Finite Group Databasebeta

← D7×#1503 #13320897

Subgroups — D7×#1503 #13320897

Order 1792.

1194 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D7×#533C211yesmaximal, characteristic
2D7×#431C211yesmaximal, characteristic
3C4×D7×C4⋊C4C211yesmaximal, characteristic
4C7×#1503C211yesmaximal, characteristic, complemented
5#11729589C211yesmaximal, characteristic, complemented
6#11728546C211yesmaximal, characteristic, complemented
7#11727225C211yesmaximal, characteristic, complemented
8D7×#328C214yesmaximal
9#11726063C214yesmaximal, complemented
10C7×#533C2211yescharacteristic
11#90419C411yescharacteristic, complemented
12#90419C411yescharacteristic, complemented
13D7×C4⋊Q8C411yescharacteristic, complemented
14D7×C4⋊Q8C411yescharacteristic, complemented
15#90379—21no—
16D7×#125—21no—
17D7×C22⋊Q8—21no—
18D7×C22⋊Q8C2212yes—
19#90313—21no—
20#90313C2212yes—
21#90269—21no—
22#90269C412yescomplemented
23C4×Q8×D7—21no—
24C4×Q8×D7C412yescomplemented
25D7×#117—21no—
26#90208—21no—
27C2×D7×C4⋊C4—21no—
28C2×C42×D7—21no—
29C2×C42×D7C2211yescharacteristic
30#90161C2211yescharacteristic
31C7×#431C2211yescharacteristic
32C4×C7×C4⋊C4C2211yescharacteristic
33C4⋊C4×Dic7—21no—
34C4×C4⋊Dic7C2211yescharacteristic
35C4×Dic7⋊C4—21no—
36#89697C2211yescharacteristic
37#89605—21no—
38D7×C4⋊C8—21no—
39D7×C22⋊C8C2212yes—
40#89490C2212yes—
41#89457—21no—
42C4×C8×D7—21no—
43D7×#95C2212yes—
44#89421C2212yes—
45C7×#328C2214yes—
46#89333C2214yes—
47#89262C2214yes—
48#89247C2214yes—
49C2×#1503—71nomaximal, Sylow
50C2×Q8×D7—21no—
51C2×Q8×D7C2×C412yes—
52C22×C4×D7—22no—
53C22×C4×D7D411yescharacteristic
54C22×C4×D7D411yescharacteristic
55C22×C4×D7C2311yescharacteristic
56C7×C4⋊Q8C2×C411yescharacteristic, complemented
57C7×C4⋊Q8C2×C411yescharacteristic, complemented
58C7×#125—21no—
59C7×C22⋊Q8—21no—
60C7×C22⋊Q8C2312yes—
61C4×C7×Q8—21no—
62C4×C7×Q8C2×C412yescomplemented
63C7×#117—21no—
64C2×C7×C4⋊C4—21no—
65C2×C42×C7—21no—
66C2×C42×C7C2311yescharacteristic
67#6509—21no—
68#6509C2×C412yes—
69Q8×Dic7—21no—
70Q8×Dic7C2×C412yescomplemented
71#6507—21no—
72#6507C2×C412yescomplemented
73#6489—21no—
74C2×C4⋊Dic7—21no—
75#6487—21no—
76#6487C2312yes—
77C2×Dic7⋊C4—22no—
78C2×C4×Dic7—21no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7D411yescharacteristic
81C2×C4×Dic7D411yescharacteristic
82C2×C4×Dic7C2311yescharacteristic
83C2×C8×D7—22no—
84#6460—21no—
85#6460C2×C412yes—
86#6459—22no—
87#6459—22no—
88#6455—21no—
89#6455—21no—
90D7×C4⋊C4—28no—
91D7×C4⋊C4—21no—
92D7×C4⋊C4—21no—
93D7×C4⋊C4—22no—
94D7×C4⋊C4—21no—
95D7×C4⋊C4—22no—
96D7×C4⋊C4C2×C412yes—
97#6453—21no—
98#6453—21no—
99#6452—22no—
100#6452—22no—
101#6451—21no—
102#6451—21no—
103#6451—21no—
104#6451C2×C412yescomplemented
105#6450—22no—
106#6450—21no—
107#6450—22no—
108#6450C2×C412yescomplemented
109D7×C22⋊C4—22no—
110#6441—22no—
111#6441—22no—
112#6440—22no—
113#6435—22no—
114C42×D7—22no—
115C42×D7—44no—
116C42×D7C2×C411yescharacteristic
117C42×D7C2×C411yescharacteristic
