Finite Group Databasebeta

← #13403293

Subgroups — #13403293

Order 1792.

954 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#459C211yesmaximal, characteristic
2#11740624C211yesmaximal, characteristic, complemented
3#11739821C211yesmaximal, characteristic, complemented
4C2×#89602C211yesmaximal, characteristic, complemented
5#11729794C212yesmaximal, complemented
6#11729792C212yesmaximal, complemented
7#11729518C211yesmaximal, characteristic, complemented
8C4×#6406C211yesmaximal, characteristic, complemented
9#11728207C211yesmaximal, characteristic, complemented
10#11727940C212yesmaximal, complemented
11#11727934C212yesmaximal, complemented
12C22×C7×D8C2212yes—
13C2×C7×#127C2211yescharacteristic
14C2×C4×C7×D4C2211yescharacteristic
15C2×#6499—21no—
16C2×#6487—21no—
17C2×C4×Dic14C2211yescharacteristic
18C7×#459—24no—
19C2×C7×C4⋊C8C2211yescharacteristic
20C2×C7×#102C2212yes—
21#89994—22no—
22#89993—21no—
23#89993C2212yes—
24#89993C2212yes—
25#89993C2212yes—
26C2×#6406C2212yes—
27C2×#6406C2211yescharacteristic
28C2×#6406C2211yescharacteristic
29C2×#6406C2212yes—
30#89984—21no—
31C2×#6392C2212yes—
32C2×Dic7⋊C8C2212yes—
33C2×C8×Dic7C2212yes—
34#89745C2212yes—
35#89720—22no—
36#89707C2211yescharacteristic
37C4×C4⋊Dic7C2211yescharacteristic
38C2×C4×C7⋊C8C2211yescharacteristic
39#89602—24no—
40#89346C2212yes—
41#89324C2211yescharacteristic
42#89324C2211yescharacteristic
43#25292—71nomaximal, Sylow
44C22×C7×D4—21no—
45C22×C7×D4—21no—
46C22×C7×D4C2312yes—
47C22×C7×D4C2311yescharacteristic
48C23×C4×C7—21no—
49C22×Dic14D411yescharacteristic
50C2×C7×D8—24no—
51C2×C7×D8—24no—
52C2×C7×D8—42no—
53C22×C7×C8C2312yes—
54C7×#127—22no—
55C7×#127—22no—
56C4×C7×D4—22no—
57C4×C7×D4—22no—
58C2×C7×C4⋊C4C2311yescharacteristic
59C2×C7×C22⋊C4—21no—
60C2×C42×C7C2311yescharacteristic
61C2×C22⋊Dic7—22no—
62C2×C22⋊Dic7—22no—
63C2×C22⋊Dic7—22no—
64C2×C22⋊Dic7—22no—
65C2×C22⋊Dic7—22no—
66C2×C22⋊Dic7—22no—
67#6499—44no—
68C2×C4⋊Dic7—21no—
69C2×C4⋊Dic7—21no—
70C2×C4⋊Dic7D411yescharacteristic
71C2×C4⋊Dic7C2311yescharacteristic
72C2×C4⋊Dic7C2312yes—
73C2×C4⋊Dic7C2311yescharacteristic
74#6487—44no—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4D412yes—
77C2×C4×Dic7—21no—
78C2×C4×Dic7C2312yes—
79C22×C7⋊C8C2311yescharacteristic
80C22×C7⋊C8C2311yescharacteristic
81C4×Dic14—22no—
82C4×Dic14—22no—
83C7×C4⋊C8D414yes—
84C7×#102—24no—
85#6406—22no—
86#6406—22no—
87#6406—24no—
88#6406—42no—
89C7⋊#95—21no—
90C7⋊#95—22no—
91#6392—42no—
92Dic7⋊C8—24no—
93C8×Dic7—24no—
94C4×C7⋊C8—22no—
95C2×#459D711yescharacteristic
96C2×C8×Q8—71no—
97#2548—71no—
98#2538—71no—
99#2067—72no—
100#2054—72no—
101#1970—72no—
102#1957—71no—
103#1947—71no—
104#1934—72no—
105C4×#102—71no—
106C24×C7—21no—
107C24×C7—22no—
108C2×C7×D4—21no—
