Finite Group Databasebeta

← #13275537

Subgroups — #13275537

Order 1792.

1598 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic
3C2×C4×Dic7⋊C4C211yesmaximal, characteristic
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic
5C2×#89704C211yesmaximal, characteristic
6#11729322C212yesmaximal
7#11729320C212yesmaximal
8C4×C7⋊#95C211yesmaximal, characteristic
9C4×C7⋊#95C211yesmaximal, characteristic
10#11727167C212yesmaximal
11#11727163C212yesmaximal
12C22×C7×C4⋊C4C2212yes—
13C22×C42×C7C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×Dic7⋊C4C2212yes—
17C22×Dic7⋊C4C2212yes—
18C22×Dic7⋊C4C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C4×C7×C4⋊C4—24no—
25C2×C7×#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36#89704—24no—
37C4×Dic7⋊C4—24no—
38C4×Dic7⋊C4—24no—
39C4×Dic7⋊C4C418yescomplemented
40#13848—71nomaximal, Sylow
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C2×C7×C4⋊C4—24no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—24no—
55C2×C42×C7—22no—
56C2×C42×C7—22no—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7—22no—
61C2×C42×C7—22no—
62C2×C42×C7C2×C414yes—
63C2×C42×C7D414yes—
64C2×Dic7⋊C4—24no—
65C2×Dic7⋊C4—24no—
66C2×Dic7⋊C4—24no—
67C2×Dic7⋊C4—24no—
68C2×Dic7⋊C4—24no—
69C2×Dic7⋊C4—24no—
70C2×Dic7⋊C4—24no—
71C2×Dic7⋊C4—24no—
72C2×Dic7⋊C4C2×C414yes—
73C2×Dic7⋊C4C2×C414yes—
74C2×C4×Dic7—22no—
75C2×C4×Dic7—22no—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—22no—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—22no—
81C2×C4×Dic7C2×C414yes—
82C2×C4×Dic7C2×C414yes—
83C2×C4×Dic7D414yes—
84C2×C4×Dic7Q814yes—
85C2×C4×Dic7Q814yes—
86C7×#95—24no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—24no—
92C7⋊#95—24no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95C2×C414yes—
96C7⋊#95C2×C414yes—
97C2×C4×C4⋊C4—71no—
98C2×C4×C4⋊C4—71no—
99C2×C4×C4⋊C4—71no—
100C2×C4×C4⋊C4D711yescharacteristic
101C2×#376—71no—
102#1444—72no—
103#1442—72no—
104#1441—72no—
105#1441—72no—
106C4×#95—71no—
107C4×#95—71no—
108C24×C7C2411yescharacteristic
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—21no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7C22×C412yes—
129C22×C4×C7C22×C412yes—
130C22×C4×C7C22×C412yes—
131C22×C4×C7C2×D414yes—
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2×Q812yes—
135C22×C4×C7C2×Q812yes—
136C22×C4×C7#4114yes—
137C22×C4×C7#4114yes—
138C22×C4×C7#4112yes—
139C22×C4×C7#4112yes—
140C22×Dic7—21no—
141C22×Dic7—21no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—21no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7C22×C412yes—
164C22×Dic7C22×C412yes—
165C22×Dic7C22×C412yes—
166C22×Dic7C22×C412yes—
167C22×Dic7C2×D412yes—
168C22×Dic7C2×D412yes—
169C22×Dic7C2×Q814yes—
170C22×Dic7C2×Q812yes—
171C22×Dic7C2×Q812yes—
172C22×Dic7#4114yes—
173C22×Dic7#4114yes—
174C7×C4⋊C4—216no—
175C42×C7—28no—
176C42×C7—28no—
177C42×C7—44no—
178Dic7⋊C4—216no—
179Dic7⋊C4—216no—
180Dic7⋊C4—28no—
181Dic7⋊C4—28no—
182C4×Dic7—28no—
183C4×Dic7—28no—
184C4×Dic7—44no—
185C4×Dic7C4⋊C4116yescomplemented
186C22×C4⋊C4—71no—
187C22×C4⋊C4—71no—
188C22×C4⋊C4—72no—
189C22×C4⋊C4—72no—
190C22×C4⋊C4C2×D712yes—
191C22×C42—71no—
192C22×C42—71no—
193C22×C42—71no—
194C22×C42—71no—
195C22×C42C2×D711yescharacteristic
196C22×C42C2×D711yescharacteristic
197C22×C42C2×D711yescharacteristic
198C4×C4⋊C4—24no—
199C4×C4⋊C4—78no—
200C4×C4⋊C4—144no—
201C4×C4⋊C4—144no—
202#376—144no—
203C2×#95—71no—
204C2×#95—71no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—72no—
