Finite Group Databasebeta

← #13249483

Subgroups — #13249483

Order 1792.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740714C211yesmaximal, characteristic
2C2×#89607C211yesmaximal, characteristic
3C2×C7×#332C211yesmaximal, characteristic, complemented
4C2×#89342C211yesmaximal, characteristic, complemented
5#11728229C211yesmaximal, characteristic
6#11725508C211yesmaximal, characteristic, complemented
7#11725508C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6509—21no—
10C2×C42×D7C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13#90002—21no—
14C2×(C2×D7)⋊C8—21no—
15C2×(C2×D7)⋊C8—21no—
16C2×#6389—21no—
17#89759—21no—
18#89759C412yes—
19#89745—21no—
20#89745C412yes—
21#89707C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4⋊(C7⋊C8)C2211yescharacteristic
24#89607—22no—
25#89607—22no—
26C7×#332—22no—
27#89345—21no—
28#89342—22no—
29#9138—71nomaximal, Sylow
30C22×C7×Q8—21no—
31C22×C4×D7C2×C411yescharacteristic
32C22×C4×D7D411yescharacteristic
33C22×C4×D7D411yescharacteristic
34C22×C7×C8—21no—
35C22×C7×C8—21no—
36C7×C4⋊Q8—21no—
37C7×C4⋊Q8—21no—
38C7×C4⋊Q8—21no—
39C7×C4⋊Q8—21no—
40C2×C7×C4⋊C4—21no—
41C2×C7×C4⋊C4C2×C412yes—
42C2×C42×C7C2311yescharacteristic
43#6509—42no—
44#6509—42no—
45C2×(C2×D7)⋊C4—22no—
46C2×C4⋊Dic7—21no—
47C2×C4⋊Dic7—21no—
48C2×C4⋊Dic7C2×C412yes—
49C2×Dic7⋊C4—22no—
50C2×C4×Dic7C2×C411yescharacteristic
51C2×C4×Dic7D411yescharacteristic
52C2×C4×Dic7D411yescharacteristic
53C22×C7⋊C8—21no—
54C22×C7⋊C8—21no—
55C42×D7—21no—
56C42×D7—21no—
57C42×D7—21no—
58C42×D7—21no—
59C7×C4⋊C8—21no—
60C7×C4⋊C8—21no—
61C7×C4⋊C8—21no—
62C7×C4⋊C8D412yes—
63C7⋊#95—22no—
64C7⋊#95—22no—
65(C2×D7)⋊C8—24no—
66(C2×D7)⋊C8—42no—
67#6389—24no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4⋊(C7⋊C8)—21no—
71C4⋊(C7⋊C8)D412yes—
72C2×#432—71no—
73#2857—71no—
74#1797—71no—
75C2×#332—71no—
76C2×#332D711yescharacteristic, complemented
77#1296—71no—
78#1296—71no—
79C23×D7C22⋊C411yescharacteristic
80C2×C7×Q8—41no—
81C2×C7×Q8—41no—
82C2×C7×Q8—41no—
83C2×C7×Q8—41no—
84C2×C7×Q8—41no—
85C2×C7×Q8—41no—
86C22×C4×C7—22no—
87C22×C4×C7C22×C411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×Dic7—22no—
91C22×Dic7C22⋊C411yescharacteristic
92C22×Dic7C22⋊C411yescharacteristic
93C22×Dic7C22⋊C411yescharacteristic
94C2×C4×D7—22no—
95C2×C4×D7—21no—
96C2×C4×D7—21no—
97C2×C4×D7—21no—
98C2×C4×D7—21no—
99C2×C4×D7—21no—
100C2×C4×D7—21no—
101C2×C4×D7—21no—
102C2×C4×D7—21no—
103C2×C4×D7—21no—
104C2×C4×D7—21no—
105C2×C4×D7—21no—
106C2×C4×D7—21no—
107C2×C4×D7—21no—
108C2×C4×D7—21no—
109C2×C4×D7—41no—
110C2×C7×C8—22no—
111C2×C7×C8—41no—
112C2×C7×C8—41no—
113C2×C7×C8—41no—
114C2×C7×C8—41no—
115C2×C7×C8—41no—
116C7×C4⋊C4—22no—
117C7×C4⋊C4—22no—
118C7×C4⋊C4—41no—
119C7×C4⋊C4—41no—
120C42×C7C2×D411yescharacteristic
121C42×C7C2×D411yescharacteristic
122C42×C7#4111yescharacteristic
123C42×C7#4111yescharacteristic
124(C2×D7)⋊C4—44no—
125C4⋊Dic7—41no—
126C4⋊Dic7—41no—
127C4⋊Dic7—41no—
128C4⋊Dic7—41no—
129C4⋊Dic7—42no—
130Dic7⋊C4—44no—
131C4×Dic7—21no—
132C4×Dic7—21no—
133C4×Dic7—21no—
134C4×Dic7—21no—
135C4×Dic7—21no—
136C4×Dic7—21no—
137C2×C7⋊C8—22no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8—41no—
140C2×C7⋊C8—41no—
141C2×C7⋊C8—41no—
142C2×C7⋊C8—41no—
143C2×C4⋊Q8C2×D711yescharacteristic
144C2×C22⋊Q8—141no—
145C22×C42—71no—
146#432—142no—
147#432—142no—
148C2×C4⋊C8—71no—
149C2×C4⋊C8—71no—
