Finite Group Databasebeta

← #13257679

Subgroups — #13257679

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×#89618C211yesmaximal, characteristic
2C2×C7×#335C211yesmaximal, characteristic, complemented
3#11728233C211yesmaximal, characteristic
4C2×#89281C211yesmaximal, characteristic, complemented
5#11727541C211yesmaximal, characteristic
6#11727525C211yesmaximal, characteristic, complemented
7#11725508C211yesmaximal, characteristic, complemented
8C2×C4×D28C2211yescharacteristic
9C2×#6432C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C4×C7×C8C2211yescharacteristic
13C2×#6395—21no—
14C2×#6395—21no—
15C2×(C2×D7)⋊C8—21no—
16C2×(C2×D7)⋊C8—21no—
17C2×#6392—21no—
18C2×#6390—21no—
19C2×#6390—21no—
20#89707C2211yescharacteristic
21C2×C4⋊(C7⋊C8)C2211yescharacteristic
22#89618—22no—
23#89618—22no—
24C7×#335—22no—
25#89346—21no—
26#89281—22no—
27#10485—71nomaximal, Sylow
28C22×D28D411yescharacteristic
29C22×C4×D7—21no—
30C22×Dic14—21no—
31C22×C7×C8—21no—
32C22×C7×C8—21no—
33C22×C7×C8D411yescharacteristic
34C22×C7×C8D411yescharacteristic
35C2×C42×C7C2311yescharacteristic
36C2×(C2×D7)⋊C4—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7—21no—
42C2×C4⋊Dic7D411yescharacteristic
43C22×C7⋊C8—21no—
44C4×D28—21no—
45C4×D28—21no—
46C4×D28—21no—
47C4×D28—21no—
48#6432—21no—
49#6432—21no—
50#6432—21no—
51#6432D412yes—
52C7×C4⋊C8—21no—
53C7×C4⋊C8—21no—
54C7×C4⋊C8—21no—
55C7×C4⋊C8D412yes—
56C4×C7×C8—21no—
57C4×C7×C8—21no—
58#6395—24no—
59#6395—42no—
60(C2×D7)⋊C8—42no—
61(C2×D7)⋊C8—42no—
62#6392—24no—
63#6390—42no—
64#6390—42no—
65C4⋊(C7⋊C8)—21no—
66C4⋊(C7⋊C8)—21no—
67C2×#474—71no—
68#1956—71no—
69#1954—71no—
70#1802—71no—
71C2×#335D711yescharacteristic, complemented
72C2×#332—71no—
73#1296—71no—
74C23×D7—21no—
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7#4111yescharacteristic
78C22×Dic7—21no—
79C22×Dic7—41no—
80C22×Dic7—41no—
81C2×D28—21no—
82C2×D28—21no—
83C2×D28—21no—
84C2×D28—21no—
85C2×D28—21no—
86C2×D28Q1612yes—
87C2×C4×D7—41no—
88C2×C4×D7—41no—
89C2×C4×D7—41no—
90C2×C4×D7—41no—
91C2×C4×D7—41no—
92C2×C4×D7—41no—
93C2×Dic14—22no—
94C2×Dic14—41no—
95C2×Dic14—41no—
96C2×Dic14—41no—
97C2×Dic14—41no—
98C2×Dic14—41no—
99C2×C7×C8—21no—
100C2×C7×C8—21no—
101C2×C7×C8—22no—
102C2×C7×C8—21no—
103C2×C7×C8—21no—
104C2×C7×C8—21no—
105C2×C7×C8—41no—
106C2×C7×C8—41no—
107C2×C7×C8—41no—
108C2×C7×C8—41no—
109C2×C7×C8—41no—
110C2×C7×C8D812yes—
111C42×C7C2×D411yescharacteristic
112C42×C7C2×D411yescharacteristic
113C42×C7#4111yescharacteristic
114C42×C7#4111yescharacteristic
115(C2×D7)⋊C4—41no—
116(C2×D7)⋊C4—41no—
117C4⋊Dic7—22no—
118C4⋊Dic7—21no—
119C4⋊Dic7—22no—
120C4⋊Dic7—21no—
121C4⋊Dic7—41no—
122C4⋊Dic7—41no—
123C4⋊Dic7—41no—
124C4⋊Dic7—41no—
