Finite Group Databasebeta

← #13253873

Subgroups — #13253873

Order 1792.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739519C211yesmaximal, characteristic
2C7×C4⋊#95C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4#11725418C212yesmaximal
5#11725418C212yesmaximal
6C22×C7×C4⋊C4—21no—
7C22×C42×C7C2211yescharacteristic
8C2×#6433C411yescharacteristic, complemented
9C2×C7×#95—21no—
10C2×C7×#95C2212yes—
11#89984C2211yescharacteristic
12#89984C2211yescharacteristic
13#89982—21no—
14#89982—21no—
15C2×C22⋊(C7⋊C8)C2212yes—
16#89708C411yescharacteristic, complemented
17#89705—21no—
18#89705—21no—
19#89700C411yescharacteristic, complemented
20#89700C411yescharacteristic, complemented
21C2×#6377—21no—
22#89319—21no—
23#9887—71nomaximal, Sylow
24C23×C4×C7—22no—
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×C4×C7C2311yescharacteristic
28C2×C7×C4⋊C4—24no—
29C2×C7×C4⋊C4—42no—
30C2×C7×C4⋊C4—42no—
31C2×C42×C7—42no—
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7C2×C411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C4⋊Dic7C2×C411yescharacteristic
39C2×C4⋊Dic7C2×C411yescharacteristic
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C22×C7⋊C8—22no—
47#6433—42no—
48C7×#95—24no—
49C7×#95—42no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C22⋊(C7⋊C8)—22no—
57C22⋊(C7⋊C8)Q814yes—
58#6377—42no—
59#2851—71no—
60#1749—71no—
61C4⋊#95D711yescharacteristic
62#1294—72no—
63#1294—72no—
64C24×C7C2×D411yescharacteristic
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—24no—
72C22×C4×C7—41no—
73C22×C4×C7—41no—
74C22×C4×C7—41no—
75C22×C4×C7—41no—
76C22×C4×C7—42no—
77C22×C4×C7—42no—
78C22×C4×C7—42no—
79C22×C4×C7—42no—
80C22×C4×C7—42no—
81C22×C4×C7—42no—
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22⋊C411yescharacteristic
84C22×C4×C7C22⋊C411yescharacteristic
85C22×C4×C7C22⋊C411yescharacteristic
86C22×C4×C7C22×C411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×C4×C7C2×Q812yes—
89C22×C4×C7#4112yes—
90C22×Dic7—21no—
91C22×Dic7—21no—
92C22×Dic7—21no—
93C22×Dic7—21no—
94C7×C4⋊C4—48no—
95C42×C7—22no—
96C42×C7—22no—
97C42×C7—41no—
98C42×C7—41no—
99C22⋊Dic7—41no—
100C22⋊Dic7—41no—
101C22⋊Dic7—41no—
102C22⋊Dic7—41no—
103C4⋊Dic7—41no—
104C4⋊Dic7—41no—
105C4⋊Dic7—41no—
106C4⋊Dic7—41no—
107Dic7⋊C4—42no—
108Dic7⋊C4—42no—
109Dic7⋊C4—42no—
110Dic7⋊C4—42no—
111C2×C7⋊C8—24no—
112C2×C7⋊C8—42no—
113C2×C7⋊C8—42no—
114C2×#125—71no—
115C22×C4⋊C4—21no—
116C22×C42C2×D711yescharacteristic
117C2×C22⋊C8—72no—
118C2×#97—141no—
119#389—71no—
120#389—71no—
121#387—141no—
122#387—141no—
123#385—141no—
124#385—141no—
125#382—71no—
126#380—71no—
127#380—71no—
128C2×#95—21no—
129C2×#95C2×D712yes—
130#336—141no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7C2×C22⋊C411yescharacteristic
136C23×C7#12411yescharacteristic
137C23×C7C4⋊Q811yescharacteristic
138C23×C7AGL(1,ℤ/8)11yescharacteristic
139C23×C7AGL(1,ℤ/8)11yescharacteristic
140C23×C7#13711yescharacteristic
141C23×C7#13711yescharacteristic
142C2×C4×C7—24no—
143C2×C4×C7—24no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—21no—
157C2×C4×C7—21no—
158C2×C4×C7—42no—
159C2×C4×C7—42no—
160C2×C4×C7—42no—
161C2×C4×C7—42no—
162C2×C4×C7—44no—
163C2×C4×C7—44no—
164C2×C4×C7—44no—
165C2×C4×C7—82no—
166C2×C4×C7—82no—
167C2×C4×C7—82no—
168C2×C4×C7—82no—
169C2×C4×C7#9912yes—
170C2×C4×C7#10412yes—
171C2×C4×C7C4×Q812yes—
172C2×C4×C7C22⋊Q812yes—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—41no—
176C2×Dic7—41no—
177C2×Dic7—41no—
178C2×Dic7—41no—
179C2×Dic7—41no—
180C2×Dic7—41no—
181C2×Dic7—41no—
182C2×Dic7—41no—
183C2×Dic7—41no—
184C2×Dic7—41no—
185C7⋊C8—44no—
186C23×C4—22no—
187C23×C4C22⋊D711yescharacteristic
188C23×C4C22⋊D711yescharacteristic
189C23×C4C22×D711yescharacteristic
190C22×C8—142no—
191#125—282no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—71no—
196C2×C4⋊C4—71no—
197C2×C4⋊C4—71no—
198C2×C4⋊C4—71no—
199C2×C4⋊C4—141no—
200C2×C4⋊C4—141no—
201C2×C4⋊C4—141no—
202C2×C4⋊C4—141no—
203C2×C22⋊C4—141no—
204C2×C22⋊C4—141no—
