Finite Group Databasebeta

← #13249558

Subgroups — #13249558

Order 1792.

586 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740255C211yesmaximal, characteristic
2C2×#89423C211yesmaximal, characteristic
3C2×C7×#328C211yesmaximal, characteristic
4C2×#89333C211yesmaximal, characteristic
5#11727664C211yesmaximal, characteristic
6#11725481C211yesmaximal, characteristic
7#11725418C211yesmaximal, characteristic
8C2×C7×C22⋊Q8C2211yescharacteristic
9C22×C4×Dic7C2211yescharacteristic
10C2×C7×C22⋊C8C2211yescharacteristic
11C2×C7×#95C2211yescharacteristic
12#90002C412yescomplemented
13#89984C2211yescharacteristic
14C2×C7⋊#95—21no—
15C2×C7⋊#95—21no—
16C2×C7⋊#95C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18#89750—22no—
19#89745C412yescomplemented
20#89718—21no—
21#89715—21no—
22#89423—22no—
23#89423—22no—
24C7×#328—22no—
25#89345—22no—
26#89333—22no—
27#9153—71nomaximal, Sylow
28C22×C7×Q8C2×C411yescharacteristic
29C23×C4×C7—21no—
30C23×C4×C7C2311yescharacteristic
31C23×Dic7—21no—
32C23×Dic7D411yescharacteristic
33C23×Dic7D411yescharacteristic
34C22×C7×C8—21no—
35C7×C22⋊Q8—21no—
36C7×C22⋊Q8—21no—
37C7×C22⋊Q8—21no—
38C7×C22⋊Q8—21no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4C2×C411yescharacteristic
41C2×C7×C22⋊C4—21no—
42C2×C22⋊Dic7—21no—
43C2×C4⋊Dic7C2×C412yes—
44C2×Dic7⋊C4—22no—
45C2×C4×Dic7—21no—
46C2×C4×Dic7—21no—
47C2×C4×Dic7—21no—
48C2×C4×Dic7—21no—
49C2×C4×Dic7C2×C412yes—
50C2×C4×Dic7D412yes—
51C22×C7⋊C8—21no—
52C7×C22⋊C8—21no—
53C7×C22⋊C8—21no—
54C7×#95—21no—
55C7×#95D412yes—
56C7⋊#95—24no—
57C7⋊#95—24no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—22no—
61C7⋊#95—22no—
62C7⋊#95—22no—
63C7⋊#95D412yes—
64C22⋊(C7⋊C8)—21no—
65C22⋊(C7⋊C8)—21no—
66#2855—71no—
67C2×#383—71no—
68#1817—71no—
69C2×#328—71no—
70C2×#328D711yescharacteristic
71#1294—71no—
72#1294—71no—
73C24×C7C2×D411yescharacteristic
74C2×C7×Q8—21no—
75C2×C7×Q8—21no—
76C2×C7×Q8—42no—
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—22no—
80C22×C4×C7—42no—
81C22×C4×C7—42no—
82C22×C4×C7—42no—
83C22×C4×C7—41no—
84C22×C4×C7—41no—
85C22×C4×C7C22×C411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7#4111yescharacteristic
90C22×C4×C7#4111yescharacteristic
91C22×Dic7—21no—
92C22×Dic7—21no—
93C22×Dic7—21no—
94C22×Dic7—21no—
95C22×Dic7—21no—
96C22×Dic7—21no—
97C22×Dic7—21no—
98C22×Dic7—21no—
99C22×Dic7—22no—
100C22×Dic7—22no—
101C22×Dic7—42no—
102C22×Dic7—42no—
103C22×Dic7—42no—
104C22×Dic7—41no—
105C22×Dic7—41no—
106C22×Dic7C22⋊C412yes—
107C22×Dic7C22⋊C412yes—
108C2×C7×C8—42no—
109C2×C7×C8—41no—
110C7×C4⋊C4—21no—
111C7×C4⋊C4—21no—
112C7×C4⋊C4—41no—
113C7×C4⋊C4—41no—
114C7×C22⋊C4—41no—
115C7×C22⋊C4—41no—
116C22⋊Dic7—41no—
117C22⋊Dic7—41no—
118C4⋊Dic7—42no—
119Dic7⋊C4—44no—
120C4×Dic7—22no—
121C4×Dic7—22no—
122C4×Dic7—22no—
123C4×Dic7—22no—
