Finite Group Databasebeta

← #13361377

Subgroups — #13361377

Order 1792.

880 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×Dic7C211yesmaximal, characteristic
2C2×#89563C211yesmaximal, characteristic
3#11733412C211yesmaximal, characteristic
4C7×#1865C211yesmaximal, characteristic
5#11729383C211yesmaximal, characteristic
6#11728317C211yesmaximal, characteristic
7Dic7×#106C211yesmaximal, characteristic
8#11727975C211yesmaximal, characteristic
9Dic7×#103C211yesmaximal, characteristic
10Dic7×#103C211yesmaximal, characteristic
11#11727355C211yesmaximal, characteristic
12#11726554C211yesmaximal, characteristic
13#11726538C211yesmaximal, characteristic
14#11726376C211yesmaximal, characteristic
15#11726356C211yesmaximal, characteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×Q8×Dic7C2211yescharacteristic
19C2×#6451C2211yescharacteristic
20C2×#6450—21no—
21C2×C7×#106C2211yescharacteristic
22C2×C7×#103C2211yescharacteristic
23C2×C7×#103C2211yescharacteristic
24C7×#389C2211yescharacteristic
25C2×#6409C2211yescharacteristic
26C2×#6409C2211yescharacteristic
27C2×#6391C2211yescharacteristic
28C2×Dic7⋊C8C2211yescharacteristic
29C2×Dic7⋊C8C2211yescharacteristic
30C2×C8×Dic7C2211yescharacteristic
31C2×C8×Dic7C2211yescharacteristic
32#89748C2211yescharacteristic
33C4⋊C4×Dic7—21no—
34C4⋊C4×Dic7—21no—
35C4⋊C4×Dic7C2211yescharacteristic
36C4⋊C4×Dic7C2211yescharacteristic
37C4⋊C4×Dic7C2211yescharacteristic
38C4⋊C4×Dic7C2211yescharacteristic
39#89744—21no—
40C2×#6382C2211yescharacteristic
41C2×#6382C2211yescharacteristic
42C4×C4⋊Dic7—21no—
43C4×C4⋊Dic7C2211yescharacteristic
44C42×Dic7—21no—
45C42×Dic7C2211yescharacteristic
46#89700C2211yescharacteristic
47#89563C418yescomplemented
48#89421—21no—
49#89418—21no—
50C7×#340C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89319C2211yescharacteristic
60C4×#475—71nomaximal, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×Dic14—21no—
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C4×C7×Q8—22no—
66C4×C7×Q8—22no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C42×C7—21no—
73C2×C42×C7C2311yescharacteristic
74Q8×Dic7—22no—
75Q8×Dic7—22no—
76Q8×Dic7C2×C414yes—
77Q8×Dic7Q814yescomplemented
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7—21no—
80C2×C4⋊Dic7C2311yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×Dic7⋊C4—21no—
85C2×Dic7⋊C4—21no—
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—21no—
88C2×C4×Dic7—21no—
89C2×C4×Dic7—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7D411yescharacteristic
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7D411yescharacteristic
99C2×C4×Dic7C2311yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103#6451—22no—
104#6451C2×C414yes—
105#6450—44no—
106C7×#106—22no—
107C7×#103—22no—
108C7×#103C2×C414yes—
109C7×#95—21no—
110#6409—22no—
111#6409C2×C414yes—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118#6391C2×C414yes—
119Dic7⋊C8—22no—
120Dic7⋊C8C2×C414yes—
121C8×Dic7—22no—
122C8×Dic7—22no—
123#6382—22no—
124#6382C2×C414yes—
125C2×#475—71no—
126C4×C4⋊Q8—71no—
127C42×Q8—71no—
128#1988—71no—
129#1948—71no—
130#1919—71no—
131#1919—71no—
132#1865—71no—
133#1865D711yescharacteristic
134#1803—71no—
135C4×#106—71no—
136C4×#106—71no—
137C4×C4⋊C8—71no—
138C4×#103—71no—
139C4×#103—71no—
140C2×C7×Q8—21no—
141C2×C7×Q8—21no—
142C2×C7×Q8—21no—
143C2×C7×Q8C22×C412yes—
144C2×C7×Q8C2×Q812yes—
145C2×C7×Q8#4112yes—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2411yescharacteristic
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7C2×D411yescharacteristic
158C22×Dic7C2×D411yescharacteristic
159C22×Dic7C2×D411yescharacteristic
160C22×Dic7C2×D411yescharacteristic
161C2×Dic14—24no—
162C2×Dic14—42no—
163C2×Dic14—42no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8C22×C412yes—
170C7×C4⋊C4—24no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—42no—
176C7×C4⋊C4C22×C412yes—