109C2×C7×D4—22no—
110C2×C7×D4—21no—
111C2×C7×D4—21no—
112C2×C7×D4—22no—
113C2×C7×D4—22no—
114C2×C7×D4—22no—
115C2×C7×D4—21no—
116C2×C7×D4—22no—
117C2×C7×D4—21no—
118C2×C7×D4—22no—
119C2×C7×D4—42no—
120C2×C7×D4—42no—
121C2×C7×D4—42no—
122C2×C7×D4—42no—
123C2×C7×D4—81no—
124C2×C7×D4—81no—
125C2×C7×D4#4112yes—
126C22×C4×C7—21no—
127C22×C4×C7—42no—
128C22×C4×C7—42no—
129C22×C4×C7—42no—
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2411yescharacteristic
133C22×Dic7—21no—
134C22×Dic7—21no—
135C22×Dic7—22no—
136C22×Dic7C2×D412yes—
137C22×Dic7C2×D412yes—
138C2×Dic14—22no—
139C2×Dic14—22no—
140C2×Dic14D814yescomplemented
141C7×D8—48no—
142C2×C7×C8—22no—
143C2×C7×C8—22no—
144C2×C7×C8C2×D414yes—
145C7×C4⋊C4—21no—
146C7×C4⋊C4—21no—
147C7×C22⋊C4—42no—
148C42×C7C2×D412yes—
149C42×C7#4112yes—
150C22⋊Dic7—44no—
151C22⋊Dic7—44no—
152C22⋊Dic7—44no—
153C22⋊Dic7—82no—
154C22⋊Dic7—82no—
155C22⋊Dic7—82no—
156C4⋊Dic7—22no—
157C4⋊Dic7—21no—
158C4⋊Dic7—22no—
159C4⋊Dic7—21no—
160C4⋊Dic7—22no—
161C4⋊Dic7—21no—
162C4⋊Dic7—21no—
163C4⋊Dic7—42no—
164C4⋊Dic7—81no—
165Dic7⋊C4—24no—
166Dic7⋊C4—44no—
167C4×Dic7—22no—
168C4×Dic7—22no—
169C4×Dic7—42no—
170C2×C7⋊C8—21no—
171C2×C7⋊C8—21no—
172C2×C7⋊C8—21no—
173C2×C7⋊C8—21no—
174C2×C7⋊C8—21no—
175C2×C7⋊C8#4112yes—
176C22×D8C2×D712yes—
177C2×#127C2×D711yescharacteristic
178C2×#124—141no—
179C2×C22⋊Q8—141no—
180C2×C4×Q8—71no—
181C2×C4×D4C2×D711yescharacteristic
182#459—24no—
183C8×Q8—144no—
184C2×#107—72no—
185C2×C4⋊C8—72no—
186C2×C4⋊C8C2×D711yescharacteristic
187C2×#102—71no—
188C2×#102—72no—
189C2×#102—71no—
190C2×#102—72no—
191C2×#102C2×D712yes—
192C2×C4×C8—72no—
193C2×C4×C8—71no—
194#396—142no—
195#394—142no—
196#390—72no—
197#390—72no—
198#390—72no—
199#390—141no—
200#389—72no—
201#384—71no—
202#380—141no—
203C4×C4⋊C4—71no—
204#340—72no—
205#340—71no—
206#340—71no—
207C23×C7—22no—
208C23×C7—41no—
209C23×C7—41no—
210C23×C7—41no—
211C23×C7—41no—
212C23×C7—41no—
213C23×C7—41no—
214C23×C7—42no—
215C23×C7—42no—
216C23×C7—42no—
217C23×C7—42no—
218C23×C7—42no—
219C23×C7—42no—
220C23×C7—42no—
221C23×C7C22×D411yescharacteristic
222C7×D4—22no—
223C7×D4—22no—
224C7×D4—42no—
225C7×D4—41no—
226C7×D4—42no—
227C7×D4—42no—
228C7×D4—41no—
229C7×D4—42no—
230C7×D4—84no—
231C7×D4—84no—
232C2×C4×C7—21no—
233C2×C4×C7—21no—
234C2×C4×C7—41no—
235C2×C4×C7—41no—
236C2×C4×C7—41no—
237C2×C4×C7—84no—
238C2×C4×C7#12112yes—
239C2×C4×C7#12112yes—
240C2×C4×C7C2×D812yes—
241C2×C4×C7#13512yes—
242C2×C4×C7C22×D411yescharacteristic
243C2×C4×C7C2×#4111yescharacteristic
244C2×C4×C7C2×#4111yescharacteristic
245C2×C4×C7C2×#4111yescharacteristic
246C2×C4×C7H(5,𝔽2)11yescharacteristic
247C2×C4×C72−1+411yescharacteristic
248C2×Dic7—22no—
249C2×Dic7—22no—
250C2×Dic7—22no—
251C2×Dic7—22no—
