Finite Group Databasebeta

← C2×#11727015 #13508364

Subgroups — C2×#11727015 #13508364

Order 1792.

658 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×#89932C211yesmaximal, characteristic
2C22×#6401C211yesmaximal, characteristic, complemented
3C2×#89679C211yesmaximal, characteristic, complemented
4C2×#89668C211yesmaximal, characteristic, complemented
5C2×C7×#361C211yesmaximal, characteristic, complemented
6C2×#89312C211yesmaximal, characteristic, complemented
7C2×#89288C211yesmaximal, characteristic, complemented
8#11727015C218yesmaximal, direct product factor
9C22×C7×D8C2211yescharacteristic
10C2×#6495—21no—
11C2×#6472—21no—
12C22×Dic28C2211yescharacteristic
13C2×#6464C2211yescharacteristic
14C2×C7×M32C2211yescharacteristic
15C2×C7×#108C2211yescharacteristic
16C2×#6407—21no—
17#89932—22no—
18#89932C2214yes—
19C2×#6401—21no—
20C2×#6401—21no—
21C2×#6401—22no—
22C2×#6401C2214yescomplemented
23C2×#6398—21no—
24C2×#6393C2211yescharacteristic
25C22×C7⋊C16C2211yescharacteristic
26#89679—22no—
27#89679C2214yescomplemented
28C2×#6372—21no—
29C2×D7×C16—21no—
30#89668—22no—
31#89668C2214yescomplemented
32C7×#361C2214yescomplemented
33#89312C2214yescomplemented
34#89288C2214yescomplemented
35C2×#2223—71nomaximal, Sylow
36C22×C7×D4—21no—
37C2×#1157D411yescharacteristic
38C22×Dic14—21no—
39C2×C7×D8—21no—
40C2×C7×D8—21no—
41C2×C7×D8—21no—
42C2×C7×D8—21no—
43C2×C7×D8—21no—
44C2×C7×D8C2312yes—
45C2×C7×M16—21no—
46C22×C7×C8C2311yescharacteristic
47C2×#1142—41no—
48#6495—24no—
49#6495—42no—
50C2×#1141—41no—
51C2×#1136—21no—
52C2×#1136D411yescharacteristic
53#6472—24no—
54#6472—42no—
55C2×Dic28—21no—
56C2×Dic28—21no—
57C2×Dic28—21no—
58C2×Dic28—21no—
59C2×Dic28—21no—
60C2×Dic28—41no—
61C2×Dic28C2312yes—
62C2×#1132—41no—
63#6464—21no—
64#6464—21no—
65#6464D412yes—
66#6464C2312yes—
67C2×#1131—21no—
68C2×C8×D7—21no—
69C7×M32—21no—
70C7×M32C2312yes—
71C2×C7×C16—21no—
72C7×#108—21no—
73C7×#108C2312yes—
74#6407—24no—
75#6401—24no—
76#6401—24no—
77#6398—24no—
78#6393—21no—
79#6393C2312yes—
80C2×C7⋊C16D411yescharacteristic
81C2×C7⋊C16D411yescharacteristic
82C2×C7⋊C16D412yes—
83C2×C7⋊C16C2312yes—
84#6372—24no—
85D7×C16—24no—
86C22×SD32—71no—
87C2×#504—71no—
88C2×#473—71no—
89C2×#472—71no—
90#2223—78no—
91C2×#368—71no—
92C2×#362—71no—
93C2×#361D711yescharacteristic, complemented
94C24×C7—41no—
95C2×C7×D4—22no—
96C2×C7×D4—41no—
97C2×C7×D4—41no—
98C2×C7×D4—41no—
99C2×C7×D4—41no—
100C2×C7×D4—41no—
101C22×C4×C7C2×D411yescharacteristic
102C2×C22⋊D7—21no—
103C22×Dic7—41no—
104#1157—21no—
105#1157—21no—
106#1157D812yes—
107#1157C2×D412yes—
108C2×D28D811yescharacteristic
109C2×C4×D7—21no—
110C2×Dic14—22no—
111C2×Dic14—41no—
112C2×Dic14—41no—
113C2×Dic14—41no—
114C2×Dic14—41no—
115C2×Dic14—41no—
116C2×Dic14D811yescharacteristic
117C7×D8—22no—
118C7×D8—22no—
119C7×D8—41no—
120C7×D8—41no—
121C7×M16—22no—
122C7×M16—41no—
123C2×C7×C8—41no—
124C2×C7×C8C2×D411yescharacteristic
125C2×C7×C8C2×D411yescharacteristic
126C2×C7×C8C2×D411yescharacteristic
127C2×C7×C8#4111yescharacteristic