177C7×C4⋊C4#4112yes—
178C42×C7—24no—
179C42×C7—21no—
180C42×C7—21no—
181C4⋊Dic7—21no—
182C4⋊Dic7—21no—
183C4⋊Dic7—21no—
184C4⋊Dic7—24no—
185C4⋊Dic7—24no—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7C22×C412yes—
189C4⋊Dic7C22×C412yes—
190C4⋊Dic7C2×Q812yes—
191Dic7⋊C4—24no—
192Dic7⋊C4—42no—
193Dic7⋊C4—42no—
194Dic7⋊C4—42no—
195C4×Dic7—24no—
196C4×Dic7—24no—
197C4×Dic7—22no—
198C4×Dic7—22no—
199C4×Dic7—41no—
200C4×Dic7—42no—
201C4×Dic7—42no—
202C4×Dic7—42no—
203C4×Dic7—42no—
204C4×Dic7—42no—
205C4×Dic7SD1614yes—
206C4×Dic7C22×C412yes—
207C4×Dic7C2×Q812yes—
208C4×Dic7#4112yes—
209C4×Dic7#4112yes—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8C22×C412yes—
216C2×C4⋊Q8—71no—
217C2×C4×Q8—71no—
218C2×C4×Q8—71no—
219C2×C4×Q8—141no—
220C2×C4×Q8C2×D711yescharacteristic
221#475—78no—
222C2×#106—71no—
223C2×#106—71no—
224C2×#106—71no—
225C2×#106C2×D711yescharacteristic
226C2×C4⋊C8—71no—
227C2×C4⋊C8—71no—
228C2×#103—71no—
229C2×#103—71no—
230C2×#103C2×D711yescharacteristic
231C2×#103C2×D711yescharacteristic
232C2×C4×C8—71no—
233C2×C4×C8—71no—
234#391—141no—
235#389—71no—
236#389—141no—
237#389C2×D711yescharacteristic
238#384—71no—
239C4×C4⋊C4—71no—
240C4×C4⋊C4—71no—
241C4×C4⋊C4—71no—
242C4×C4⋊C4—71no—
243C4×C4⋊C4—71no—
244C4×C4⋊C4—141no—
245C4×C4⋊C4—141no—
246C4×C4⋊C4—141no—
247C4×C4⋊C4—141no—
248C43—71no—
249C43—141no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#340C2×D711yescharacteristic
258#336—71no—
259#336C2×D711yescharacteristic
260C23×C7C22×D411yescharacteristic
261C7×Q8—22no—
262C7×Q8—22no—
263C7×Q8—22no—
264C7×Q8C4×Q814yescomplemented
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—21no—
268C2×C4×C7—22no—
269C2×C4×C7—21no—
270C2×C4×C7—22no—
271C2×C4×C7—21no—
272C2×C4×C7—22no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7C2×SD1612yes—
283C2×C4×C7C23×C411yescharacteristic
284C2×C4×C7C22×Q811yescharacteristic
285C2×C4×C7C2×#4111yescharacteristic
286C2×C4×C7C2×#4111yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C2×C4×C7C2×#4111yescharacteristic
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—21no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—41no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7C4×D412yes—
306C2×Dic7C4×D412yes—
307C2×Dic7C22⋊Q812yes—
308C2×Dic7C22⋊Q812yes—
309C2×Dic7C2×SD1612yes—
310C2×Dic7C2×SD1612yes—
311C2×Dic7#13512yes—
312C2×Dic7#13712yes—
313Dic14—48no—
314C7×C8—22no—
315C7×C8—41no—
316C7⋊C8—22no—
317C7⋊C8—41no—
318C22×Q8—141no—
319C22×Q8C22×D711yescharacteristic
320C22×C8—71no—
321C22×C8—71no—
322C22×C8C22×D711yescharacteristic
323C22×C8C22×D711yescharacteristic
324C4⋊Q8—74no—
325C4⋊Q8—142no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—74no—
329C4×Q8—74no—
330C4×Q8—142no—
331C4×Q8—142no—
332C4×Q8—284no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—71no—
337C2×C4⋊C4—71no—
338C2×C4⋊C4—71no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4—141no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—141no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4C22×D711yescharacteristic
346C2×C4⋊C4C22×D711yescharacteristic
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C42—21no—
349C2×C42—71no—
350C2×C42—71no—
351C2×C42—71no—
352C2×C42—71no—
353C2×C42—71no—
354C2×C42—71no—
355C2×C42—141no—
356C2×C42—141no—
357C2×C42—141no—
358C2×C42—141no—
359C2×C42—141no—
360C2×C42—141no—
361C2×C42—141no—
362C2×C42C22×D711yescharacteristic
363#106—22no—
364#106—74no—
365#106—74no—
366#106—142no—
367C4⋊C8—74no—
368C4⋊C8—142no—
369#103—22no—
370#103—74no—
371#103—142no—
372#103C4×D714yes—
373C4×C8—142no—
374C4×C8—142no—
375#95—21no—
376#95—141no—
377#95—141no—
378#95—141no—
379#95—141no—
380#95—141no—
381#95—141no—
382C22×C7C2×C4×D411yescharacteristic
383C22×C7C2×C22⋊Q811yescharacteristic
384C22×C7#52511yescharacteristic
385C22×C7C22×SD1611yescharacteristic
386C22×C7C2×#13511yescharacteristic
