Finite Group Databasebeta

← #13319705

Subgroups — #13319705

Order 1792.

1210 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90195C211yesmaximal, characteristic
2#11736047C212yesmaximal, complemented
3C2×C7×#324C211yesmaximal, characteristic, complemented
4C2×#89323C211yesmaximal, characteristic, complemented
5#11727673C212yesmaximal, complemented
6#11725899C212yesmaximal, complemented
7#11725898C212yesmaximal, complemented
8#11725881C212yesmaximal, complemented
9#11725880C212yesmaximal, complemented
10C22×#1157C411yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C2×C4×C22⋊D7C411yescharacteristic
13C2×C4×C22⋊D7C411yescharacteristic
14C2×C4×C22⋊D7C2211yescharacteristic
15C2×C4×C22⋊D7C2211yescharacteristic
16C2×#6489C411yescharacteristic
17#90195—24no—
18#90195—24no—
19C2×#6456C411yescharacteristic
20C2×#6456C2211yescharacteristic
21C2×#6455C411yescharacteristic
22C2×#6455C2211yescharacteristic
23C2×D7×C4⋊C4C411yescharacteristic
24C2×D7×C4⋊C4C2211yescharacteristic
25C2×#6450C411yescharacteristic
26C2×#6450C2211yescharacteristic
27C2×C7×C22⋊C8C2212yes—
28C2×C22⋊(C7⋊C8)C2212yes—
29#89883—24no—
30#89502—24no—
31#89498C2214yes—
32#89491C2214yes—
33C7×#324C2212yes—
34C7×#324C2212yes—
35#89323C2212yes—
36#89323C2212yes—
37#89264C2214yes—
38#89263C2214yes—
39#17368—71nomaximal, Sylow
40C23×C4×C7C2×C411yescharacteristic
41C23×C4×C7C2×C411yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C22×C22⋊D7C2×C411yescharacteristic
44C22×C22⋊D7C2×C411yescharacteristic
45C2×#1157—24no—
46C2×#1157—22no—
47C2×#1157—22no—
48C2×#1157—24no—
49C22×D28C2×C411yescharacteristic
50C22×C4×D7C2×C411yescharacteristic
51C22×C4×D7C2×C411yescharacteristic
52C22×C4×D7C2×C411yescharacteristic
53C22×C4×D7C2×C411yescharacteristic
54C22×C4×D7C2×C411yescharacteristic
55C22×C4×D7C2311yescharacteristic
56C22×Dic14C2×C411yescharacteristic
57C22×C7×C8—22no—
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4C2×C411yescharacteristic
61C2×C7×C4⋊C4C2×C411yescharacteristic
62C2×C7×C4⋊C4C2311yescharacteristic
63C2×C7×C4⋊C4C2311yescharacteristic
64C2×C22⋊Dic7C2×C411yescharacteristic
65C2×C22⋊Dic7C2×C411yescharacteristic
66C4×C22⋊D7—22no—
67C4×C22⋊D7—22no—
68C4×C22⋊D7—22no—
69C4×C22⋊D7—22no—
70C4×C22⋊D7—22no—
71C4×C22⋊D7—22no—
72C4×C22⋊D7D414yes—
73C4×C22⋊D7D414yes—
74C2×(C2×D7)⋊C4C2×C411yescharacteristic
75C2×(C2×D7)⋊C4C2×C411yescharacteristic
76C2×(C2×D7)⋊C4C2×C411yescharacteristic
77C2×(C2×D7)⋊C4C2311yescharacteristic
78#6489—22no—
79#6489—22no—
80C2×C4⋊Dic7C2×C411yescharacteristic
81C2×C4⋊Dic7C2×C411yescharacteristic
82C2×Dic7⋊C4C2×C411yescharacteristic
83C2×Dic7⋊C4C2×C411yescharacteristic
84C2×Dic7⋊C4C2×C411yescharacteristic
85C2×Dic7⋊C4C2311yescharacteristic
86C2×C4×Dic7C2×C411yescharacteristic
87C2×C4×Dic7C2×C411yescharacteristic
88C2×C4×Dic7C2×C411yescharacteristic
89C2×C4×Dic7C2×C411yescharacteristic
90C2×C4×Dic7C2×C411yescharacteristic
91C2×C4×Dic7C2311yescharacteristic
92C22×C7⋊C8—22no—
93C2×#1131—24no—
94#6456—24no—
95#6456—24no—
96#6455—24no—
97#6455—24no—
98D7×C4⋊C4—24no—
99D7×C4⋊C4—24no—
100#6450—24no—
101#6450—24no—
102C7×C22⋊C8—22no—
103C7×C22⋊C8C2314yes—
104C22⋊(C7⋊C8)—22no—
105C22⋊(C7⋊C8)C2314yes—
106(C2×D7)⋊C8—24no—