125C4⋊Dic7—41no—
126C4⋊Dic7—41no—
127C4⋊Dic7—81no—
128C2×C7⋊C8—41no—
129C2×C7⋊C8—41no—
130C2×C7⋊C8—41no—
131C2×C4⋊Q8—71no—
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×C8C2×D711yescharacteristic
146#384—71no—
147#340—141no—
148#335—22no—
149#332—142no—
150C23×C7#12111yescharacteristic
151C22×D7—22no—
152C22×D7—41no—
153C22×D7—41no—
154C22×D7—41no—
155C22×D7—41no—
156C22×D7—41no—
157C22×D7—41no—
158C2×C4×C7—21no—
159C2×C4×C7—21no—
160C2×C4×C7#12011yescharacteristic
161C2×C4×C7#12111yescharacteristic
162C2×C4×C7#12111yescharacteristic
163C2×C4×C7#12311yescharacteristic
164C2×C4×C7#12311yescharacteristic
165C2×C4×C7#12411yescharacteristic
166C2×C4×C7C2×D811yescharacteristic
167C2×C4×C7C2×Q1611yescharacteristic
168C2×C4×C7#13511yescharacteristic
169C2×C4×C7#13511yescharacteristic
170C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C7#13711yescharacteristic
174C2×Dic7—42no—
175C2×Dic7—41no—
176C2×Dic7—41no—
177C2×Dic7—41no—
178C2×Dic7—81no—
179C2×Dic7—81no—
180C2×Dic7—81no—
181C2×Dic7—81no—
182C2×Dic7—81no—
183D28—22no—
184D28—22no—
185D28—41no—
186D28—41no—
187C4×D7—81no—
188C4×D7—81no—
189C4×D7—81no—
190C4×D7—81no—
191Dic14—42no—
192Dic14—42no—
193Dic14—81no—
194Dic14—81no—
195C7×C8—22no—
196C7×C8—42no—
197C7×C8—41no—
198C7×C8—81no—
199C7⋊C8—81no—
200C22×Q8—141no—
201C22×D4—71no—
202C23×C4—141no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—141no—
206C22×C8D2811yescharacteristic
207C22×C8D2811yescharacteristic
208C4⋊Q8—72no—
209C4⋊Q8—141no—
210C4⋊Q8—141no—
211C4⋊Q8—141no—
212C4×D4—141no—
213C4×D4—141no—
214C4×D4—141no—
215C4×D4—141no—
216C2×C4⋊C4—71no—
217C2×C4⋊C4—141no—
218C2×C4⋊C4—141no—
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—141no—
229C4⋊C8—141no—
230C4⋊C8C22⋊D712yes—
231#103—282no—
232#103—282no—
233#102—144no—
234#102—282no—
235C22⋊C8—282no—
236C22⋊C8—282no—
237C4×C8—21no—
238C4×C8—21no—
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#44911yescharacteristic
256C4×C7#45111yescharacteristic
257C4×C7#45911yescharacteristic
258C4×C7#46311yescharacteristic
259C4×C7#46611yescharacteristic
260C4×C7#46911yescharacteristic
261C4×C7#48411yescharacteristic
262C4×C7#48511yescharacteristic
263Dic7—82no—
264Dic7—81no—
265Dic7—161no—
266C24—141no—
267C2×Q8—142no—
268C2×Q8—281no—
269C2×Q8—281no—
270C2×Q8—281no—
271C2×Q8—281no—
272C2×Q8—281no—
273C2×D4—72no—
274C2×D4—141no—
275C2×D4—141no—
276C2×D4—141no—
277C2×D4—141no—
278C2×D4—141no—
279C22×C4—141no—
280C22×C4—281no—
281C22×C4—281no—
282C22×C4—281no—
283C22×C4—281no—
284C22×C4—281no—
285C22×C4—281no—
286C22×C4—281no—
287C22×C4—281no—
288C22×C4C2×D2811yescharacteristic
289C22×C4D4×D711yescharacteristic
290C22×C4#116111yescharacteristic
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—281no—