124C2×C7⋊C8—42no—
125C2×C7⋊C8—41no—
126C2×C22⋊Q8C2×D711yescharacteristic
127C22×C42—71no—
128C2×C22⋊C8—71no—
129C2×C22⋊C8C2×D711yescharacteristic
130#391—72no—
131#389—72no—
132#387—142no—
133#385—141no—
134#383—142no—
135#383—142no—
136#381—141no—
137#380—71no—
138C2×#95—71no—
139C2×#95—141no—
140C2×#95—141no—
141C2×#95C2×D711yescharacteristic
142#336—142no—
143#328—22no—
144#328—142no—
145C23×C7—22no—
146C23×C7—22no—
147C23×C7C2×C22⋊C411yescharacteristic
148C23×C7#12011yescharacteristic
149C23×C7#12311yescharacteristic
150C23×C7#13511yescharacteristic
151C23×C7#13511yescharacteristic
152C23×C7#13711yescharacteristic
153C23×C7#13711yescharacteristic
154C7×Q8—81no—
155C7×Q8—81no—
156C2×C4×C7—22no—
157C2×C4×C7—22no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—42no—
163C2×C4×C7—42no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—42no—
167C2×C4×C7—42no—
168C2×C4×C7—42no—
169C2×C4×C7—82no—
170C2×C4×C7—82no—
171C2×C4×C7C4×D411yescharacteristic
172C2×C4×C7C4×D411yescharacteristic
173C2×C4×C7#12111yescharacteristic
174C2×C4×C7#12111yescharacteristic
175C2×Dic7—22no—
176C2×Dic7—22no—
177C2×Dic7—22no—
178C2×Dic7—22no—
179C2×Dic7—22no—
180C2×Dic7—22no—
181C2×Dic7—42no—
182C2×Dic7—42no—
183C2×Dic7—41no—
184C2×Dic7—41no—
185C2×Dic7—41no—
186C2×Dic7—41no—
187C2×Dic7—42no—
188C2×Dic7—42no—
189C2×Dic7—42no—
190C2×Dic7—42no—
191C2×Dic7—42no—
192C2×Dic7—42no—
193C2×Dic7—82no—
194C2×Dic7—82no—
195C7×C8—81no—
196C7⋊C8—81no—
197C22×Q8C4×D711yescharacteristic
198C23×C4—21no—
199C23×C4—71no—
200C23×C4—71no—
201C23×C4—141no—
202C23×C4C22×D711yescharacteristic
203C22×C8—21no—
204C22×C8—141no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—72no—
211C2×C4⋊C4—142no—
212C2×C4⋊C4C4×D711yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—141no—
215C2×C42—72no—
216C2×C42—72no—
217C2×C42—141no—
218C2×C42—141no—
219C2×C42—141no—
220C2×C42—141no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—141no—
224C22⋊C8—141no—
225#95—21no—
226#95—72no—
227#95—142no—
228#95—142no—
229#95—142no—
230#95—144no—
231#95—144no—
232#95—141no—
233#95—141no—
234#95C22⋊D712yes—
235C22×C7—21no—
236C22×C7—21no—
237C22×C7—21no—
238C22×C7—21no—
239C22×C7—22no—
240C22×C7—22no—
241C22×C7—22no—
242C22×C7—22no—
243C22×C7#38611yescharacteristic
244C22×C7#41012yes—
245C22×C7#41611yescharacteristic
246C22×C7#41911yescharacteristic
247C22×C7#42112yes—
248C22×C7#45211yescharacteristic
249C22×C7#45211yescharacteristic
250C22×C7#48511yescharacteristic
251C22×C7#48511yescharacteristic
252C4×C7—21no—
253C4×C7—21no—
254C4×C7—21no—
255C4×C7—21no—
256C4×C7—82no—
257C4×C7—81no—
258C4×C7—81no—
259Dic7—42no—
260Dic7—42no—
261Dic7—82no—
262Dic7—82no—
263C24D4×D711yescharacteristic
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—42no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—72no—
