Finite Group Databasebeta

← #13244694

Subgroups — #13244694

Order 1792.

720 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731311C211yesmaximal, characteristic
2C2×#89262C211yesmaximal, characteristic
3#11727660C211yesmaximal, characteristic
4Dic7×#95C211yesmaximal, characteristic
5C2×#89247C211yesmaximal, characteristic
6C7×#1294C211yesmaximal, characteristic
7#11725430C211yesmaximal, characteristic
8C2×#6487C2211yescharacteristic
9C22×C4×Dic7—21no—
10C22×C4×Dic7C2211yescharacteristic
11C2×#6450C411yescharacteristic, complemented
12C2×C7×C22⋊C8C2211yescharacteristic
13C7×#380C2211yescharacteristic
14C2×C7×#95C2211yescharacteristic
15C2×C7⋊#95—21no—
16C2×C7⋊#95C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18C2×#6389—21no—
19C4⋊C4×Dic7C411yescharacteristic, complemented
20#89746C411yescharacteristic, complemented
21#89745C411yescharacteristic, complemented
22#89718—21no—
23C22⋊C4×Dic7—21no—
24#89424—21no—
25#89421—21no—
26#89345—21no—
27#89262C414yescomplemented
28#89247C414yescomplemented
29#8219—71nomaximal, Sylow
30C23×C4×C7—21no—
31C23×C4×C7C2311yescharacteristic
32C23×Dic7—21no—
33C23×Dic7D411yescharacteristic
34C23×Dic7D411yescharacteristic
35C22×Dic14C2×C411yescharacteristic
36C22×C7×C8—21no—
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C22⋊C4—21no—
40C2×C22⋊Dic7—21no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42#6487—21no—
43#6487—21no—
44#6487C2×C412yes—
45#6487C2×C412yes—
46C2×Dic7⋊C4—21no—
47C2×Dic7⋊C4—21no—
48C2×Dic7⋊C4—21no—
49C2×C4×Dic7—24no—
50C2×C4×Dic7—21no—
51C2×C4×Dic7—21no—
52C2×C4×Dic7—42no—
53C2×C4×Dic7—42no—
54C2×C4×Dic7—42no—
55C2×C4×Dic7C2×C411yescharacteristic
56C2×C4×Dic7C2×C411yescharacteristic
57C2×C4×Dic7D411yescharacteristic
58C2×C4×Dic7D411yescharacteristic
59C22×C7⋊C8—21no—
60#6450—42no—
61C7×C22⋊C8—21no—
62C7×C22⋊C8C2×C412yes—
63C7×#95—21no—
64C7×#95—21no—
65C7×#95C2×C412yes—
66C7⋊#95—24no—
67C7⋊#95—21no—
68C7⋊#95—21no—
69C7⋊#95—21no—
70C7⋊#95—21no—
71C7⋊#95—21no—
72C7⋊#95C2×C412yes—
73C22⋊(C7⋊C8)—21no—
74C22⋊(C7⋊C8)C2×C412yes—
75#6389—42no—
76C4×C22⋊Q8—71no—
77#1749—71no—
78C2×#328—71no—
79C2×#328—71no—
80C4×#95—71no—
81#1294—71no—
82#1294D711yescharacteristic
83C24×C7C2×D411yescharacteristic
84C22×C4×C7—22no—
85C22×C4×C7—22no—
86C22×C4×C7—22no—
87C22×C4×C7—21no—
88C22×C4×C7—21no—
89C22×C4×C7—41no—
90C22×C4×C7—41no—
91C22×C4×C7—41no—
92C22×C4×C7—41no—
93C22×C4×C7—41no—
94C22×C4×C7—41no—
95C22×C4×C7C22×C411yescharacteristic
96C22×C4×C7C22×C411yescharacteristic
97C22×C4×C7C22×C411yescharacteristic
98C22×C4×C7C2×D411yescharacteristic
99C22×C4×C7#4111yescharacteristic
100C22×C4×C7#4111yescharacteristic
101C22×Dic7—21no—
102C22×Dic7—21no—
103C22×Dic7—22no—
104C22×Dic7—22no—
105C22×Dic7—22no—
106C22×Dic7—22no—
107C22×Dic7—21no—