150C2×C4⋊C8C2×D711yescharacteristic
151C2×C4⋊C8C2×D711yescharacteristic
152C2×C22⋊C8—141no—
153C2×C22⋊C8—141no—
154C2×#97—141no—
155#391—141no—
156#389—72no—
157#389—141no—
158#384—71no—
159#380—72no—
160#380—141no—
161#336—141no—
162#332—22no—
163#332—142no—
164C23×C7C2×C22⋊C411yescharacteristic
165C22×D7—21no—
166C22×D7—21no—
167C22×D7—21no—
168C22×D7—21no—
169C22×D7—21no—
170C22×D7—21no—
171C22×D7#10112yes—
172C7×Q8—81no—
173C7×Q8—81no—
174C7×Q8—81no—
175C7×Q8—81no—
176C2×C4×C7—21no—
177C2×C4×C7—21no—
178C2×C4×C7—42no—
179C2×C4×C7—42no—
180C2×C4×C7—42no—
181C2×C4×C7C4×D411yescharacteristic
182C2×C4×C7C4×D411yescharacteristic
183C2×C4×C7#12011yescharacteristic
184C2×C4×C7#12111yescharacteristic
185C2×C4×C7#12111yescharacteristic
186C2×C4×C7#12311yescharacteristic
187C2×C4×C7#13511yescharacteristic
188C2×C4×C7#13511yescharacteristic
189C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C7#13711yescharacteristic
193C2×C4×C7#13711yescharacteristic
194C2×C4×C7#13711yescharacteristic
195C2×Dic7—21no—
196C2×Dic7—21no—
197C2×Dic7—21no—
198C2×Dic7—21no—
199C2×Dic7—21no—
200C2×Dic7—21no—
201C2×Dic7—21no—
202C2×Dic7—21no—
203C2×Dic7—21no—
204C2×Dic7—42no—
205C2×Dic7—42no—
206C2×Dic7—42no—
207C4×D7—42no—
208C4×D7—42no—
209C4×D7—41no—
210C4×D7—41no—
211C4×D7—41no—
212C4×D7—41no—
213C4×D7—41no—
214C4×D7—41no—
215C4×D7—41no—
216C4×D7—41no—
217C7×C8—42no—
218C7×C8—81no—
219C7⋊C8—42no—
220C7⋊C8—81no—
221C22×Q8—21no—
222C23×C4—71no—
223C23×C4—71no—
224C23×C4—71no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—141no—
228C22×C8—141no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C22⋊Q8—282no—
234C22⋊Q8—282no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—72no—
237C2×C4⋊C4—142no—
238C2×C4⋊C4—141no—
239C2×C4⋊C4—141no—
240C2×C4⋊C4C4×D712yes—
241C2×C22⋊C4—142no—
242C2×C42—71no—
243C2×C42—71no—
244C2×C42—71no—
245C2×C42—141no—
246C2×C42—141no—
247C2×C42—141no—
248C2×C42—141no—
249C2×C42C22×D711yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—72no—
254C4⋊C8—141no—
255C4⋊C8—141no—
256C4⋊C8—141no—
257C4⋊C8C22⋊D712yes—
258C22⋊C8—144no—
259C22⋊C8—282no—
260#97—144no—
261#95—142no—
262#95—142no—
263C22×C7#38611yescharacteristic
264C22×C7C2×#10111yescharacteristic
265C22×C7#41311yescharacteristic
266C22×C7#41611yescharacteristic
267C22×C7#41711yescharacteristic
268C22×C7#41811yescharacteristic
269C22×C7#41911yescharacteristic
270C2×D7—22no—
271C2×D7—22no—
272C2×D7—22no—
273C2×D7—41no—
274C2×D7—41no—
275C2×D7—41no—
276C2×D7—41no—
277C4×C7—21no—
278C4×C7—21no—
279C4×C7—82no—
280C4×C7#45211yescharacteristic
281C4×C7#45211yescharacteristic
282C4×C7#46811yescharacteristic
283C4×C7#46811yescharacteristic
284C4×C7#46911yescharacteristic
285C4×C7#46911yescharacteristic
286C4×C7#48511yescharacteristic
287C4×C7#48511yescharacteristic
288Dic7—41no—
289Dic7—41no—
290Dic7—41no—
291Dic7—82no—
292C24—71no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C22×C4—22no—
300C22×C4—71no—
301C22×C4—71no—
302C22×C4—71no—
303C22×C4—142no—
304C22×C4—141no—
305C22×C4—141no—
306C22×C4—141no—
307C22×C4—141no—
308C22×C4—141no—
309C22×C4—141no—
310C22×C4—141no—
311C22×C4—141no—
312C22×C4—141no—
313C22×C4—141no—
314C22×C4—141no—
315C22×C4—141no—
316C22×C4—141no—
317C22×C4—141no—
318C22×C4—142no—
319C22×C4—281no—
320C22×C4C2×C4×D711yescharacteristic
321C22×C4D4×D711yescharacteristic