252C2×Dic7—22no—
253C2×Dic7—41no—
254C2×Dic7—42no—
255C2×Dic7—41no—
256C2×Dic7—41no—
257C2×Dic7—41no—
258C2×Dic7—42no—
259C2×Dic7—42no—
260C2×Dic7—41no—
261C2×Dic7—41no—
262C2×Dic7C2×D814yes—
263Dic14—28no—
264C7×C8—24no—
265C7⋊C8—22no—
266C7⋊C8—41no—
267C22×Q8—71no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C22×D712yes—
271C22×D4C22×D711yescharacteristic
272C23×C4—21no—
273C2×D8—24no—
274C2×D8—24no—
275C2×D8—42no—
276C22×C8—71no—
277C22×C8—71no—
278C22×C8C22×D712yes—
279#127—22no—
280#127—22no—
281#124—284no—
282C22⋊Q8—284no—
283C4×Q8—142no—
284C4×Q8—142no—
285C4×D4—22no—
286C4×D4—22no—
287C2×C4⋊C4—72no—
288C2×C4⋊C4—71no—
289C2×C4⋊C4—71no—
290C2×C4⋊C4—71no—
291C2×C4⋊C4—72no—
292C2×C4⋊C4—142no—
293C2×C4⋊C4—141no—
294C2×C4⋊C4—141no—
295C2×C4⋊C4C22×D711yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—142no—
298C2×C22⋊C4—142no—
299C2×C22⋊C4—142no—
300C2×C22⋊C4—142no—
301C2×C22⋊C4—142no—
302C2×C22⋊C4—142no—
303C2×C42—72no—
304C2×C42—141no—
305C2×C42C22×D711yescharacteristic
306#107—282no—
307C4⋊C8—144no—
308C4⋊C8C22⋊D714yes—
309#102—24no—
310#102—142no—
311#102—144no—
312#102—142no—
313#102—282no—
314C4×C8—144no—
315C4×C8—142no—
316#95—142no—
317#95—141no—
318C22×C7—42no—
319C22×C7—42no—
320C22×C7—42no—
321C22×C7—81no—
322C22×C7—81no—
323C22×C7—81no—
324C22×C7—81no—
325C22×C7—82no—
326C22×C7—82no—
327C22×C7—82no—
328C22×C7—82no—
329C22×C7—82no—
330C22×C7—82no—
331C22×C7—82no—
332C22×C7C2×#12111yescharacteristic
333C22×C7#54811yescharacteristic
334C22×C7#55011yescharacteristic
335C22×C7C22×D811yescharacteristic
336C22×C7C2×#13511yescharacteristic
337C22×C7#57611yescharacteristic
338C22×C7#57711yescharacteristic
339C4×C7—22no—
340C4×C7—81no—
341C4×C7#46614yes—
342C4×C7#52911yescharacteristic
343C4×C7#54211yescharacteristic
344C4×C7#54611yescharacteristic
345C4×C7#54811yescharacteristic
346Dic7—24no—
347Dic7—42no—
348Dic7—81no—
349Dic7—81no—
350Dic7—82no—
351C24—21no—
352C24—22no—
353C2×Q8—74no—
354C2×Q8—142no—
355C2×Q8—142no—
356C2×D4—21no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—81no—
372C2×D4—81no—
373C2×D4#115912yes—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—72no—
379C22×C4—72no—
380C22×C4—141no—
381C22×C4—141no—
382C22×C4—142no—
383C22×C4D4×D711yescharacteristic
384C22×C4D4×D711yescharacteristic
385C22×C4C23×D711yescharacteristic
386D8—48no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—72no—
390C2×C8—141no—
391C2×C8—141no—
392C2×C8—141no—
393C2×C8—141no—
394C2×C8—141no—
395C2×C8C2×C22⋊D714yes—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—144no—
399C4⋊C4—142no—
400C4⋊C4—141no—
401C4⋊C4—142no—
402C4⋊C4—141no—
403C4⋊C4—141no—
404C4⋊C4—142no—
405C4⋊C4—141no—
406C4⋊C4—284no—
407C4⋊C4—282no—
408C4⋊C4—561no—
409C22⋊C4—42no—
410C22⋊C4—284no—