108C22×Dic7—21no—
109C22×Dic7—22no—
110C22×Dic7—21no—
111C22×Dic7—21no—
112C22×Dic7—22no—
113C22×Dic7—41no—
114C22×Dic7—41no—
115C22×Dic7—41no—
116C22×Dic7—41no—
117C22×Dic7—41no—
118C22×Dic7C22⋊C411yescharacteristic
119C22×Dic7C22⋊C411yescharacteristic
120C22×Dic7C22⋊C411yescharacteristic
121C22×Dic7C22⋊C411yescharacteristic
122C2×Dic14—21no—
123C2×Dic14—41no—
124C2×Dic14—41no—
125C2×Dic14C4212yescomplemented
126C2×C7×C8—22no—
127C2×C7×C8—41no—
128C2×C7×C8—41no—
129C7×C4⋊C4—41no—
130C7×C4⋊C4—41no—
131C7×C22⋊C4—41no—
132C7×C22⋊C4—41no—
133C22⋊Dic7—22no—
134C22⋊Dic7—22no—
135C4⋊Dic7—21no—
136C4⋊Dic7C4212yescomplemented
137Dic7⋊C4—22no—
138Dic7⋊C4—22no—
139Dic7⋊C4—42no—
140Dic7⋊C4—42no—
141C4×Dic7—22no—
142C4×Dic7—22no—
143C4×Dic7—41no—
144C4×Dic7—41no—
145C4×Dic7—42no—
146C4×Dic7—48no—
147C4×Dic7—42no—
148C2×C7⋊C8—22no—
149C2×C7⋊C8—41no—
150C2×C7⋊C8—41no—
151C2×C22⋊Q8—71no—
152C2×C4×Q8—71no—
153C22×C42—71no—
154C22×C42—141no—
155C2×C22⋊C8—71no—
156C2×C22⋊C8C2×D711yescharacteristic
157C2×#97—141no—
158#391—71no—
159#389—71no—
160#387—141no—
161#385—141no—
162#380C2×D711yescharacteristic
163C4×C4⋊C4—71no—
164C4×C4⋊C4—141no—
165C4×C22⋊C4—141no—
166C2×#95—71no—
167C2×#95—141no—
168C2×#95C2×D711yescharacteristic
169#336—141no—
170#328—74no—
171#328—74no—
172C23×C7—21no—
173C23×C7—21no—
174C23×C7—21no—
175C23×C7—21no—
176C23×C7C2×C22⋊C411yescharacteristic
177C23×C7C4×D411yescharacteristic
178C23×C7C4×D411yescharacteristic
179C23×C7AGL(1,ℤ/8)11yescharacteristic
180C23×C7#13711yescharacteristic
181C23×C7#13711yescharacteristic
182C23×C7#13711yescharacteristic
183C2×C4×C7—21no—
184C2×C4×C7—21no—
185C2×C4×C7—21no—
186C2×C4×C7—21no—
187C2×C4×C7—24no—
188C2×C4×C7—41no—
189C2×C4×C7—41no—
190C2×C4×C7—41no—
191C2×C4×C7—41no—
192C2×C4×C7—42no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7—42no—
196C2×C4×C7—42no—
197C2×C4×C7—42no—
198C2×C4×C7—41no—
199C2×C4×C7—41no—
200C2×C4×C7—41no—
201C2×C4×C7—41no—
202C2×C4×C7—41no—
203C2×C4×C7—41no—
204C2×C4×C7C2×C4211yescharacteristic
205C2×C4×C7#11711yescharacteristic
206C2×C4×C7C4×D411yescharacteristic
207C2×C4×C7C4×D411yescharacteristic
208C2×Dic7—24no—
209C2×Dic7—24no—
210C2×Dic7—21no—
211C2×Dic7—21no—
212C2×Dic7—21no—
213C2×Dic7—21no—
214C2×Dic7—21no—
215C2×Dic7—21no—
216C2×Dic7—24no—
217C2×Dic7—22no—
218C2×Dic7—22no—
219C2×Dic7—21no—
220C2×Dic7—21no—
221C2×Dic7—21no—
222C2×Dic7—42no—
223C2×Dic7—42no—
224C2×Dic7—42no—
225C2×Dic7—42no—
226C2×Dic7—42no—
227C2×Dic7—42no—
228C2×Dic7—42no—
229C2×Dic7—41no—
230C2×Dic7—41no—
231C2×Dic7—41no—
232C2×Dic7—41no—
233C2×Dic7—42no—
234C2×Dic7#9912yes—
235C2×Dic7#10412yes—
236C2×Dic7#10412yes—
237Dic14—42no—
238Dic14—42no—
239C7×C8—42no—
240C7⋊C8—42no—
241C22×Q8—71no—
242C23×C4—21no—
243C23×C4—71no—
244C23×C4—71no—
