Finite Group Databasebeta

← #13253984

Subgroups — #13253984

Order 1792.

548 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731443C211yesmaximal, characteristic
2#11727662C211yesmaximal, characteristic
3#11727155C211yesmaximal, characteristic
4C7×#1294C211yesmaximal, characteristic
5#11725481C211yesmaximal, characteristic
6#11725430C211yesmaximal, characteristic
7#11725418C211yesmaximal, characteristic
8C22×C4×Dic7C2211yescharacteristic
9C2×#6453C411yescharacteristic, complemented
10C2×C7×C22⋊C8C2211yescharacteristic
11C7×#380C2211yescharacteristic
12C2×C7×#95C2211yescharacteristic
13#89984C2211yescharacteristic
14C2×C7⋊#95—21no—
15C2×C7⋊#95—21no—
16C2×C7⋊#95C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18C2×Dic7⋊C8—21no—
19#89757C411yescharacteristic, complemented
20#89749C411yescharacteristic, complemented
21#89745C411yescharacteristic, complemented
22#89722—21no—
23#89718—21no—
24#89427—21no—
25#89426—21no—
26#89345—21no—
27#9913—71nomaximal, Sylow
28C23×C4×C7—21no—
29C23×C4×C7C2311yescharacteristic
30C23×Dic7—21no—
31C23×Dic7D411yescharacteristic
32C23×Dic7D411yescharacteristic
33C22×C7×C8—21no—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C22⋊C4—21no—
37C2×C22⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×C4×Dic7—42no—
45C2×C4×Dic7C2×C411yescharacteristic
46C2×C4×Dic7C2×C411yescharacteristic
47C2×C4×Dic7D411yescharacteristic
48C2×C4×Dic7D411yescharacteristic
49C22×C7⋊C8—21no—
50#6453—42no—
51C7×C22⋊C8—21no—
52C7×C22⋊C8—21no—
53C7×#95—21no—
54C7×#95—21no—
55C7×#95Q812yes—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C7⋊#95—21no—
62C7⋊#95—42no—
63C7⋊#95—42no—
64C7⋊#95Q812yes—
65C22⋊(C7⋊C8)—21no—
66C22⋊(C7⋊C8)—21no—
67Dic7⋊C8—42no—
68#2851—71no—
69#1797—71no—
70#1434—71no—
71#1294—71no—
72#1294—71no—
73#1294—71no—
74#1294D711yescharacteristic
75C24×C7C2×D411yescharacteristic
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7—22no—
79C22×C4×C7—41no—
80C22×C4×C7—41no—
81C22×C4×C7—41no—
82C22×C4×C7—41no—
83C22×C4×C7—41no—
84C22×C4×C7—41no—
85C22×C4×C7—41no—
86C22×C4×C7—41no—
87C22×C4×C7C22×C411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×Q811yescharacteristic
90C22×C4×C7C2×Q811yescharacteristic
91C22×C4×C7#4111yescharacteristic
92C22×C4×C7#4111yescharacteristic
93C22×Dic7—21no—
94C22×Dic7—21no—
95C22×Dic7—21no—
96C22×Dic7—21no—
97C22×Dic7—22no—
98C22×Dic7—21no—
99C22×Dic7—21no—
100C22×Dic7—22no—
101C22×Dic7—41no—
102C22×Dic7—41no—
103C22×Dic7—41no—
104C22×Dic7—41no—
105C22×Dic7—41no—
106C22×Dic7—41no—
107C22×Dic7—41no—
108C22×Dic7—41no—
109C22×Dic7—41no—
110C22×Dic7C22⋊C411yescharacteristic
111C22×Dic7C22⋊C411yescharacteristic
112C22×Dic7C22⋊C411yescharacteristic
113C22×Dic7C22⋊C411yescharacteristic
114C2×C7×C8—41no—
115C2×C7×C8—41no—
116C2×C7×C8—41no—
117C7×C4⋊C4—41no—
118C7×C4⋊C4—41no—
119C7×C22⋊C4—41no—
120C7×C22⋊C4—41no—
121C22⋊Dic7—41no—
122C22⋊Dic7—41no—
123C4⋊Dic7—42no—
124C4⋊Dic7—42no—
125C4⋊Dic7—41no—
126C4⋊Dic7—41no—
127Dic7⋊C4—42no—
128Dic7⋊C4—42no—
129C4×Dic7—22no—
130C4×Dic7—22no—
131C4×Dic7—41no—
132C4×Dic7—41no—
133C2×C7⋊C8—41no—
134C2×C7⋊C8—41no—
135C2×C7⋊C8—41no—
136C2×#125—71no—
137C22×C42—71no—
138C2×C4⋊C8—141no—
139C2×C22⋊C8—71no—
140C2×C22⋊C8C2×D711yescharacteristic
141#389—71no—
142#389—71no—
143#387—141no—
144#387—141no—
145#385—141no—
146#385—141no—
147#382—71no—
