Finite Group Databasebeta

← #13249551

Subgroups — #13249551

Order 1792.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#380C211yesmaximal, characteristic
2#11741476C211yesmaximal, characteristic
3#11729880C211yesmaximal, characteristic
4C2×#89247C212yesmaximal, complemented
5#11725418C212yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C22×C7×C4⋊C4—21no—
8C22×C7×C22⋊C4—21no—
9C2×#6487C412yescomplemented
10C2×#6487C2211yescharacteristic
11C7×#380—24no—
12C2×C7×#95C2212yes—
13#90019—21no—
14#89984C412yescomplemented
15#89984C2211yescharacteristic
16#89982—21no—
17#89982—22no—
18C2×C22⋊(C7⋊C8)—22no—
19C2×C22⋊(C7⋊C8)C2212yes—
20#89247—24no—
21#9151—71nomaximal, Sylow
22C25×C7D411yescharacteristic
23C23×C4×C7—22no—
24C23×C4×C7—22no—
25C23×C4×C7—22no—
26C23×C4×C7—44no—
27C23×C4×C7C2×C412yes—
28C23×C4×C7D412yes—
29C23×C4×C7D411yescharacteristic
30C23×C4×C7C2311yescharacteristic
31C22×Dic14C2×C411yescharacteristic
32C2×C7×C4⋊C4—24no—
33C2×C7×C4⋊C4—44no—
34C2×C7×C22⋊C4—24no—
35C2×C7×C22⋊C4—42no—
36C2×C7×C22⋊C4—42no—
37C2×C22⋊Dic7—22no—
38C2×C22⋊Dic7—22no—
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—21no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×C4⋊Dic7C2×C412yes—
43#6487—22no—
44#6487—22no—
45#6487—44no—
46C2×Dic7⋊C4—22no—
47C2×Dic7⋊C4—21no—
48C22×C7⋊C8—22no—
49C7×#95—22no—
50C7×#95D414yes—
51C7⋊#95—22no—
52C7⋊#95—21no—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—22no—
55C22⋊(C7⋊C8)—44no—
56#2848—71no—
57C2×#380D711yescharacteristic
58#1779—71no—
59C2×#328—72no—
60#1294—72no—
61C24×C7—21no—
62C24×C7—21no—
63C24×C7—21no—
64C24×C7—21no—
65C24×C7—42no—
66C24×C7—42no—
67C24×C7C22⋊C412yes—
68C24×C7SD1612yes—
69C24×C7Q1612yes—
70C24×C7C2×D411yescharacteristic
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—24no—
74C22×C4×C7—24no—
75C22×C4×C7—24no—
76C22×C4×C7—24no—
77C22×C4×C7—24no—
78C22×C4×C7—24no—
79C22×C4×C7—42no—
80C22×C4×C7—42no—
81C22×C4×C7—42no—
82C22×C4×C7—48no—
83C22×C4×C7—48no—
84C22×C4×C7—44no—
85C22×C4×C7—44no—
86C22×C4×C7—42no—
87C22×C4×C7—42no—
88C22×C4×C7C22⋊C412yes—
89C22×C4×C7C22×C411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7C2×D412yes—
92C22×C4×C7#4112yes—
93C22×Dic7—21no—
94C22×Dic7—22no—
95C22×Dic7—21no—
96C2×Dic14—22no—
97C2×Dic14—42no—
98C7×C4⋊C4—48no—
99C7×C22⋊C4—48no—
100C22⋊Dic7—44no—
101C22⋊Dic7—44no—
102C22⋊Dic7—41no—
103C22⋊Dic7—41no—
104C22⋊Dic7—41no—
105C22⋊Dic7—41no—
106C4⋊Dic7—22no—
107C4⋊Dic7—42no—
108Dic7⋊C4—44no—
109Dic7⋊C4—42no—
110C2×C7⋊C8—44no—
111C2×C7⋊C8—42no—
112C24×C4C2×D711yescharacteristic
113C2×C22⋊Q8—71no—
114C2×C22⋊Q8—72no—
115C22×C4⋊C4—21no—
116C22×C22⋊C4—21no—
117C2×C22⋊C8—72no—
118C2×C22⋊C8—142no—
119#385—142no—
120#385—141no—
121#380—24no—
122#380—72no—
123#380—71no—
124#379—141no—
125C2×#95C2×D712yes—
126#328—144no—
127C23×C7—22no—
128C23×C7—22no—
129C23×C7—22no—
130C23×C7—22no—
131C23×C7—22no—
132C23×C7—22no—
133C23×C7—22no—
134C23×C7—22no—
135C23×C7—22no—
136C23×C7—22no—
137C23×C7—22no—
138C23×C7—22no—
139C23×C7—44no—
140C23×C7—44no—
141C23×C7—42no—
142C23×C7—42no—
143C23×C7—42no—
144C23×C7—42no—
145C23×C7—44no—
146C23×C7—44no—
147C23×C7#10314yes—
148C23×C7C2×C22⋊C411yescharacteristic
149C23×C7#12011yescharacteristic
150C23×C7#12311yescharacteristic
151C23×C7C2×SD1611yescharacteristic
152C23×C7C2×Q1611yescharacteristic
153C23×C7AGL(1,ℤ/8)11yescharacteristic
154C23×C7#13711yescharacteristic
155C2×C4×C7—24no—
156C2×C4×C7—24no—
157C2×C4×C7—22no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—22no—
161C2×C4×C7—42no—
162C2×C4×C7—42no—
163C2×C4×C7—48no—
164C2×C4×C7—48no—
165C2×C4×C7—44no—
166C2×C4×C7—44no—
167C2×C4×C7—44no—
168C2×C4×C7—84no—
169C2×C4×C7—84no—
170C2×C4×C7#9914yes—
171C2×C4×C7C4×D412yes—
172C2×C4×C7#12112yes—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—42no—
176C2×Dic7—42no—
177C2×Dic7—42no—
178C2×Dic7—42no—
179C2×Dic7—42no—
180Dic14—82no—
181C7⋊C8—82no—
182C25C22⋊D711yescharacteristic
183C22×Q8—71no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—44no—
188C23×C4C4×D712yes—