107#6389—24no—
108Dic7⋊C8—24no—
109C2×#520—71no—
110#2973—72no—
111#1467—72no—
112#1465—72no—
113#1464—72no—
114#1463—72no—
115#1459—72no—
116C2×#324—71no—
117C2×#324D711yescharacteristic, complemented
118C24×C7C22×C411yescharacteristic
119C23×D7C22×C411yescharacteristic
120C23×D7C22×C411yescharacteristic
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—81no—
127C22×C4×C7—81no—
128C22×C4×C7M1614yescomplemented
129C22×C4×C7C22×C411yescharacteristic
130C22×C4×C7C22×C411yescharacteristic
131C22×C4×C7C22×C411yescharacteristic
132C22×C4×C7C22×C411yescharacteristic
133C22×C4×C7C22×C411yescharacteristic
134C22×C4×C7C2×D412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7C2411yescharacteristic
137C2×C22⋊D7—21no—
138C2×C22⋊D7—21no—
139C2×C22⋊D7—22no—
140C2×C22⋊D7—22no—
141C2×C22⋊D7—22no—
142C2×C22⋊D7C22⋊C412yes—
143C2×C22⋊D7C22⋊C412yes—
144C2×C22⋊D7M1614yescomplemented
145C22×Dic7C22×C411yescharacteristic
146C22×Dic7C22×C411yescharacteristic
147C22×Dic7C22×C411yescharacteristic
148C22×Dic7C22×C411yescharacteristic
149C22×Dic7C22×C411yescharacteristic
150C22×Dic7C22×C411yescharacteristic
151#1157—216no—
152#1157—216no—
153C2×D28—22no—
154C2×D28—22no—
155C2×D28—22no—
156C2×C4×D7—22no—
157C2×C4×D7—22no—
158C2×C4×D7—22no—
159C2×C4×D7—22no—
160C2×C4×D7—22no—
161C2×C4×D7—22no—
162C2×C4×D7—22no—
163C2×C4×D7—22no—
164C2×C4×D7—22no—
165C2×C4×D7—81no—
166C2×C4×D7—81no—
167C2×C4×D7—81no—
168C2×C4×D7—81no—
169C2×C4×D7C2×D414yes—
170C2×Dic14—22no—
171C2×Dic14—22no—
172C2×Dic14—22no—
173C2×C7×C8—24no—
174C2×C7×C8—82no—
175C7×C4⋊C4—22no—
176C7×C4⋊C4—22no—
177C7×C4⋊C4—22no—
178C7×C4⋊C4—22no—
179C22⋊Dic7—21no—
180C22⋊Dic7—21no—
181C22⋊Dic7C22⋊C412yes—
182C22⋊Dic7C22⋊C412yes—
183(C2×D7)⋊C4—22no—
184(C2×D7)⋊C4—22no—
185(C2×D7)⋊C4—22no—
186(C2×D7)⋊C4C22⋊C414yes—
187C4⋊Dic7—22no—
188C4⋊Dic7—22no—
189Dic7⋊C4—22no—
190Dic7⋊C4—22no—
191Dic7⋊C4—22no—
192Dic7⋊C4C22⋊C414yes—
193C4×Dic7—22no—
194C4×Dic7—22no—
195C4×Dic7—22no—
196C4×Dic7—22no—
197C4×Dic7—22no—
198C4×Dic7C2×D414yes—
199C2×C7⋊C8—24no—
200C2×C7⋊C8—82no—
201#1131—84no—
202C22×#41—71no—
203#520—144no—
204#520—144no—
205C2×C4×Q8—71no—
206C2×C4×Q8—71no—
207C2×C4×D4—71no—
208C2×C4×D4—71no—
209C2×C4×D4—71no—
210C2×C4×D4—71no—
211C2×C4×D4—71no—
212C2×C4×D4—71no—
213C2×#117—71no—
214C2×#117—71no—
215C2×#117—71no—
216C22×C4⋊C4—71no—
217C22×C4⋊C4—71no—
218C22×C4⋊C4C2×D711yescharacteristic
219#435—144no—
220#435—144no—
221#432—74no—
222#407—74no—
223C2×C22⋊C8—72no—
224C2×C22⋊C8C2×D712yes—
225#324—72no—
226#324—72no—
227#324—74no—
228#324C2×D712yes—
229#324C2×D712yes—
230#323—74no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7C2×C22⋊C411yescharacteristic
234C23×C7C2×C22⋊C411yescharacteristic
235C23×C7C2×M1612yes—
236C23×C7C2×M1612yes—
237C23×C7C23×C411yescharacteristic
238C22×D7—21no—
239C22×D7—21no—
240C22×D7—21no—
241C22×D7—21no—
242C22×D7—41no—
243C22×D7—41no—
244C22×D7—41no—
245C22×D7—41no—
246C22×D7C2×C22⋊C412yes—
247C22×D7C2×M1612yes—
248C2×C4×C7—21no—
249C2×C4×C7—21no—
250C2×C4×C7—21no—
251C2×C4×C7—21no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
254C2×C4×C7—21no—
255C2×C4×C7—21no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—81no—
263C2×C4×C7—81no—
