Finite Group Databasebeta

← #13245246

Subgroups — #13245246

Order 1792.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#529C211yesmaximal, characteristic
2C2×#89333C212yesmaximal, complemented
3C2×#89332C212yesmaximal
4#11729288C211yesmaximal, characteristic, complemented
5#11729285C211yesmaximal, characteristic, complemented
6C7×#529—24no—
7C7×#529—24no—
8C2×C7×#126—21no—
9C2×C7×#125C411yescharacteristic, complemented
10C2×C7×#124C411yescharacteristic, complemented
11C2×C7×#123—21no—
12C2×C7×C22⋊Q8C2211yescharacteristic
13C2×C7×#121C2211yescharacteristic
14C2×C4×C7×Q8C411yescharacteristic, complemented
15C2×C4×C7×D4—21no—
16C2×C4×C7×D4C411yescharacteristic, complemented
17C2×C7×#117—21no—
18C22×C42×C7C2211yescharacteristic
19C2×C7⋊#95—21no—
20C2×C7⋊#95—21no—
21C2×C7⋊#95C2212yes—
22C2×C22⋊(C7⋊C8)C2212yes—
23#89333—24no—
24#89332—24no—
25#89319—21no—
26#89319—21no—
27#8330—71nomaximal, Sylow
28C22×C7×Q8C2×C411yescharacteristic
29C22×C7×D4—21no—
30C22×C7×D4C2×C411yescharacteristic
31C23×C4×C7—21no—
32C23×C4×C7D411yescharacteristic
33C23×C4×C7D411yescharacteristic
34C23×C4×C7C2311yescharacteristic
35C23×Dic7—22no—
36C7×#126—28no—
37C7×#125—22no—
38C7×#125—22no—
39C7×#124—22no—
40C7×#124—22no—
41C7×#123—28no—
42C7×C22⋊Q8—22no—
43C7×C22⋊Q8D414yes—
44C7×#121—22no—
45C7×#121D414yes—
46C4×C7×Q8—22no—
47C4×C7×Q8—22no—
48C4×C7×D4—28no—
49C4×C7×D4—22no—
50C4×C7×D4—22no—
51C7×#117—28no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4C2×C411yescharacteristic
57C2×C7×C4⋊C4C2×C411yescharacteristic
58C2×C7×C22⋊C4—21no—
59C2×C7×C22⋊C4—21no—
60C2×C7×C22⋊C4—21no—
61C2×C7×C22⋊C4—21no—
62C2×C7×C22⋊C4—21no—
63C2×C42×C7—21no—
64C2×C42×C7—22no—
65C2×C42×C7—22no—
66C2×C42×C7C2×C411yescharacteristic
67C2×C42×C7C2×C411yescharacteristic
68C2×C42×C7D411yescharacteristic
69C2×C42×C7D411yescharacteristic
70C22×C7⋊C8—22no—
71C7⋊#95—24no—
72C7⋊#95—22no—
73C7⋊#95—22no—
74C7⋊#95—42no—
75C22⋊(C7⋊C8)—22no—
76C22⋊(C7⋊C8)—22no—
77C2×#529D711yescharacteristic
78#1817—71no—
79C2×#328—72no—
80C2×#327—72no—
81#1434—71no—
82C24×C7—21no—
83C24×C7C2×D411yescharacteristic
84C2×C7×Q8—21no—
85C2×C7×Q8—41no—
86C2×C7×Q8—41no—
87C2×C7×Q8C22⋊C412yes—
88C2×C7×D4—24no—
89C2×C7×D4—21no—
90C2×C7×D4—41no—
91C2×C7×D4—41no—
92C2×C7×D4—42no—
93C2×C7×D4—41no—
94C2×C7×D4—41no—
95C2×C7×D4C22⋊C412yes—
96C22×C4×C7—24no—
97C22×C4×C7—21no—
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—22no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—22no—
106C22×C4×C7—41no—
107C22×C4×C7—41no—
108C22×C4×C7—41no—
109C22×C4×C7—42no—
110C22×C4×C7—42no—
111C22×C4×C7C22⋊C411yescharacteristic
112C22×C4×C7C22⋊C411yescharacteristic
113C22×C4×C7C22⋊C411yescharacteristic
114C22×C4×C7C22⋊C411yescharacteristic
115C22×C4×C7C22×C411yescharacteristic
116C22×C4×C7C2×D411yescharacteristic
117C22×C4×C7C2×D412yes—
118C22×C4×C7C2×D412yes—
119C22×Dic7—24no—
120C22×Dic7—42no—
121C22×Dic7—42no—
122C22×Dic7—42no—
123C22×Dic7—42no—
124C22×Dic7—42no—
125C22×Dic7—42no—
126C7×C4⋊C4—24no—
127C7×C4⋊C4—24no—
128C7×C4⋊C4—24no—
129C7×C4⋊C4—21no—
130C7×C4⋊C4—21no—
131C7×C4⋊C4—24no—
132C7×C4⋊C4C22⋊C412yes—
133C7×C4⋊C4C22⋊C412yes—
134C7×C22⋊C4—24no—
135C7×C22⋊C4—24no—
136C7×C22⋊C4—24no—
137C7×C22⋊C4—24no—
138C7×C22⋊C4—24no—
139C42×C7—24no—
140C42×C7—21no—
141C42×C7—21no—
142C42×C7—21no—
143C42×C7—21no—
144C42×C7—22no—
145C42×C7—22no—
146C2×C7⋊C8—42no—
