Finite Group Databasebeta

← #13249518

Subgroups — #13249518

Order 1792.

694 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740255C211yesmaximal, characteristic
2C2×#89420C211yesmaximal, characteristic
3C2×C7×#328C211yesmaximal, characteristic
4C2×#89333C211yesmaximal, characteristic
5#11727664C211yesmaximal, characteristic
6#11725481C211yesmaximal, characteristic
7#11725418C211yesmaximal, characteristic
8C2×C7×C22⋊Q8C2211yescharacteristic
9C22×C4×Dic7—21no—
10C22×C4×Dic7C2211yescharacteristic
11C2×C7×C22⋊C8C2211yescharacteristic
12C2×C7×#95C2211yescharacteristic
13#90002C412yescomplemented
14#89984C2211yescharacteristic
15C2×C7⋊#95—21no—
16C2×C7⋊#95C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18#89750—22no—
19#89745C412yescomplemented
20#89718—21no—
21#89715—21no—
22#89420—22no—
23#89420—22no—
24C7×#328—22no—
25#89345—22no—
26#89333—22no—
27#9145—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—24no—
46C2×C4×Dic7—28no—
47C2×C4×Dic7—21no—
48C2×C4×Dic7—21no—
49C2×C4×Dic7—21no—
50C2×C4×Dic7—21no—
51C2×C4×Dic7C2×C412yes—
52C2×C4×Dic7D412yes—
53C22×C7⋊C8—21no—
54C7×C22⋊C8—21no—
55C7×C22⋊C8—21no—
56C7×#95—21no—
57C7×#95D412yes—
58C7⋊#95—24no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C7⋊#95—22no—
62C7⋊#95—22no—
63C7⋊#95—22no—
64C7⋊#95D412yes—
65C22⋊(C7⋊C8)—21no—
66C22⋊(C7⋊C8)—21no—
67#2855—71no—
68C2×#376—71no—
69#1817—71no—
70C2×#328—71no—
71C2×#328D711yescharacteristic
72#1294—71no—
73#1294—71no—
74C24×C7C2×D411yescharacteristic
75C2×C7×Q8—21no—
76C2×C7×Q8—21no—
77C2×C7×Q8—42no—
78C22×C4×C7—24no—
79C22×C4×C7—22no—
80C22×C4×C7—21no—
81C22×C4×C7—21no—
82C22×C4×C7—42no—
83C22×C4×C7—42no—
84C22×C4×C7—41no—
85C22×C4×C7—41no—
86C22×C4×C7C22×C411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7#4111yescharacteristic
91C22×C4×C7#4111yescharacteristic
92C22×Dic7—21no—
93C22×Dic7—21no—
94C22×Dic7—24no—
95C22×Dic7—24no—
96C22×Dic7—21no—
97C22×Dic7—22no—
98C22×Dic7—21no—
99C22×Dic7—21no—
100C22×Dic7—21no—
101C22×Dic7—21no—
102C22×Dic7—21no—
103C22×Dic7—22no—
104C22×Dic7—42no—
105C22×Dic7—41no—
106C22×Dic7—41no—
107C22×Dic7C22⋊C412yes—
108C22×Dic7C22⋊C412yes—
109C2×C7×C8—42no—
110C2×C7×C8—41no—
111C7×C4⋊C4—21no—
112C7×C4⋊C4—21no—
113C7×C4⋊C4—41no—
114C7×C4⋊C4—41no—
115C7×C22⋊C4—41no—
116C7×C22⋊C4—41no—
117C22⋊Dic7—41no—
118C22⋊Dic7—41no—
119C4⋊Dic7—42no—
120Dic7⋊C4—44no—
121C4×Dic7—216no—
122C4×Dic7—22no—
123C4×Dic7—22no—
124C4×Dic7—22no—
125C4×Dic7—22no—
126C2×C7⋊C8—42no—
127C2×C7⋊C8—41no—
128C2×C22⋊Q8C2×D711yescharacteristic
129C22×C42—71no—
130C22×C42—141no—
131C2×C22⋊C8—71no—
132C2×C22⋊C8C2×D711yescharacteristic
133#391—72no—
134#389—72no—
135#387—142no—
136#385—141no—
137#381—141no—
138#380—71no—
139#376—142no—
140#376—142no—
141C2×#95—71no—
142C2×#95—141no—
143C2×#95C2×D711yescharacteristic
144#336—142no—
145#328—22no—
146#328—142no—
147C23×C7—22no—
148C23×C7—22no—
149C23×C7C2×C22⋊C411yescharacteristic
150C23×C7#12011yescharacteristic
151C23×C7#12311yescharacteristic
152C23×C7#13511yescharacteristic
153C23×C7#13511yescharacteristic
154C23×C7#13711yescharacteristic
155C23×C7#13711yescharacteristic
156C7×Q8—81no—
157C7×Q8—81no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—24no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—42no—
166C2×C4×C7—44no—
167C2×C4×C7—44no—
168C2×C4×C7—42no—
169C2×C4×C7—41no—
170C2×C4×C7—41no—
171C2×C4×C7—42no—
172C2×C4×C7—42no—
173C2×C4×C7C4×D411yescharacteristic
174C2×C4×C7C4×D411yescharacteristic
175C2×C4×C7#12111yescharacteristic
176C2×C4×C7#12111yescharacteristic
177C2×Dic7—24no—
178C2×Dic7—24no—
179C2×Dic7—22no—
180C2×Dic7—22no—
181C2×Dic7—24no—
182C2×Dic7—22no—
183C2×Dic7—22no—
184C2×Dic7—22no—
185C2×Dic7—42no—
186C2×Dic7—44no—
187C2×Dic7—44no—
188C2×Dic7—41no—
189C2×Dic7—41no—
190C2×Dic7—42no—
191C2×Dic7—41no—
192C2×Dic7—41no—
193C2×Dic7—42no—
194C2×Dic7—42no—
195C2×Dic7—42no—
196C2×Dic7#10414yes—
197C7×C8—81no—
198C7⋊C8—81no—
199C22×Q8C4×D711yescharacteristic
200C23×C4—21no—
201C23×C4—71no—
202C23×C4—71no—
203C23×C4—141no—
204C23×C4C22×D711yescharacteristic