245C23×C4—141no—
246C23×C4C22×D711yescharacteristic
247C22×C8—21no—
248C22×C8—141no—
249C22⋊Q8—72no—
250C22⋊Q8—72no—
251C22⋊Q8—141no—
252C22⋊Q8—141no—
253C4×Q8—282no—
254C2×C4⋊C4—71no—
255C2×C4⋊C4—141no—
256C2×C4⋊C4—141no—
257C2×C4⋊C4—141no—
258C2×C4⋊C4C4×D711yescharacteristic
259C2×C4⋊C4C4×D711yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—141no—
262C2×C42—71no—
263C2×C42—71no—
264C2×C42—71no—
265C2×C42—71no—
266C2×C42—141no—
267C2×C42—141no—
268C2×C42—144no—
269C2×C42—282no—
270C2×C42—282no—
271C2×C42—282no—
272C22⋊C8—21no—
273C22⋊C8—72no—
274C22⋊C8—141no—
275C22⋊C8C4×D712yes—
276#97—282no—
277#95—21no—
278#95—21no—
279#95—72no—
280#95—141no—
281#95—141no—
282#95—141no—
283#95—141no—
284#95—144no—
285#95—141no—
286#95C4×D712yes—
287C22×C7—21no—
288C22×C7—21no—
289C22×C7—21no—
290C22×C7—21no—
291C22×C7—21no—
292C22×C7—21no—
293C22×C7—21no—
294C22×C7—21no—
295C22×C7—21no—
296C22×C7—21no—
297C22×C7—21no—
298C22×C7—21no—
299C22×C7C4×C22⋊C411yescharacteristic
300C22×C7C2×#9911yescharacteristic
301C22×C7#41011yescharacteristic
302C22×C7#41711yescharacteristic
303C22×C7#41911yescharacteristic
304C22×C7C2×#10411yescharacteristic
305C22×C7C2×#10411yescharacteristic
306C22×C7#44011yescharacteristic
307C22×C7#44011yescharacteristic
308C22×C7#44111yescharacteristic
309C22×C7#44111yescharacteristic
310C4×C7—21no—
311C4×C7—21no—
312C4×C7—21no—
313C4×C7—21no—
314C4×C7—44no—
315C4×C7—81no—
316C4×C7—81no—
317Dic7—22no—
318Dic7—22no—
319Dic7—22no—
320Dic7—44no—
321Dic7—42no—
322Dic7—42no—
323Dic7—41no—
324C24D4×D711yescharacteristic
325C2×Q8—72no—
326C2×Q8—141no—
327C2×Q8—281no—
328C2×Q8—281no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—71no—
341C22×C4—71no—
342C22×C4—71no—
343C22×C4—71no—
344C22×C4—142no—
345C22×C4—142no—
346C22×C4—142no—
347C22×C4—141no—
348C22×C4—141no—
349C22×C4—142no—
350C22×C4—142no—
351C22×C4—141no—
352C22×C4—141no—
353C22×C4—142no—
354C22×C4—141no—
355C22×C4—141no—
356C22×C4—281no—
357C22×C4—281no—
358C22×C4—281no—
359C22×C4—281no—
360C22×C4—281no—
361C22×C4C2×C4×D711yescharacteristic
362C22×C4C2×C4×D711yescharacteristic
363C22×C4C2×C4×D711yescharacteristic
364C22×C4D4×D711yescharacteristic
365C22×C4#115911yescharacteristic
366C22×C4#116111yescharacteristic
367C2×C8—22no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—142no—
371C2×C8—281no—
372C2×C8—281no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—72no—
376C4⋊C4—142no—
377C4⋊C4—141no—
378C4⋊C4—142no—
379C4⋊C4—282no—
380C4⋊C4—282no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—142no—
384C22⋊C4—142no—
385C42—142no—
386C42—142no—
387C42—281no—
388C42—281no—
389C42—282no—
390C42—288no—
391C42—282no—
392C2×C7—21no—
393C2×C7—21no—
394C2×C7—21no—
395C2×C7—21no—
396C2×C7#150411yescharacteristic