264C2×C4×C7C2×C22⋊C412yes—
265C2×C4×C7C2×M1612yes—
266C2×C4×C7C2×M1612yes—
267C2×C4×C7C22×D412yes—
268C22⋊D7—24no—
269C22⋊D7—24no—
270C22⋊D7—24no—
271C22⋊D7—24no—
272C2×Dic7—21no—
273C2×Dic7—21no—
274C2×Dic7—21no—
275C2×Dic7—21no—
276C2×Dic7—21no—
277C2×Dic7—21no—
278C2×Dic7—41no—
279C2×Dic7—41no—
280C2×Dic7—41no—
281C2×Dic7—41no—
282C2×Dic7C2×C22⋊C412yes—
283C2×Dic7C2×C22⋊C412yes—
284C2×Dic7C2×C22⋊C412yes—
285C2×Dic7C2×M1612yes—
286D28—28no—
287C4×D7—28no—
288C4×D7—28no—
289C4×D7—44no—
290C4×D7—82no—
291C4×D7—82no—
292C4×D7—82no—
293Dic14—28no—
294C7×C8—44no—
295C7⋊C8—44no—
296C2×#41—142no—
297C2×#41—142no—
298C2×#41—144no—
299C2×#41—144no—
300C22×Q8—71no—
301C22×D4—71no—
302C22×D4—71no—
303C22×D4—71no—
304C23×C4—71no—
305C23×C4—71no—
306C23×C4—71no—
307C23×C4—71no—
308C23×C4—71no—
309C23×C4—71no—
310C23×C4C4×D711yescharacteristic
311C23×C4C4×D711yescharacteristic
312C23×C4C22×D711yescharacteristic
313C2×M16—144no—
314C22×C8—22no—
315C22×C8—142no—
316C4×Q8—144no—
317C4×Q8—144no—
318C4×D4—74no—
319C4×D4—74no—
320C4×D4—144no—
321C4×D4—142no—
322C4×D4—142no—
323C4×D4—144no—
324C4×D4—142no—
325C4×D4—142no—
326C4×D4—142no—
327C4×D4—142no—
328#117—144no—
329#117—144no—
330#117—142no—
331#117—142no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—71no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—71no—
337C2×C4⋊C4—71no—
338C2×C4⋊C4—71no—
339C2×C4⋊C4—71no—
340C2×C4⋊C4—144no—
341C2×C4⋊C4—144no—
342C2×C4⋊C4C4×D711yescharacteristic
343C2×C4⋊C4C4×D711yescharacteristic
344C2×C4⋊C4C22×D711yescharacteristic
345C2×C4⋊C4C22×D711yescharacteristic
346C2×C22⋊C4—71no—
347C2×C22⋊C4—71no—
348C2×C22⋊C4—71no—
349C2×C22⋊C4—71no—
350C2×C22⋊C4—71no—
351C2×C22⋊C4—71no—
352C2×C42—71no—
353C2×C42—71no—
354C2×C42—71no—
355C2×C42—71no—
356C2×C42—71no—
357C2×C42—71no—
358C4⋊C8—144no—
359C22⋊C8—22no—
360C22⋊C8—74no—
361C22⋊C8—144no—
362C22⋊C8—142no—
363C22⋊C8C22×D714yes—
364#97—144no—
365C22×C7—21no—
366C22×C7—21no—
367C22×C7—21no—
368C22×C7—21no—
369C22×C7—21no—
370C22×C7—21no—
371C22×C7—42no—
372C22×C7—42no—
373C22×C7#40712yes—
374C22×C7#40712yes—
375C22×C7C22×C22⋊C411yescharacteristic
376C22×C7C22×M1611yescharacteristic
377C22×C7C22×M1611yescharacteristic
378C2×D7—22no—
379C2×D7—22no—
380C2×D7—22no—
381C2×D7—22no—
382C2×D7—42no—
383C2×D7—42no—
384C2×D7—42no—
385C2×D7—41no—
386C2×D7—41no—
387C2×D7—42no—
388C4×C7—22no—
389C4×C7—22no—
390C4×C7—22no—
391C4×C7—22no—
392C4×C7—41no—
393C4×C7—41no—
394Dic7—22no—
395Dic7—22no—
396Dic7—22no—
397Dic7—22no—
398Dic7—41no—
399Dic7—41no—
400C24—71no—
401C24—71no—
402C24C2×C4×D711yescharacteristic
403#41—1416no—
404#41—1416no—
405C2×Q8—142no—
406C2×Q8—142no—
407C2×Q8—142no—
408C2×D4—72no—
409C2×D4—72no—
410C2×D4—74no—
411C2×D4—142no—
412C2×D4—142no—
413C2×D4—141no—
414C2×D4—141no—
415C2×D4—142no—
416C2×D4—142no—
417C2×D4—142no—
418C2×D4—142no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—71no—
425C22×C4—71no—
426C22×C4—71no—
427C22×C4—71no—
428C22×C4—74no—
429C22×C4—71no—
430C22×C4—71no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4—142no—
434C22×C4—142no—
435C22×C4—142no—
436C22×C4—142no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—142no—
442C22×C4—561no—
443C22×C4—561no—