303C2×C8—281no—
304C2×C8—281no—
305C2×C8D5612yes—
306C4⋊C4—141no—
307C4⋊C4—142no—
308C4⋊C4—142no—
309C4⋊C4—141no—
310C4⋊C4—281no—
311C4⋊C4—281no—
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#116111yescharacteristic
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#645811yescharacteristic
339Q8—282no—
340Q8—282no—
341Q8—561no—
342Q8—561no—
343D4—142no—
344D4—142no—
345D4—281no—
346D4—281no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—281no—
350C2×C4—281no—
351C2×C4—281no—
352C2×C4—282no—
353C2×C4—561no—
354C2×C4—561no—
355C2×C4—561no—
356C2×C4—561no—
357C2×C4—561no—
358C2×C4—561no—
359C2×C4—561no—
360C2×C4—561no—
361C2×C4—561no—
362C2×C4#645711yescharacteristic
363C2×C4#645711yescharacteristic
364C2×C4#645811yescharacteristic
365C2×C4C2×D5611yescharacteristic
366C2×C4#646711yescharacteristic
367C2×C4#647111yescharacteristic
368C2×C4#647111yescharacteristic
369C2×C4#647411yescharacteristic
370C2×C4#647511yescharacteristic
371C2×C4D7×Q1611yescharacteristic
372C2×C4#648111yescharacteristic
373C2×C4#649311yescharacteristic
374C2×C4#650011yescharacteristic
375C2×C4#651011yescharacteristic
376C8—22no—
377C8—41no—
378C8—42no—
379C8—81no—
380C8—561no—
381C7#1048511yescharacteristic, complemented, Sylow
382C22—282no—
383C22—282no—
384C22—282no—
385C22—561no—
386C22—561no—
387C22—561no—
388C22—561no—
389C22#8961511yescharacteristic
390C22#8961611yescharacteristic
391C22#8965811yescharacteristic
392C22#8965911yescharacteristic
393C22#8966811yescharacteristic
394C22#8967011yescharacteristic
395C22#8976311yescharacteristic
396C4—21no—
397C4—21no—
398C4—561no—
399C4—562no—
400C4—1121no—
401C4#8961511yescharacteristic
402C4#8961611yescharacteristic
403C4#8965611yescharacteristic
404C4#8966011yescharacteristic
405C4#8988711yescharacteristic
406C4#8990711yescharacteristic
407C4#8993011yescharacteristic
408C4#8995811yescharacteristic
409C2—562no—
410C2#1172633111yescharacteristic
411C2#1172633511yescharacteristic
412C2#1172633611yescharacteristic
413C2#1172633911yescharacteristic
414C2#1172823511yescharacteristic
415C2#1172838911yescharacteristic
416C2#1172847011yescharacteristic
subgroupG/H
centerC23#6458
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC2×C7×#335C2
socleC23×C7#121
prime radicalC22×D28D4
hypercenterC2×#335D7
hypocenterC7#10485
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. C2×C7×#335C2semidirect
4. C2×#89281C2semidirect
6. #11727525C2semidirect
7. #11725508C2semidirect
71. C2×#335D7semidirect
381. C7#10485semidirect

Maximal subgroups

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

subgroupindex
C2×#896182
C2×C7×#3352
#117282332
C2×#892812
#117275412
#117275252
#117255082
#104857