128C2×C7×C8#4111yescharacteristic
129C2×C7×C8C2411yescharacteristic
130#1142—44no—
131#1141—44no—
132#1136—21no—
133#1136—22no—
134#1136—41no—
135#1136C2×D412yes—
136C2×C7⋊C8—21no—
137C2×C7⋊C8—41no—
138Dic28—22no—
139Dic28—22no—
140Dic28—44no—
141Dic28—41no—
142Dic28—41no—
143#1132—44no—
144#1131—22no—
145#1131—22no—
146C8×D7—22no—
147C8×D7—22no—
148C7×C16—22no—
149C7⋊C16C2×D412yes—
150C7⋊C16C2×D412yes—
151C2×#137—141no—
152C2×AGL(1,ℤ/8)—141no—
153C22×Q16—71no—
154C22×D8C2×D711yescharacteristic
155C2×#131—71no—
156C2×SD32—74no—
157C2×SD32—141no—
158C2×SD32—141no—
159C2×SD32—142no—
160#504—74no—
161#504—142no—
162C2×M32—141no—
163C2×M32C2×D711yescharacteristic
164C22×C16—71no—
165C22×C16—141no—
166#473—74no—
167#473—142no—
168#472—74no—
169#472—142no—
170C2×#108—71no—
171C2×#108C2×D711yescharacteristic
172C2×#101—141no—
173C2×#100—141no—
174#368—74no—
175#362—74no—
176#361C2×D714yescomplemented
177C23×C7—42no—
178C23×C7—81no—
179C23×C7—81no—
180C23×C7—162no—
181C23×C7#13511yescharacteristic
182C22×D7—21no—
183C7×D4—42no—
184C7×D4—42no—
185C7×D4—81no—
186C7×D4—81no—
187C2×C4×C7#12111yescharacteristic
188C2×C4×C7#12111yescharacteristic
189C2×C4×C7C2×D811yescharacteristic
190C2×C4×C7C2×D811yescharacteristic
191C2×C4×C7#13511yescharacteristic
192C2×C4×C7C22×D411yescharacteristic
193C22⋊D7—22no—
194C22⋊D7—22no—
195C2×Dic7—21no—
196C2×Dic7—42no—
197C2×Dic7—81no—
198C2×Dic7—81no—
199D28—21no—
200D28C2×D812yes—
201C4×D7—22no—
202C4×D7—22no—
203Dic14—21no—
204Dic14—42no—
205Dic14—42no—
206Dic14—81no—
207Dic14—81no—
208Dic14C2×D812yes—
209C7×C8—42no—
210C7×C8#12111yescharacteristic
211C7×C8#12111yescharacteristic
212C7×C8C22×D411yescharacteristic
213C7×C8C2×#4111yescharacteristic
214C7⋊C8—22no—
215C7⋊C8—42no—
216C2×#41—71no—
217C22×Q8—141no—
218C22×D4—21no—
219#137—144no—
220#137—282no—
221AGL(1,ℤ/8)—144no—
222AGL(1,ℤ/8)—282no—
223C2×Q16—72no—
224C2×Q16—141no—
225C2×Q16—141no—
226C2×Q16—141no—
227C2×Q16—141no—
228C2×Q16—141no—
229C2×Q16—281no—
230C2×SD16—281no—
231C2×SD16—281no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—281no—
238C2×D8C22×D712yes—
239#131—72no—
240#131—72no—
241#131—141no—
242#131—141no—
243C2×M16—21no—
244C2×M16—71no—
245C2×M16—141no—
246C2×M16—141no—
247C22×C8—141no—
248C22×C8C22×D711yescharacteristic
249SD32—144no—
250SD32—144no—
251M32—21no—
252M32—144no—
253M32C22×D712yes—
254C2×C16—21no—
255C2×C16—71no—
256C2×C16—71no—
257C2×C16—72no—
258C2×C16—72no—
259C2×C16—144no—
260#108—21no—
261#108—72no—
262#108—141no—
263#108C22×D712yes—
264#101—144no—
265#100—144no—
266C22×C7—22no—
267C22×C7—82no—
268C22×C7—162no—
269C22×C7—162no—
270C22×C7—162no—
271C22×C7#46611yescharacteristic
272C22×C7#46611yescharacteristic
273C22×C7C2×#13511yescharacteristic
274C2×D7—22no—
275C2×D7—42no—
276C4×C7#46611yescharacteristic
277C4×C7#46611yescharacteristic
278C4×C7C2×#12111yescharacteristic
279C4×C7C22×D811yescharacteristic
280Dic7—22no—
281Dic7—82no—
282C24—41no—
283#41—72no—
284#41—72no—
285#41—141no—
286#41—141no—
287C2×Q8—71no—
288C2×Q8—142no—
289C2×Q8—281no—