147C2×C7⋊C8—42no—
148C2×C7⋊C8—42no—
149#529—24no—
150#529—24no—
151C2×#126—21no—
152C2×#125Dic711yescharacteristic, complemented
153C2×#124Dic711yescharacteristic, complemented
154C2×#123—21no—
155C2×C22⋊Q8C2×D711yescharacteristic
156C2×#121C2×D711yescharacteristic
157C2×C4×Q8Dic711yescharacteristic, complemented
158C2×C4×D4—21no—
159C2×C4×D4Dic711yescharacteristic, complemented
160C2×#117—21no—
161C22×C42C2×D711yescharacteristic
162C2×C22⋊C8—72no—
163C2×#95—72no—
164C2×#95—141no—
165C2×#95—141no—
166#336—141no—
167#336—141no—
168#328—144no—
169#327—144no—
170C23×C7—21no—
171C23×C7—21no—
172C23×C7—21no—
173C23×C7—21no—
174C23×C7—22no—
175C23×C7—41no—
176C23×C7—41no—
177C23×C7—41no—
178C23×C7—41no—
179C23×C7—41no—
180C23×C7—41no—
181C23×C7C2×C22⋊C411yescharacteristic
182C23×C7#12012yes—
183C23×C7#13512yes—
184C23×C7AGL(1,ℤ/8)11yescharacteristic
185C23×C7#13711yescharacteristic
186C7×Q8—42no—
187C7×Q8—42no—
188C7×D4—42no—
189C7×D4—42no—
190C7×D4—44no—
191C7×D4—44no—
192C2×C4×C7—21no—
193C2×C4×C7—21no—
194C2×C4×C7—21no—
195C2×C4×C7—21no—
196C2×C4×C7—21no—
197C2×C4×C7—21no—
198C2×C4×C7—21no—
199C2×C4×C7—21no—
200C2×C4×C7—21no—
201C2×C4×C7—22no—
202C2×C4×C7—22no—
203C2×C4×C7—22no—
204C2×C4×C7—21no—
205C2×C4×C7—21no—
206C2×C4×C7—21no—
207C2×C4×C7—21no—
208C2×C4×C7—21no—
209C2×C4×C7—21no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—44no—
213C2×C4×C7—48no—
214C2×C4×C7—41no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7—41no—
218C2×C4×C7—41no—
219C2×C4×C7—41no—
220C2×C4×C7—42no—
221C2×C4×C7—42no—
222C2×C4×C7#10412yes—
223C2×C4×C7C2×C22⋊C411yescharacteristic
224C2×C4×C7C2×C22⋊C411yescharacteristic
225C2×C4×C7#12012yes—
226C2×Dic7—44no—
227C2×Dic7—44no—
228C2×Dic7—44no—
229C2×Dic7—82no—
230C2×Dic7—82no—
231C2×Dic7—82no—
232C2×Dic7—82no—
233C7⋊C8—82no—
234C22×Q8C2×Dic711yescharacteristic
235C22×D4—21no—
236C22×D4C2×Dic711yescharacteristic
237C23×C4—21no—
238C23×C4—142no—
239C23×C4C22⋊D711yescharacteristic
240C23×C4C22⋊D711yescharacteristic
241C23×C4C22×D711yescharacteristic
242C22×C8—142no—
243#126—28no—
244#125—22no—
245#125—22no—
246#124—22no—
247#124—22no—
248#123—28no—
249C22⋊Q8—22no—
250C22⋊Q8C22⋊D714yes—
251#121—22no—
252#121C22⋊D714yes—
253C4×Q8—22no—
254C4×Q8—22no—
255C4×D4—28no—
256C4×D4—22no—
257C4×D4—22no—
258#117—28no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4C2×Dic711yescharacteristic
264C2×C4⋊C4C2×Dic711yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42C2×Dic711yescharacteristic
274C2×C42C2×Dic711yescharacteristic
275C2×C42C22⋊D711yescharacteristic
276C2×C42C22⋊D711yescharacteristic
277C22⋊C8—142no—
278C22⋊C8—142no—
279#95—144no—
280#95—142no—
281#95—142no—
282#95—282no—
283C22×C7—22no—
284C22×C7—21no—
285C22×C7—21no—
286C22×C7—21no—
287C22×C7—21no—
288C22×C7—22no—
289C22×C7—22no—
290C22×C7—22no—
291C22×C7—42no—
292C22×C7—42no—
293C22×C7—42no—
294C22×C7—81no—
295C22×C7—81no—
296C22×C7—81no—
297C22×C7—81no—
298C22×C7#37911yescharacteristic
299C22×C7#41011yescharacteristic
300C22×C7#41011yescharacteristic
301C22×C7#41611yescharacteristic
302C22×C7#41711yescharacteristic
303C22×C7C2×#10411yescharacteristic
304C22×C7#42111yescharacteristic
305C22×C7#44912yes—
306C22×C7#45212yes—
307C4×C7—22no—
308C4×C7—21no—
309C4×C7—21no—
310C4×C7—22no—
311C4×C7—42no—
312C4×C7—41no—
313C4×C7—41no—
314C4×C7—42no—
315C4×C7—41no—
316C4×C7—42no—
