Finite Group Databasebeta

← #13284511

Subgroups — #13284511

Order 1792.

1326 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#399C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic, complemented
3C2×#89723C211yesmaximal, characteristic
4#11729323C211yesmaximal, characteristic, complemented
5#11729319C212yesmaximal, complemented
6#11729319C212yesmaximal, complemented
7#11729302C212yesmaximal
8#11729300C211yesmaximal, characteristic
9#11729300C212yesmaximal
10#11727166C211yesmaximal, characteristic, complemented
11#11727155C211yesmaximal, characteristic, complemented
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C22⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C7×#399C418yescomplemented
24C2×C7×#95C2211yescharacteristic
25C2×C7⋊#95C2211yescharacteristic
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89757—24no—
37#89723—24no—
38#14628—71nomaximal, Sylow
39C25×C7C2311yescharacteristic
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2312yes—
45C23×Dic7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—42no—
53C2×C7×C4⋊C4—42no—
54C2×C7×C4⋊C4C2×C414yes—
55C2×C7×C4⋊C4C2×C418yes—
56C2×C7×C22⋊C4—22no—
57C2×C7×C22⋊C4—22no—
58C2×C7×C22⋊C4—42no—
59C2×C7×C22⋊C4—42no—
60C2×C7×C22⋊C4C2×C414yes—
61C2×C7×C22⋊C4C2×C418yes—
62C2×C22⋊Dic7—22no—
63C2×C22⋊Dic7—22no—
64C2×C22⋊Dic7—42no—
65C2×C22⋊Dic7—42no—
66C2×C22⋊Dic7—42no—
67C2×C22⋊Dic7—42no—
68C2×C22⋊Dic7—42no—
69C2×C4⋊Dic7—22no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—24no—
72C2×C4⋊Dic7—42no—
73C2×C4⋊Dic7—42no—
74C2×C4⋊Dic7—42no—
75C2×C4⋊Dic7—42no—
76C2×C4×Dic7—42no—
77C2×C4×Dic7D414yes—
78C7×#95C2×C414yes—
79C7⋊#95—22no—
80C7⋊#95—22no—
81C7⋊#95—22no—
82C7⋊#95—24no—
83C7⋊#95—42no—
84C7⋊#95—42no—
85C7⋊#95—42no—
86C7⋊#95—42no—
87C7⋊#95—42no—
88C7⋊#95—42no—
89C7⋊#95—42no—
90C2×#399D711yescharacteristic
91C2×#389—71no—
92C2×#388—71no—
93#1445—71no—
94#1442—71no—
95#1441—72no—
96#1441—72no—
97#1440—72no—
98#1439—72no—
99#1439—71no—
100#1434—71no—
101C24×C7—21no—
102C24×C7—21no—
103C24×C7—22no—
104C24×C7—21no—
105C24×C7—22no—
106C24×C7—22no—
107C24×C7—21no—
108C24×C7—21no—
109C24×C7—22no—
110C24×C7—21no—
111C24×C7C22×C412yes—
112C24×C7C2411yescharacteristic
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7C22×C414yes—
132C22×C4×C7C22×C412yes—
133C22×C4×C7C22×C414yes—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7#4112yes—
137C22×Dic7—21no—
138C22×Dic7—22no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—21no—
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—22no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—21no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—21no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7C2×D412yes—
170C22×Dic7C2×D412yes—
171C7×C4⋊C4—28no—
172C7×C4⋊C4—48no—
173C7×C22⋊C4—28no—
174C7×C22⋊C4—48no—
175C22⋊Dic7—44no—
176C22⋊Dic7—44no—
177C22⋊Dic7—48no—
178C4⋊Dic7—48no—
179C4⋊Dic7—44no—
180C4⋊Dic7—44no—
181C4×Dic7—44no—
182C22×C4⋊C4—72no—
183C22×C4⋊C4—71no—
184C22×C4⋊C4—71no—
185C22×C4⋊C4C2×D711yescharacteristic
186C22×C4⋊C4C2×D712yes—
187C22×C22⋊C4—71no—
188C22×C22⋊C4—71no—
189C22×C22⋊C4—72no—
190C22×C22⋊C4C2×D711yescharacteristic
191C22×C22⋊C4C2×D712yes—
192C22×C42—71no—
193#399Dic718yescomplemented
194#389—144no—
195#388—144no—
196C2×#95—71no—
197C2×#95—72no—
198C2×#95—71no—
199C2×#95—71no—
200C2×#95—72no—
201C2×#95—72no—
202C2×#95—72no—
203C2×#95—72no—
204C2×#95—72no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95C2×D711yescharacteristic
208C23×C7—22no—
209C23×C7—24no—
210C23×C7—22no—
211C23×C7—24no—
212C23×C7—22no—
213C23×C7—41no—
214C23×C7—41no—
