Finite Group Databasebeta

← #13403920

Subgroups — #13403920

Order 1792.

958 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2537C211yesmaximal, characteristic
2#11739829C211yesmaximal, characteristic, complemented
3C2×D4×C7⋊C8C211yesmaximal, characteristic, complemented
4C2×#89780C211yesmaximal, characteristic, complemented
5#11729435C212yesmaximal, complemented
6#11729434C212yesmaximal, complemented
7C4×#6406C211yesmaximal, characteristic, complemented
8#11727336C211yesmaximal, characteristic, complemented
9#11727322C211yesmaximal, characteristic, complemented
10#11727274C212yesmaximal, complemented
11#11727265C212yesmaximal, complemented
12C2×C7×#121—21no—
13C2×C7×#121C2212yes—
14C2×C4×C7×D4C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C23×C7⋊C8C2212yes—
17C2×#6432C2211yescharacteristic
18C7×#394—22no—
19C7×#384C2211yescharacteristic
20C7×#380—21no—
21C7×#380C2212yes—
22#89993—21no—
23C2×#6406C2211yescharacteristic
24C2×#6406C2212yes—
25C2×#6406C2211yescharacteristic
26#89984C2212yes—
27#89984C2212yes—
28C2×C22⋊(C7⋊C8)C2212yes—
29D4×C7⋊C8—24no—
30#89780—24no—
31#89749—21no—
32C2×#6382C2212yes—
33C2×#6382C2212yes—
34#89719—22no—
35C4×C4⋊Dic7C2211yescharacteristic
36C2×C4⋊(C7⋊C8)C2211yescharacteristic
37C2×C4×C7⋊C8C2211yescharacteristic
38#89324C2212yes—
39#89324C2212yes—
40#89324C2212yes—
41#89324C2211yescharacteristic
42#89324C2211yescharacteristic
43#25339—71nomaximal, Sylow
44C22×C7×D4—22no—
45C22×C7×D4D411yescharacteristic
46C22×C7×D4C2311yescharacteristic
47C23×C4×C7—21no—
48C23×C4×C7C2312yes—
49C22×Dic14—21no—
50C7×#121—24no—
51C7×#121—42no—
52C7×#121—44no—
53C4×C7×D4—22no—
54C4×C7×D4—22no—
55C4×C7×D4—22no—
56C4×C7×D4—22no—
57C2×C7×C4⋊C4—21no—
58C2×C7×C4⋊C4—21no—
59C2×C7×C4⋊C4D411yescharacteristic
60C2×C7×C4⋊C4C2311yescharacteristic
61C2×C7×C4⋊C4C2312yes—
62C2×C7×C22⋊C4—22no—
63C2×C7×C22⋊C4—21no—
64C2×C7×C22⋊C4—22no—
65C2×C7×C22⋊C4D412yes—
66C2×C42×C7C2311yescharacteristic
67C2×C22⋊Dic7—22no—
68C2×C22⋊Dic7—22no—
69C2×C4⋊Dic7—21no—
70C2×C4⋊Dic7C2312yes—
71C2×C4⋊Dic7C2311yescharacteristic
72C2×C4⋊Dic7C2311yescharacteristic
73C2×C4×Dic7—21no—
74C22×C7⋊C8—24no—
75C22×C7⋊C8—24no—
76C22×C7⋊C8—42no—
77C22×C7⋊C8C2311yescharacteristic
78C22×C7⋊C8C2312yes—
79C22×C7⋊C8C2311yescharacteristic
80#6432—22no—
81#6432—22no—
82C7×#95—22no—
83#6406—22no—
84#6406—24no—
85#6406—22no—
86C7⋊#95—21no—
87C7⋊#95—22no—
88C7⋊#95—22no—
89C22⋊(C7⋊C8)—24no—
90#6382—24no—
91#6382—42no—
92C4⋊(C7⋊C8)D414yescomplemented
93C4×C7⋊C8—22no—
94C2×#476—71no—
95C2×C8×D4—71no—
96#2563—71no—
97#2537D711yescharacteristic
98#2077—72no—
99#2034—72no—
100#1990—71no—
101#1948—71no—
102#1893—72no—
103#1807—72no—
