Finite Group Databasebeta

← #13256111

Subgroups — #13256111

Order 1792.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2537C211yesmaximal, characteristic
2C2×#89791C211yesmaximal, characteristic, complemented
3C2×#89779C211yesmaximal, characteristic, complemented
4C2×D4⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
5C2×D4⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
6#11727336C211yesmaximal, characteristic, complemented
7#11725440C211yesmaximal, characteristic, complemented
8C2×C7×#121—21no—
9C2×C7×#121—21no—
10C2×C4×C7×D4C2211yescharacteristic
11C2×C4×C7×D4C2211yescharacteristic
12C22×#1142—21no—
13C2×#6432C2211yescharacteristic
14C7×#394—22no—
15C7×#384C2211yescharacteristic
16C7×#380—21no—
17C7×#380—21no—
18C2×#6406—21no—
19#89791—22no—
20#89791—22no—
21#89779—22no—
22#89779—22no—
23C2×#6384—21no—
24C2×#6381—21no—
25C2×C4⋊(C7⋊C8)C2211yescharacteristic
26C2×C4⋊(C7⋊C8)C2211yescharacteristic
27C2×C4×C7⋊C8C2211yescharacteristic
28D4⋊(C7⋊C8)—22no—
29D4⋊(C7⋊C8)—22no—
30#89324—22no—
31#10231—71nomaximal, Sylow
32C22×C7×D4—22no—
33C22×C7×D4D411yescharacteristic
34C22×C7×D4D411yescharacteristic
35C23×C4×C7—21no—
36C23×C4×C7—21no—
37C22×Dic14—21no—
38C7×#121—42no—
39C7×#121—42no—
40C7×#121—42no—
41C7×#121—42no—
42C4×C7×D4—21no—
43C4×C7×D4—21no—
44C4×C7×D4—21no—
45C4×C7×D4—21no—
46C4×C7×D4—21no—
47C4×C7×D4—21no—
48C4×C7×D4—21no—
49C4×C7×D4—21no—
50C2×C7×C4⋊C4—21no—
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4D411yescharacteristic
53C2×C7×C4⋊C4D411yescharacteristic
54C2×C7×C4⋊C4D412yes—
55C2×C7×C22⋊C4—22no—
56C2×C7×C22⋊C4—22no—
57C2×C7×C22⋊C4—21no—
58C2×C7×C22⋊C4—21no—
59C2×C42×C7C2311yescharacteristic
60C2×#1142—24no—
61C2×#1142—42no—
62C2×#1142—42no—
63C2×C4⋊Dic7—21no—
64C2×C4⋊Dic7—21no—
65C22×C7⋊C8—21no—
66C22×C7⋊C8—21no—
67C22×C7⋊C8—21no—
68#6432—21no—
69#6432—21no—
70#6432—21no—
71#6432D412yescomplemented
72C7×#95—22no—
73#6406—24no—
74#6384—24no—
75#6381—24no—
76C4⋊(C7⋊C8)—21no—
77C4⋊(C7⋊C8)—21no—
78C4⋊(C7⋊C8)D412yescomplemented
79C4⋊(C7⋊C8)D412yescomplemented
80C4×C7⋊C8—21no—
81C4×C7⋊C8—21no—
82C2×#474—71no—
83C2×#461—71no—
84#2537D711yescharacteristic
85#1990—71no—
86C2×D4⋊C8—71no—
87C2×D4⋊C8—71no—
88#1296—71no—
89C24×C7—21no—
90C24×C7—21no—
91C2×C7×D4—21no—
92C2×C7×D4—21no—
93C2×C7×D4—21no—
94C2×C7×D4—21no—
95C2×C7×D4—21no—
96C2×C7×D4—21no—
97C2×C7×D4—21no—
98C2×C7×D4—21no—
99C2×C7×D4—21no—
100C2×C7×D4—21no—
101C2×C7×D4—44no—
102C2×C7×D4—44no—
103C2×C7×D4—82no—
104C2×C7×D4D812yes—
105C2×C7×D4SD1612yescomplemented
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—22no—
109C22×C4×C7—41no—
110C22×C4×C7—41no—
111C22×C4×C7—41no—
112C22×C4×C7—41no—
113C22×C4×C7—41no—
114C22×C4×C7—41no—
115C22×C4×C7—41no—
