Finite Group Databasebeta

← #13258366

Subgroups — #13258366

Order 1792.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#1948C211yesmaximal, characteristic, complemented
2C2×#89280C211yesmaximal, characteristic
3C2×#89275C211yesmaximal, characteristic, complemented
4#11727334C211yesmaximal, characteristic
5#11727241C211yesmaximal, characteristic
6#11727238C211yesmaximal, characteristic, complemented
7#11725440C211yesmaximal, characteristic, complemented
8C2×#6437C2211yescharacteristic
9C2×C7×#106—21no—
10C2×C7×C4⋊C8C2211yescharacteristic
11C7×#384C2211yescharacteristic
12C4×C7×C4⋊C4C2211yescharacteristic
13C2×#6383—21no—
14C2×#6383—21no—
15C2×#6383—21no—
16C2×#6383—21no—
17C2×C4⋊(C7⋊C8)—21no—
18C2×C4⋊(C7⋊C8)C2211yescharacteristic
19C2×C4⋊(C7⋊C8)C2211yescharacteristic
20C2×C4×C7⋊C8C2211yescharacteristic
21C7×#340—21no—
22#89319—21no—
23#89280—22no—
24#89275—22no—
25#10595—71nomaximal, Sylow
26C22×D28—21no—
27C22×D28—21no—
28C22×D28—21no—
29C22×C7×C8—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C42×C7—21no—
36C2×C42×C7C2311yescharacteristic
37C22×C7⋊C8—21no—
38C22×C7⋊C8—21no—
39C22×C7⋊C8D411yescharacteristic
40C22×C7⋊C8D411yescharacteristic
41#6437—21no—
42#6437—21no—
43#6437—21no—
44#6437Q812yes—
45C7×#106—42no—
46C7×C4⋊C8—21no—
47C7×C4⋊C8D412yes—
48C7×#95—21no—
49#6383—42no—
50#6383—42no—
51#6383—42no—
52#6383—42no—
53C4⋊(C7⋊C8)—21no—
54C4⋊(C7⋊C8)—21no—
55C4⋊(C7⋊C8)—21no—
56C4⋊(C7⋊C8)—21no—
57C4⋊(C7⋊C8)—42no—
58C4×C7⋊C8—21no—
59C4×C7⋊C8—21no—
60#1982—71no—
61#1957—71no—
62#1948D711yescharacteristic, complemented
63#1939—71no—
64C2×#334—71no—
65C2×#331—71no—
66#1296—71no—
67C23×D7—41no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—41no—
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7#4111yescharacteristic
74C2×D28—22no—
75C2×D28—22no—
76C2×D28—22no—
77C2×D28—41no—
78C2×D28—41no—
79C2×D28—41no—
80C2×D28—41no—
81C2×D28—41no—
82C2×D28—41no—
83C2×D28—41no—
84C2×D28—41no—
85C2×D28—41no—
86C2×D28—41no—
87C2×D28—41no—
88C2×D28—81no—
89C2×D28—81no—
90C2×C7×C8—22no—
91C2×C7×C8—41no—
92C2×C7×C8—41no—
93C7×C4⋊C4—21no—
94C7×C4⋊C4—21no—
95C7×C4⋊C4—21no—
96C7×C4⋊C4—41no—
97C7×C4⋊C4—41no—
98C7×C4⋊C4—41no—
99C7×C4⋊C4—41no—
100C7×C4⋊C4—81no—
101C7×C4⋊C4SD1612yes—
102C42×C7—41no—
103C42×C7—41no—
104C42×C7C2×D411yescharacteristic
105C42×C7C2×Q811yescharacteristic
106C42×C7#4111yescharacteristic
107C42×C7#4111yescharacteristic
108C2×C7⋊C8—21no—
109C2×C7⋊C8—21no—
110C2×C7⋊C8—21no—
111C2×C7⋊C8—21no—
112C2×C7⋊C8—21no—
113C2×C7⋊C8—41no—
114C2×C7⋊C8—41no—
115C2×C7⋊C8—41no—
116C2×C7⋊C8—41no—
117C2×C7⋊C8—41no—
118C2×C7⋊C8—41no—
119C2×C7⋊C8SD1612yes—
120C2×#127—71no—
121C2×#106—21no—
122C2×C4⋊C8—71no—
123C2×C4⋊C8—71no—
124C2×C4⋊C8—141no—
125C2×C4⋊C8C2×D711yescharacteristic
126C2×#102—141no—
127C2×#102—141no—
128C2×#102—141no—
129C2×#102—141no—
130C2×C4×C8—71no—
131#384C2×D711yescharacteristic