104C4×#102—71no—
105C24×C7—21no—
106C24×C7C2×D412yes—
107C2×C7×D4—22no—
108C2×C7×D4—22no—
109C2×C7×D4—21no—
110C2×C7×D4—21no—
111C2×C7×D4—21no—
112C2×C7×D4—21no—
113C2×C7×D4—21no—
114C2×C7×D4—44no—
115C2×C7×D4—44no—
116C2×C7×D4—82no—
117C2×C7×D4SD1614yes—
118C2×C7×D4#4112yes—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—42no—
128C22×C4×C7—42no—
129C22×C4×C7—42no—
130C22×C4×C7C2×D412yes—
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2411yescharacteristic
134C22×Dic7—21no—
135C22×Dic7—21no—
136C22×Dic7—22no—
137C2×Dic14—42no—
138C2×Dic14—81no—
139C2×Dic14—81no—
140C7×C4⋊C4—22no—
141C7×C4⋊C4—21no—
142C7×C4⋊C4—21no—
143C7×C4⋊C4—22no—
144C7×C4⋊C4—22no—
145C7×C4⋊C4—42no—
146C7×C4⋊C4—81no—
147C7×C22⋊C4—24no—
148C7×C22⋊C4—44no—
149C7×C22⋊C4—44no—
150C7×C22⋊C4—42no—
151C42×C7C2×D412yes—
152C42×C7#4112yes—
153C22⋊Dic7—82no—
154C22⋊Dic7—82no—
155C4⋊Dic7—22no—
156C4⋊Dic7—21no—
157C4⋊Dic7—21no—
158C4⋊Dic7—22no—
159C4⋊Dic7—21no—
160C4⋊Dic7—21no—
161C4⋊Dic7—42no—
162C4×Dic7—42no—
163C2×C7⋊C8—21no—
164C2×C7⋊C8—22no—
165C2×C7⋊C8—21no—
166C2×C7⋊C8—22no—
167C2×C7⋊C8—21no—
168C2×C7⋊C8—21no—
169C2×C7⋊C8—21no—
170C2×C7⋊C8—48no—
171C2×C7⋊C8C2×D414yes—
172C2×C7⋊C8#4112yes—
173C23×C8—72no—
174C2×C4⋊Q8—71no—
175C2×#121—21no—
176C2×#121C2×D712yes—
177C2×C4×D4C2×D711yescharacteristic
178C2×C4×D4C2×D711yescharacteristic
179#476—144no—
180C8×D4—144no—
181C2×#106—72no—
182C2×#106—72no—
183C2×C4⋊C8—71no—
184C2×#102—71no—
185C2×#102—72no—
186C2×#102—71no—
187C2×C22⋊C8—72no—
188C2×C4×C8—71no—
189#394—22no—
190#393—142no—
191#390—141no—
192#384C2×D711yescharacteristic
193#382—141no—
194#380—21no—
195#380—72no—
196#380—72no—
197#380C2×D712yes—
198C4×C4⋊C4—71no—
199#340—71no—
200#340—72no—
201#340—71no—
202#340—72no—
203#340—72no—
204C23×C7—22no—
205C23×C7—22no—
206C23×C7—22no—
207C23×C7—22no—
208C23×C7—22no—
209C23×C7—22no—
210C23×C7—22no—
211C23×C7—41no—
212C23×C7—41no—
213C23×C7—41no—
214C23×C7—41no—
215C23×C7—41no—
216C23×C7—41no—
217C23×C7C2×SD1614yes—
218C23×C7C22×D411yescharacteristic
219C7×D4—22no—
220C7×D4—22no—
221C7×D4—28no—
222C7×D4—41no—
223C7×D4—41no—
224C7×D4—88no—
225C2×C4×C7—21no—
226C2×C4×C7—21no—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—42no—
233C2×C4×C7—42no—
234C2×C4×C7—41no—
235C2×C4×C7—42no—
236C2×C4×C7—41no—
237C2×C4×C7—42no—
238C2×C4×C7—41no—
239C2×C4×C7—42no—
240C2×C4×C7—84no—
241C2×C4×C7#12112yes—
242C2×C4×C7#12112yes—
243C2×C4×C7C2×SD1612yes—
244C2×C4×C7#13512yes—
245C2×C4×C7C22×D411yescharacteristic
246C2×C4×C7C2×#4111yescharacteristic
247C2×C4×C7C2×#4111yescharacteristic
248C2×C4×C7C2×#4111yescharacteristic
249C2×C4×C7H(5,𝔽2)11yescharacteristic
250C2×C4×C72−1+411yescharacteristic