189C23×C4D2812yes—
190C23×C4C22⋊D711yescharacteristic
191C23×C4C22×D711yescharacteristic
192C22×C8—142no—
193C22⋊Q8—142no—
194C22⋊Q8—142no—
195C22⋊Q8—284no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—71no—
199C2×C4⋊C4—72no—
200C2×C4⋊C4—142no—
201C2×C4⋊C4—141no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—42no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—142no—
206C2×C22⋊C4—142no—
207C2×C22⋊C4—141no—
208C2×C22⋊C4—141no—
209C22⋊C8—142no—
210C22⋊C8—142no—
211C22⋊C8—284no—
212#95—22no—
213#95—142no—
214#95—141no—
215#95C22⋊D714yes—
216C22×C7—21no—
217C22×C7—21no—
218C22×C7—21no—
219C22×C7—21no—
220C22×C7—22no—
221C22×C7—22no—
222C22×C7—22no—
223C22×C7—22no—
224C22×C7—24no—
225C22×C7—24no—
226C22×C7—24no—
227C22×C7—44no—
228C22×C7—44no—
229C22×C7—44no—
230C22×C7—44no—
231C22×C7—42no—
232C22×C7—42no—
233C22×C7—42no—
234C22×C7—42no—
235C22×C7#38611yescharacteristic
236C22×C7C2×#9912yes—
237C22×C7C2×#10311yescharacteristic
238C22×C7#41711yescharacteristic
239C22×C7#42112yes—
240C22×C7#45011yescharacteristic
241C22×C7#45111yescharacteristic
242C22×C7#48311yescharacteristic
243C22×C7#48411yescharacteristic
244C4×C7—22no—
245C4×C7—22no—
246C4×C7—24no—
247C4×C7—84no—
248Dic7—81no—
249Dic7—81no—
250Dic7—82no—
251C24—21no—
252C24—21no—
253C24—21no—
254C24—21no—
255C24—42no—
256C24—42no—
257C24(C2×D7)⋊C412yes—
258C24#114212yes—
259C24#114412yes—
260C24C2×C22⋊D711yescharacteristic
261C2×Q8—142no—
262C2×Q8—282no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—48no—
275C22×C4—48no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—142no—
281C22×C4—141no—
282C22×C4—141no—
283C22×C4(C2×D7)⋊C412yes—
284C22×C4C2×C4×D711yescharacteristic
285C22×C4C2×D2811yescharacteristic
286C22×C4#115712yes—
287C22×C4C2×C22⋊D712yes—
288C2×C8—284no—
289C2×C8—282no—
290C4⋊C4—48no—
291C4⋊C4—142no—
292C4⋊C4—282no—
293C4⋊C4—282no—
294C4⋊C4—284no—
295C22⋊C4—48no—
296C22⋊C4—284no—
297C22⋊C4—284no—
298C22⋊C4—281no—
299C22⋊C4—281no—
300C22⋊C4—281no—
301C22⋊C4—281no—
302C2×C7—21no—
303C2×C7—21no—
304C2×C7—21no—
305C2×C7—21no—
306C2×C7—44no—
307C2×C7#151312yes—
308C2×C7#152012yes—
309C2×C7#187211yescharacteristic
310C2×C7#189711yescharacteristic
311C2×C7#189811yescharacteristic
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—44no—
325C23—44no—
326C23—42no—
327C23—42no—
328C23—44no—
329C23—44no—
330C23—42no—
331C23—42no—
332C23#638414yes—
333C23C2×(C2×D7)⋊C411yescharacteristic
334C23#649211yescharacteristic
335C23#649511yescharacteristic
336C23C2×#114211yescharacteristic
337C23#650511yescharacteristic
338C23C2×#114411yescharacteristic
339C23#651611yescharacteristic
340Q8—562no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—48no—
350C2×C4—48no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—84no—
355C2×C4—84no—
356C2×C4—282no—
357C2×C4—282no—
358C2×C4—281no—
359C2×C4—281no—
360C2×C4—282no—
361C2×C4—282no—
362C2×C4—282no—
363C2×C4#638014yes—
364C2×C4C4×C22⋊D712yes—
365C2×C4#649312yes—
366C8—562no—
367C7#915111yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C2×#638012yes—
388C22#8973811yescharacteristic
389C22C2×#638411yescharacteristic
390C22#8974211yescharacteristic
391C22#8974311yescharacteristic
392C22#8977712yes—
393C22#8998511yescharacteristic
394C22#8999011yescharacteristic
395C22#9000011yescharacteristic
396C4—22no—
397C4—24no—
398C4—22no—
399C4—84no—
400C4—561no—
401C4—562no—
402C4—561no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2#1172726212yes—
409C2#1172726412yes—
410C2#1172929711yescharacteristic
411C2#1172931311yescharacteristic
412C2#1172934511yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#380C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7D4
cosocleC23×C4×C7C23
hypercenterC2×#380D7
hypocenterC7#9151
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#89247C2semidirect
5. #11725418C2semidirect
9. C2×#6487C4semidirect
14. #89984C4semidirect
367. C7#9151semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3802
#117414762
#117298802
C2×#892472
#117254182
#91517