118C42×D7C2×C411yescharacteristic
119C42×D7C2×C411yescharacteristic
120C42×D7D411yescharacteristic
121C42×D7D411yescharacteristic
122C42×D7D411yescharacteristic
123C42×D7D411yescharacteristic
124#6433—21no—
125#6432C2×C411yescharacteristic, complemented
126#6432C2×C411yescharacteristic, complemented
127C4×Dic14—21no—
128C4×Dic14—22no—
129C4×Dic14—22no—
130C4×Dic14C2×C412yescomplemented
131C7×C4⋊C8—21no—
132C7×C22⋊C8C2312yes—
133C4×C7×C8—21no—
134C7×#95C2312yes—
135C7⋊#95—22no—
136C7⋊#95C2312yes—
137C22⋊(C7⋊C8)C2312yes—
138(C2×D7)⋊C8—22no—
139Dic7⋊C8—22no—
140C8×Dic7—22no—
141C4⋊(C7⋊C8)—21no—
142C4×C7⋊C8—21no—
143C2×#533—71no—
144C2×#431—71no—
145C2×C4×C4⋊C4—71no—
146#1503—71no—
147#1503—71no—
148#1503—74no—
149#1503—71no—
150#1503D711yescharacteristic, direct product factor
151C2×#328—74no—
152C23×D7C2×D411yescharacteristic
153C2×C7×Q8—21no—
154C2×C7×Q8C22×C412yes—
155C22×C4×C7—22no—
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2411yescharacteristic
159C22×Dic7—22no—
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163Q8×D7—44no—
164Q8×D7—44no—
165C2×C4×D7—24no—
166C2×C4×D7—28no—
167C2×C4×D7—22no—
168C2×C4×D7—22no—
169C2×C4×D7—42no—
170C2×C4×D7—44no—
171C2×C4×D7—44no—
172C2×C4×D7C22⋊C411yescharacteristic
173C2×C4×D7C22⋊C411yescharacteristic
174C2×C4×D7C22⋊C411yescharacteristic
175C2×C4×D7C22⋊C411yescharacteristic
176C2×C4×D7C22⋊C411yescharacteristic
177C2×C4×D7C22⋊C411yescharacteristic
178C2×C4×D7C22⋊C411yescharacteristic
179C2×C4×D7C22⋊C411yescharacteristic
180C2×C4×D7SD1614yes—
181C2×C4×D7Q1614yes—
182C2×C4×D7C22×C411yescharacteristic
183C2×C4×D7C22×C411yescharacteristic
184C2×C4×D7C2×D411yescharacteristic
185C2×C4×D7C2×D411yescharacteristic
186C2×Dic14—21no—
187C2×Dic14—22no—
188C2×Dic14—22no—
189C2×Dic14C22×C412yes—
190C2×C7×C8—22no—
191C7×C4⋊C4—24no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—22no—
197C7×C4⋊C4C22×C412yes—
198C7×C22⋊C4—22no—
199C42×C7—22no—
200C42×C7—42no—
201C42×C7C22×C411yescharacteristic
202C42×C7C22×C411yescharacteristic
203C42×C7C2×D411yescharacteristic
204C42×C7C2×D411yescharacteristic
205C22⋊Dic7—22no—
206(C2×D7)⋊C4—22no—
207(C2×D7)⋊C4—22no—
208C4⋊Dic7—24no—
209C4⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4⋊Dic7—21no—
212C4⋊Dic7—22no—
213C4⋊Dic7—22no—
214C4⋊Dic7C22×C412yes—
215Dic7⋊C4—28no—
216Dic7⋊C4—22no—
217Dic7⋊C4—22no—
218Dic7⋊C4—22no—
219Dic7⋊C4—22no—
220Dic7⋊C4—22no—
221Dic7⋊C4—22no—
222Dic7⋊C4—22no—
223Dic7⋊C4—22no—
224C4×Dic7—22no—
225C4×Dic7—22no—
226C4×Dic7—22no—
227C4×Dic7—42no—
228C4×Dic7—44no—
229C4×Dic7C22⋊C411yescharacteristic
230C4×Dic7C22⋊C411yescharacteristic
231C4×Dic7C22⋊C411yescharacteristic
232C4×Dic7C22⋊C411yescharacteristic
233C4×Dic7C22⋊C411yescharacteristic
234C4×Dic7C22⋊C411yescharacteristic
235C4×Dic7C22⋊C411yescharacteristic
236C4×Dic7C22⋊C411yescharacteristic
237C4×Dic7C22×C411yescharacteristic
238C4×Dic7C22×C411yescharacteristic
239C4×Dic7C2×D411yescharacteristic
240C4×Dic7C2×D411yescharacteristic
241C2×C7⋊C8—22no—