411C22⋊C4—284no—
412C22⋊C4—284no—
413C22⋊C4—562no—
414C22⋊C4—562no—
415C22⋊C4—562no—
416C42—142no—
417C42—142no—
418C42—282no—
419C42#115912yes—
420C42C2×C22⋊D712yes—
421C2×C7—82no—
422C2×C7—162no—
423C2×C7#242611yescharacteristic
424C2×C7C2×#46611yescharacteristic
425C2×C7#306211yescharacteristic
426C2×C7#335811yescharacteristic
427C2×C7#336111yescharacteristic
428C2×C7#339111yescharacteristic
429C2×C7#339411yescharacteristic
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23C2×D4×D711yescharacteristic
445Q8—148no—
446D4—22no—
447D4—22no—
448D4—42no—
449D4—41no—
450D4—42no—
451D4—42no—
452D4—41no—
453D4—42no—
454D4—84no—
455D4—84no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—74no—
462C2×C4—84no—
463C2×C4—142no—
464C2×C4—142no—
465C2×C4—142no—
466C2×C4—142no—
467C2×C4—142no—
468C2×C4—281no—
469C2×C4—281no—
470C2×C4—282no—
471C2×C4—281no—
472C2×C4—282no—
473C2×C4—281no—
474C2×C4—281no—
475C2×C4—282no—
476C2×C4—281no—
477C2×C4D7×D812yes—
478C2×C4#647512yes—
479C2×C4#650112yes—
480C2×C4#650112yes—
481C2×C4C2×#115911yescharacteristic
482C2×C4C2×#115911yescharacteristic
483C2×C4#654811yescharacteristic
484C2×C4D7×#4111yescharacteristic
485C2×C4#655411yescharacteristic
486C2×C4C22×C22⋊D711yescharacteristic
487C8—24no—
488C8—142no—
489C8—281no—
490C7#2529211yescharacteristic, complemented, Sylow
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22#9028911yescharacteristic
506C22#9029011yescharacteristic
507C22C2×D7×D811yescharacteristic
508C22C2×#647511yescharacteristic
509C22#9046511yescharacteristic
510C22#9046611yescharacteristic
511C22C2×#650111yescharacteristic
512C4—22no—
513C4—81no—
514C4—144no—
515C4—282no—
516C4—561no—
517C4—561no—
518C4—562no—
519C4#8992914yes—
520C4#9029111yescharacteristic
521C4#9029411yescharacteristic
522C4#9049711yescharacteristic
523C4#9052211yescharacteristic
524C2—82no—
525C2—162no—
526C2#1173776311yescharacteristic
527C2#1173776411yescharacteristic
528C2#1173776911yescharacteristic
529C2#1173777011yescharacteristic
530C2#1174009111yescharacteristic
531C2C2×#8992911yescharacteristic
532C2#1174139611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#459C2
socleC23×C7C22×D4
hypercenterC2×#459D7
hypocenterC7#25292
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
2. #11740624C2semidirect
3. #11739821C2semidirect
4. C2×#89602C2semidirect
5. #11729794C2semidirect
6. #11729792C2semidirect
7. #11729518C2semidirect
8. C4×#6406C2semidirect
9. #11728207C2semidirect
10. #11727940C2semidirect
11. #11727934C2semidirect
140. C2×Dic14D8semidirect
490. C7#25292semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4592
#117406242
#117398212
C2×#896022
#117297942
#117297922
#117295182
C4×#64062
#117282072
#117279402
#117279342
#252927