132C4×C4⋊C4C2×D711yescharacteristic
133#340—21no—
134#336—141no—
135#334—142no—
136#331—142no—
137C23×C7#12111yescharacteristic
138C22×D7—42no—
139C22×D7—81no—
140C22×D7—81no—
141C22×D7—81no—
142C22×D7—81no—
143C22×D7—81no—
144C22×D7—81no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—22no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—81no—
154C2×C4×C7—81no—
155C2×C4×C7—81no—
156C2×C4×C7#12111yescharacteristic
157C2×C4×C7#12111yescharacteristic
158C2×C4×C7C22⋊Q811yescharacteristic
159C2×C4×C7C22⋊Q811yescharacteristic
160C2×C4×C7C22⋊Q811yescharacteristic
161C2×C4×C7#12611yescharacteristic
162C2×C4×C7C2×SD1611yescharacteristic
163C2×C4×C7C2×SD1611yescharacteristic
164C2×C4×C7#13511yescharacteristic
165C2×C4×C7#13511yescharacteristic
166C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
170D28—42no—
171D28—42no—
172D28—42no—
173D28—42no—
174D28—82no—
175D28—82no—
176D28—81no—
177D28—81no—
178D28—81no—
179D28—81no—
180C7×C8—42no—
181C7⋊C8—22no—
182C7⋊C8—41no—
183C7⋊C8—81no—
184C7⋊C8—81no—
185C22×D4—141no—
186C22×D4—141no—
187C22×D4—141no—
188C22×C8—21no—
189C22×C8—71no—
190C22×C8—71no—
191C22×C8—141no—
192C22×C8—141no—
193#127—72no—
194#127—141no—
195#127—141no—
196#127—141no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C22⋊D711yescharacteristic
201C2×C4⋊C4C22⋊D711yescharacteristic
202C2×C42—21no—
203C2×C42C22×D711yescharacteristic
204#106—42no—
205C4⋊C8—21no—
206C4⋊C8—141no—
207C4⋊C8—141no—
208C4⋊C8—141no—
209C4⋊C8—141no—
210C4⋊C8—282no—
211C4⋊C8D2812yes—
212#102—282no—
213#102—282no—
214#102—282no—
215#102—282no—
216C4×C8—141no—
217C4×C8—141no—
218#95—21no—
219C22×C7#39611yescharacteristic
220C22×C7#46011yescharacteristic
221C22×C7#46311yescharacteristic
222C22×C7#46511yescharacteristic
223C22×C7#46911yescharacteristic
224C22×C7#47111yescharacteristic
225C22×C7#47211yescharacteristic
226C2×D7—82no—
227C2×D7—82no—
228C2×D7—82no—
229C2×D7—161no—
230C2×D7—161no—
231C2×D7—161no—
232C2×D7—161no—
233C4×C7—21no—
234C4×C7—21no—
235C4×C7—42no—
236C4×C7—81no—
237C4×C7—161no—
238C4×C7#46011yescharacteristic
239C4×C7#46311yescharacteristic
240C4×C7#46511yescharacteristic
241C4×C7#46911yescharacteristic
242C4×C7#47611yescharacteristic
243C4×C7#47611yescharacteristic
244C4×C7#47811yescharacteristic
245C4×C7#47811yescharacteristic
246C24—281no—
247C2×D4—142no—
248C2×D4—142no—
249C2×D4—142no—
250C2×D4—281no—
251C2×D4—281no—
252C2×D4—281no—
253C2×D4—281no—
254C2×D4—281no—
255C2×D4—281no—
256C2×D4—281no—
257C2×D4—281no—
258C2×D4—281no—
259C2×D4—281no—
260C2×D4—281no—
261C2×D4—561no—
262C2×D4—561no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4D4×D711yescharacteristic
267C22×C4#115911yescharacteristic
268C22×C4C2×C22⋊D711yescharacteristic
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—72no—
273C2×C8—141no—
274C2×C8—141no—
275C2×C8—141no—
276C2×C8—141no—
277C2×C8—141no—