387C22×C7C2×#13711yescharacteristic
388C22×C7#57511yescharacteristic
389C4×C7—22no—
390C4×C7—24no—
391C4×C7—41no—
392C4×C7—42no—
393C4×C7—42no—
394C4×C7—81no—
395C4×C7C2×C4×Q811yescharacteristic
396C4×C7C4×#4111yescharacteristic
397C4×C7#52911yescharacteristic
398C4×C7#53311yescharacteristic
399Dic7—22no—
400Dic7—22no—
401Dic7—42no—
402Dic7—42no—
403Dic7—42no—
404Dic7—81no—
405Dic7C4×SD1614yes—
406Dic7#47514yescomplemented
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—144no—
411C2×Q8—282no—
412C2×Q8—282no—
413C2×Q8C2×C4×D712yes—
414C2×Q8#115912yes—
415C2×Q8Q8×D712yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—71no—
421C22×C4—71no—
422C22×C4—71no—
423C22×C4—71no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—141no—
427C22×C4—141no—
428C22×C4D4×D711yescharacteristic
429C22×C4D4×D711yescharacteristic
430C22×C4C23×D711yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—72no—
437C2×C8—141no—
438C2×C8—141no—
439C2×C8—141no—
440C2×C8—141no—
441C2×C8—141no—
442C2×C8C2×C4×D712yes—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—72no—
450C4⋊C4—72no—
451C4⋊C4—72no—
452C4⋊C4—144no—
453C4⋊C4—144no—
454C4⋊C4—144no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—282no—
461C4⋊C4—282no—
462C4⋊C4—282no—
463C4⋊C4C2×C4×D712yes—
464C4⋊C4#115912yes—
465C42—24no—
466C42—21no—
467C42—21no—
468C42—74no—
469C42—72no—
470C42—72no—
471C42—72no—
472C42—72no—
473C42—142no—
474C42—142no—
475C42—144no—
476C42—144no—
477C42—281no—
478C42—282no—
479C42—282no—
480C42—282no—
481C42—282no—
482C42—282no—
483C2×C7C4×C22⋊Q811yescharacteristic
484C2×C7C2×C4×SD1611yescharacteristic
485C2×C7C4×#13711yescharacteristic
486C2×C7C2×#47511yescharacteristic
487C2×C7#307611yescharacteristic
488C2×C7#310311yescharacteristic
489C2×C7#310711yescharacteristic
490C23C2×D4×D711yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—22no—
494Q8—288no—
495Q8#645014yescomplemented
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—72no—
514C2×C4—72no—
515C2×C4—72no—
516C2×C4—72no—
517C2×C4—72no—
518C2×C4—72no—
519C2×C4—72no—
520C2×C4—72no—
521C2×C4—141no—
522C2×C4—141no—
523C2×C4—141no—
524C2×C4—141no—
525C2×C4—142no—
526C2×C4—142no—
527C2×C4—142no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4D7×SD1612yes—
538C2×C4C22×C4×D711yescharacteristic
539C2×C4C2×#115911yescharacteristic
540C2×C4C2×#115911yescharacteristic
541C2×C4C2×Q8×D711yescharacteristic
542C2×C4D7×#4111yescharacteristic
543C2×C4D7×#4111yescharacteristic
544C8—22no—
545C8—41no—
546C8—142no—
547C8—281no—
548C7C4×#47511yescharacteristic, complemented, Sylow
549C22C4×D4×D711yescharacteristic
550C22#9027711yescharacteristic
551C22D7×C22⋊Q811yescharacteristic
552C22C2×D7×SD1611yescharacteristic
553C22D7×#13511yescharacteristic
554C22D7×#13711yescharacteristic
555C22#9046811yescharacteristic
556C4—24no—
557C4—22no—
558C4—42no—
559C4—41no—
560C4—42no—
561C4—74no—
562C4—74no—
563C4—81no—
564C4—142no—
565C4—142no—
566C4—282no—
567C4—282no—
568C4—282no—
569C4—561no—
570C4C2×#645011yescharacteristic
571C4C4×#115911yescharacteristic
572C4#9031311yescharacteristic
573C4#9034011yescharacteristic
574C2#1173182611yescharacteristic
575C2C4×D7×SD1611yescharacteristic
576C2#1173727411yescharacteristic
577C2#1173747311yescharacteristic
578C2#1173765811yescharacteristic
579C2D7×#47511yescharacteristic
580C2#1173867411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1865C2
socle, prime radicalC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenter#1865D7
hypocenterC7C4×#475
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
47. #89563C4semidirect
77. Q8×Dic7Q8semidirect
264. C7×Q8C4×Q8semidirect
406. Dic7#475semidirect
495. Q8#6450semidirect
548. C7C4×#475semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×Dic72
C2×#895632
#117334122
C7×#18652
#117293832
#117283172
Dic7×#1062
#117279752
Dic7×#1032
#117273552
#117265542
#117265382
#117263762
#117263562
C4×#4757