Finite Group Databasebeta

← #13358444

Subgroups — #13358444

Order 1792.

1338 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×#90174C211yesmaximal, characteristic
2#11739540C211yesmaximal, characteristic
3#11739528C211yesmaximal, characteristic
4C2×C7×#342C211yesmaximal, characteristic
5C2×#89322C211yesmaximal, characteristic
6C2×#89322C211yesmaximal, characteristic
7C2×#89321C211yesmaximal, characteristic
8#11726709C218yesmaximal, complemented
9C22×C7×C22⋊C4C2211yescharacteristic
10C22×C7×C22⋊C4C2211yescharacteristic
11C22×C7×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic7C2211yescharacteristic
13C22×C22⋊Dic7C2211yescharacteristic
14C22×C22⋊Dic7C2211yescharacteristic
15C22×C22⋊Dic7C2211yescharacteristic
16C2×#6487C414yescomplemented
17#90174—22no—
18#90174—22no—
19#90174—22no—
20#90174—22no—
21C2×#6441C414yescomplemented
22C2×#6441C2214yes—
23#89982—22no—
24C4×C22⋊Dic7—22no—
25#89718—22no—
26#89714C2214yes—
27C22⋊C4×Dic7—22no—
28C22⋊C4×Dic7C2214yes—
29C7×#342C2214yes—
30#89322C2214yes—
31#89322C2214yes—
32#89321C2214yes—
33#21333—71nomaximal, Sylow
34C25×C7C2311yescharacteristic
35C23×C4×C7—21no—
36C23×C4×C7—21no—
37C23×C4×C7C2×C412yes—
38C23×Dic7—21no—
39C23×Dic7—21no—
40C23×Dic7C2×C412yes—
41C23×Dic7C2312yes—
42C22×Dic14C2×C414yescomplemented
43C2×C7×C22⋊C4—21no—
44C2×C7×C22⋊C4—21no—
45C2×C7×C22⋊C4—21no—
46C2×C7×C22⋊C4—21no—
47C2×C7×C22⋊C4—21no—
48C2×C7×C22⋊C4—22no—
49C2×C7×C22⋊C4—22no—
50C2×C7×C22⋊C4—22no—
51C2×C7×C22⋊C4—21no—
52C2×C7×C22⋊C4C2×C412yes—
53C2×C7×C22⋊C4Q814yescomplemented
54C2×C7×C22⋊C4C2312yes—
55C2×C7×C22⋊C4C2312yes—
56C2×C7×C22⋊C4C2312yes—
57C2×C22⋊Dic7—21no—
58C2×C22⋊Dic7—21no—
59C2×C22⋊Dic7—21no—
60C2×C22⋊Dic7—21no—
61C2×C22⋊Dic7—21no—
62C2×C22⋊Dic7—22no—
63C2×C22⋊Dic7—22no—
64C2×C22⋊Dic7—22no—
65C2×C22⋊Dic7—21no—
66C2×C22⋊Dic7C2×C412yes—
67C2×C22⋊Dic7C2×C412yes—
68C2×C22⋊Dic7C2×C412yes—
69C2×C22⋊Dic7D412yes—
70C2×C22⋊Dic7D412yes—
71C2×C22⋊Dic7D412yes—
72C2×C22⋊Dic7D412yes—
73C2×C22⋊Dic7Q814yescomplemented
74C2×C22⋊Dic7C2312yes—
75C2×C22⋊Dic7C2312yes—
76C2×C22⋊Dic7C2312yes—
77C2×C4⋊Dic7C2×C414yescomplemented
78#6487—28no—
79#6487—28no—
80C2×Dic7⋊C4—24no—
81C2×Dic7⋊C4C2×C418yescomplemented
82C2×C4×Dic7—24no—
83#6441—28no—
84#6441—28no—
85#6441—28no—
86#6441—28no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C2×#543—71no—
90#2315—71no—
91#2273—71no—
92#1996—78no—
93C2×#342—71no—
94C2×#342—71no—
95C2×#342—71no—
96C2×#342D711yescharacteristic
97C24×C7—82no—
98C24×C7C22×C411yescharacteristic
99C24×C7C22×C411yescharacteristic
100C24×C7C2×D411yescharacteristic
101C24×C7C2×D411yescharacteristic
102C24×C7C2×D411yescharacteristic
103C24×C7C2×D411yescharacteristic
104C24×C7C2×Q812yes—
105C24×C7C2×Q812yes—
106C24×C7#4112yes—
107C24×C7#4112yes—
