Finite Group Databasebeta

← #13257675

Subgroups — #13257675

Order 1792.

490 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
1C2×#89859C211yesmaximal, characteristic
2C2×C7×#332C211yesmaximal, characteristic, complemented
3#11729539C211yesmaximal, characteristic, complemented
4#11728233C211yesmaximal, characteristic
5#11728224C211yesmaximal, characteristic
6C2×#89274C211yesmaximal, characteristic, complemented
7#11725508C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C4×D28C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×#6409—21no—
13C2×#6409—21no—
14C2×#6395—21no—
15C2×(C2×D7)⋊C8—21no—
16C2×(C2×D7)⋊C8—21no—
17#89859—22no—
18#89859—22no—
19C2×#6383—21no—
20C2×#6381—21no—
21#89707C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4×C7⋊C8C2211yescharacteristic
24C7×#332—22no—
25#89346—21no—
26#89274—22no—
27#10485—71nomaximal, Sylow
28C22×C7×Q8—21no—
29C22×D28D411yescharacteristic
30C22×C4×D7—21no—
31C22×C7×C8—21no—
32C22×C7×C8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8—21no—
36C7×C4⋊Q8D412yes—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C42×C7C2311yescharacteristic
40C2×(C2×D7)⋊C4—21no—
41C2×C4⋊Dic7—21no—
42C2×C4⋊Dic7—21no—
43C2×C4⋊Dic7—21no—
44C2×C4⋊Dic7D411yescharacteristic
45C22×C7⋊C8—21no—
46C22×C7⋊C8D411yescharacteristic
47C22×C7⋊C8D411yescharacteristic
48C4×D28—21no—
49C4×D28—21no—
50C4×D28—21no—
51C4×D28—21no—
52C7×C4⋊C8—21no—
53C7×C4⋊C8—21no—
54C7×C4⋊C8—21no—
55C7×C4⋊C8—21no—
56#6409—42no—
57#6409—42no—
58#6395—42no—
59(C2×D7)⋊C8—42no—
60(C2×D7)⋊C8—42no—
61#6383—24no—
62#6381—24no—
63C4⋊(C7⋊C8)—21no—
64C4⋊(C7⋊C8)D412yes—
65C4×C7⋊C8—21no—
66C4×C7⋊C8—21no—
67C2×#474—71no—
68#1956—71no—
69#1954—71no—
70#1802—71no—
71C2×#335—71no—
72C2×#332D711yescharacteristic, complemented
73#1296—71no—
74C23×D7—21no—
75C2×C7×Q8—22no—
76C2×C7×Q8—41no—
77C2×C7×Q8—41no—
78C2×C7×Q8—41no—
79C2×C7×Q8—41no—
80C2×C7×Q8—41no—
81C22×C4×C7—41no—
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C22×C4×C7#4111yescharacteristic
85C22×Dic7—21no—
86C22×Dic7—41no—
87C2×D28—21no—
88C2×D28—21no—
89C2×D28—21no—
90C2×D28—21no—
91C2×D28—21no—
92C2×D28Q1612yes—
93C2×C4×D7—41no—
94C2×C4×D7—41no—
95C2×C4×D7—41no—
96C2×C4×D7—41no—
97C2×C4×D7—41no—
98C2×C4×D7—41no—
99C2×C7×C8—41no—
100C2×C7×C8—41no—
101C2×C7×C8—41no—
102C2×C7×C8—41no—
103C2×C7×C8—41no—
104C2×C7×C8—41no—
105C7×C4⋊C4—22no—
106C7×C4⋊C4—22no—
107C7×C4⋊C4—41no—
108C7×C4⋊C4—41no—
109C42×C7C2×D411yescharacteristic
110C42×C7C2×D411yescharacteristic
111C42×C7#4111yescharacteristic
112C42×C7#4111yescharacteristic
113(C2×D7)⋊C4—41no—
114(C2×D7)⋊C4—41no—
115C4⋊Dic7—21no—
116C4⋊Dic7—21no—
117C4⋊Dic7—41no—
118C4⋊Dic7—41no—
119C4⋊Dic7—41no—
120C4⋊Dic7—41no—
121C4⋊Dic7—81no—
122C2×C7⋊C8—21no—
123C2×C7⋊C8—21no—
124C2×C7⋊C8—22no—
125C2×C7⋊C8—21no—
126C2×C7⋊C8—21no—
127C2×C7⋊C8—21no—
128C2×C7⋊C8—41no—
129C2×C7⋊C8—41no—
130C2×C7⋊C8D812yes—
131C2×C4⋊Q8C2×D711yescharacteristic
132C2×C4×D4—71no—
133#474—142no—
134#474—142no—
135C2×#107—141no—
136C2×C4⋊C8—71no—
137C2×C4⋊C8C2×D711yescharacteristic
138C2×C4⋊C8C2×D711yescharacteristic
139C2×#103—141no—