210C2×#95—72no—
211C2×#95—72no—
212C2×#95—72no—
213C2×#95C2×D712yes—
214C23×C7C23×C411yescharacteristic
215C23×C7C22×D411yescharacteristic
216C23×C7C22×D411yescharacteristic
217C23×C7C22×Q811yescharacteristic
218C23×C7C22×Q811yescharacteristic
219C23×C7C2×#4112yes—
220C23×C7C2×#4111yescharacteristic
221C23×C7C2×#4112yes—
222C23×C7C2×#4111yescharacteristic
223C23×C7C2×#4112yes—
224C23×C7C2×#4112yes—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—24no—
228C2×C4×C7—24no—
229C2×C4×C7—22no—
230C2×C4×C7—22no—
231C2×C4×C7—22no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7C2×C4⋊C414yes—
249C2×C4×C7#11714yes—
250C2×C4×C7C4×D414yes—
251C2×C4×C7C4×Q814yes—
252C2×C4×C7#12114yes—
253C2×C4×C7C22⋊Q814yes—
254C2×C4×C7#12514yes—
255C2×C4×C7C4⋊Q814yes—
256C2×Dic7—22no—
257C2×Dic7—22no—
258C2×Dic7—22no—
259C2×Dic7—22no—
260C2×Dic7—22no—
261C2×Dic7—22no—
262C2×Dic7—24no—
263C2×Dic7—24no—
264C2×Dic7—24no—
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—24no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—24no—
272C2×Dic7—24no—
273C2×Dic7—24no—
274C2×Dic7—24no—
275C2×Dic7—24no—
276C2×Dic7—24no—
277C2×Dic7—42no—
278C2×Dic7—42no—
279C2×Dic7—42no—
280C2×Dic7—42no—
281C2×Dic7—42no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7C2×C4⋊C414yes—
288C2×Dic7C2×C4⋊C414yes—
289C2×Dic7#11714yes—
290C23×C4—71no—
291C23×C4—71no—
292C23×C4—71no—
293C23×C4—72no—
294C23×C4—71no—
295C23×C4—72no—
296C23×C4C22×D711yescharacteristic
297C23×C4C22×D712yes—
298C23×C4C22×D712yes—
299C23×C4C22×D711yescharacteristic
300C23×C4C22×D711yescharacteristic
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—74no—
305C2×C4⋊C4—74no—
306C2×C4⋊C4—144no—
307C2×C4⋊C4—144no—
308C2×C4⋊C4—144no—
309C2×C4⋊C4—144no—
310C2×C4⋊C4—144no—
311C2×C4⋊C4—144no—
312C2×C4⋊C4—144no—
313C2×C4⋊C4—144no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—74no—
322C2×C42—74no—
323C2×C42—74no—
324C2×C42—74no—
325C2×C42—74no—
326C2×C42—142no—
327C2×C42—142no—
328C2×C42—142no—
329C2×C42—142no—
330C2×C42—142no—
331C2×C42—142no—
332C2×C42—142no—
333C2×C42C4×D714yes—
334C2×C42C22⋊D714yes—
335#95—24no—
336#95—74no—
337#95—74no—
338#95—144no—
339#95—144no—
340#95—144no—
341#95—144no—
342#95—144no—
343#95—144no—
344#95—144no—
345#95—144no—
346C22×C7C22×C4⋊C411yescharacteristic
347C22×C7C2×#11711yescharacteristic
348C22×C7C2×#11711yescharacteristic
349C22×C7C2×C4×D411yescharacteristic
350C22×C7C2×C4×Q811yescharacteristic
351C22×C7C4×#4111yescharacteristic
352C22×C7C4×#4111yescharacteristic
353C22×C7C2×#12111yescharacteristic
354C22×C7C2×C22⋊Q811yescharacteristic
355C22×C7#52512yes—
356C22×C7#52512yes—
357C22×C7#52512yes—
358C22×C7C2×#12511yescharacteristic
359C22×C7#52912yes—
360C22×C7#52912yes—
361C22×C7#52912yes—
362C22×C7#52912yes—
363C22×C7C2×C4⋊Q811yescharacteristic
364C22×C7#53212yes—
365C22×C7#53312yes—
366C22×C7#53312yes—
367C22×C7#53312yes—
368C22×C7#53312yes—
369C4×C7—24no—
370C4×C7—44no—
371C4×C7—44no—
372C4×C7—42no—
373C4×C7#38918yes—
374Dic7—24no—
375Dic7—24no—
376Dic7—24no—
377Dic7—44no—
378Dic7—44no—
379Dic7—42no—
380C24C23×D711yescharacteristic
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—72no—
401C22×C4—72no—
402C22×C4—72no—
403C22×C4—72no—
404C22×C4—72no—
405C22×C4—72no—
406C22×C4—72no—
407C22×C4—74no—
408C22×C4—72no—
409C22×C4—74no—
410C22×C4—74no—
411C22×C4—141no—
412C22×C4—142no—
413C22×C4—142no—
414C22×C4—142no—
415C22×C4—142no—
416C22×C4—142no—
417C22×C4—141no—
418C22×C4—142no—
419C22×C4—142no—