108C24×C7C2411yescharacteristic
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—24no—
113C22×C4×C7—22no—
114C22×C4×C7—42no—
115C22×C4×C7—82no—
116C22×C4×C7—82no—
117C22×C4×C7—82no—
118C22×C4×C7C22×C414yes—
119C22×Dic7—22no—
120C22×Dic7—22no—
121C22×Dic7—22no—
122C22×Dic7—24no—
123C22×Dic7—22no—
124C22×Dic7—42no—
125C22×Dic7—82no—
126C22×Dic7—82no—
127C22×Dic7—82no—
128C22×Dic7—82no—
129C22×Dic7C22×C414yes—
130C22×Dic7C22×C414yes—
131C22×Dic7C2×D414yes—
132C22×Dic7C2×D414yes—
133C2×Dic14—28no—
134C2×Dic14—84no—
135C7×C22⋊C4—22no—
136C7×C22⋊C4—22no—
137C7×C22⋊C4—24no—
138C7×C22⋊C4—22no—
139C7×C22⋊C4—22no—
140C7×C22⋊C4—22no—
141C7×C22⋊C4—22no—
142C7×C22⋊C4—22no—
143C7×C22⋊C4—42no—
144C7×C22⋊C4C2×Q814yes—
145C22⋊Dic7—22no—
146C22⋊Dic7—22no—
147C22⋊Dic7—24no—
148C22⋊Dic7—22no—
149C22⋊Dic7—22no—
150C22⋊Dic7—22no—
151C22⋊Dic7—22no—
152C22⋊Dic7—22no—
153C22⋊Dic7—42no—
154C22⋊Dic7C22⋊C414yes—
155C22⋊Dic7C22⋊C414yes—
156C22⋊Dic7C22⋊C414yes—
157C22⋊Dic7C22⋊C414yes—
158C22⋊Dic7C2×Q814yes—
159C4⋊Dic7—28no—
160Dic7⋊C4—216no—
161Dic7⋊C4—84no—
162C4×Dic7—84no—
163#543—142no—
164#543—142no—
165#543—142no—
166#543—142no—
167C2×C22⋊Q8—74no—
168C2×C22⋊Q8—74no—
169C2×C22⋊Q8—74no—
170C22×C22⋊C4—71no—
171C22×C22⋊C4—71no—
172C22×C22⋊C4—71no—
173C22×C22⋊C4—71no—
174C22×C22⋊C4C2×D711yescharacteristic
175C22×C22⋊C4C2×D711yescharacteristic
176C22×C22⋊C4C2×D711yescharacteristic
177#385—142no—
178#385—142no—
179#380—74no—
180C4×C22⋊C4—74no—
181C4×C22⋊C4—142no—
182C4×C22⋊C4—142no—
183#342—74no—
184#342—74no—
185#342—74no—
186#342C2×D714yes—
187C23×C7—42no—
188C23×C7—42no—
189C23×C7—42no—
190C23×C7—42no—
191C23×C7—42no—
192C23×C7—42no—
193C23×C7—42no—
194C23×C7—82no—
195C23×C7—82no—
196C23×C7—82no—
197C23×C7—82no—
198C23×C7C2×C22⋊C411yescharacteristic
199C23×C7C2×C22⋊C411yescharacteristic
200C23×C7C2×C22⋊C411yescharacteristic
201C23×C7C2×C22⋊C411yescharacteristic
202C23×C7C4×Q812yes—
203C23×C7C4×Q812yes—
204C23×C7C4×Q812yes—
205C23×C7C4×Q812yes—
206C23×C7C22⋊Q812yes—
207C23×C7C22⋊Q812yes—
208C23×C7C22⋊Q812yes—
209C23×C7C22⋊Q812yes—
210C23×C7#12412yes—
211C23×C7#12412yes—
212C23×C7C4⋊Q812yes—
213C23×C7C4⋊Q812yes—
214C23×C7C23×C411yescharacteristic
215C23×C7C22×D411yescharacteristic
216C23×C7C22×D411yescharacteristic
217C23×C7C22×Q811yescharacteristic
218C23×C7C22×Q811yescharacteristic
219C23×C7C2×#4111yescharacteristic
220C23×C7C2×#4111yescharacteristic
221C2×C4×C7—24no—
222C2×C4×C7—24no—
223C2×C4×C7—44no—
224C2×C4×C7—44no—
225C2×C4×C7—44no—
226C2×C4×C7—42no—
227C2×C4×C7—82no—
228C2×C4×C7—82no—
229C2×C4×C7—84no—
230C2×C4×C7—84no—
231C2×Dic7—24no—
232C2×Dic7—24no—
233C2×Dic7—44no—
234C2×Dic7—44no—
235C2×Dic7—44no—
236C2×Dic7—44no—
237C2×Dic7—44no—
238C2×Dic7—44no—
239C2×Dic7—42no—
240C2×Dic7—82no—
241C2×Dic7—82no—