140C2×#103—141no—
141C2×#102—141no—
142C2×#102—141no—
143C2×C22⋊C8—141no—
144C2×C22⋊C8—141no—
145C2×C4×C8—71no—
146#384—71no—
147#340—141no—
148#335—142no—
149#332—22no—
150C23×C7#12111yescharacteristic
151C22×D7—22no—
152C22×D7—41no—
153C22×D7—41no—
154C22×D7—41no—
155C22×D7—41no—
156C22×D7—41no—
157C22×D7—41no—
158C7×Q8—42no—
159C7×Q8—42no—
160C7×Q8—81no—
161C7×Q8—81no—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—42no—
165C2×C4×C7—81no—
166C2×C4×C7—81no—
167C2×C4×C7#12011yescharacteristic
168C2×C4×C7#12111yescharacteristic
169C2×C4×C7#12111yescharacteristic
170C2×C4×C7#12311yescharacteristic
171C2×C4×C7#12311yescharacteristic
172C2×C4×C7#12411yescharacteristic
173C2×C4×C7C2×D811yescharacteristic
174C2×C4×C7C2×Q1611yescharacteristic
175C2×C4×C7#13511yescharacteristic
176C2×C4×C7#13511yescharacteristic
177C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C7#13711yescharacteristic
181C2×Dic7—41no—
182C2×Dic7—41no—
183C2×Dic7—41no—
184C2×Dic7—81no—
185C2×Dic7—81no—
186C2×Dic7—81no—
187D28—22no—
188D28—22no—
189D28—41no—
190D28—41no—
191C4×D7—81no—
192C4×D7—81no—
193C4×D7—81no—
194C4×D7—81no—
195C7×C8—81no—
196C7×C8—81no—
197C7⋊C8—22no—
198C7⋊C8—42no—
199C7⋊C8—41no—
200C22×Q8—21no—
201C22×D4—71no—
202C23×C4—141no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—71no—
206C22×C8—71no—
207C22×C8—141no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C22⋊D712yes—
212C4×D4—141no—
213C4×D4—141no—
214C4×D4—141no—
215C4×D4—141no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—71no—
219C2×C4⋊C4—141no—
220C2×C4⋊C4—141no—
221C2×C4⋊C4—141no—
222C2×C22⋊C4—141no—
223C2×C42C22×D711yescharacteristic
224#107—144no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—72no—
230C4⋊C8—141no—
231#103—282no—
232#103—282no—
233#102—144no—
234#102—282no—
235C22⋊C8—282no—
236C22⋊C8—282no—
237C4×C8—141no—
238C4×C8—141no—
239C22×C7#39411yescharacteristic
240C22×C7#45911yescharacteristic
241C22×C7#46311yescharacteristic
242C22×C7#46711yescharacteristic
243C22×C7#46811yescharacteristic
244C22×C7#47111yescharacteristic
245C22×C7#47311yescharacteristic
246C2×D7—42no—
247C2×D7—42no—
248C2×D7—42no—
249C2×D7—81no—
250C2×D7—81no—
251C2×D7—81no—
252C2×D7—81no—
253C4×C7—21no—
254C4×C7—21no—
255C4×C7—82no—
256C4×C7#44911yescharacteristic
257C4×C7#45111yescharacteristic
258C4×C7#45911yescharacteristic
259C4×C7#46311yescharacteristic
260C4×C7#46611yescharacteristic
261C4×C7#46911yescharacteristic
262C4×C7#48411yescharacteristic
263C4×C7#48511yescharacteristic
264Dic7—81no—
265Dic7—161no—
266C24—141no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×D4—72no—
274C2×D4—141no—
275C2×D4—141no—
276C2×D4—141no—
277C2×D4—141no—
278C2×D4—141no—
279C22×C4—41no—
280C22×C4—141no—
281C22×C4—281no—
282C22×C4—281no—
283C22×C4—281no—
284C22×C4—281no—
285C22×C4—281no—
286C22×C4—281no—
287C22×C4—281no—
288C22×C4#115711yescharacteristic
289C22×C4D4×D711yescharacteristic
290C22×C4D4×D711yescharacteristic
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—72no—
298C2×C8—141no—
299C2×C8—141no—
300C2×C8—141no—
301C2×C8—141no—
