317C22×C4C24×C13913yes—
318C22×C4C24×C13911yescharacteristic
319C22×C4C24×C13913yes—
320C22×C4C24×C13913yes—
321C22×C4C24×C13912yes—
322C22×C4C24×C13913yes—
323C4⋊C4—26no—
324C4⋊C4—26no—
325C4⋊C4—26no—
326C4⋊C4—22no—
327C4⋊C4—212no—
328C4⋊C4—212no—
329C4⋊C4—212no—
330C4⋊C4—212no—
331C4⋊C4—212no—
332C4⋊C4—24no—
333C4⋊C4—46no—
334C4⋊C4—412no—
335C4⋊C4C2×D4×C139112yes—
336C22⋊C4—26no—
337C22⋊C4—22no—
338C22⋊C4—24no—
339C22⋊C4—46no—
340C42—212no—
341C42—26no—
342C42—212no—
343C42—212no—
344C42C2×D4×C139112yes—
345C23—21no—
346C23—21no—
347C23—22no—
348C23—22no—
349C23C22×Q8×C13912yes—
350C23C25×C13911yescharacteristic
351Q8—224no—
352Q8—412no—
353Q8C22⋊Q8×C139116yes—
354C2×C4—23no—
355C2×C4—22no—
356C2×C4—23no—
357C2×C4—26no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—224no—
361C2×C4—23no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—26no—
370C2×C4—26no—
371C2×C4—26no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4C22×D4×C13916yes—
375C2×C4C22×D4×C13912yes—
376C2×C4C22×D4×C13916yes—
377C2×C4C22×Q8×C13916yes—
378C2×C4C22×Q8×C13916yes—
379C2×C4C2×#41×C13916yes—
380C2×C42−1+4×C13914yes—
381C22—22no—
382C22—24no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22C23×D4×C13911yescharacteristic
387C22C23×Q8×C13911yescharacteristic
388C22C22×#41×C13911yescharacteristic
389C22C2×2−1+4×C13912yes—
390C22#585×C13912yes—
391C4—26no—
392C4—22no—
393C4—26no—
394C4—24no—
395C4—46no—
396C4—43no—
397C4—41no—
398C4—42no—
399C4—46no—
400C4C2×C22⋊Q8×C139112yes—
401C2—42no—
402C2C22×C22⋊Q8×C13911yescharacteristic
403C2#3487×C13911yescharacteristic
404C2#3499×C13911yescharacteristic
405C2#3502×C13912yes—
406C2#3516×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC24×C139C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#557×C139C2semidirect
4. #2581×C139C2semidirect
5. #2567×C139C2semidirect
6. #2453×C139C2semidirect
9. #2351×C139C2semidirect
10. Q8×C4⋊C4×C139C2semidirect
50. C22×Q8×C139Q8semidirect
203. #35845C139direct (N × H)
204. C139#35845direct (N × H)
205. C2×#557C2×C139semidirect
208. #2581C2×C139semidirect
209. #2567C2×C139semidirect
210. #2453C2×C139semidirect
213. #2351C2×C139semidirect
214. Q8×C4⋊C4C2×C139semidirect
254. C22×Q8Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1392
C2×#519×C1392
#2628×C1392
#2581×C1392
#2567×C1392
#2453×C1392
#2441×C1392
#2396×C1392
#2351×C1392
Q8×C4⋊C4×C1392
Q8×C22⋊C4×C1392
#35845139