Finite Group Databasebeta

← #13276468

Subgroups — #13276468

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89744C212yesmaximal
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic
3C2×#89419C212yesmaximal
4C2×#89422C211yesmaximal, characteristic
5C2×#89421C211yesmaximal, characteristic
6C7×#1444C211yesmaximal, characteristic
7#11729322C211yesmaximal, characteristic
8#11729317C212yesmaximal
9#11727174C211yesmaximal, characteristic
10#11727173C211yesmaximal, characteristic
11Dic7⋊#95C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4⋊Dic7C2212yes—
16C22×Dic7⋊C4C2211yescharacteristic
17C22×Dic7⋊C4C2211yescharacteristic
18C22×Dic7⋊C4C2212yes—
19C22×Dic7⋊C4C2212yes—
20C22×Dic7⋊C4C2212yes—
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C2×C7×#95C2212yes—
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C4⋊C4×Dic7—24no—
36#89744—28no—
37#89422—24no—
38#89421C418yescomplemented
39#89419—28no—
40#13954—71nomaximal, Sylow
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2312yes—
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2311yescharacteristic
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4—42no—
57C2×C4⋊Dic7—22no—
58C2×C4⋊Dic7—24no—
59C2×C4⋊Dic7—24no—
60C2×C4⋊Dic7—24no—
61C2×C4⋊Dic7—42no—
62C2×Dic7⋊C4—24no—
63C2×Dic7⋊C4—24no—
64C2×Dic7⋊C4—24no—
65C2×Dic7⋊C4—22no—
66C2×Dic7⋊C4—22no—
67C2×Dic7⋊C4—24no—
68C2×Dic7⋊C4—24no—
69C2×Dic7⋊C4—24no—
70C2×Dic7⋊C4—42no—
71C2×Dic7⋊C4—42no—
72C2×Dic7⋊C4C2×C418yes—
73C2×Dic7⋊C4D418yes—
74C2×Dic7⋊C4Q818yes—
75C2×C4×Dic7—24no—
76C2×C4×Dic7—24no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—42no—
79C2×C4×Dic7—42no—
80C2×C4×Dic7C2×C418yes—
81C2×C4×Dic7C2×C414yes—
82C2×C4×Dic7D414yes—
83C2×C4×Dic7Q814yes—
84C7×#95—24no—
85C7×#95—22no—
86C7×#95C2×C414yes—
87C7⋊#95—22no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—22no—
91C7⋊#95—22no—
92C7⋊#95—24no—
93C7⋊#95—24no—
94C7⋊#95C2×C414yes—
95C2×#389—72no—
96C2×#389—72no—
97C2×#382—71no—
98C2×C4×C4⋊C4—71no—
99C2×C4×C4⋊C4—71no—
100#1444—71no—
101#1444—71no—
102#1444—71no—
103#1444D711yescharacteristic
104C4⋊#95—72no—
105C4⋊#95—72no—
106C24×C7C2411yescharacteristic
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7C22×C412yes—
130C22×C4×C7C22×C414yes—
131C22×C4×C7C2×D412yes—
132C22×C4×C7C2×D414yes—
133C22×C4×C7C2×Q812yes—
134C22×C4×C7C2×Q814yes—
135C22×C4×C7#4114yes—
136C22×Dic7—22no—
137C22×Dic7—22no—
138C22×Dic7—21no—
139C22×Dic7—21no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—21no—
143C22×Dic7—21no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7C22×C414yes—
161C22×Dic7C22×C412yes—
162C22×Dic7C22×C412yes—
163C22×Dic7C2×D412yes—
164C22×Dic7C2×D414yes—
165C22×Dic7C2×D412yes—
166C22×Dic7C2×D414yes—
167C22×Dic7C2×Q812yes—
168C22×Dic7C2×Q814yes—
169C22×Dic7C2×Q812yes—
170C22×Dic7C2×Q814yes—
171C22×Dic7#4114yes—
172C7×C4⋊C4—28no—
173C7×C4⋊C4—48no—
174C4⋊Dic7—28no—
175C4⋊Dic7—48no—
176Dic7⋊C4—48no—
177Dic7⋊C4—48no—
178Dic7⋊C4—44no—
179Dic7⋊C4—44no—
180Dic7⋊C4C4⋊C4132yescomplemented
181C4×Dic7—48no—
182C4×Dic7—48no—
183C4×Dic7C4⋊C4116yescomplemented
184C22×C4⋊C4—72no—
185C22×C4⋊C4—71no—
186C22×C4⋊C4—71no—
187C22×C4⋊C4—71no—
188C22×C4⋊C4—72no—
189C22×C4⋊C4—72no—
190C22×C4⋊C4—72no—
191C22×C4⋊C4C2×D711yescharacteristic
192C22×C4⋊C4C2×D712yes—
193C22×C42—71no—
194C22×C42—72no—
195C22×C42—72no—
196#389—148no—
197#389—148no—
198#382—144no—
199C4×C4⋊C4—78no—
200C4×C4⋊C4—144no—
201C2×#95—71no—
202C2×#95—72no—
203C2×#95—71no—