317Dic7—84no—
318C24—21no—
319C24C2×C22⋊D711yescharacteristic
320C2×Q8—21no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8C22⋊Dic712yes—
324C2×D4—24no—
325C2×D4—21no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4C22⋊Dic712yes—
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—144no—
348C22×C4—282no—
349C22×C4—282no—
350C22×C4—282no—
351C22×C4—282no—
352C22×C4—282no—
353C22×C4—282no—
354C22×C4C22⋊Dic711yescharacteristic
355C22×C4C22⋊Dic711yescharacteristic
356C22×C4C22⋊Dic711yescharacteristic
357C22×C4C22⋊Dic711yescharacteristic
358C22×C4C22×Dic711yescharacteristic
359C22×C4C2×C22⋊D711yescharacteristic
360C22×C4C2×C22⋊D712yes—
361C22×C4C2×C22⋊D712yes—
362C2×C8—282no—
363C2×C8—282no—
364C2×C8—282no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—24no—
371C4⋊C4C22⋊Dic712yes—
372C4⋊C4C22⋊Dic712yes—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C42—24no—
379C42—21no—
380C42—21no—
381C42—21no—
382C42—21no—
383C42—22no—
384C42—22no—
385C2×C7—22no—
386C2×C7—22no—
387C2×C7—82no—
388C2×C7#150011yescharacteristic
389C2×C7#150911yescharacteristic
390C2×C7#151211yescharacteristic
391C2×C7#152111yescharacteristic
392C2×C7#178211yescharacteristic
393C2×C7#178811yescharacteristic
394C2×C7#178911yescharacteristic
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—22no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23#651211yescharacteristic
407C23#651312yes—
408C23#651411yescharacteristic
409C23C2×C22⋊Dic711yescharacteristic
410C23#651612yes—
411Q8—42no—
412Q8—42no—
413D4—42no—
414D4—42no—
415D4—44no—
416D4—44no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—48no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—284no—
448C2×C4—284no—
449C2×C4—284no—
450C2×C4—562no—
451C2×C4—562no—
452C2×C4—562no—
453C2×C4—562no—
454C2×C4#641112yes—
455C2×C4C2×C22⋊Dic711yescharacteristic
456C2×C4C2×C22⋊Dic711yescharacteristic
457C2×C4#651612yes—
458C8—562no—
459C7#833011yescharacteristic, complemented, Sylow
460C22—22no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22#9000411yescharacteristic
476C22#9000511yescharacteristic
477C22C2×#641111yescharacteristic
478C22#9000811yescharacteristic
479C22#9001012yes—
480C22#9001112yes—
481C22#9001211yescharacteristic
482C22#9001211yescharacteristic
483C22#9001911yescharacteristic
484C4—22no—
485C4—22no—
486C4—21no—
487C4—21no—
488C4—41no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—42no—
493C4—42no—
494C4—564no—
495C2—22no—
496C2—22no—
497C2—82no—
498C2#1172950811yescharacteristic
499C2#1172950911yescharacteristic
500C2#1172951011yescharacteristic
501C2#1172951111yescharacteristic
502C2#1172988911yescharacteristic
503C2#1172989211yescharacteristic
504C2#1172989311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#529C2
socleC23×C7C2×C22⋊C4
prime radicalC2×C7×#121C22
cosocleC23×C4×C7C23
hypercenterC2×#529D7
hypocenterC7#8330
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
2. C2×#89333C2semidirect
4. #11729288C2semidirect
5. #11729285C2semidirect
9. C2×C7×#125C4semidirect
10. C2×C7×#124C4semidirect
14. C2×C4×C7×Q8C4semidirect
16. C2×C4×C7×D4C4semidirect
152. C2×#125Dic7semidirect
153. C2×#124Dic7semidirect
157. C2×C4×Q8Dic7semidirect
159. C2×C4×D4Dic7semidirect
459. C7#8330semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5292
C2×#893332
C2×#893322
#117292882
#117292852
#83307