278C2×C8—281no—
279C2×C8—281no—
280C2×C8—281no—
281C2×C8—281no—
282C2×C8—281no—
283C2×C8—281no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C4⋊C4#114312yes—
293C42—41no—
294C42—41no—
295C42C2×D2811yescharacteristic
296C42#115711yescharacteristic
297C42Q8×D711yescharacteristic
298C42#116111yescharacteristic
299C2×C7#166611yescharacteristic
300C2×C7#167711yescharacteristic
301C2×C7#168811yescharacteristic
302C2×C7#170111yescharacteristic
303C2×C7#206311yescharacteristic
304C2×C7#206511yescharacteristic
305C2×C7#206511yescharacteristic
306D7—162no—
307C23—282no—
308C23—561no—
309C23—561no—
310C23—561no—
311C23—561no—
312C23—561no—
313C23—561no—
314C23#650211yescharacteristic
315D4—282no—
316D4—282no—
317D4—282no—
318D4—282no—
319D4—562no—
320D4—562no—
321D4—561no—
322D4—561no—
323D4—561no—
324D4—561no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4#645811yescharacteristic
337C2×C4#645911yescharacteristic
338C2×C4#646011yescharacteristic
339C2×C4#646111yescharacteristic
340C2×C4D7×SD1611yescharacteristic
341C2×C4#647711yescharacteristic
342C2×C4#647711yescharacteristic
343C2×C4#647911yescharacteristic
344C2×C4#649311yescharacteristic
345C2×C4#649511yescharacteristic
346C2×C4C2×#114311yescharacteristic
347C2×C4#650911yescharacteristic
348C2×C4#651211yescharacteristic
349C2×C4#651311yescharacteristic
350C8—42no—
351C8—142no—
352C8—281no—
353C8—561no—
354C8—561no—
355C7#1059511yescharacteristic, complemented, Sylow
356C22—562no—
357C22—562no—
358C22—562no—
359C22—1121no—
360C22—1121no—
361C22—1121no—
362C22—1121no—
363C22#8976611yescharacteristic
364C22#8981111yescharacteristic
365C22#8982011yescharacteristic
366C22#8993511yescharacteristic
367C22#8993711yescharacteristic
368C22#8997111yescharacteristic
369C22#8997511yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#8963611yescharacteristic
376C4#8963711yescharacteristic
377C4#8964211yescharacteristic
378C4#8964311yescharacteristic
379C4#8978811yescharacteristic
380C4#8979911yescharacteristic
381C4#8983811yescharacteristic
382C4#8985611yescharacteristic
383C2—1122no—
384C2#1172738311yescharacteristic
385C2#1172833911yescharacteristic
386C2#1172843011yescharacteristic
387C2#1172877911yescharacteristic
388C2#1172879711yescharacteristic
389C2#1172887011yescharacteristic
390C2#1172888811yescharacteristic
subgroupG/H
centerC23#6502
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1948C2
socleC23×C7#121
prime radicalC2×#6437C22
hypercenter#1948D7
hypocenterC7#10595
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C7×#1948C2semidirect
3. C2×#89275C2semidirect
6. #11727238C2semidirect
7. #11725440C2semidirect
62. #1948D7semidirect
355. C7#10595semidirect

Maximal subgroups

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

subgroupindex
C7×#19482
C2×#892802
C2×#892752
#117273342
#117272412
#117272382
#117254402
#105957