Finite Group Databasebeta

← #13319733

Subgroups — #13319733

Order 1792.

1174 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90237C211yesmaximal, characteristic
2#11736759C212yesmaximal, complemented
3C7×#1466C211yesmaximal, characteristic, complemented
4#11729357C211yesmaximal, characteristic, complemented
5#11728580C212yesmaximal, complemented
6#11725857C212yesmaximal, complemented
7#11725856C212yesmaximal, complemented
8#11725855C212yesmaximal, complemented
9#11725854C212yesmaximal, complemented
10C22×#1159C411yescharacteristic
11C2×C4×C7×D4C2211yescharacteristic
12C2×D4×Dic7C411yescharacteristic
13C2×C4×C22⋊D7C411yescharacteristic
14C2×C4×C22⋊D7C411yescharacteristic
15C22×Dic7⋊C4C411yescharacteristic
16C22×Dic7⋊C4C411yescharacteristic
17#90237—24no—
18#90237—24no—
19C2×D7×C4⋊C4C411yescharacteristic
20C2×#6450C411yescharacteristic
21C2×(C22⋊D7)⋊C4C2211yescharacteristic
22C2×(C22⋊D7)⋊C4C2211yescharacteristic
23C2×#6440C2211yescharacteristic
24C2×#6440C2211yescharacteristic
25C2×#6435C2211yescharacteristic
26C2×C4×Dic14C2211yescharacteristic
27C7×#432C2212yes—
28#89698C2212yes—
29#89600—24no—
30#89491C2214yes—
31#89490C2214yes—
32#89473—24no—
33C7×#323C2212yes—
34C7×#323C2212yes—
35#89320C2212yes—
36#89320C2212yes—
37#89264C2214yes—
38#89263C2214yes—
39#17372—71nomaximal, Sylow
40C22×C7×D4C2×C411yescharacteristic
41C23×C4×C7C2×C411yescharacteristic
42C23×C4×C7C2×C411yescharacteristic
43C22×C22⋊D7C2×C411yescharacteristic
44C22×C22⋊D7C2×C411yescharacteristic
45C23×Dic7C2×C411yescharacteristic
46C23×Dic7C2×C411yescharacteristic
47C23×Dic7C2×C411yescharacteristic
48C23×Dic7C2×C411yescharacteristic
49C2×#1159—24no—
50C2×#1159—24no—
51C2×#1159—24no—
52C22×C4×D7C2×C411yescharacteristic
53C22×C4×D7C2×C411yescharacteristic
54C22×C4×D7C2×C411yescharacteristic
55C22×Dic14C2×C411yescharacteristic
56C4×C7×D4—22no—
57C4×C7×D4—22no—
58C2×C7×C4⋊C4C2×C411yescharacteristic
59C2×C7×C22⋊C4C2311yescharacteristic
60C2×C7×C22⋊C4C2311yescharacteristic
61C2×C42×C7C2311yescharacteristic
62C2×C22⋊Dic7C2×C411yescharacteristic
63C2×C22⋊Dic7C2×C411yescharacteristic
64D4×Dic7—24no—
65C4×C22⋊D7—22no—
66C4×C22⋊D7—22no—
67C4×C22⋊D7—22no—
68C4×C22⋊D7—22no—
69C2×(C2×D7)⋊C4C2×C411yescharacteristic
70C2×(C2×D7)⋊C4C2311yescharacteristic
71C2×C4⋊Dic7C2×C411yescharacteristic
72C2×Dic7⋊C4—22no—
73C2×Dic7⋊C4—22no—
74C2×Dic7⋊C4—22no—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4C2×C411yescharacteristic
77C2×Dic7⋊C4C2×C411yescharacteristic
78C2×Dic7⋊C4C2×C411yescharacteristic
79C2×Dic7⋊C4C2×C411yescharacteristic
80C2×Dic7⋊C4C2×C411yescharacteristic
81C2×Dic7⋊C4C2×C411yescharacteristic
82C2×Dic7⋊C4C2×C411yescharacteristic
83C2×Dic7⋊C4C2311yescharacteristic
84C2×C4×Dic7C2×C411yescharacteristic
85C2×C4×Dic7C2×C411yescharacteristic
86C2×C4×Dic7C2×C411yescharacteristic
87C2×C4×Dic7C2311yescharacteristic
88C2×C4×Dic7C2311yescharacteristic
89D7×C4⋊C4—24no—
90#6450—24no—
91(C22⋊D7)⋊C4—24no—
92(C22⋊D7)⋊C4—24no—
93#6440—24no—
94#6440—24no—
95#6435—22no—
96#6435—22no—
97C4×Dic14D414yes—