322C22×C4D4×D711yescharacteristic
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—142no—
330C2×C8—281no—
331C2×C8—281no—
332C2×C8—281no—
333C2×C8—281no—
334C2×C8—281no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—282no—
340C4⋊C4—284no—
341C4⋊C4—281no—
342C4⋊C4—281no—
343C4⋊C4—281no—
344C4⋊C4—281no—
345C22⋊C4—284no—
346C42—141no—
347C42—141no—
348C42—141no—
349C42—141no—
350C42—141no—
351C42—141no—
352C42#115711yescharacteristic
353C42D4×D711yescharacteristic
354C42#115911yescharacteristic
355C42C2×C22⋊D711yescharacteristic
356C2×C7#155211yescharacteristic
357C2×C7#155311yescharacteristic
358C2×C7#155611yescharacteristic
359C2×C7#155911yescharacteristic
360C2×C7#187311yescharacteristic
361C2×C7#189511yescharacteristic
362C2×C7#190111yescharacteristic
363D7—42no—
364C23—72no—
365C23—141no—
366C23—141no—
367C23—141no—
368C23—141no—
369C23—141no—
370C23—141no—
371C23D7×C22⋊C411yescharacteristic
372Q8—81no—
373Q8—81no—
374Q8—81no—
375Q8—81no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—141no—
382C2×C4—141no—
383C2×C4—141no—
384C2×C4—141no—
385C2×C4—141no—
386C2×C4—141no—
387C2×C4—141no—
388C2×C4—141no—
389C2×C4—141no—
390C2×C4—282no—
391C2×C4—282no—
392C2×C4—281no—
393C2×C4—281no—
394C2×C4—281no—
395C2×C4—281no—
396C2×C4—281no—
397C2×C4—281no—
398C2×C4—281no—
399C2×C4—281no—
400C2×C4—282no—
401C2×C4—282no—
402C2×C4—282no—
403C2×C4(C22⋊D7)⋊C411yescharacteristic
404C2×C4#644611yescharacteristic
405C2×C4#644711yescharacteristic
406C2×C4#647411yescharacteristic
407C2×C4#647411yescharacteristic
408C2×C4#647711yescharacteristic
409C2×C4#647811yescharacteristic
410C2×C4#647811yescharacteristic
411C2×C4#647911yescharacteristic
412C2×C4#648111yescharacteristic
413C2×C4#648211yescharacteristic
414C2×C4C4×C22⋊D711yescharacteristic
415C2×C4#650011yescharacteristic
416C2×C4#650111yescharacteristic
417C8—42no—
418C8—81no—
419C8—282no—
420C8—561no—
421C7#913811yescharacteristic, complemented, Sylow
422C22—142no—
423C22—142no—
424C22—142no—
425C22—281no—
426C22—281no—
427C22—281no—
428C22—281no—
429C22D7×#10111yescharacteristic
430C22#8952311yescharacteristic
431C22#8954211yescharacteristic
432C22#8954311yescharacteristic
433C22#8957411yescharacteristic
434C22#8957611yescharacteristic
435C22#8972811yescharacteristic
436C4—21no—
437C4—21no—
438C4—82no—
439C4—281no—
440C4—281no—
441C4—281no—
442C4—562no—
443C4#8955211yescharacteristic
444C4#8955411yescharacteristic
445C4#8958611yescharacteristic
446C4#8958711yescharacteristic
447C4#8993111yescharacteristic
448C4#8994511yescharacteristic
449C4#8994611yescharacteristic
450C4#8995911yescharacteristic
451C2—282no—
452C2#1172617911yescharacteristic
453C2#1172618011yescharacteristic
454C2#1172618211yescharacteristic
455C2#1172618411yescharacteristic
456C2#1172786911yescharacteristic
457C2#1172795711yescharacteristic
458C2#1172802311yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#332C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#332D7
hypocenterC7#9138
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. C2×C7×#332C2semidirect
4. C2×#89342C2semidirect
6. #11725508C2semidirect
7. #11725508C2semidirect
76. C2×#332D7semidirect
421. C7#9138semidirect

Maximal subgroups

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

subgroupindex
#117407142
C2×#896072
C2×C7×#3322
C2×#893422
#117282292
#117255082
#91387