251C2×Dic7—42no—
252C2×Dic7—41no—
253C2×Dic7—41no—
254C2×Dic7—41no—
255C2×Dic7—41no—
256C2×Dic7—41no—
257C2×Dic7—42no—
258C2×Dic7—41no—
259C2×Dic7—42no—
260Dic14—84no—
261C7⋊C8—22no—
262C7⋊C8—24no—
263C7⋊C8—41no—
264C22×Q8—141no—
265C22×D4—22no—
266C22×D4C22⋊D711yescharacteristic
267C22×D4C22×D711yescharacteristic
268C23×C4—21no—
269C23×C4C22×D712yes—
270C22×C8—71no—
271C22×C8—72no—
272C22×C8—71no—
273C22×C8—144no—
274C22×C8—144no—
275C22×C8—282no—
276C4⋊Q8—142no—
277C4⋊Q8—142no—
278#121—24no—
279#121—42no—
280#121—44no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—22no—
284C4×D4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—72no—
288C2×C4⋊C4—71no—
289C2×C4⋊C4—71no—
290C2×C4⋊C4—141no—
291C2×C4⋊C4C22⋊D711yescharacteristic
292C2×C4⋊C4C22×D711yescharacteristic
293C2×C4⋊C4C22×D712yes—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—142no—
298C2×C22⋊C4—142no—
299C2×C22⋊C4C22⋊D712yes—
300C2×C42—141no—
301C2×C42C22×D711yescharacteristic
302#106—144no—
303#106—282no—
304C4⋊C8—74no—
305#102—142no—
306#102—144no—
307#102—142no—
308C22⋊C8—144no—
309C4×C8—142no—
310#95—22no—
311#95—141no—
312#95—142no—
313#95—142no—
314C22×C7—24no—
315C22×C7—24no—
316C22×C7—24no—
317C22×C7—42no—
318C22×C7—42no—
319C22×C7—42no—
320C22×C7—42no—
321C22×C7—42no—
322C22×C7—42no—
323C22×C7—42no—
324C22×C7—81no—
325C22×C7—81no—
326C22×C7—81no—
327C22×C7—81no—
328C22×C7C2×#12111yescharacteristic
329C22×C7#54611yescharacteristic
330C22×C7#54711yescharacteristic
331C22×C7C22×SD1611yescharacteristic
332C22×C7C2×#13511yescharacteristic
333C22×C7#57611yescharacteristic
334C22×C7#57711yescharacteristic
335C4×C7—22no—
336C4×C7—42no—
337C4×C7—82no—
338C4×C7—81no—
339C4×C7#46514yes—
340C4×C7#52911yescharacteristic
341C4×C7#54211yescharacteristic
342C4×C7#54611yescharacteristic
343C4×C7#54811yescharacteristic
344Dic7—81no—
345Dic7—81no—
346Dic7—82no—
347C24—21no—
348C24C2×C22⋊D712yes—
349C2×Q8—282no—
350C2×Q8—561no—
351C2×Q8—561no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4—82no—
362C2×D4#114214yes—
363C2×D4#115912yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—141no—
376C22×C4—141no—
377C22×C4—142no—
378C22×C4C2×C22⋊D712yes—
379C22×C4C2×C22⋊D711yescharacteristic
380C22×C4C2×C22⋊D711yescharacteristic
381C22×C4C23×D711yescharacteristic
382C2×C8—74no—
383C2×C8—72no—
384C2×C8—141no—
385C2×C8—142no—
386C2×C8—141no—
387C2×C8—142no—
388C2×C8—141no—
389C2×C8—141no—
390C2×C8—141no—
391C2×C8—288no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—81no—
399C4⋊C4—142no—
400C4⋊C4—141no—
401C4⋊C4—142no—
402C4⋊C4—141no—
403C4⋊C4—141no—
404C4⋊C4—141no—
405C4⋊C4—282no—