98C4×Dic14D414yes—
99C7×C4⋊C8—22no—
100C7×C22⋊C8C2314yes—
101C7×#97—22no—
102C22⋊(C7⋊C8)C2314yes—
103#6389—24no—
104Dic7⋊C8—24no—
105Dic7⋊C8—24no—
106C8×Dic7—24no—
107C4⋊(C7⋊C8)—22no—
108#6377—22no—
109C2×#520—71no—
110#2983—72no—
111#1466—72no—
112#1466—71no—
113#1466D711yescharacteristic, complemented
114#1464—72no—
115#1464—72no—
116#1460—72no—
117#1458—72no—
118C24×C7C22×C411yescharacteristic
119C24×C7C22×C411yescharacteristic
120C23×D7C22×C411yescharacteristic
121C2×C7×D4—22no—
122C2×C7×D4—22no—
123C2×C7×D4—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—81no—
129C22×C4×C7—81no—
130C22×C4×C7C22×C411yescharacteristic
131C22×C4×C7C22×C411yescharacteristic
132C22×C4×C7C22×C411yescharacteristic
133C22×C4×C7C22×C411yescharacteristic
134C22×C4×C7C2411yescharacteristic
135C2×C22⋊D7—22no—
136C2×C22⋊D7—22no—
137C2×C22⋊D7—22no—
138C2×C22⋊D7—22no—
139C2×C22⋊D7—22no—
140C2×C22⋊D7M1614yes—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—81no—
149C22×Dic7—81no—
150C22×Dic7M1614yes—
151C22×Dic7C22×C411yescharacteristic
152C22×Dic7C22×C411yescharacteristic
153C22×Dic7C22×C411yescharacteristic
154C22×Dic7C22×C411yescharacteristic
155C22×Dic7C22×C411yescharacteristic
156C22×Dic7C22×C411yescharacteristic
157C22×Dic7C22×C411yescharacteristic
158#1159—232no—
159C2×C4×D7—22no—
160C2×C4×D7—22no—
161C2×C4×D7—22no—
162C2×C4×D7—22no—
163C2×C4×D7—22no—
164C2×C4×D7—81no—
165C2×C4×D7—81no—
166C2×Dic14—22no—
167C2×Dic14—22no—
168C2×Dic14C22⋊C414yes—
169C2×C7×C8—24no—
170C7×C4⋊C4—22no—
171C7×C22⋊C4—22no—
172C7×C22⋊C4—22no—
173C42×C7C2×D412yes—
174C42×C7C2×D412yes—
175C22⋊Dic7—22no—
176C22⋊Dic7—22no—
177(C2×D7)⋊C4—21no—
178(C2×D7)⋊C4—21no—
179(C2×D7)⋊C4—22no—
180C4⋊Dic7C22⋊C414yes—
181Dic7⋊C4—21no—
182Dic7⋊C4—21no—
183Dic7⋊C4—22no—
184Dic7⋊C4—22no—
185Dic7⋊C4—22no—
186Dic7⋊C4—22no—
187Dic7⋊C4—22no—
188Dic7⋊C4C22⋊C412yes—
189Dic7⋊C4C22⋊C412yes—
190Dic7⋊C4C22⋊C412yes—
191Dic7⋊C4C22⋊C412yes—
192C4×Dic7—22no—
193C4×Dic7—22no—
194C4×Dic7—22no—
195C4×Dic7C2×D414yes—
196C4×Dic7C2×D414yes—
197C2×C7⋊C8—24no—
198C22×#41—71no—
199#520—144no—
200#520—144no—
201C2×C4×Q8—71no—
202C2×C4×Q8—71no—
203C2×C4×D4—71no—
204C2×C4×D4—71no—
205C2×C4×D4—71no—
206C2×C4×D4—71no—
207C2×C4×D4—71no—
208C2×C4×D4C2×D711yescharacteristic
209C2×#117—71no—
210C2×#117—71no—
211C2×#117—71no—
212C22×C4⋊C4—71no—
213C22×C4⋊C4—71no—
214C22×C4⋊C4—71no—
215#446—144no—
216#446—144no—
217#432—72no—
218#432—74no—
219#432C2×D712yes—
220#431—74no—
221#324—74no—
222#323—72no—
223#323—72no—
224#323—74no—
225#323C2×D712yes—
226#323C2×D712yes—
227C23×C7—21no—
228C23×C7—21no—
229C23×C7—21no—
230C23×C7—21no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—41no—
234C23×C7—41no—
235C23×C7C2×M1612yes—
236C23×C7C2×M1612yes—
237C23×C7C23×C411yescharacteristic
238C22×D7—21no—
239C22×D7—21no—
240C22×D7—41no—
241C22×D7—41no—
242C22×D7C2×M1612yes—
243C7×D4—28no—
244C2×C4×C7—21no—
245C2×C4×C7—21no—
246C2×C4×C7—21no—
247C2×C4×C7—21no—
248C2×C4×C7—41no—
249C2×C4×C7—41no—
250C2×C4×C7—41no—
251C2×C4×C7—41no—
252C2×C4×C7—81no—