242C8×D7—44no—
243#533—71no—
244#533—71no—
245#533—72no—
246#533—72no—
247#533—71no—
248#533—141no—
249#533—141no—
250#533—141no—
251#533—141no—
252#533C2×D711yescharacteristic
253C2×C4⋊Q8—71no—
254C2×C4⋊Q8—71no—
255C2×#125—141no—
256C2×C22⋊Q8—72no—
257C2×C22⋊Q8—141no—
258C2×C4×Q8—72no—
259C2×C4×Q8—141no—
260C2×#117—141no—
261C22×C4⋊C4—141no—
262C22×C42—71no—
263C22×C42—141no—
264#431—71no—
265#431—72no—
266#431—141no—
267#431—141no—
268#431C2×D711yescharacteristic
269C2×C4⋊C8—141no—
270C2×C22⋊C8—72no—
271C2×C4×C8—141no—
272C4×C4⋊C4—71no—
273C4×C4⋊C4—72no—
274C4×C4⋊C4—141no—
275C4×C4⋊C4—141no—
276C4×C4⋊C4C2×D711yescharacteristic
277C2×#95—72no—
278#328—74no—
279#328—74no—
280#328—74no—
281#328C2×D714yes—
282C23×C7C22×D411yescharacteristic
283C22×D7—22no—
284C22×D7—22no—
285C22×D7C2×C22⋊C411yescharacteristic
286C22×D7C2×C22⋊C411yescharacteristic
287C22×D7C2×SD1612yes—
288C22×D7C2×Q1612yes—
289C7×Q8—42no—
290C7×Q8—42no—
291C2×C4×C7—22no—
292C2×C4×C7—24no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—41no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7C2×C22⋊C411yescharacteristic
299C2×C4×C7C2×C22⋊C411yescharacteristic
300C2×C4×C7C2×C22⋊C411yescharacteristic
301C2×C4×C7C2×C22⋊C411yescharacteristic
302C2×C4×C7C2×SD1612yes—
303C2×C4×C7C2×Q1612yes—
304C2×C4×C7C23×C411yescharacteristic
305C2×C4×C7C22×D411yescharacteristic
306C2×Dic7—22no—
307C2×Dic7—24no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—41no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7C2×C22⋊C411yescharacteristic
314C2×Dic7C2×C22⋊C411yescharacteristic
315C2×Dic7C2×C22⋊C411yescharacteristic
316C2×Dic7C2×C22⋊C411yescharacteristic
317C2×Dic7C2×C22⋊C411yescharacteristic
318C2×Dic7C2×C22⋊C411yescharacteristic
319C2×Dic7C2×SD1612yes—
320C2×Dic7C2×Q1612yes—
321C4×D7—22no—
322C4×D7—22no—
323C4×D7—22no—
324C4×D7—22no—
325C4×D7—22no—
326C4×D7—41no—
327C4×D7—41no—
328C4×D7—416no—
329C4×D7—44no—
330C4×D7—44no—
331C4×D7#10314yes—
332C4×D7#10314yes—
333C4×D7#10314yes—
334C4×D7#10314yes—
335C4×D7#10414yes—
336Dic14—44no—
337Dic14—42no—
338Dic14—44no—
339Dic14—42no—
340C7×C8—42no—
341C7⋊C8—42no—
342C22×Q8—72no—
343C22×Q8—141no—
344C23×C4—71no—
345C23×C4—71no—
346C23×C4—71no—
347C23×C4—142no—
348C22×C8—142no—
349C4⋊Q8—72no—
350C4⋊Q8—72no—
351C4⋊Q8—71no—
352C4⋊Q8—71no—
353C4⋊Q8—141no—
354C4⋊Q8—141no—
355C4⋊Q8—141no—
356C4⋊Q8—141no—
357C4⋊Q8C4×D711yescharacteristic, complemented
358C4⋊Q8C4×D711yescharacteristic, complemented
359#125—21no—
360#125—142no—
361#125—142no—
362#125—141no—
363#125—141no—
364#125—141no—
365C22⋊Q8—21no—
366C22⋊Q8—72no—
367C22⋊Q8—72no—
368C22⋊Q8—72no—
369C22⋊Q8—142no—
370C22⋊Q8—142no—
371C22⋊Q8—142no—
372C22⋊Q8—142no—
373C22⋊Q8—141no—
374C22⋊Q8—141no—
375C22⋊Q8—141no—
376C22⋊Q8C22×D712yes—
377C4×Q8—21no—
378C4×Q8—72no—
379C4×Q8—72no—
380C4×Q8—72no—
381C4×Q8—142no—
382C4×Q8—142no—
383C4×Q8—142no—
384C4×Q8—141no—
385C4×Q8—142no—
386C4×Q8—141no—
387C4×Q8—141no—
388C4×Q8C4×D712yescomplemented
389#117—21no—