205C2×C42—42no—
206C2×C42C4×D711yescharacteristic
207C2×C42C4×D711yescharacteristic
208C2×C42D2811yescharacteristic
209C2×C42D2811yescharacteristic
210C22⋊C8—74no—
211C22⋊C8—142no—
212#97—282no—
213#95—24no—
214#95—42no—
215#95—141no—
216#95—141no—
217#95—141no—
218#95—141no—
219#95—141no—
220#95—141no—
221C22×C7—21no—
222C22×C7—21no—
223C22×C7—21no—
224C22×C7—21no—
225C22×C7—21no—
226C22×C7—21no—
227C22×C7—21no—
228C22×C7—21no—
229C22×C7—21no—
230C22×C7—21no—
231C22×C7—21no—
232C22×C7—21no—
233C22×C7#39111yescharacteristic
234C22×C7C2×#9911yescharacteristic
235C22×C7#41011yescharacteristic
236C22×C7#41711yescharacteristic
237C22×C7#41711yescharacteristic
238C22×C7C2×#10411yescharacteristic
239C22×C7#42111yescharacteristic
240C22×C7#49011yescharacteristic
241C22×C7#49111yescharacteristic
242C22×C7#50111yescharacteristic
243C22×C7#50111yescharacteristic
244C4×C7—22no—
245C4×C7—22no—
246C4×C7—22no—
247C4×C7—22no—
248C4×C7—41no—
249C4×C7—41no—
250C4×C7—84no—
251Dic7—81no—
252Dic7—81no—
253Dic7—81no—
254Dic7—81no—
255C24C2×C22⋊D711yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—24no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—141no—
274C22×C4—141no—
275C22×C4—141no—
276C22×C4—141no—
277C22×C4(C2×D7)⋊C411yescharacteristic
278C22×C4(C2×D7)⋊C411yescharacteristic
279C22×C4(C2×D7)⋊C411yescharacteristic
280C22×C4(C2×D7)⋊C411yescharacteristic
281C22×C4C2×C4×D711yescharacteristic
282C22×C4C2×D2811yescharacteristic
283C22×C4#115912yes—
284C22×C4Q8×D712yes—
285C2×C8—144no—
286C2×C8—282no—
287C2×C8—282no—
288C4⋊C4—48no—
289C4⋊C4—281no—
290C4⋊C4—281no—
291C4⋊C4—281no—
292C4⋊C4—281no—
293C4⋊C4—282no—
294C4⋊C4—282no—
295C4⋊C4—282no—
296C4⋊C4—282no—
297C22⋊C4—281no—
298C22⋊C4—281no—
299C22⋊C4—281no—
300C22⋊C4—281no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C2×C7—21no—
306C2×C7—21no—
307C2×C7—21no—
308C2×C7—21no—
309C2×C7#150411yescharacteristic
310C2×C7#150911yescharacteristic
311C2×C7#151211yescharacteristic
312C2×C7#151311yescharacteristic
313C2×C7#198611yescharacteristic
314C2×C7#199211yescharacteristic
315C2×C7#199611yescharacteristic
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×(C2×D7)⋊C411yescharacteristic
321C23#649511yescharacteristic
322C23#649511yescharacteristic
323C23#649911yescharacteristic
324C23#650511yescharacteristic
325C23#650511yescharacteristic
326C23#650711yescharacteristic
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—281no—
355C2×C4—281no—
356C2×C4—281no—
357C2×C4—281no—
358C2×C4—281no—
359C2×C4—281no—
360C2×C4—281no—
361C2×C4—281no—
362C2×C4—281no—
363C2×C4—281no—
364C2×C4—281no—
365C2×C4—281no—
366C2×C4#637912yes—
367C2×C4#638012yes—
368C2×C4#645012yes—
369C2×C4#646012yes—
370C8—284no—
371C7#988711yescharacteristic, complemented, Sylow
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22C2×#637911yescharacteristic
385C22C2×#638011yescharacteristic
386C22#8973811yescharacteristic
387C22#8973811yescharacteristic
388C22#8974611yescharacteristic
389C22#8977711yescharacteristic
390C22#8977811yescharacteristic
391C22#8984311yescharacteristic
392C22#8985211yescharacteristic
393C22#8985211yescharacteristic
394C22#8985411yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—84no—
402C4—561no—
403C4—561no—
404C4—561no—
405C4—561no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2#1172715211yescharacteristic
411C2#1172722411yescharacteristic
412C2#1172724711yescharacteristic
413C2#1172726211yescharacteristic
414C2#1172728311yescharacteristic
415C2#1172729811yescharacteristic
416C2#1172733711yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×C4⋊#95C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC4⋊#95D7
hypocenterC7#9887
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
8. C2×#6433C4semidirect
16. #89708C4semidirect
19. #89700C4semidirect
20. #89700C4semidirect
371. C7#9887semidirect

Maximal subgroups

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

subgroupindex
#117395192
C7×C4⋊#952
#117292832
#117254182
#98877