Finite Group Databasebeta

← #13257191

Subgroups — #13257191

Order 1792.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731252C211yesmaximal, characteristic
2C7×#1947C211yesmaximal, characteristic, complemented
3C2×#89276C211yesmaximal, characteristic, complemented
4C2×#89278C211yesmaximal, characteristic
5#11727338C211yesmaximal, characteristic
6#11727333C211yesmaximal, characteristic, complemented
7#11725425C211yesmaximal, characteristic, complemented
8C2×C4×D28C2211yescharacteristic
9C2×#6432C2211yescharacteristic
10C2×C7×#107—21no—
11C2×C7×C4⋊C8C2211yescharacteristic
12C7×#384C2211yescharacteristic
13C4×C7×C4⋊C4C2211yescharacteristic
14#89759—21no—
15#89759—21no—
16C2×#6384—22no—
17C2×#6383—21no—
18#89711—21no—
19#89708—21no—
20C2×C4⋊(C7⋊C8)C2211yescharacteristic
21C2×C4×C7⋊C8C2211yescharacteristic
22#89445—22no—
23C7×#340—21no—
24#89324—21no—
25#89278—22no—
26#89276—22no—
27#10413—71nomaximal, Sylow
28C22×D28D411yescharacteristic
29C22×C4×D7—21no—
30C22×Dic14D412yes—
31C22×C7×C8—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C42×C7—21no—
38C2×C42×C7C2311yescharacteristic
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—22no—
41C2×(C2×D7)⋊C4—22no—
42C2×C4⋊Dic7—21no—
43C2×C4⋊Dic7—21no—
44C2×C4⋊Dic7D411yescharacteristic
45C22×C7⋊C8—21no—
46C22×C7⋊C8—21no—
47C4×D28—21no—
48C4×D28—21no—
49C4×D28—21no—
50C4×D28—21no—
51#6432—21no—
52#6432—21no—
53#6432—21no—
54#6432—21no—
55C7×#107—42no—
56C7×C4⋊C8—21no—
57C7×C4⋊C8D412yes—
58C7×#95—21no—
59C7⋊#95—22no—
60C7⋊#95—22no—
61#6384—44no—
62#6383—42no—
63C4⋊(C7⋊C8)—21no—
64C4⋊(C7⋊C8)—21no—
65C4×C7⋊C8—21no—
66C4×C7⋊C8—21no—
67#2563—71no—
68#1956—71no—
69#1947D711yescharacteristic, complemented
70#1802—71no—
71C2×#333—71no—
72C2×D4⋊C8—71no—
73#1279—71no—
74C23×D7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—41no—
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×Dic7—21no—
82C22×Dic7—22no—
83C2×D28—21no—
84C2×D28—21no—
85C2×D28—21no—
86C2×D28—21no—
87C2×D28—21no—
88C2×D28Q1612yes—
89C2×C4×D7—41no—
90C2×C4×D7—41no—
91C2×C4×D7—41no—
92C2×C4×D7—41no—
93C2×C4×D7—41no—
94C2×C4×D7—41no—
95C2×Dic14—22no—
96C2×Dic14—22no—
97C2×Dic14—42no—
98C2×Dic14—42no—
99C2×C7×C8—22no—
100C2×C7×C8—41no—
101C2×C7×C8—41no—
102C7×C4⋊C4—21no—
103C7×C4⋊C4—21no—
104C7×C4⋊C4—21no—
105C7×C4⋊C4—21no—
106C7×C4⋊C4—42no—
107C7×C4⋊C4—41no—
108C7×C4⋊C4—41no—
109C7×C4⋊C4—41no—
110C7×C4⋊C4—41no—
111C42×C7—41no—
112C42×C7—41no—
113C42×C7C2×D411yescharacteristic
114C42×C7#4111yescharacteristic
115C42×C7#4111yescharacteristic
116C42×C7#4111yescharacteristic
117(C2×D7)⋊C4—41no—
118(C2×D7)⋊C4—41no—
119(C2×D7)⋊C4—82no—
120(C2×D7)⋊C4—82no—
121C4⋊Dic7—21no—
122C4⋊Dic7—21no—
123C4⋊Dic7—41no—
124C4⋊Dic7—41no—
125C4⋊Dic7—41no—
126C4⋊Dic7—41no—
127C2×C7⋊C8—22no—
128C2×C7⋊C8—41no—
129C2×C7⋊C8—41no—
130C2×C7⋊C8—41no—
131C2×C7⋊C8—41no—
132C2×C7⋊C8—41no—
133C2×C4⋊Q8—71no—
134C2×C4×D4—71no—
135C2×#107—21no—
136C2×C4⋊C8—71no—
137C2×C4⋊C8C2×D711yescharacteristic
138C2×#103—142no—
139C2×#102—141no—
140C2×C4×C8—71no—
141#393—142no—
142#390—141no—
143#384C2×D711yescharacteristic
144#382—141no—