215C23×C7—41no—
216C23×C7—41no—
217C23×C7—41no—
218C23×C7—41no—
219C23×C7—42no—
220C23×C7—42no—
221C23×C7—41no—
222C23×C7—41no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—42no—
229C23×C7—42no—
230C23×C7—42no—
231C23×C7C23×C411yescharacteristic
232C23×C7C22×D411yescharacteristic
233C23×C7C2×#4111yescharacteristic
234C23×C7H(5,𝔽2)12yes—
235C23×C7H(5,𝔽2)12yes—
236C23×C7H(5,𝔽2)12yes—
237C23×C7H(5,𝔽2)11yescharacteristic
238C23×C72−1+411yescharacteristic
239C23×C72−1+411yescharacteristic
240C23×C72−1+412yes—
241C23×C72−1+411yescharacteristic
242C2×C4×C7—24no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—24no—
246C2×C4×C7—22no—
247C2×C4×C7—24no—
248C2×C4×C7—24no—
249C2×C4×C7—24no—
250C2×C4×C7—24no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
254C2×C4×C7—41no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—41no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7C4×D414yes—
266C2×Dic7—22no—
267C2×Dic7—22no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—22no—
272C2×Dic7—42no—
273C2×Dic7—42no—
274C2×Dic7—42no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—41no—
278C2×Dic7—41no—
279C2×Dic7—42no—
280C2×Dic7—41no—
281C2×Dic7—41no—
282C2×Dic7—41no—
283C2×Dic7—41no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C25C22×D711yescharacteristic
301C23×C4—71no—
302C23×C4—71no—
303C23×C4—72no—
304C23×C4—71no—
305C23×C4—71no—
306C23×C4—72no—
307C23×C4C22×D711yescharacteristic
308C23×C4C22×D712yes—
309C23×C4C22×D712yes—
310C23×C4C22×D711yescharacteristic
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—142no—
316C2×C4⋊C4—144no—
317C2×C4⋊C4—142no—
318C2×C4⋊C4—282no—
319C2×C4⋊C4—282no—
320C2×C4⋊C4—282no—
321C2×C4⋊C4—282no—
322C2×C4⋊C4C2×Dic714yes—
323C2×C4⋊C4C2×Dic718yes—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—142no—
329C2×C22⋊C4—142no—
330C2×C22⋊C4—282no—
331C2×C22⋊C4—282no—
332C2×C22⋊C4—282no—
333C2×C22⋊C4—282no—
334C2×C22⋊C4—282no—
335C2×C22⋊C4C2×Dic714yes—
336C2×C22⋊C4C2×Dic718yes—
337C2×C42—74no—
338C2×C42—282no—
339#95—142no—
340#95—144no—
341#95—142no—
342#95—142no—
343#95—282no—
344#95—282no—
345#95—282no—
346#95—282no—
347#95—282no—
348#95—282no—
349#95—282no—
350#95C2×Dic714yes—
351C22×C7—42no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—44no—
355C22×C7—44no—
356C22×C7—81no—
357C22×C7—81no—
358C22×C7—81no—
359C22×C7—82no—
360C22×C7—82no—
361C22×C7—81no—
362C22×C7C2×C4×D411yescharacteristic
363C22×C7#51812yes—
364C22×C7#51911yescharacteristic
365C22×C7#52012yes—
366C22×C7#52011yescharacteristic
367C22×C7#53411yescharacteristic
368C22×C7#53511yescharacteristic
369C22×C7#53511yescharacteristic
370C22×C7#53611yescharacteristic
371C22×C7#53611yescharacteristic
372C22×C7#53711yescharacteristic
373C22×C7#53912yes—
374C22×C7#54012yes—
375C22×C7#54111yescharacteristic
376C22×C7#54211yescharacteristic
377C22×C7#56012yes—
378C22×C7#56212yes—
379C22×C7#56212yes—
380C22×C7#56212yes—
381C22×C7#56212yes—
382C22×C7#56312yes—
383C22×C7#56312yes—
384C22×C7#56312yes—
385C4×C7—24no—
386C4×C7—42no—
387C4×C7—44no—
388C4×C7—44no—
389Dic7—42no—
390Dic7—42no—
391Dic7—81no—
392Dic7—81no—
393Dic7—82no—
394Dic7—82no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24C22×Dic712yes—
406C24C23×D711yescharacteristic
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—72no—
426C22×C4—72no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—142no—
433C22×C4—142no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—142no—
442C22×C4—142no—
443C22×C4—142no—
444C22×C4—142no—
445C22×C4—141no—
446C22×C4—141no—
447C22×C4—142no—
448C22×C4—142no—
449C22×C4—141no—