116C22×C4×C7—41no—
117C22×C4×C7—41no—
118C22×C4×C7—41no—
119C22×C4×C7—41no—
120C22×C4×C7—41no—
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×Dic7—41no—
125C2×Dic14—22no—
126C2×Dic14—41no—
127C2×Dic14—41no—
128C2×Dic14—41no—
129C2×Dic14—41no—
130C2×Dic14—41no—
131C7×C4⋊C4—21no—
132C7×C4⋊C4—21no—
133C7×C4⋊C4—21no—
134C7×C4⋊C4—21no—
135C7×C4⋊C4—42no—
136C7×C4⋊C4—41no—
137C7×C4⋊C4—41no—
138C7×C4⋊C4—41no—
139C7×C4⋊C4—41no—
140C7×C22⋊C4—44no—
141C7×C22⋊C4—44no—
142C7×C22⋊C4—41no—
143C7×C22⋊C4—41no—
144C7×C22⋊C4—41no—
145C7×C22⋊C4—41no—
146C42×C7C2×D411yescharacteristic
147C42×C7C2×D411yescharacteristic
148C42×C7C2×D411yescharacteristic
149C42×C7#4111yescharacteristic
150#1142—48no—
151C4⋊Dic7—22no—
152C4⋊Dic7—22no—
153C4⋊Dic7—41no—
154C4⋊Dic7—41no—
155C2×C7⋊C8—22no—
156C2×C7⋊C8—22no—
157C2×C7⋊C8—22no—
158C2×C7⋊C8—41no—
159C2×C7⋊C8—41no—
160C2×C7⋊C8—41no—
161C2×C7⋊C8—41no—
162C2×C7⋊C8—41no—
163C2×C7⋊C8—41no—
164C22×SD16—141no—
165C2×C4⋊Q8—71no—
166C2×#121—21no—
167C2×#121—21no—
168C2×C4×D4C2×D711yescharacteristic
169C2×C4×D4C2×D711yescharacteristic
170#474—142no—
171#474—142no—
172#461—142no—
173#461—142no—
174C2×#107—141no—
175C2×C4⋊C8—71no—
176C2×C4⋊C8—71no—
177C2×#103—141no—
178C2×#102—141no—
179C2×C4×C8—71no—
180#394—22no—
181#384C2×D711yescharacteristic
182#380—21no—
183#380—21no—
184#340—142no—
185D4⋊C8—142no—
186D4⋊C8—142no—
187C23×C7—22no—
188C23×C7—22no—
189C23×C7—41no—
190C23×C7—41no—
191C23×C7—41no—
192C23×C7—41no—
193C23×C7—41no—
194C23×C7—41no—
195C23×C7—41no—
196C23×C7—41no—
197C23×C7—41no—
198C23×C7—41no—
199C23×C7—41no—
200C23×C7—41no—
201C23×C7#12011yescharacteristic
202C7×D4—22no—
203C7×D4—22no—
204C7×D4—22no—
205C7×D4—22no—
206C7×D4—41no—
207C7×D4—41no—
208C7×D4—41no—
209C7×D4—41no—
210C7×D4—88no—
211C2×C4×C7—21no—
212C2×C4×C7—21no—
213C2×C4×C7—41no—
214C2×C4×C7—41no—
215C2×C4×C7—41no—
216C2×C4×C7—42no—
217C2×C4×C7—41no—
218C2×C4×C7—41no—
219C2×C4×C7—42no—
220C2×C4×C7—41no—
221C2×C4×C7—42no—
222C2×C4×C7—81no—
223C2×C4×C7—81no—
224C2×C4×C7—81no—
225C2×C4×C7—81no—
226C2×C4×C7—81no—
227C2×C4×C7—81no—
228C2×C4×C7—81no—
229C2×C4×C7—81no—
230C2×C4×C7#12011yescharacteristic
231C2×C4×C7#12011yescharacteristic
232C2×C4×C7#12111yescharacteristic
233C2×C4×C7#12111yescharacteristic
234C2×C4×C7#12111yescharacteristic
235C2×C4×C7#12711yescharacteristic
236C2×C4×C7C2×D811yescharacteristic
237C2×C4×C7C2×SD1611yescharacteristic
238C2×C4×C7#13511yescharacteristic
239C2×C4×C7#13511yescharacteristic
240C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
241C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
242C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
243C2×C4×C7#13711yescharacteristic
244C2×Dic7—42no—
245C2×Dic7—81no—
246C2×Dic7—81no—