204C2×#95—71no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—71no—
209C2×#95C2×D712yes—
210C2×#95C2×D711yescharacteristic
211C2×#95C2×D711yescharacteristic
212C23×C7C23×C411yescharacteristic
213C23×C7C22×D411yescharacteristic
214C23×C7C22×D412yes—
215C23×C7C22×Q811yescharacteristic
216C23×C7C22×Q812yes—
217C23×C7C2×#4112yes—
218C23×C7C2×#4112yes—
219C23×C7H(5,𝔽2)11yescharacteristic
220C23×C7H(5,𝔽2)11yescharacteristic
221C23×C72−1+411yescharacteristic
222C23×C72−1+411yescharacteristic
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—41no—
241C2×C4×C7—41no—
242C2×C4×C7—41no—
243C2×C4×C7—41no—
244C2×C4×C7—41no—
245C2×C4×C7—41no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7C2×C4⋊C414yes—
251C2×C4×C7C2×C4⋊C418yes—
252C2×Dic7—24no—
253C2×Dic7—22no—
254C2×Dic7—24no—
255C2×Dic7—22no—
256C2×Dic7—22no—
257C2×Dic7—22no—
258C2×Dic7—22no—
259C2×Dic7—22no—
260C2×Dic7—24no—
261C2×Dic7—24no—
262C2×Dic7—24no—
263C2×Dic7—24no—
264C2×Dic7—24no—
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—42no—
268C2×Dic7—42no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7—41no—
272C2×Dic7—41no—
273C2×Dic7—41no—
274C2×Dic7—41no—
275C2×Dic7—41no—
276C2×Dic7—41no—
277C2×Dic7—42no—
278C2×Dic7—42no—
279C2×Dic7—42no—
280C2×Dic7—42no—
281C2×Dic7C2×C4⋊C414yes—
282C2×Dic7C2×C4⋊C418yes—
283C2×Dic7C2×C4⋊C414yes—
284C2×Dic7C2×C4⋊C418yes—
285C2×Dic7#12714yes—
286C2×Dic7C4⋊Q814yes—
287C2×Dic7C4⋊Q818yes—
288C23×C4—71no—
289C23×C4—72no—
290C23×C4—71no—
291C23×C4—72no—
292C23×C4—71no—
293C23×C4—71no—
294C23×C4C22×D711yescharacteristic
295C23×C4C22×D711yescharacteristic
296C23×C4C22×D712yes—
297C23×C4C22×D712yes—
298C23×C4C22×D711yescharacteristic
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—78no—
305C2×C4⋊C4—78no—
306C2×C4⋊C4—78no—
307C2×C4⋊C4—144no—
308C2×C4⋊C4—142no—
309C2×C4⋊C4—144no—
310C2×C4⋊C4—142no—
311C2×C4⋊C4—142no—
312C2×C4⋊C4—144no—
313C2×C4⋊C4—144no—
314C2×C4⋊C4—144no—
315C2×C4⋊C4—144no—
316C2×C4⋊C4—144no—
317C2×C4⋊C4—144no—
318C2×C4⋊C4—144no—
319C2×C4⋊C4—282no—
320C2×C4⋊C4—282no—
321C2×C4⋊C4—282no—
322C2×C42—74no—
323C2×C42—74no—
324C2×C42—74no—
325C2×C42—78no—
326C2×C42—144no—
327C2×C42—144no—
328C2×C42—144no—
329C2×C42—282no—
330C2×C42—282no—
331#95—22no—
332#95—24no—
333#95—74no—
334#95—144no—
335#95—142no—
336#95—142no—
337#95—144no—
338#95—144no—
339#95—142no—
340#95—144no—
341#95C4×D714yes—
342C22×C7C22×C4⋊C411yescharacteristic
343C22×C7C22×C4⋊C412yes—
344C22×C7C4×#4112yes—
345C22×C7#51811yescharacteristic
346C22×C7#51911yescharacteristic
347C22×C7#52511yescharacteristic
348C22×C7#52511yescharacteristic
349C22×C7C2×#12711yescharacteristic
350C22×C7C2×C4⋊Q811yescharacteristic
351C22×C7C2×C4⋊Q812yes—
352C22×C7#53312yes—
353C22×C7#53711yescharacteristic
354C22×C7#53711yescharacteristic
355C22×C7#54411yescharacteristic
356C22×C7#54411yescharacteristic
357C22×C7#54612yes—
358C22×C7#54612yes—
359C22×C7#54812yes—
360C22×C7#54812yes—
361C22×C7#55412yes—
362C22×C7#55412yes—
363C22×C7#55712yes—
364C22×C7#55712yes—
365C4×C7—28no—
366C4×C7—24no—
367C4×C7—44no—
368C4×C7—81no—
369C4×C7—81no—
370Dic7—24no—
371Dic7—28no—
372Dic7—44no—
373Dic7—81no—
374Dic7—81no—
375Dic7#38418yes—
376C24C23×D711yescharacteristic
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—72no—
400C22×C4—72no—
401C22×C4—74no—
402C22×C4—72no—
403C22×C4—74no—
404C22×C4—74no—
405C22×C4—72no—
406C22×C4—72no—
407C22×C4—74no—
408C22×C4—72no—
409C22×C4—74no—
410C22×C4—74no—
411C22×C4—142no—
412C22×C4—141no—
413C22×C4—142no—
414C22×C4—141no—