253C2×C4×C7—81no—
254C2×C4×C7—81no—
255C2×C4×C7—81no—
256C2×C4×C7C2×C22⋊C412yes—
257C2×C4×C7C2×C22⋊C411yescharacteristic
258C2×C4×C7C2×C22⋊C411yescharacteristic
259C2×C4×C7C22×D412yes—
260C22⋊D7—28no—
261C22⋊D7—28no—
262C2×Dic7—28no—
263C2×Dic7—21no—
264C2×Dic7—21no—
265C2×Dic7—21no—
266C2×Dic7—21no—
267C2×Dic7—28no—
268C2×Dic7—21no—
269C2×Dic7—21no—
270C2×Dic7—41no—
271C2×Dic7—41no—
272C2×Dic7—41no—
273C2×Dic7—41no—
274C2×Dic7—82no—
275C2×Dic7—82no—
276C2×Dic7C2×C22⋊C412yes—
277C2×Dic7C2×C22⋊C412yes—
278C2×Dic7C2×C22⋊C412yes—
279C2×Dic7C2×C22⋊C412yes—
280C2×Dic7C2×M1612yes—
281C2×Dic7C2×M1612yes—
282C2×Dic7C2×M1612yes—
283C4×D7—28no—
284C4×D7—82no—
285C4×D7—82no—
286Dic14—28no—
287C7×C8—44no—
288C7⋊C8—44no—
289C2×#41—144no—
290C2×#41—144no—
291C2×#41—144no—
292C22×Q8—71no—
293C22×D4—71no—
294C22×D4—71no—
295C22×D4C4×D711yescharacteristic
296C23×C4—71no—
297C23×C4—71no—
298C23×C4—71no—
299C23×C4—71no—
300C23×C4—71no—
301C23×C4—71no—
302C23×C4—71no—
303C23×C4C4×D711yescharacteristic
304C23×C4C4×D711yescharacteristic
305C4×Q8—74no—
306C4×Q8—74no—
307C4×Q8—144no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—144no—
311C4×D4—144no—
312C4×D4—142no—
313C4×D4—142no—
314C4×D4—142no—
315C4×D4—142no—
316C4×D4—144no—
317#117—144no—
318#117—144no—
319#117—142no—
320#117—142no—
321C2×C4⋊C4—71no—
322C2×C4⋊C4—71no—
323C2×C4⋊C4—71no—
324C2×C4⋊C4—71no—
325C2×C4⋊C4—71no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—144no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4C4×D711yescharacteristic
336C2×C22⋊C4—71no—
337C2×C22⋊C4—71no—
338C2×C22⋊C4—71no—
339C2×C22⋊C4—71no—
340C2×C22⋊C4C22×D711yescharacteristic
341C2×C22⋊C4C22×D711yescharacteristic
342C2×C42—71no—
343C2×C42—71no—
344C2×C42—71no—
345C2×C42—71no—
346C2×C42—71no—
347C2×C42C22×D711yescharacteristic
348C4⋊C8—22no—
349C4⋊C8—144no—
350C4⋊C8—144no—
351C4⋊C8—142no—
352C22⋊C8—74no—
353C22⋊C8C22×D714yes—
354#97—22no—
355#97—144no—
356#97—142no—
357C4×C8—144no—
358C22×C7—21no—
359C22×C7—21no—
360C22×C7—22no—
361C22×C7—22no—
362C22×C7—42no—
363C22×C7—42no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7—41no—
367C22×C7—41no—
368C22×C7—41no—
369C22×C7—41no—
370C22×C7C22×C22⋊C411yescharacteristic
371C22×C7C22×M1611yescharacteristic
372C22×C7C22×M1611yescharacteristic
373C2×D7—22no—
374C2×D7—42no—
375C2×D7—41no—
376C2×D7—41no—
377C2×D7—42no—
378C4×C7—22no—
379C4×C7—22no—
380C4×C7—21no—
381C4×C7—21no—
382C4×C7—41no—
383C4×C7—41no—
384Dic7—22no—
385Dic7—22no—
386Dic7—22no—
387Dic7—22no—
388Dic7—41no—
389Dic7—41no—
390Dic7#40714yes—
391C24—71no—
392C24C2×C4×D711yescharacteristic
393C24C2×C4×D711yescharacteristic
394#41—1432no—
395C2×Q8—74no—
396C2×Q8—142no—
397C2×Q8—142no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—74no—
402C2×D4—142no—
403C2×D4—142no—
404C2×D4—142no—
405C2×D4—142no—
406C2×D4—142no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—71no—
412C22×C4—74no—
413C22×C4—71no—
414C22×C4—71no—
415C22×C4—71no—
416C22×C4—71no—
417C22×C4—71no—