247Dic14—42no—
248Dic14—42no—
249Dic14—81no—
250Dic14—81no—
251C7⋊C8—42no—
252C7⋊C8—42no—
253C7⋊C8—42no—
254C22×Q8—141no—
255C22×D4—22no—
256C22×D4C22⋊D711yescharacteristic
257C22×D4C22⋊D711yescharacteristic
258C23×C4—21no—
259C23×C4—21no—
260C2×SD16—144no—
261C2×SD16—282no—
262C2×SD16—282no—
263C22×C8—141no—
264C22×C8—141no—
265C22×C8—141no—
266C4⋊Q8—72no—
267C4⋊Q8—141no—
268C4⋊Q8—141no—
269C4⋊Q8—141no—
270#121—42no—
271#121—42no—
272#121—42no—
273#121—42no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—141no—
285C2×C4⋊C4—141no—
286C2×C4⋊C4C22⋊D711yescharacteristic
287C2×C4⋊C4C22⋊D711yescharacteristic
288C2×C4⋊C4C22⋊D712yes—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C42C22×D711yescharacteristic
294#107—144no—
295C4⋊C8—72no—
296C4⋊C8—72no—
297C4⋊C8—141no—
298C4⋊C8—141no—
299#103—144no—
300#102—144no—
301C4×C8—141no—
302C4×C8—141no—
303#95—22no—
304C22×C7—42no—
305C22×C7—42no—
306C22×C7—42no—
307C22×C7—42no—
308C22×C7—42no—
309C22×C7—42no—
310C22×C7—81no—
311C22×C7—81no—
312C22×C7—81no—
313C22×C7—81no—
314C22×C7—81no—
315C22×C7—81no—
316C22×C7—81no—
317C22×C7—81no—
318C22×C7#39211yescharacteristic
319C22×C7#44711yescharacteristic
320C22×C7#44911yescharacteristic
321C22×C7#45011yescharacteristic
322C22×C7#45211yescharacteristic
323C22×C7#45511yescharacteristic
324C22×C7#45611yescharacteristic
325C4×C7—21no—
326C4×C7—21no—
327C4×C7—82no—
328C4×C7—81no—
329C4×C7—81no—
330C4×C7#44711yescharacteristic
331C4×C7#44811yescharacteristic
332C4×C7#44911yescharacteristic
333C4×C7#44911yescharacteristic
334C4×C7#46511yescharacteristic
335C4×C7#46611yescharacteristic
336C4×C7#46811yescharacteristic
337C4×C7#46911yescharacteristic
338Dic7—82no—
339C24—21no—
340C24—21no—
341C2×Q8—142no—
342C2×Q8—281no—
343C2×Q8—281no—
344C2×Q8—281no—
345C2×Q8—281no—
346C2×Q8—281no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—44no—
358C2×D4—44no—
359C2×D4—82no—
360C2×D4#114112yes—
361C2×D4#114212yescomplemented
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—281no—
378C22×C4C2×C22⋊D711yescharacteristic
379C22×C4C2×C22⋊D711yescharacteristic
380C22×C4C2×C22⋊D711yescharacteristic
381SD16—288no—
382C2×C8—142no—
383C2×C8—142no—
384C2×C8—142no—
385C2×C8—281no—
386C2×C8—281no—
387C2×C8—281no—
388C2×C8—281no—
389C2×C8—281no—
390C2×C8—281no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—42no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—142no—
401C4⋊C4—142no—
402C4⋊C4—281no—
403C4⋊C4—281no—
404C22⋊C4—44no—
405C22⋊C4—44no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C42D4×D711yescharacteristic
411C42D4×D711yescharacteristic
412C42D4×D711yescharacteristic
413C42#115911yescharacteristic
414C2×C7—82no—
415C2×C7—82no—
416C2×C7#163911yescharacteristic