415C22×C4—142no—
416C22×C4—141no—
417C22×C4—142no—
418C22×C4—141no—
419C22×C4—142no—
420C22×C4—142no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—141no—
426C22×C4—141no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—142no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4C2×C4×D712yes—
436C22×C4C2×C4×D714yes—
437C22×C4D4×D712yes—
438C22×C4D4×D714yes—
439C22×C4#115914yes—
440C22×C4Q8×D712yes—
441C22×C4Q8×D714yes—
442C4⋊C4—28no—
443C4⋊C4—48no—
444C4⋊C4—732no—
445C4⋊C4—148no—
446C4⋊C4—288no—
447C4⋊C4—288no—
448C4⋊C4—284no—
449C4⋊C4—284no—
450C4⋊C4—288no—
451C42—716no—
452C42—288no—
453C42—288no—
454C2×C7C2×#38411yescharacteristic
455C2×C7#229611yescharacteristic
456C2×C7#231611yescharacteristic
457C2×C7#234912yes—
458C2×C7#235112yes—
459C2×C7#254011yescharacteristic
460C2×C7#254011yescharacteristic
461C2×C7#255012yes—
462C2×C7#255012yes—
463C2×C7#258411yescharacteristic
464C2×C7#258411yescharacteristic
465C23C22×C4×D711yescharacteristic
466C23C2×D4×D711yescharacteristic
467C23C2×D4×D712yes—
468C23C2×#115912yes—
469C23#654811yescharacteristic
470C23C2×Q8×D712yes—
471C23C2×Q8×D711yescharacteristic
472C23#655111yescharacteristic
473C23D7×#4112yes—
474C23#655311yescharacteristic
475C23#655411yescharacteristic
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—74no—
504C2×C4—78no—
505C2×C4—74no—
506C2×C4—74no—
507C2×C4—78no—
508C2×C4—74no—
509C2×C4—78no—
510C2×C4—142no—
511C2×C4—142no—
512C2×C4—144no—
513C2×C4—142no—
514C2×C4—144no—
515C2×C4—142no—
516C2×C4—144no—
517C2×C4—142no—
518C2×C4—142no—
519C2×C4—144no—
520C2×C4—144no—
521C2×C4—144no—
522C2×C4—144no—
523C2×C4—144no—
524C2×C4—144no—
525C2×C4—282no—
526C2×C4—282no—
527C2×C4—282no—
528C2×C4—282no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—282no—
533C2×C4—282no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—282no—
537C2×C4—282no—
538C2×C4—281no—
539C2×C4D7×C4⋊C414yes—
540C2×C4D7×C4⋊C418yes—
541C7#1395411yescharacteristic, complemented, Sylow
542C22C2×D7×C4⋊C411yescharacteristic
543C22C2×D7×C4⋊C412yes—
544C22C4×#115912yes—
545C22#9023611yescharacteristic
546C22#9026311yescharacteristic
547C22#9027711yescharacteristic
548C22#9028212yes—
549C22#9028912yes—
550C22#9029911yescharacteristic
551C22#9031312yes—
552C22#9032011yescharacteristic
553C22#9032412yes—
554C22#9032612yes—
555C22#9032712yes—
556C22#9034512yes—
557C22#9034711yescharacteristic
558C22#9037612yes—
559C22#9038011yescharacteristic
560C22D7×#12711yescharacteristic
561C22#9041212yes—
562C22D7×C4⋊Q812yes—
563C22D7×C4⋊Q811yescharacteristic
564C22#9042011yescharacteristic
565C4—24no—
566C4—28no—
567C4—44no—
568C4—78no—
569C4—81no—
570C4—81no—
571C4—148no—
572C4—144no—
573C4—284no—
574C4—561no—
575C4—561no—
576C2D7×#38411yescharacteristic
577C2#1173182311yescharacteristic
578C2#1173183912yes—
579C2#1173342712yes—
580C2#1173364011yescharacteristic
581C2#1173413211yescharacteristic
582C2#1173463012yes—
583C2#1173463711yescharacteristic
584C2#1173523112yes—
585C2#1173524211yescharacteristic
586C2#1173548111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1444C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1444D7
hypocenterC7#13954
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
38. #89421C4semidirect
180. Dic7⋊C4C4⋊C4semidirect
183. C4×Dic7C4⋊C4semidirect
541. C7#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#897442
C2×C4⋊C4×Dic72
C2×#894192
C2×#894222
C2×#894212
C7×#14442
#117293222
#117293172
#117271742
#117271732
Dic7⋊#952
#139547