Finite Group Databasebeta

← #13248878

Subgroups — #13248878

Order 1792.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#11739937C211yesmaximal, characteristic
2#11739881C211yesmaximal, characteristic, complemented
3C4×C7×#101C211yesmaximal, characteristic, complemented
4#11727609C212yesmaximal
5#11725471C212yesmaximal, complemented
6C2×C4×C7×Q8C2211yescharacteristic
7C2×C4×D28C2211yescharacteristic
8C2×C7×#101—21no—
9C4×C7×M16C2212yes—
10#90003—21no—
11#89796—24no—
12#89765—21no—
13#89763C411yescharacteristic
14#89763C411yescharacteristic
15#89758C411yescharacteristic
16#89758C411yescharacteristic
17C4×(C2×D7)⋊C4—21no—
18C4×(C2×D7)⋊C4—21no—
19#89704C2211yescharacteristic
20#89698—21no—
21#89698C2212yes—
22#89697—21no—
23C7×#343—21no—
24#89254—24no—
25#9032—71nomaximal, Sylow
26C22×C7×Q8D411yescharacteristic
27C22×D28C2×C411yescharacteristic
28C22×C4×D7—21no—
29C2×C7×M16—22no—
30C4×C7×Q8—22no—
31C4×C7×Q8—22no—
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C42×C7C2311yescharacteristic
38C2×(C2×D7)⋊C4—21no—
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×C4⋊Dic7C2×C411yescharacteristic
44C2×C4×Dic7—21no—
45C4×D28—22no—
46C4×D28—22no—
47C7×#101—24no—
48C7×#97—22no—
49C4×C7×C8—22no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95C2×C411yescharacteristic
56C7⋊#95C2×C411yescharacteristic
57C22⋊(C7⋊C8)—22no—
58C4⋊(C7⋊C8)—22no—
59C4⋊(C7⋊C8)—22no—
60C4⋊(C7⋊C8)D414yes—
61#6377—22no—
62#6377—22no—
63C4×C7⋊C8—22no—
64#2983—71no—
65#2398—71no—
66C4×#101D711yescharacteristic, complemented
67#1490—72no—
68#1300—72no—
69C23×D7—21no—
70C2×C7×Q8—22no—
71C2×C7×Q8—22no—
72C2×C7×Q8—41no—
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C2×D28—22no—
84C2×D28—42no—
85C2×C4×D7—42no—
86C2×C4×D7—42no—
87C2×C4×D7—41no—
88C2×C4×D7—41no—
89C7×M16—24no—
90C7×M16—42no—
91C2×C7×C8—42no—
92C7×C4⋊C4—22no—
93C7×C4⋊C4—22no—
94C7×C4⋊C4—22no—
95C42×C7—21no—
96C42×C7—21no—
97C42×C7—21no—
98C42×C7—21no—
99C42×C7C2×D412yes—
100C42×C7#4112yes—
101(C2×D7)⋊C4—42no—
102(C2×D7)⋊C4—42no—
103(C2×D7)⋊C4—42no—
104(C2×D7)⋊C4—42no—
105(C2×D7)⋊C4—42no—
106C4⋊Dic7—22no—
107C4×Dic7—42no—
108C2×C7⋊C8—24no—
109C2×C4×Q8C2×D711yescharacteristic
110C2×C4×D4—71no—
111#446—144no—
112#432—72no—
113#432—141no—
114#431—141no—
115C2×#101—21no—
116C4×M16C2×D712yes—
117#400—71no—
118#400—71no—
119#397—141no—
120#394—71no—
121#394—71no—
122#393—141no—
123C4×C22⋊C4—141no—
124C4×C22⋊C4—141no—
125#376—71no—
126#343—21no—
127D4⋊C8—144no—
128C23×C7C2×C22⋊C411yescharacteristic
129C22×D7—22no—
130C22×D7—41no—
131C22×D7—41no—
132C22×D7—41no—
133C22×D7—41no—
134C22×D7—41no—
135C22×D7—41no—
136C7×Q8—44no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—22no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7#10412yes—
151C2×C4×C7C4×D412yes—
152C2×C4×C7#12011yescharacteristic
153C2×C4×C7#12112yes—
154C2×C4×C7#12311yescharacteristic
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164D28—24no—
165D28—42no—
166C4×D7—82no—
167C4×D7—82no—
168C7×C8—44no—
169C7⋊C8—44no—
170C22×Q8C22⋊D711yescharacteristic
171C22×D4—71no—
172C23×C4—141no—
173C2×M16—22no—
174C4×Q8—22no—
175C4×Q8—22no—
176C4×D4—142no—
177C4×D4—142no—
178C2×C4⋊C4—71no—
179C2×C4⋊C4C4×D711yescharacteristic
180C2×C4⋊C4C4×D711yescharacteristic
181C2×C4⋊C4C22⋊D711yescharacteristic