290C2×Q8—281no—
291C2×Q8—281no—
292C2×Q8—281no—
293C2×Q8—281no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—71no—
301C2×D4—141no—
302C22×C4—141no—
303C22×C4—281no—
304C22×C4D4×D711yescharacteristic
305Q16—142no—
306Q16—142no—
307Q16—284no—
308Q16—281no—
309Q16—281no—
310SD16—284no—
311SD16—284no—
312D8—22no—
313D8—22no—
314D8—41no—
315D8—41no—
316D8—284no—
317M16—22no—
318M16—41no—
319M16—72no—
320M16—141no—
321M16—142no—
322M16—142no—
323M16—142no—
324M16—281no—
325C2×C8—41no—
326C2×C8—141no—
327C2×C8—142no—
328C2×C8—142no—
329C2×C8—281no—
330C2×C8#115711yescharacteristic
331C2×C8#115711yescharacteristic
332C2×C8D4×D711yescharacteristic
333C2×C8D4×D711yescharacteristic
334C2×C8D4×D711yescharacteristic
335C2×C8C23×D711yescharacteristic
336C16—22no—
337C16—72no—
338C16—72no—
339C2×C7—21no—
340C2×C7—21no—
341C2×C7—162no—
342C2×C7#222312yescomplemented
343C2×C7C2×#46611yescharacteristic
344D7—42no—
345C23—42no—
346C23—81no—
347C23—81no—
348C23—141no—
349C23—162no—
350C23#647911yescharacteristic
351Q8—72no—
352Q8—141no—
353Q8—282no—
354Q8—282no—
355Q8—561no—
356Q8—561no—
357D4—42no—
358D4—42no—
359D4—72no—
360D4—81no—
361D4—81no—
362D4—142no—
363D4—142no—
364D4—141no—
365C2×C4—141no—
366C2×C4—142no—
367C2×C4—142no—
368C2×C4—282no—
369C2×C4—561no—
370C2×C4—561no—
371C2×C4#644711yescharacteristic
372C2×C4#644711yescharacteristic
373C2×C4D7×D811yescharacteristic
374C2×C4D7×D811yescharacteristic
375C2×C4#647911yescharacteristic
376C2×C4C2×D4×D711yescharacteristic
377C8—42no—
378C8—142no—
379C8—282no—
380C8#644711yescharacteristic
381C8#644711yescharacteristic
382C8C2×#115711yescharacteristic
383C8C2×D4×D711yescharacteristic
384C7C2×#222311yescharacteristic, complemented, Sylow
385C22—22no—
386C22—82no—
387C22—142no—
388C22—162no—
389C22—162no—
390C22—162no—
391C22—282no—
392C22#8954711yescharacteristic
393C22#8954711yescharacteristic
394C22C2×#647911yescharacteristic
395C4—142no—
396C4—562no—
397C4#8954711yescharacteristic
398C4#8954711yescharacteristic
399C4C2×#644711yescharacteristic
400C4C2×D7×D811yescharacteristic
401C2—21no—
402C2—21no—
403C2—162no—
404C2—282no—
405C2#1172701512yesdirect product factor
406C2C2×#8954711yescharacteristic
subgroupG/H
centerC22#89547
commutator, cosocleC2×C7×C8C24
FrattiniC2×C8C23×D7
FittingC2×C7×#361C2
socleC22×C7#466
prime radicalC2×#89932C2
hypercenterC2×#361D7
hypocenterC7C2×#2223
LCSG ▷ C2×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C22×#6401C2semidirect
3. C2×#89679C2semidirect
4. C2×#89668C2semidirect
5. C2×C7×#361C2semidirect
6. C2×#89312C2semidirect
7. C2×#89288C2semidirect
8. #11727015C2direct (N × H)
22. C2×#6401C22semidirect
27. #89679C22semidirect
31. #89668C22semidirect
32. C7×#361C22semidirect
33. #89312C22semidirect
34. #89288C22semidirect
93. C2×#361D7semidirect
176. #361C2×D7semidirect
342. C2×C7#2223semidirect
384. C7C2×#2223semidirect
405. C2#11727015direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#899322
C22×#64012
C2×#896792
C2×#896682
C2×C7×#3612
C2×#893122
C2×#892882
#117270152
C2×#22237