418C22×C4—71no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—142no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—561no—
434C22×C4—561no—
435C22×C4—561no—
436C22×C4—561no—
437C22×C4C2×C4×D711yescharacteristic
438C22×C4C2×C4×D711yescharacteristic
439C22×C4C2×C4×D711yescharacteristic
440C22×C4C2×C4×D711yescharacteristic
441C22×C4C23×D711yescharacteristic
442C2×C8—24no—
443C2×C8—144no—
444C4⋊C4—22no—
445C4⋊C4—72no—
446C4⋊C4—72no—
447C4⋊C4—72no—
448C4⋊C4—72no—
449C4⋊C4—74no—
450C4⋊C4—142no—
451C4⋊C4—142no—
452C4⋊C4—142no—
453C4⋊C4—142no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—142no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—142no—
460C22⋊C4—142no—
461C22⋊C4—141no—
462C22⋊C4—141no—
463C22⋊C4—142no—
464C42—74no—
465C42—74no—
466C42—142no—
467C42—142no—
468C42—142no—
469C42D4×D712yes—
470C42D4×D712yes—
471C2×C7—21no—
472C2×C7—21no—
473C2×C7—42no—
474C2×C7—42no—
475C2×C7C2×#40711yescharacteristic
476C2×C7#288411yescharacteristic
477C2×C7#288811yescharacteristic
478D7—42no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—72no—
488C23—141no—
489C23—141no—
490C23—281no—
491C23—281no—
492C23D7×M1612yes—
493C23D7×M1612yes—
494C23C22×C4×D711yescharacteristic
495Q8—148no—
496D4—28no—
497D4—148no—
498D4—148no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—72no—
508C2×C4—72no—
509C2×C4—72no—
510C2×C4—72no—
511C2×C4—72no—
512C2×C4—72no—
513C2×C4—72no—
514C2×C4—81no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—148no—
519C2×C4—148no—
520C2×C4—148no—
521C2×C4—141no—
522C2×C4—141no—
523C2×C4—141no—
524C2×C4—141no—
525C2×C4—141no—
526C2×C4—141no—
527C2×C4—281no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—562no—
532C2×C4—562no—
533C2×C4—562no—
534C2×C4—562no—
535C2×C4D7×C22⋊C412yes—
536C2×C4D7×C22⋊C411yescharacteristic
537C2×C4D7×C22⋊C411yescharacteristic
538C2×C4C2×D4×D712yes—
539C8—44no—
540C8—284no—
541C7#1737211yescharacteristic, complemented, Sylow
542C22—21no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—142no—
555C22—282no—
556C22—282no—
557C22—281no—
558C22—281no—
559C22C2×D7×C22⋊C411yescharacteristic
560C22C2×D7×M1611yescharacteristic
561C22C2×D7×M1611yescharacteristic
562C4—22no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—74no—
569C4—142no—
570C4—142no—
571C4—142no—
572C4—142no—
573C4—281no—
574C4—281no—
575C2—21no—
576C2—21no—
577C2—42no—
578C2—42no—
579C2—282no—
580C2D7×#40711yescharacteristic
581C2#1173613411yescharacteristic
582C2#1173614211yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1466C2
socleC22×C7C22×C22⋊C4
prime radicalC22×#1159C4
cosocleC22×C4×C7C24
hypercenter#1466D7
hypocenterC7#17372
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #11736759C2semidirect
3. C7×#1466C2semidirect
4. #11729357C2semidirect
5. #11728580C2semidirect
6. #11725857C2semidirect
7. #11725856C2semidirect
8. #11725855C2semidirect
9. #11725854C2semidirect
113. #1466D7semidirect
541. C7#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#902372
#117367592
C7×#14662
#117293572
#117285802
#117258572
#117258562
#117258552
#117258542
#173727