145#380—141no—
146#380—141no—
147C4×C4⋊C4C2×D711yescharacteristic
148#340—21no—
149#340—141no—
150#333—142no—
151D4⋊C8—142no—
152C23×C7#12011yescharacteristic
153C22×D7—22no—
154C22×D7—41no—
155C22×D7—41no—
156C22×D7—41no—
157C22×D7—41no—
158C22×D7—41no—
159C22×D7—41no—
160C2×C4×C7—21no—
161C2×C4×C7—21no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7—81no—
169C2×C4×C7—81no—
170C2×C4×C7—81no—
171C2×C4×C7#12111yescharacteristic
172C2×C4×C7#12111yescharacteristic
173C2×C4×C7#12111yescharacteristic
174C2×C4×C7#12311yescharacteristic
175C2×C4×C7#12311yescharacteristic
176C2×C4×C7#12411yescharacteristic
177C2×C4×C7C2×Q1611yescharacteristic
178C2×C4×C7#13511yescharacteristic
179C2×C4×C7#13511yescharacteristic
180C2×C4×C7#13511yescharacteristic
181C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C7#13711yescharacteristic
184C2×C4×C7#13711yescharacteristic
185C2×Dic7—41no—
186C2×Dic7—42no—
187C2×Dic7—41no—
188C2×Dic7—41no—
189C2×Dic7—42no—
190C2×Dic7—42no—
191D28—22no—
192D28—22no—
193D28—41no—
194D28—41no—
195C4×D7—81no—
196C4×D7—81no—
197C4×D7—81no—
198C4×D7—81no—
199Dic14—44no—
200Dic14—82no—
201C7×C8—42no—
202C7⋊C8—42no—
203C7⋊C8—81no—
204C22×Q8—72no—
205C22×D4—71no—
206C23×C4—141no—
207C22×C8—21no—
208C22×C8—141no—
209C22×C8—141no—
210C4⋊Q8—141no—
211C4⋊Q8—141no—
212C4⋊Q8—141no—
213C4⋊Q8—141no—
214C4×D4—141no—
215C4×D4—141no—
216C4×D4—141no—
217C4×D4—141no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—71no—
222C2×C4⋊C4—141no—
223C2×C4⋊C4—141no—
224C2×C4⋊C4C22⋊D711yescharacteristic
225C2×C4⋊C4C22⋊D711yescharacteristic
226C2×C22⋊C4—141no—
227C2×C22⋊C4—142no—
228C2×C22⋊C4—142no—
229C2×C42—21no—
230C2×C42C22×D711yescharacteristic
231#107—42no—
232C4⋊C8—21no—
233C4⋊C8—141no—
234C4⋊C8—141no—
235C4⋊C8D2812yes—
236#103—284no—
237#102—282no—
238C4×C8—141no—
239C4×C8—141no—
240#95—21no—
241#95—142no—
242#95—142no—
243C22×C7#39411yescharacteristic
244C22×C7#44911yescharacteristic
245C22×C7#44911yescharacteristic
246C22×C7#45111yescharacteristic
247C22×C7#45211yescharacteristic
248C22×C7#45311yescharacteristic
249C22×C7#45511yescharacteristic
250C2×D7—42no—
251C2×D7—42no—
252C2×D7—42no—
253C2×D7—81no—
254C2×D7—81no—
255C2×D7—81no—
256C2×D7—81no—
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—81no—
260C4×C7—81no—
261C4×C7—161no—
262C4×C7#46311yescharacteristic
263C4×C7#46411yescharacteristic
264C4×C7#46711yescharacteristic
265C4×C7#46811yescharacteristic
266C4×C7#48411yescharacteristic
267C4×C7#48511yescharacteristic
268C4×C7#48811yescharacteristic
269C4×C7#48911yescharacteristic
270Dic7—82no—
271Dic7—81no—
272C24—141no—
273C2×Q8—142no—
274C2×Q8—142no—
275C2×Q8—282no—
276C2×Q8—282no—
277C2×D4—72no—
278C2×D4—141no—
279C2×D4—141no—
280C2×D4—141no—
281C2×D4—141no—
282C2×D4—141no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—141no—
287C22×C4—142no—
288C22×C4—281no—
289C22×C4—281no—
290C22×C4—281no—
291C22×C4—281no—
292C22×C4—281no—
293C22×C4—281no—
294C22×C4D4×D711yescharacteristic
295C22×C4D4×D711yescharacteristic
296C22×C4C2×C22⋊D711yescharacteristic
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—142no—