148#380—71no—
149#380C2×D711yescharacteristic
150C2×#95—71no—
151C2×#95—141no—
152C2×#95—141no—
153C2×#95C2×D711yescharacteristic
154#336—141no—
155C23×C7—21no—
156C23×C7—21no—
157C23×C7—21no—
158C23×C7—21no—
159C23×C7C2×C22⋊C411yescharacteristic
160C23×C7C22⋊Q811yescharacteristic
161C23×C7C22⋊Q811yescharacteristic
162C23×C7#13511yescharacteristic
163C23×C7#13511yescharacteristic
164C23×C7AGL(1,ℤ/8)11yescharacteristic
165C23×C7#13711yescharacteristic
166C2×C4×C7—21no—
167C2×C4×C7—21no—
168C2×C4×C7—21no—
169C2×C4×C7—21no—
170C2×C4×C7—41no—
171C2×C4×C7—41no—
172C2×C4×C7—41no—
173C2×C4×C7—41no—
174C2×C4×C7—42no—
175C2×C4×C7—42no—
176C2×C4×C7—41no—
177C2×C4×C7—41no—
178C2×C4×C7—41no—
179C2×C4×C7—41no—
180C2×C4×C7—41no—
181C2×C4×C7—41no—
182C2×C4×C7—42no—
183C2×C4×C7—81no—
184C2×C4×C7—81no—
185C2×C4×C7—81no—
186C2×C4×C7—81no—
187C2×C4×C7C4×Q811yescharacteristic
188C2×C4×C7C4×Q811yescharacteristic
189C2×C4×C7#12411yescharacteristic
190C2×C4×C7C4⋊Q811yescharacteristic
191C2×Dic7—21no—
192C2×Dic7—21no—
193C2×Dic7—21no—
194C2×Dic7—21no—
195C2×Dic7—21no—
196C2×Dic7—21no—
197C2×Dic7—21no—
198C2×Dic7—21no—
199C2×Dic7—21no—
200C2×Dic7—21no—
201C2×Dic7—21no—
202C2×Dic7—42no—
203C2×Dic7—42no—
204C2×Dic7—42no—
205C2×Dic7—42no—
206C2×Dic7—42no—
207C2×Dic7—42no—
208C2×Dic7—41no—
209C2×Dic7—41no—
210C2×Dic7—41no—
211C2×Dic7—41no—
212C2×Dic7—41no—
213C2×Dic7—41no—
214C2×Dic7—42no—
215C2×Dic7—81no—
216C2×Dic7—81no—
217C2×Dic7—81no—
218C2×Dic7—81no—
219C2×Dic7#9912yes—
220C7×C8—81no—
221C7⋊C8—81no—
222C23×C4—21no—
223C23×C4—71no—
224C23×C4—71no—
225C23×C4—141no—
226C23×C4C22×D711yescharacteristic
227C22×C8—21no—
228C22×C8—141no—
229#125—282no—
230C2×C4⋊C4—71no—
231C2×C4⋊C4—71no—
232C2×C4⋊C4—141no—
233C2×C4⋊C4—141no—
234C2×C4⋊C4—141no—
235C2×C4⋊C4—141no—
236C2×C4⋊C4C4×D711yescharacteristic
237C2×C4⋊C4C4×D711yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—141no—
240C2×C42—71no—
241C2×C42—71no—
242C2×C42—71no—
243C2×C42—71no—
244C2×C42—282no—
245C4⋊C8—282no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—141no—
249C22⋊C8—141no—
250#95—21no—
251#95—21no—
252#95—72no—
253#95—141no—
254#95—141no—
255#95—141no—
256#95—141no—
257#95—141no—
258#95—141no—
259#95—282no—
260#95—282no—
261#95Dic1412yes—
262C22×C7—21no—
263C22×C7—21no—
264C22×C7—21no—
265C22×C7—21no—
266C22×C7—21no—
267C22×C7—21no—
268C22×C7—21no—
269C22×C7—21no—
270C22×C7—21no—
271C22×C7—21no—
272C22×C7—21no—
273C22×C7—21no—
274C22×C7#39111yescharacteristic
275C22×C7C2×#9911yescharacteristic
276C22×C7#41011yescharacteristic
277C22×C7#41611yescharacteristic
278C22×C7#41711yescharacteristic
279C22×C7#42111yescharacteristic
280C22×C7#42111yescharacteristic
281C22×C7#47811yescharacteristic
282C22×C7#47811yescharacteristic
283C22×C7#47911yescharacteristic
284C22×C7#47911yescharacteristic
285C4×C7—21no—
286C4×C7—21no—
287C4×C7—21no—
288C4×C7—21no—
289C4×C7—82no—
290C4×C7—81no—
291C4×C7—81no—
292Dic7—22no—
293Dic7—41no—
294Dic7—41no—
295Dic7—41no—
296Dic7—82no—
297Dic7—81no—
298Dic7—81no—
299C24D4×D711yescharacteristic
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—71no—
312C22×C4—71no—
313C22×C4—71no—
314C22×C4—71no—
315C22×C4—142no—
316C22×C4—141no—
317C22×C4—141no—
318C22×C4—141no—
319C22×C4—141no—
320C22×C4—141no—
321C22×C4—141no—
322C22×C4—142no—
323C22×C4—281no—
324C22×C4—281no—