390#117—142no—
391#117—142no—
392#117—141no—
393#117—141no—
394#117—141no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—72no—
397C2×C4⋊C4—141no—
398C2×C4⋊C4—141no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—142no—
401C2×C4⋊C4—141no—
402C2×C4⋊C4—148no—
403C2×C4⋊C4—142no—
404C2×C4⋊C4—141no—
405C2×C22⋊C4—142no—
406C2×C42—21no—
407C2×C42—71no—
408C2×C42—71no—
409C2×C42—71no—
410C2×C42—71no—
411C2×C42—71no—
412C2×C42—71no—
413C2×C42—71no—
414C2×C42—71no—
415C2×C42—71no—
416C2×C42—71no—
417C2×C42—71no—
418C2×C42—142no—
419C2×C42—142no—
420C2×C42—141no—
421C2×C42—284no—
422C2×C42C22×D711yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—142no—
425C4⋊C8—141no—
426C22⋊C8—72no—
427C22⋊C8—142no—
428C22⋊C8C22×D712yes—
429C4×C8—21no—
430C4×C8—142no—
431C4×C8—141no—
432#95—72no—
433#95—142no—
434#95C22×D712yes—
435C22×C7—21no—
436C22×C7—21no—
437C22×C7C22×C22⋊C411yescharacteristic
438C22×C7C22×SD1611yescharacteristic
439C22×C7C22×Q1611yescharacteristic
440C2×D7—21no—
441C2×D7—21no—
442C2×D7—24no—
443C2×D7—24no—
444C2×D7#41012yes—
445C2×D7C2×#10312yes—
446C2×D7C2×#10312yes—
447C2×D7C2×#10412yes—
448C4×C7—21no—
449C4×C7—21no—
450C4×C7—21no—
451C4×C7—44no—
452C4×C7—42no—
453C4×C7—42no—
454C4×C7C2×#10312yes—
455C4×C7C2×#10312yes—
456C4×C7C2×#10412yes—
457Dic7—21no—
458Dic7—21no—
459Dic7—21no—
460Dic7—44no—
461Dic7—42no—
462Dic7—42no—
463Dic7C2×#10312yes—
464Dic7C2×#10312yes—
465Dic7C2×#10412yes—
466C24—71no—
467C2×Q8—21no—
468C2×Q8—72no—
469C2×Q8—142no—
470C2×Q8—142no—
471C2×Q8—141no—
472C2×Q8—284no—
473C2×Q8—284no—
474C2×Q8C2×C4×D712yes—
475C22×C4—22no—
476C22×C4—71no—
477C22×C4—71no—
478C22×C4—71no—
479C22×C4—71no—
480C22×C4—71no—
481C22×C4—71no—
482C22×C4—74no—
483C22×C4—74no—
484C22×C4—71no—
485C22×C4—71no—
486C22×C4—71no—
487C22×C4—71no—
488C22×C4—71no—
489C22×C4—71no—
490C22×C4—71no—
491C22×C4—71no—
492C22×C4—71no—
493C22×C4—144no—
494C22×C4—142no—
495C22×C4—142no—
496C22×C4—148no—
497C22×C4—142no—
498C22×C4—282no—
499C22×C4—284no—
500C22×C4—284no—
501C22×C4D4×D711yescharacteristic
502C22×C4D4×D711yescharacteristic
503C22×C4C23×D711yescharacteristic
504C2×C8—22no—
505C2×C8—142no—
506C2×C8—284no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—72no—
514C4⋊C4—142no—
515C4⋊C4—142no—
516C4⋊C4—142no—
517C4⋊C4—142no—
518C4⋊C4—142no—
519C4⋊C4—142no—
520C4⋊C4—142no—
521C4⋊C4—142no—
522C4⋊C4—148no—
523C4⋊C4—144no—
524C4⋊C4—142no—
525C4⋊C4—141no—
526C4⋊C4—141no—
527C4⋊C4—141no—
528C4⋊C4—142no—
529C4⋊C4C2×C4×D712yes—
530C22⋊C4—22no—
531C22⋊C4—142no—
532C22⋊C4—142no—
533C22⋊C4—142no—
534C42—22no—
535C42—42no—
536C42—71no—
537C42—71no—
538C42—71no—
539C42—71no—
540C42—71no—
541C42—71no—
542C42—71no—
543C42—71no—
544C42—71no—
545C42—71no—
546C42—71no—
547C42—71no—
548C42—142no—
549C42—142no—
550C42—142no—
551C42—284no—
552C42—282no—
553C42C2×C4×D711yescharacteristic
554C42C2×C4×D711yescharacteristic
555C42D4×D711yescharacteristic
556C42D4×D711yescharacteristic
557C2×C7—21no—
558C2×C7—21no—