276C22×C4—72no—
277C22×C4—141no—
278C22×C4—141no—
279C22×C4—141no—
280C22×C4—141no—
281C22×C4—141no—
282C22×C4—141no—
283C22×C4—141no—
284C22×C4—141no—
285C22×C4—142no—
286C22×C4—142no—
287C22×C4—282no—
288C22×C4—282no—
289C22×C4—282no—
290C22×C4—281no—
291C22×C4—281no—
292C22×C4C2×C4×D711yescharacteristic
293C22×C4#115711yescharacteristic
294C22×C4D4×D711yescharacteristic
295C22×C4D4×D711yescharacteristic
296C22×C4#115911yescharacteristic
297C22×C4C2×C22⋊D711yescharacteristic
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—282no—
301C2×C8—281no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—282no—
307C4⋊C4—284no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—281no—
311C22⋊C4—281no—
312C42—142no—
313C42—142no—
314C42—142no—
315C42—142no—
316C2×C7—21no—
317C2×C7—21no—
318C2×C7—21no—
319C2×C7—21no—
320C2×C7#151512yes—
321C2×C7#152112yes—
322C2×C7#187311yescharacteristic
323C2×C7#189711yescharacteristic
324C2×C7#189911yescharacteristic
325C23—22no—
326C23—22no—
327C23D7×C22⋊C411yescharacteristic
328C23#644611yescharacteristic
329C23#647811yescharacteristic
330C23#647911yescharacteristic
331C23#648111yescharacteristic
332C23#648211yescharacteristic
333C23#650011yescharacteristic
334Q8—81no—
335Q8—81no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—142no—
352C2×C4—142no—
353C2×C4—142no—
354C2×C4—142no—
355C2×C4—142no—
356C2×C4—142no—
357C2×C4—282no—
358C2×C4—282no—
359C2×C4—281no—
360C2×C4—281no—
361C2×C4—281no—
362C2×C4—281no—
363C2×C4—282no—
364C2×C4—282no—
365C2×C4—282no—
366C2×C4—282no—
367C2×C4—282no—
368C2×C4—282no—
369C2×C4—562no—
370C2×C4—562no—
371C2×C4(C22⋊D7)⋊C411yescharacteristic
372C2×C4#644711yescharacteristic
373C2×C4C4×C22⋊D711yescharacteristic
374C2×C4#650111yescharacteristic
375C8—81no—
376C8—561no—
377C7#915311yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22#8951212yes—
387C22#8957411yescharacteristic
388C22#8957611yescharacteristic
389C22#8958611yescharacteristic
390C22#8958711yescharacteristic
391C22#8959312yes—
392C22#8972811yescharacteristic
393C22#8994511yescharacteristic
394C22#8995911yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—81no—
401C4—81no—
402C4—282no—
403C4—282no—
404C4—562no—
405C4—562no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2#1172606712yes—
411C2#1172606912yes—
412C2#1172778311yescharacteristic
413C2#1172802311yescharacteristic
414C2#1172813711yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC2×#328D7
hypocenterC7#9153
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
12. #90002C4semidirect
19. #89745C4semidirect
377. C7#9153semidirect

Maximal subgroups

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

subgroupindex
#117402552
C2×#894232
C2×C7×#3282
C2×#893332
#117276642
#117254812
#117254182
#91537