406C22⋊C4—24no—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C22⋊C4—42no—
410C22⋊C4—562no—
411C22⋊C4—562no—
412C42—282no—
413C42D4×D712yes—
414C42#115912yes—
415C2×C7—44no—
416C2×C7—82no—
417C2×C7#242711yescharacteristic
418C2×C7C2×#46511yescharacteristic
419C2×C7#306211yescharacteristic
420C2×C7#329511yescharacteristic
421C2×C7#330311yescharacteristic
422C2×C7#333511yescharacteristic
423C2×C7#334111yescharacteristic
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C2×#114214yes—
438C23C22×C22⋊D711yescharacteristic
439Q8—564no—
440D4—22no—
441D4—22no—
442D4—28no—
443D4—41no—
444D4—41no—
445D4—88no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—84no—
462C2×C4—282no—
463C2×C4—281no—
464C2×C4—281no—
465C2×C4—281no—
466C2×C4—281no—
467C2×C4—281no—
468C2×C4—282no—
469C2×C4—281no—
470C2×C4—282no—
471C2×C4C2×#114212yes—
472C2×C4#650212yes—
473C2×C4#650212yes—
474C2×C4#651312yes—
475C2×C4C2×D4×D711yescharacteristic
476C2×C4C2×#115911yescharacteristic
477C2×C4C2×#115911yescharacteristic
478C2×C4#654811yescharacteristic
479C2×C4D7×#4111yescharacteristic
480C2×C4#655411yescharacteristic
481C8—144no—
482C8—142no—
483C8—281no—
484C7#2533911yescharacteristic, complemented, Sylow
485C22—24no—
486C22—24no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22C22×#114211yescharacteristic
500C22C2×#650211yescharacteristic
501C22#9049711yescharacteristic
502C22C2×#651311yescharacteristic
503C22#9051511yescharacteristic
504C22#9052611yescharacteristic
505C22#9052811yescharacteristic
506C4—22no—
507C4—42no—
508C4—82no—
509C4—81no—
510C4—561no—
511C4—561no—
512C4—562no—
513C4#8981314yes—
514C4#9028911yescharacteristic
515C4#9029111yescharacteristic
516C4#9029411yescharacteristic
517C4#9030311yescharacteristic
518C2—44no—
519C2—82no—
520C2C2×#8981311yescharacteristic
521C2#1174009211yescharacteristic
522C2#1174086711yescharacteristic
523C2#1174092811yescharacteristic
524C2#1174095611yescharacteristic
525C2#1174096211yescharacteristic
526C2#1174109211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC7×#2537C2
socleC23×C7C22×D4
hypercenter#2537D7
hypocenterC7#25339
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
2. #11739829C2semidirect
3. C2×D4×C7⋊C8C2semidirect
4. C2×#89780C2semidirect
5. #11729435C2semidirect
6. #11729434C2semidirect
7. C4×#6406C2semidirect
8. #11727336C2semidirect
9. #11727322C2semidirect
10. #11727274C2semidirect
11. #11727265C2semidirect
92. C4⋊(C7⋊C8)D4semidirect
484. C7#25339semidirect

Maximal subgroups

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

subgroupindex
C7×#25372
#117398292
C2×D4×C7⋊C82
C2×#897802
#117294352
#117294342
C4×#64062
#117273362
#117273222
#117272742
#117272652
#253397