242C2×Dic7—84no—
243C2×Dic7—84no—
244C2×Dic7C2×C22⋊C418yes—
245Dic14—88no—
246C25C22×D711yescharacteristic
247C22×Q8—74no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—72no—
251C23×C4—72no—
252C23×C4—141no—
253C23×C4—141no—
254C23×C4C4×D712yes—
255C22⋊Q8—148no—
256C22⋊Q8—148no—
257C22⋊Q8—148no—
258C22⋊Q8—148no—
259C22⋊Q8—148no—
260C22⋊Q8—148no—
261C2×C4⋊C4—78no—
262C2×C4⋊C4—74no—
263C2×C4⋊C4—144no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—72no—
274C2×C22⋊C4—72no—
275C2×C22⋊C4—72no—
276C2×C22⋊C4—72no—
277C2×C22⋊C4—72no—
278C2×C22⋊C4—72no—
279C2×C22⋊C4—74no—
280C2×C22⋊C4—72no—
281C2×C22⋊C4—72no—
282C2×C22⋊C4—72no—
283C2×C22⋊C4—72no—
284C2×C22⋊C4—142no—
285C2×C22⋊C4—141no—
286C2×C22⋊C4—141no—
287C2×C22⋊C4—141no—
288C2×C22⋊C4—141no—
289C2×C22⋊C4—141no—
290C2×C22⋊C4—142no—
291C2×C22⋊C4—142no—
292C2×C22⋊C4—141no—
293C2×C22⋊C4Dic1414yescomplemented
294C2×C22⋊C4C4×D712yes—
295C2×C22⋊C4C22×D712yes—
296C2×C22⋊C4C22×D712yes—
297C2×C22⋊C4C22×D712yes—
298C2×C42—144no—
299#95—144no—
300#95—144no—
301C22×C7—22no—
302C22×C7—22no—
303C22×C7—22no—
304C22×C7—22no—
305C22×C7—22no—
306C22×C7—22no—
307C22×C7—22no—
308C22×C7—42no—
309C22×C7—42no—
310C22×C7—42no—
311C22×C7—42no—
312C22×C7—42no—
313C22×C7—42no—
314C22×C7—42no—
315C22×C7—42no—
316C22×C7—42no—
317C22×C7—42no—
318C22×C7—42no—
319C22×C7—42no—
320C22×C7—41no—
321C22×C7—41no—
322C22×C7—41no—
323C22×C7—41no—
324C22×C7#39112yes—
325C22×C7#39112yes—
326C22×C7#39112yes—
327C22×C7#39112yes—
328C22×C7C22×C22⋊C411yescharacteristic
329C22×C7C2×C4×Q811yescharacteristic
330C22×C7C2×C4×Q811yescharacteristic
331C22×C7C2×C22⋊Q811yescharacteristic
332C22×C7C2×C22⋊Q811yescharacteristic
333C22×C7C2×#12411yescharacteristic
334C22×C7C2×C4⋊Q811yescharacteristic
335C4×C7—44no—
336C4×C7—44no—
337C4×C7—82no—
338Dic7—28no—
339Dic7—44no—
340Dic7—44no—
341Dic7—82no—
342C24—82no—
343C24C2×Dic1412yes—
344C24C2×C4×D711yescharacteristic
345C24C2×C4×D711yescharacteristic
346C24#115712yes—
347C24D4×D711yescharacteristic
348C24D4×D711yescharacteristic
349C24D4×D711yescharacteristic
350C24D4×D711yescharacteristic
351C24#115912yes—
352C24Q8×D712yes—
353C24C23×D711yescharacteristic
354C2×Q8—148no—
355C2×Q8—564no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—42no—
362C22×C4—74no—
363C22×C4—74no—
364C22×C4—74no—
365C22×C4—74no—
366C22×C4—82no—
367C22×C4—82no—
368C22×C4—82no—
369C22×C4—142no—
370C22×C4—142no—
371C22×C4—142no—
372C22×C4—144no—
373C22×C4—142no—
374C22×C4—282no—
375C22×C4—562no—
376C22×C4—562no—
377C22×C4—562no—
378C22×C4—562no—
379C22×C4C2×C4×D714yes—
380C4⋊C4—1416no—
381C4⋊C4—148no—
382C4⋊C4—564no—
383C22⋊C4—24no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—42no—
392C22⋊C4—74no—
393C22⋊C4—74no—
394C22⋊C4—74no—
395C22⋊C4—74no—
396C22⋊C4—74no—