182C2×C22⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4—141no—
186C2×C22⋊C4—141no—
187C2×C42—141no—
188C2×C42D2811yescharacteristic
189C2×C42D2811yescharacteristic
190C2×C42C22×D711yescharacteristic
191C4⋊C8—74no—
192C4⋊C8—142no—
193C4⋊C8—142no—
194#101—24no—
195C22⋊C8—142no—
196#97—22no—
197#97—142no—
198#97—142no—
199C4×C8—22no—
200C4×C8—142no—
201#95—71no—
202#95—71no—
203#95—141no—
204#95—141no—
205#95—141no—
206#95—141no—
207#95—141no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7#38611yescharacteristic
211C22×C7C2×#10411yescharacteristic
212C22×C7#42111yescharacteristic
213C2×D7—42no—
214C2×D7—42no—
215C2×D7—42no—
216C2×D7—81no—
217C2×D7—81no—
218C2×D7—81no—
219C2×D7—81no—
220C4×C7—22no—
221C4×C7—22no—
222C4×C7—21no—
223C4×C7—22no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227C4×C7#45412yes—
228Dic7—81no—
229Dic7—81no—
230Dic7—81no—
231C24—141no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×D4—142no—
236C2×D4—282no—
237C22×C4—141no—
238C22×C4—141no—
239C22×C4—141no—
240C22×C4—282no—
241C22×C4—282no—
242C22×C4—281no—
243C22×C4—281no—
244C22×C4(C2×D7)⋊C411yescharacteristic
245C22×C4(C2×D7)⋊C411yescharacteristic
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4C2×C4×D711yescharacteristic
249C22×C4C2×D2811yescharacteristic
250C22×C4C2×C22⋊D711yescharacteristic
251M16—24no—
252M16—42no—
253C2×C8—42no—
254C2×C8—144no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—142no—
259C22⋊C4—282no—
260C22⋊C4—282no—
261C22⋊C4—282no—
262C22⋊C4—282no—
263C22⋊C4—282no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—282no—
269C42D4×D712yes—
270C42#115912yes—
271C2×C7—21no—
272C2×C7—21no—
273C2×C7#187111yescharacteristic
274C2×C7#188811yescharacteristic
275C2×C7#189111yescharacteristic
276D7—82no—
277C23—142no—
278C23—281no—
279C23—281no—
280C23—281no—
281C23—281no—
282C23—281no—
283C23—281no—
284C23C2×(C2×D7)⋊C411yescharacteristic
285Q8—44no—
286D4—144no—
287D4—282no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—562no—
311C2×C4—562no—
312C2×C4#637912yes—
313C2×C4(C22⋊D7)⋊C412yes—
314C2×C4#644511yescharacteristic
315C2×C4#644911yescharacteristic
316C2×C4#650212yes—
317C8—44no—
318C8—284no—
319C7#903211yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—282no—
323C22—282no—
324C22—282no—
325C22—561no—
326C22—561no—
327C22—561no—
328C22—561no—
329C22C2×#637911yescharacteristic
330C22#8973011yescharacteristic
331C22#8977711yescharacteristic
332C4—22no—
333C4—22no—
334C4—22no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—561no—
340C4—561no—
341C4—561no—
342C4#8952512yes—
343C2—21no—
344C2—21no—
345C2—562no—
346C2#1172720711yescharacteristic
347C2#1172785811yescharacteristic
348C2#1172789011yescharacteristic
subgroupG/H
centerC2×C4#6445
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC4×C7×#101C2
socleC22×C7#386
prime radicalC22×D28C2×C4
cosocleC2×C42×C7C23
hypercenterC4×#101D7
hypocenterC7#9032
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #11739881C2semidirect
3. C4×C7×#101C2semidirect
5. #11725471C2semidirect
66. C4×#101D7semidirect
319. C7#9032semidirect

Maximal subgroups

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

subgroupindex
#117399372
#117398812
C4×C7×#1012
#117276092
#117254712
#90327