397C2×C7#150611yescharacteristic
398C2×C7#150811yescharacteristic
399C2×C7#150911yescharacteristic
400C2×C7C4×#9911yescharacteristic
401C2×C7C4×#10411yescharacteristic
402C2×C7#176311yescharacteristic
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23D7×C22⋊C411yescharacteristic
408C23(C22⋊D7)⋊C411yescharacteristic
409C23#645611yescharacteristic
410C23#647411yescharacteristic
411C23#647811yescharacteristic
412C23#647811yescharacteristic
413C23#648111yescharacteristic
414Q8—282no—
415Q8—282no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—24no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—72no—
438C2×C4—72no—
439C2×C4—72no—
440C2×C4—144no—
441C2×C4—144no—
442C2×C4—141no—
443C2×C4—141no—
444C2×C4—141no—
445C2×C4—141no—
446C2×C4—141no—
447C2×C4—141no—
448C2×C4—144no—
449C2×C4—142no—
450C2×C4—142no—
451C2×C4—141no—
452C2×C4—141no—
453C2×C4—141no—
454C2×C4—282no—
455C2×C4—282no—
456C2×C4—282no—
457C2×C4—282no—
458C2×C4—282no—
459C2×C4—282no—
460C2×C4—282no—
461C2×C4—282no—
462C2×C4—281no—
463C2×C4—281no—
464C2×C4—281no—
465C2×C4—281no—
466C2×C4C42×D711yescharacteristic
467C2×C4(C22⋊D7)⋊C411yescharacteristic
468C2×C4#645511yescharacteristic
469C2×C4#645611yescharacteristic
470C8—42no—
471C8—282no—
472C7#821911yescharacteristic, complemented, Sylow
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22#8943811yescharacteristic
486C22#8951211yescharacteristic
487C22D7×#9911yescharacteristic
488C22#8952911yescharacteristic
489C22#8954311yescharacteristic
490C22#8956111yescharacteristic
491C22#8957411yescharacteristic
492C22D7×#10411yescharacteristic
493C22D7×#10411yescharacteristic
494C22#8962511yescharacteristic
495C22#8966111yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—44no—
501C4—81no—
502C4—81no—
503C4—142no—
504C4—142no—
505C4—142no—
506C4—284no—
507C4—281no—
508C4—282no—
509C4—282no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2#1172603311yescharacteristic
515C2#1172605611yescharacteristic
516C2#1172606411yescharacteristic
517C2#1172608911yescharacteristic
518C2#1172648211yescharacteristic
519C2#1172653711yescharacteristic
520C2#1172670611yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC2×C4×C7C2×C42
FrattiniC23×C4C22×D7
FittingC7×#1294C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1294D7
hypocenterC7#8219
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
11. C2×#6450C4semidirect
19. C4⋊C4×Dic7C4semidirect
20. #89746C4semidirect
21. #89745C4semidirect
27. #89262C4semidirect
28. #89247C4semidirect
125. C2×Dic14C42semidirect
136. C4⋊Dic7C42semidirect
472. C7#8219semidirect

Maximal subgroups

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

subgroupindex
#117313112
C2×#892622
#117276602
Dic7×#952
C2×#892472
C7×#12942
#117254302
#82197