205C22×C8—21no—
206C22×C8—141no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—72no—
213C2×C4⋊C4—142no—
214C2×C4⋊C4C4×D711yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—141no—
217C2×C42—72no—
218C2×C42—72no—
219C2×C42—144no—
220C2×C42—148no—
221C2×C42—141no—
222C2×C42—141no—
223C2×C42—141no—
224C2×C42—141no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—141no—
228C22⋊C8—141no—
229#95—21no—
230#95—72no—
231#95—142no—
232#95—142no—
233#95—142no—
234#95—144no—
235#95—141no—
236#95—141no—
237#95C22⋊D712yes—
238C22×C7—21no—
239C22×C7—21no—
240C22×C7—21no—
241C22×C7—21no—
242C22×C7—22no—
243C22×C7—22no—
244C22×C7—22no—
245C22×C7—22no—
246C22×C7#38611yescharacteristic
247C22×C7#41012yes—
248C22×C7#41611yescharacteristic
249C22×C7#41911yescharacteristic
250C22×C7C2×#10412yes—
251C22×C7#45211yescharacteristic
252C22×C7#45211yescharacteristic
253C22×C7#48511yescharacteristic
254C22×C7#48511yescharacteristic
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—44no—
260C4×C7—81no—
261C4×C7—81no—
262Dic7—24no—
263Dic7—44no—
264Dic7—42no—
265Dic7—82no—
266C24D4×D711yescharacteristic
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—42no—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—72no—
279C22×C4—72no—
280C22×C4—144no—
281C22×C4—141no—
282C22×C4—141no—
283C22×C4—144no—
284C22×C4—141no—
285C22×C4—141no—
286C22×C4—141no—
287C22×C4—141no—
288C22×C4—141no—
289C22×C4—142no—
290C22×C4—141no—
291C22×C4—142no—
292C22×C4—282no—
293C22×C4—281no—
294C22×C4—281no—
295C22×C4C2×C4×D711yescharacteristic
296C22×C4#115711yescharacteristic
297C22×C4D4×D711yescharacteristic
298C22×C4D4×D711yescharacteristic
299C22×C4#115911yescharacteristic
300C22×C4C2×C22⋊D711yescharacteristic
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—282no—
304C2×C8—281no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—282no—
310C4⋊C4—284no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—281no—
314C22⋊C4—281no—
315C42—1416no—
316C42—142no—
317C42—142no—
318C42—142no—
319C42—142no—
320C2×C7—21no—
321C2×C7—21no—
322C2×C7—21no—
323C2×C7—21no—
324C2×C7#150012yes—
325C2×C7#150612yes—
326C2×C7#187311yescharacteristic
327C2×C7#189611yescharacteristic
328C2×C7#189911yescharacteristic
329C23—22no—
330C23—22no—
331C23D7×C22⋊C411yescharacteristic
332C23#644611yescharacteristic
333C23#647811yescharacteristic
334C23#647911yescharacteristic
335C23#648111yescharacteristic
336C23#648211yescharacteristic
337C23#650011yescharacteristic
338Q8—81no—
339Q8—81no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—74no—
356C2×C4—144no—
357C2×C4—144no—
358C2×C4—142no—
359C2×C4—142no—
360C2×C4—144no—
361C2×C4—142no—
362C2×C4—142no—
363C2×C4—142no—
364C2×C4—282no—
365C2×C4—284no—
366C2×C4—284no—
367C2×C4—281no—
368C2×C4—281no—
369C2×C4—282no—
370C2×C4—281no—
371C2×C4—281no—
372C2×C4—282no—
373C2×C4—282no—
374C2×C4—282no—
375C2×C4(C22⋊D7)⋊C411yescharacteristic
376C2×C4#644711yescharacteristic
377C2×C4C4×C22⋊D711yescharacteristic
378C2×C4#650111yescharacteristic
379C8—81no—
380C8—561no—
381C7#914511yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22#8951212yes—
391C22#8957411yescharacteristic
392C22#8957611yescharacteristic
393C22#8958611yescharacteristic
394C22#8958711yescharacteristic
395C22D7×#10412yes—
396C22#8972811yescharacteristic
397C22#8994511yescharacteristic
398C22#8995911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—81no—
405C4—81no—
406C4—144no—
407C4—284no—
408C4—282no—
409C4—562no—
410C2—21no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2#1172606212yes—
415C2#1172606412yes—
416C2#1172778311yescharacteristic
417C2#1172802311yescharacteristic
418C2#1172813611yescharacteristic
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#9145
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
13. #90002C4semidirect
19. #89745C4semidirect
381. C7#9145semidirect

Maximal subgroups

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

subgroupindex
#117402552
C2×#894202
C2×C7×#3282
C2×#893332
#117276642
#117254812
#117254182
#91457