420C22×C4—142no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—141no—
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—141no—
433C22×C4—142no—
434C22×C4C2×C4×D712yes—
435C22×C4C2×C4×D712yes—
436C22×C4C2×C4×D712yes—
437C22×C4#115714yes—
438C22×C4#115714yes—
439C22×C4#115712yes—
440C22×C4D4×D712yes—
441C22×C4#115912yes—
442C22×C4Q8×D712yes—
443C22×C4Q8×D712yes—
444C22×C4C2×C22⋊D714yes—
445C22×C4C2×C22⋊D712yes—
446C4⋊C4—216no—
447C4⋊C4—148no—
448C4⋊C4—1416no—
449C4⋊C4—1416no—
450C4⋊C4—148no—
451C42—28no—
452C42—28no—
453C42—44no—
454C42—716no—
455C42—148no—
456C42—148no—
457C42—284no—
458C2×C7#228511yescharacteristic
459C2×C7#229011yescharacteristic
460C2×C7#229011yescharacteristic
461C2×C7C2×#38911yescharacteristic
462C2×C7#229511yescharacteristic
463C2×C7#229511yescharacteristic
464C2×C7#229611yescharacteristic
465C2×C7#239212yes—
466C2×C7#239612yes—
467C2×C7#239912yes—
468C2×C7#240212yes—
469C23C22×C4×D711yescharacteristic
470C23C2×#115712yes—
471C23C2×#115712yes—
472C23C2×#115711yescharacteristic
473C23C2×D4×D711yescharacteristic
474C23C2×#115911yescharacteristic
475C23C2×Q8×D711yescharacteristic
476C23C2×Q8×D711yescharacteristic
477C23D7×#4112yes—
478C23D7×#4112yes—
479C23C22×C22⋊D711yescharacteristic
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—74no—
504C2×C4—74no—
505C2×C4—74no—
506C2×C4—142no—
507C2×C4—142no—
508C2×C4—142no—
509C2×C4—142no—
510C2×C4—142no—
511C2×C4—144no—
512C2×C4—142no—
513C2×C4—144no—
514C2×C4—144no—
515C2×C4—144no—
516C2×C4—144no—
517C2×C4—144no—
518C2×C4—142no—
519C2×C4—142no—
520C2×C4—144no—
521C2×C4—142no—
522C2×C4—144no—
523C2×C4—144no—
524C2×C4—144no—
525C2×C4—144no—
526C2×C4—144no—
527C2×C4—282no—
528C2×C4—282no—
529C2×C4—282no—
530C2×C4—282no—
531C2×C4—282no—
532C2×C4—282no—
533C2×C4—282no—
534C2×C4—282no—
535C2×C4—282no—
536C2×C4—282no—
537C2×C4#643514yes—
538C2×C4#645014yes—
539C2×C4#645214yes—
540C2×C4D7×C4⋊C414yes—
541C2×C4#645914yes—
542C2×C4C4×C22⋊D714yes—
543C2×C4#650214yes—
544C2×C4#650714yes—
545C7#1384811yescharacteristic, complemented, Sylow
546C22C2×#643511yescharacteristic
547C22C4×#115711yescharacteristic
548C22#9017012yes—
549C22C2×#645011yescharacteristic
550C22C2×#645211yescharacteristic
551C22C2×D7×C4⋊C411yescharacteristic
552C22C2×#645911yescharacteristic
553C22D7×#11711yescharacteristic
554C22#9021311yescharacteristic
555C22#9021912yes—
556C22#9022912yes—
557C22#9023812yes—
558C22#9023912yes—
559C22#9024812yes—
560C22#9026912yes—
561C22#9026912yes—
562C22#9026912yes—
563C22#9026912yes—
564C22C2×C4×C22⋊D711yescharacteristic
565C22#9048212yes—
566C22C2×#650211yescharacteristic
567C22C2×#650711yescharacteristic
568C22#9051912yes—
569C4—24no—
570C4—42no—
571C4—44no—
572C4—44no—
573C4—144no—
574C4—144no—
575C4—144no—
576C4—284no—
577C4—282no—
578C4—284no—
579C4#8974418yes—
580C2#1173106311yescharacteristic
581C2#1173106411yescharacteristic
582C2#1173111512yes—
583C2#1173119811yescharacteristic
584C2#1173120011yescharacteristic
585C2#1173122312yes—
586C2#1173951011yescharacteristic
587C2C2×#8974411yescharacteristic
588C2#1173971311yescharacteristic
589C2#1173979012yes—
590C2#1173991212yes—
subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#13848
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
39. C4×Dic7⋊C4C4semidirect
185. C4×Dic7C4⋊C4semidirect
545. C7#13848semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×C4×Dic7⋊C42
C2×#897042
#117293222
#117293202
C4×C7⋊#952
#117271672
#117271632
#138487