417C2×C7#164611yescharacteristic
418C2×C7#164711yescharacteristic
419C2×C7#165411yescharacteristic
420C2×C7#199911yescharacteristic
421C2×C7#200011yescharacteristic
422C2×C7#200711yescharacteristic
423C23—22no—
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23#651611yescharacteristic
438Q8—282no—
439Q8—282no—
440Q8—561no—
441Q8—561no—
442D4—22no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—41no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—88no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—282no—
471C2×C4—561no—
472C2×C4—561no—
473C2×C4C2×#114111yescharacteristic
474C2×C4#649511yescharacteristic
475C2×C4#649511yescharacteristic
476C2×C4C2×#114211yescharacteristic
477C2×C4#650011yescharacteristic
478C2×C4#650011yescharacteristic
479C2×C4#650111yescharacteristic
480C2×C4#650211yescharacteristic
481C2×C4#650211yescharacteristic
482C2×C4#650311yescharacteristic
483C2×C4#651211yescharacteristic
484C2×C4#651311yescharacteristic
485C2×C4#651311yescharacteristic
486C2×C4#651411yescharacteristic
487C8—282no—
488C8—282no—
489C8—282no—
490C7#1023111yescharacteristic, complemented, Sylow
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22#8998911yescharacteristic
506C22#8999011yescharacteristic
507C22#8999511yescharacteristic
508C22#9001011yescharacteristic
509C22#9001111yescharacteristic
510C22#9001411yescharacteristic
511C22#9001811yescharacteristic
512C4—21no—
513C4—21no—
514C4—81no—
515C4—81no—
516C4—82no—
517C4—562no—
518C4#8980811yescharacteristic
519C4#8980911yescharacteristic
520C4#8980911yescharacteristic
521C4#8981011yescharacteristic
522C4#8981111yescharacteristic
523C4#8981211yescharacteristic
524C4#8981311yescharacteristic
525C4#8981411yescharacteristic
526C2—82no—
527C2—82no—
528C2#1172943811yescharacteristic
529C2#1172943911yescharacteristic
530C2#1172963511yescharacteristic
531C2#1172966211yescharacteristic
532C2#1172966611yescharacteristic
533C2#1172966711yescharacteristic
534C2#1172968311yescharacteristic
subgroupG/H
centerC23#6516
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
Fitting, prime radicalC7×#2537C2
socleC23×C7#120
hypercenter#2537D7
hypocenterC7#10231
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
2. C2×#89791C2semidirect
3. C2×#89779C2semidirect
4. C2×D4⋊(C7⋊C8)C2semidirect
5. C2×D4⋊(C7⋊C8)C2semidirect
6. #11727336C2semidirect
7. #11725440C2semidirect
71. #6432D4semidirect
78. C4⋊(C7⋊C8)D4semidirect
79. C4⋊(C7⋊C8)D4semidirect
105. C2×C7×D4SD16semidirect
361. C2×D4#1142semidirect
490. C7#10231semidirect

Maximal subgroups

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

subgroupindex
C7×#25372
C2×#897912
C2×#897792
C2×D4⋊(C7⋊C8)2
#117273362
#117254402
#102317