450C22×C4—142no—
451C22×C4—142no—
452C22×C4—142no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—141no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4D4×D712yes—
460C22×C4#115912yes—
461C22×C4C22×Dic714yes—
462C22×C4C22×Dic712yes—
463C22×C4C22×Dic714yes—
464C22×C4C22×Dic712yes—
465C4⋊C4—28no—
466C4⋊C4—48no—
467C4⋊C4—284no—
468C4⋊C4—284no—
469C4⋊C4—288no—
470C22⋊C4—28no—
471C22⋊C4—48no—
472C22⋊C4—284no—
473C22⋊C4—284no—
474C22⋊C4—288no—
475C42—284no—
476C2×C7—82no—
477C2×C7#232211yescharacteristic
478C2×C7#232311yescharacteristic
479C2×C7#232811yescharacteristic
480C2×C7#237612yes—
481C2×C7#237812yes—
482C2×C7#281311yescharacteristic
483C2×C7#281611yescharacteristic
484C2×C7#282011yescharacteristic
485C2×C7#282111yescharacteristic
486C2×C7#283612yes—
487C2×C7#283712yes—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—42no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C2×D4×D711yescharacteristic
512C23C2×#115911yescharacteristic
513C23#654812yes—
514C23#654812yes—
515C23#655111yescharacteristic
516C23#655111yescharacteristic
517C23#655311yescharacteristic
518C23#655312yes—
519C23#655411yescharacteristic
520C23#655412yes—
521C23C23×Dic711yescharacteristic
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—142no—
546C2×C4—142no—
547C2×C4—142no—
548C2×C4—142no—
549C2×C4—142no—
550C2×C4—142no—
551C2×C4—282no—
552C2×C4—282no—
553C2×C4—282no—
554C2×C4—282no—
555C2×C4—281no—
556C2×C4—282no—
557C2×C4—281no—
558C2×C4—282no—
559C2×C4—281no—
560C2×C4—282no—
561C2×C4—281no—
562C2×C4—282no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4—282no—
567C2×C4—282no—
568C2×C4—282no—
569C2×C4—281no—
570C2×C4—281no—
571C2×C4—282no—
572C2×C4—282no—
573C2×C4—282no—
574C2×C4—282no—
575C2×C4—282no—
576C2×C4—282no—
577C2×C4—282no—
578C2×C4—282no—
579C2×C4D4×Dic714yes—
580C7#1462811yescharacteristic, complemented, Sylow
581C22—42no—
582C22—44no—
583C22—42no—
584C22—44no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—82no—
591C22—82no—
592C22#9031611yescharacteristic
593C22#9031911yescharacteristic
594C22#9032011yescharacteristic
595C22#9033411yescharacteristic
596C22#9033712yes—
597C22#9033712yes—
598C22#9033812yes—
599C22#9033812yes—
600C22#9033911yescharacteristic
601C22#9034212yes—
602C22#9034411yescharacteristic
603C22#9035612yes—
604C22#9035712yes—
605C22#9035812yes—
606C22#9035812yes—
607C22#9040611yescharacteristic
608C22#9040611yescharacteristic
609C22#9041012yes—
610C22C2×D4×Dic711yescharacteristic
611C22#9048912yes—
612C22#9050311yescharacteristic
613C22#9051811yescharacteristic
614C22#9051812yes—
615C4—24no—
616C4—44no—
617C4—42no—
618C4—44no—
619C4—282no—
620C4—282no—
621C4—562no—
622C4—561no—
623C4—561no—
624C4—562no—
625C2—82no—
626C2#1173553511yescharacteristic
627C2#1173553611yescharacteristic
628C2#1173553711yescharacteristic
629C2#1173554012yes—
630C2#1173554112yes—
631C2#1173557011yescharacteristic
632C2#1174018911yescharacteristic
633C2#1174019512yes—
634C2#1174028111yescharacteristic
635C2#1174028512yes—
636C2#1174061711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#399C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#399D7
hypocenterC7#14628
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×#89757C2semidirect
4. #11729323C2semidirect
5. #11729319C2semidirect
6. #11729319C2semidirect
10. #11727166C2semidirect
11. #11727155C2semidirect
23. C7×#399C4semidirect
193. #399Dic7semidirect
580. C7#14628semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3992
C2×#897572
C2×#897232
#117293232
#117293192
#117293022
#117293002
#117271662
#117271552
#146287