301C2×C8—281no—
302C2×C8—281no—
303C2×C8—281no—
304C2×C8—281no—
305C2×C8—281no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—141no—
316C4⋊C4—141no—
317C4⋊C4—281no—
318C4⋊C4—281no—
319C4⋊C4—281no—
320C4⋊C4—281no—
321C22⋊C4—281no—
322C22⋊C4—281no—
323C22⋊C4—562no—
324C22⋊C4—562no—
325C42—41no—
326C42—41no—
327C42C2×D2811yescharacteristic
328C42#115711yescharacteristic
329C42#116111yescharacteristic
330C42#116111yescharacteristic
331C2×C7#162411yescharacteristic
332C2×C7#163211yescharacteristic
333C2×C7#164411yescharacteristic
334C2×C7#164611yescharacteristic
335C2×C7#203611yescharacteristic
336C2×C7#203711yescharacteristic
337C2×C7#204211yescharacteristic
338D7—82no—
339C23—142no—
340C23—281no—
341C23—281no—
342C23—281no—
343C23—281no—
344C23—281no—
345C23—281no—
346C23#650011yescharacteristic
347Q8—284no—
348Q8—562no—
349D4—142no—
350D4—142no—
351D4—281no—
352D4—281no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—282no—
365C2×C4—282no—
366C2×C4—281no—
367C2×C4—282no—
368C2×C4—281no—
369C2×C4—281no—
370C2×C4—561no—
371C2×C4—561no—
372C2×C4—561no—
373C2×C4—561no—
374C2×C4#645711yescharacteristic
375C2×C4#645711yescharacteristic
376C2×C4#645811yescharacteristic
377C2×C4#645811yescharacteristic
378C2×C4#647411yescharacteristic
379C2×C4#647511yescharacteristic
380C2×C4D7×Q1611yescharacteristic
381C2×C4#648111yescharacteristic
382C2×C4#649311yescharacteristic
383C2×C4#649511yescharacteristic
384C2×C4#650511yescharacteristic
385C2×C4#651011yescharacteristic
386C2×C4#651311yescharacteristic
387C2×C4#651311yescharacteristic
388C8—42no—
389C8—282no—
390C8—561no—
391C7#1041311yescharacteristic, complemented, Sylow
392C22—282no—
393C22—282no—
394C22—282no—
395C22—561no—
396C22—561no—
397C22—561no—
398C22—561no—
399C22#8976311yescharacteristic
400C22#8980911yescharacteristic
401C22#8981911yescharacteristic
402C22#8993011yescharacteristic
403C22#8995811yescharacteristic
404C22#8997011yescharacteristic
405C22#8997411yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—161no—
411C4—561no—
412C4—562no—
413C4#8965611yescharacteristic
414C4#8965811yescharacteristic
415C4#8965911yescharacteristic
416C4#8966011yescharacteristic
417C4#8978811yescharacteristic
418C4#8980011yescharacteristic
419C4#8984011yescharacteristic
420C4#8986111yescharacteristic
421C2—562no—
422C2#1172738211yescharacteristic
423C2#1172838911yescharacteristic
424C2#1172842911yescharacteristic
425C2#1172877111yescharacteristic
426C2#1172881611yescharacteristic
427C2#1172886311yescharacteristic
428C2#1172891011yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1947C2
socleC23×C7#120
prime radicalC22×D28D4
hypercenter#1947D7
hypocenterC7#10413
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. C7×#1947C2semidirect
3. C2×#89276C2semidirect
6. #11727333C2semidirect
7. #11725425C2semidirect
69. #1947D7semidirect
391. C7#10413semidirect

Maximal subgroups

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

subgroupindex
#117312522
C7×#19472
C2×#892762
C2×#892782
#117273382
#117273332
#117254252
#104137