559C2×C7C2×#41011yescharacteristic
560C2×C7C22×#10311yescharacteristic
561C2×C7C22×#10411yescharacteristic
562D7—22no—
563D7#150314yesdirect product factor
564C23—71no—
565C23—71no—
566C23—72no—
567C23—72no—
568C23—142no—
569C23—142no—
570C23C2×D4×D711yescharacteristic
571Q8—42no—
572Q8—42no—
573Q8—282no—
574Q8—284no—
575Q8—284no—
576Q8—282no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—71no—
585C2×C4—71no—
586C2×C4—71no—
587C2×C4—72no—
588C2×C4—72no—
589C2×C4—74no—
590C2×C4—74no—
591C2×C4—74no—
592C2×C4—74no—
593C2×C4—74no—
594C2×C4—71no—
595C2×C4—71no—
596C2×C4—71no—
597C2×C4—142no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—142no—
601C2×C4—142no—
602C2×C4—142no—
603C2×C4—144no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4—284no—
609C2×C4—284no—
610C2×C4—2816no—
611C2×C4—281no—
612C2×C4—282no—
613C2×C4—282no—
614C2×C4D7×C22⋊C411yescharacteristic
615C2×C4D7×C22⋊C411yescharacteristic
616C2×C4D7×C22⋊C411yescharacteristic
617C2×C4D7×C22⋊C411yescharacteristic
618C2×C4D7×SD1612yes—
619C2×C4D7×Q1612yes—
620C2×C4C22×C4×D711yescharacteristic
621C2×C4C2×D4×D711yescharacteristic
622C8—42no—
623C8—282no—
624C7C2×#150311yescharacteristic, complemented, Sylow
625C22—21no—
626C22—21no—
627C22—72no—
628C22—72no—
629C22—72no—
630C22—72no—
631C22—144no—
632C22—144no—
633C22—141no—
634C22—141no—
635C22C2×D7×C22⋊C411yescharacteristic
636C22C2×D7×SD1611yescharacteristic
637C22C2×D7×Q1611yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—44no—
642C4—42no—
643C4—42no—
644C4—72no—
645C4—72no—
646C4—72no—
647C4—141no—
648C4—141no—
649C4—141no—
650C4—284no—
651C4—282no—
652C4—282no—
653C4D7×#10312yes—
654C4D7×#10312yes—
655C4D7×#10412yes—
656C2—21no—
657C2—21no—
658C2—74no—
659C2—142no—
660C2D7×#41011yescharacteristic
661C2C2×D7×#10311yescharacteristic
662C2C2×D7×#10411yescharacteristic
subgroupG/H
centerC2×C4D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1503C2
socleC22×C7C22×C22⋊C4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1503D7
hypocenterC7C2×#1503
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
4. C7×#1503C2semidirect
5. #11729589C2semidirect
6. #11728546C2semidirect
7. #11727225C2semidirect
9. #11726063C2semidirect
11. #90419C4semidirect
12. #90419C4semidirect
13. D7×C4⋊Q8C4semidirect
14. D7×C4⋊Q8C4semidirect
22. #90269C4semidirect
24. C4×Q8×D7C4semidirect
56. C7×C4⋊Q8C2×C4semidirect
57. C7×C4⋊Q8C2×C4semidirect
62. C4×C7×Q8C2×C4semidirect
70. Q8×Dic7C2×C4semidirect
72. #6507C2×C4semidirect
104. #6451C2×C4semidirect
108. #6450C2×C4semidirect
125. #6432C2×C4semidirect
126. #6432C2×C4semidirect
130. C4×Dic14C2×C4semidirect
150. #1503D7direct (N × H)
357. C4⋊Q8C4×D7semidirect
358. C4⋊Q8C4×D7semidirect
388. C4×Q8C4×D7semidirect
563. D7#1503direct (N × H)
624. C7C2×#1503semidirect

Maximal subgroups

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

subgroupindex
D7×#5332
D7×#4312
C4×D7×C4⋊C42
C7×#15032
#117295892
#117285462
#117272252
D7×#3282
#117260632
C2×#15037