444C22×C4—561no—
445C22×C4—561no—
446C22×C4#113114yescomplemented
447C22×C4C2×C4×D711yescharacteristic
448C22×C4C2×C4×D711yescharacteristic
449C22×C4C2×C4×D711yescharacteristic
450C22×C4C2×C4×D711yescharacteristic
451C22×C4C2×C4×D711yescharacteristic
452C22×C4D4×D712yes—
453C22×C4D4×D712yes—
454C22×C4C23×D711yescharacteristic
455M16—564no—
456C2×C8—24no—
457C2×C8—82no—
458C2×C8—144no—
459C2×C8—562no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—74no—
465C4⋊C4—142no—
466C4⋊C4—142no—
467C4⋊C4—142no—
468C4⋊C4—142no—
469C4⋊C4—142no—
470C22⋊C4—72no—
471C22⋊C4—72no—
472C22⋊C4—74no—
473C22⋊C4—142no—
474C22⋊C4—142no—
475C22⋊C4—141no—
476C22⋊C4—141no—
477C22⋊C4—142no—
478C42—74no—
479C42—142no—
480C42—142no—
481C42—142no—
482C42—142no—
483C42—142no—
484C2×C7—21no—
485C2×C7—21no—
486C2×C7—22no—
487C2×C7—22no—
488C2×C7C2×#40711yescharacteristic
489C2×C7#288311yescharacteristic
490C2×C7#288911yescharacteristic
491D7—42no—
492D7—42no—
493C23—41no—
494C23—41no—
495C23—72no—
496C23—72no—
497C23—141no—
498C23—141no—
499C23—141no—
500C23—141no—
501C23—281no—
502C23—281no—
503C23—281no—
504C23—281no—
505C23D7×C22⋊C411yescharacteristic
506C23D7×C22⋊C411yescharacteristic
507C23C2×#113112yes—
508C23D7×M1612yes—
509C23C22×C4×D711yescharacteristic
510Q8—148no—
511D4—148no—
512D4—144no—
513D4—144no—
514D4—144no—
515D4—144no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—72no—
531C2×C4—72no—
532C2×C4—72no—
533C2×C4—72no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—148no—
537C2×C4—148no—
538C2×C4—141no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—141no—
543C2×C4—141no—
544C2×C4—284no—
545C2×C4—281no—
546C2×C4—281no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—562no—
550C2×C4—562no—
551C2×C4—562no—
552C2×C4D7×C22⋊C412yes—
553C2×C4C2×#113112yes—
554C2×C4C2×#113112yes—
555C2×C4C2×D4×D712yes—
556C8—44no—
557C8—284no—
558C7#1736811yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—142no—
568C22—142no—
569C22—142no—
570C22—142no—
571C22—282no—
572C22—282no—
573C22—282no—
574C22—282no—
575C22—281no—
576C22—281no—
577C22#8949812yes—
578C22#8949812yes—
579C22C2×D7×C22⋊C411yescharacteristic
580C22C22×#113111yescharacteristic
581C22C2×D7×M1611yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—142no—
589C4—142no—
590C4—142no—
591C4—142no—
592C4—281no—
593C4—281no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—282no—
599C2—282no—
600C2C2×#8949811yescharacteristic
601C2#1173613311yescharacteristic
602C2#1173615111yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#324C2
socleC22×C7C22×C22⋊C4
prime radicalC22×#1157C4
cosocleC22×C4×C7C24
hypercenterC2×#324D7
hypocenterC7#17368
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #11736047C2semidirect
3. C2×C7×#324C2semidirect
4. C2×#89323C2semidirect
5. #11727673C2semidirect
6. #11725899C2semidirect
7. #11725898C2semidirect
8. #11725881C2semidirect
9. #11725880C2semidirect
117. C2×#324D7semidirect
128. C22×C4×C7M16semidirect
144. C2×C22⋊D7M16semidirect
446. C22×C4#1131semidirect
558. C7#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#901952
#117360472
C2×C7×#3242
C2×#893232
#117276732
#117258992
#117258982
#117258812
#117258802
#173687