397C22⋊C4—142no—
398C22⋊C4—142no—
399C22⋊C4—144no—
400C22⋊C4—142no—
401C22⋊C4—142no—
402C22⋊C4—142no—
403C22⋊C4—142no—
404C22⋊C4—142no—
405C22⋊C4—282no—
406C22⋊C4C2×Dic1414yes—
407C42—564no—
408C2×C7—21no—
409C2×C7—21no—
410C2×C7—21no—
411C2×C7—21no—
412C2×C7—21no—
413C2×C7—21no—
414C2×C7—22no—
415C2×C7—22no—
416C2×C7—22no—
417C2×C7—22no—
418C2×C7C2×#39111yescharacteristic
419C2×C7#288312yes—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—82no—
428C23—82no—
429C23—82no—
430C23—82no—
431C23C4×Dic1412yes—
432C23C4×Dic1412yes—
433C23#644112yes—
434C23#644112yes—
435C23D7×C22⋊C411yescharacteristic
436C23D7×C22⋊C411yescharacteristic
437C23D7×C22⋊C411yescharacteristic
438C23D7×C22⋊C411yescharacteristic
439C23#644812yes—
440C23#644812yes—
441C23#645012yes—
442C23#645012yes—
443C23#645112yes—
444C23#645112yes—
445C23#645912yes—
446C23#645912yes—
447C23C22×Dic1411yescharacteristic
448C23C22×C4×D711yescharacteristic
449C23C2×#115711yescharacteristic
450C23C2×D4×D711yescharacteristic
451C23C2×D4×D711yescharacteristic
452C23C2×#115911yescharacteristic
453C23C2×Q8×D711yescharacteristic
454Q8—568no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—78no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—144no—
467C2×C4—144no—
468C2×C4—284no—
469C2×C4—284no—
470C2×C4—284no—
471C2×C4—284no—
472C2×C4—284no—
473C2×C4—284no—
474C2×C4—282no—
475C2×C4—562no—
476C2×C4—562no—
477C2×C4—564no—
478C2×C4—564no—
479C7#2133311yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22#8941812yes—
504C22#8941812yes—
505C22#8941812yes—
506C22#8941812yes—
507C22C2×C4×Dic1411yescharacteristic
508C22C2×#644111yescharacteristic
509C22C2×D7×C22⋊C411yescharacteristic
510C22C2×#644811yescharacteristic
511C22C2×#645011yescharacteristic
512C22C2×#645111yescharacteristic
513C22C2×#645911yescharacteristic
514C4—44no—
515C4—44no—
516C4—82no—
517C4—148no—
518C4—284no—
519C4—284no—
520C4—562no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—22no—
526C2—22no—
527C2—22no—
528C2—22no—
529C2—21no—
530C2—21no—
531C2C2×#8941811yescharacteristic
532C2#1173613312yes—
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C7×#342C2
socleC22×C7C22×C22⋊C4
prime radicalC25×C7C23
cosocleC24×C7C24
hypercenterC2×#342D7
hypocenterC7#21333
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
8. #11726709C2semidirect
16. C2×#6487C4semidirect
21. C2×#6441C4semidirect
42. C22×Dic14C2×C4semidirect
53. C2×C7×C22⋊C4Q8semidirect
73. C2×C22⋊Dic7Q8semidirect
77. C2×C4⋊Dic7C2×C4semidirect
81. C2×Dic7⋊C4C2×C4semidirect
293. C2×C22⋊C4Dic14semidirect
479. C7#21333semidirect

Maximal subgroups

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

subgroupindex
C2×#901742
#117395402
#117395282
C2×C7×#3422
C2×#893222
C2×#893212
#117267092
#213337