302C2×C8—141no—
303C2×C8—142no—
304C2×C8—281no—
305C2×C8—281no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—141no—
311C4⋊C4—141no—
312C4⋊C4—281no—
313C4⋊C4—281no—
314C4⋊C4—281no—
315C4⋊C4—281no—
316C4⋊C4—561no—
317C22⋊C4—281no—
318C22⋊C4—281no—
319C42#115711yescharacteristic
320C42D4×D711yescharacteristic
321C42#115911yescharacteristic
322C42C2×C22⋊D711yescharacteristic
323C2×C7#166911yescharacteristic
324C2×C7#168311yescharacteristic
325C2×C7#168511yescharacteristic
326C2×C7#169911yescharacteristic
327C2×C7#203611yescharacteristic
328C2×C7#205211yescharacteristic
329C2×C7#205411yescharacteristic
330D7—82no—
331C23—142no—
332C23—281no—
333C23—281no—
334C23—281no—
335C23—281no—
336C23—281no—
337C23—281no—
338C23#644711yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343D4—142no—
344D4—142no—
345D4—281no—
346D4—281no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—281no—
353C2×C4—281no—
354C2×C4—281no—
355C2×C4—561no—
356C2×C4—561no—
357C2×C4—561no—
358C2×C4—561no—
359C2×C4—561no—
360C2×C4—561no—
361C2×C4—561no—
362C2×C4#644611yescharacteristic
363C2×C4#644711yescharacteristic
364C2×C4#644811yescharacteristic
365C2×C4D7×D811yescharacteristic
366C2×C4#647411yescharacteristic
367C2×C4#647711yescharacteristic
368C2×C4#647711yescharacteristic
369C2×C4#647911yescharacteristic
370C2×C4#647911yescharacteristic
371C2×C4D7×Q1611yescharacteristic
372C2×C4#648111yescharacteristic
373C2×C4#649211yescharacteristic
374C2×C4#650011yescharacteristic
375C2×C4#650211yescharacteristic
376C8—81no—
377C8—81no—
378C8—142no—
379C8—282no—
380C8—281no—
381C7#1048511yescharacteristic, complemented, Sylow
382C22—282no—
383C22—282no—
384C22—282no—
385C22—561no—
386C22—561no—
387C22—561no—
388C22—561no—
389C22#8952611yescharacteristic
390C22#8952711yescharacteristic
391C22#8955811yescharacteristic
392C22#8955911yescharacteristic
393C22#8958411yescharacteristic
394C22#8958511yescharacteristic
395C22#8973111yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—561no—
400C4—1121no—
401C4#8954711yescharacteristic
402C4#8955411yescharacteristic
403C4#8958111yescharacteristic
404C4#8958711yescharacteristic
405C4#8992211yescharacteristic
406C4#8993711yescharacteristic
407C4#8994411yescharacteristic
408C4#8995811yescharacteristic
409C2—562no—
410C2#1172619511yescharacteristic
411C2#1172620111yescharacteristic
412C2#1172620211yescharacteristic
413C2#1172620611yescharacteristic
414C2#1172788011yescharacteristic
415C2#1172796611yescharacteristic
416C2#1172802911yescharacteristic
subgroupG/H
centerC23#6447
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC2×C7×#332C2
socleC23×C7#121
prime radicalC22×D28D4
hypercenterC2×#332D7
hypocenterC7#10485
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×C7×#332C2semidirect
3. #11729539C2semidirect
6. C2×#89274C2semidirect
7. #11725508C2semidirect
72. C2×#332D7semidirect
381. C7#10485semidirect

Maximal subgroups

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

subgroupindex
C2×#898592
C2×C7×#3322
#117295392
#117282332
#117282242
C2×#892742
#117255082
#104857