325C22×C4—281no—
326C22×C4—281no—
327C22×C4—281no—
328C22×C4—281no—
329C22×C4—281no—
330C22×C4—281no—
331C22×C4—281no—
332C22×C4C2×Dic1411yescharacteristic
333C22×C4C2×C4×D711yescharacteristic
334C22×C4#115711yescharacteristic
335C22×C4D4×D711yescharacteristic
336C22×C4#115911yescharacteristic
337C22×C4Q8×D711yescharacteristic
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—281no—
342C2×C8—281no—
343C2×C8—281no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—281no—
347C4⋊C4—281no—
348C4⋊C4—282no—
349C4⋊C4—282no—
350C4⋊C4—282no—
351C4⋊C4—282no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—281no—
355C22⋊C4—281no—
356C42—142no—
357C42—142no—
358C42—281no—
359C42—281no—
360C2×C7—21no—
361C2×C7—21no—
362C2×C7—21no—
363C2×C7—21no—
364C2×C7#151211yescharacteristic
365C2×C7#151311yescharacteristic
366C2×C7#151611yescharacteristic
367C2×C7#152111yescharacteristic
368C2×C7#198911yescharacteristic
369C2×C7#199511yescharacteristic
370C2×C7#199611yescharacteristic
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23#644111yescharacteristic
376C23D7×C22⋊C411yescharacteristic
377C23#645911yescharacteristic
378C23#647411yescharacteristic
379C23#647811yescharacteristic
380C23#647911yescharacteristic
381C23#648211yescharacteristic
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—72no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—141no—
405C2×C4—141no—
406C2×C4—141no—
407C2×C4—141no—
408C2×C4—141no—
409C2×C4—141no—
410C2×C4—141no—
411C2×C4—141no—
412C2×C4—141no—
413C2×C4—141no—
414C2×C4—141no—
415C2×C4—282no—
416C2×C4—282no—
417C2×C4—282no—
418C2×C4—282no—
419C2×C4—282no—
420C2×C4—282no—
421C2×C4—282no—
422C2×C4—281no—
423C2×C4—281no—
424C2×C4—281no—
425C2×C4—281no—
426C2×C4—281no—
427C2×C4—281no—
428C2×C4—561no—
429C2×C4—561no—
430C2×C4—561no—
431C2×C4—561no—
432C2×C4C4×Dic1411yescharacteristic
433C2×C4#644811yescharacteristic
434C2×C4#645011yescharacteristic
435C2×C4#645111yescharacteristic
436C8—81no—
437C8—561no—
438C7#991311yescharacteristic, complemented, Sylow
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22#8941811yescharacteristic
452C22#8951211yescharacteristic
453C22D7×#9911yescharacteristic
454C22#8953511yescharacteristic
455C22#8954311yescharacteristic
456C22#8956811yescharacteristic
457C22#8957611yescharacteristic
458C22#8959311yescharacteristic
459C22#8959311yescharacteristic
460C22#8962911yescharacteristic
461C22#8966311yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—142no—
470C4—281no—
471C4—281no—
472C4—281no—
473C4—562no—
474C4—561no—
475C4—561no—
476C2—21no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2#1172603411yescharacteristic
481C2#1172605911yescharacteristic
482C2#1172606911yescharacteristic
483C2#1172609211yescharacteristic
484C2#1172648611yescharacteristic
485C2#1172655511yescharacteristic
486C2#1172670911yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1294C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1294D7
hypocenterC7#9913
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
9. C2×#6453C4semidirect
19. #89757C4semidirect
20. #89749C4semidirect
21. #89745C4semidirect
438. C7#9913semidirect

Maximal subgroups

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

subgroupindex
#117314432
#117276622
#117271552
C7×#12942
#117254812
#117254302
#117254182
#99137