Finite Group Databasebeta

← #13360099

Subgroups — #13360099

Order 1792.

1004 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×#124C211yesmaximal, characteristic
2C2×#89826C211yesmaximal, characteristic
3C2×#89802C211yesmaximal, characteristic, complemented
4C2×#89790C211yesmaximal, characteristic
5C42×Dic14C211yesmaximal, characteristic, complemented
6#11729475C211yesmaximal, characteristic
7#11729385C211yesmaximal, characteristic, complemented
8#11729363C211yesmaximal, characteristic
9#11727444C211yesmaximal, characteristic, complemented
10#11727421C211yesmaximal, characteristic, complemented
11#11727414C211yesmaximal, characteristic
12#11727391C211yesmaximal, characteristic
13#11727313C211yesmaximal, characteristic, complemented
14#11727294C211yesmaximal, characteristic, complemented
15#11727145C211yesmaximal, characteristic, complemented
16C2×C7×#124C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1142C2211yescharacteristic
21C2×C4×Dic14C2211yescharacteristic
22C2×C4×Dic14C2211yescharacteristic
23C2×C4×Dic14C2211yescharacteristic
24C7×#391C2211yescharacteristic
25C7×#390C2211yescharacteristic
26C7×#388—21no—
27C7×#388—21no—
28C7×#382C2211yescharacteristic
29C4×C7×C22⋊C4—21no—
30C4×C7×C22⋊C4—21no—
31C43×C7C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38#89826C418yescomplemented
39#89802—24no—
40#89790—24no—
41C2×#6384C2211yescharacteristic
42C2×#6384C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46C4×C4⋊Dic7C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48C4×Dic7⋊C4—21no—
49C4×Dic7⋊C4—21no—
50C4×Dic7⋊C4—21no—
51C42×Dic7—21no—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54C2×#6377C2211yescharacteristic
55C2×#6377C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#21508—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C22×Dic14C2311yescharacteristic
67C7×#124—22no—
68C7×#124C2×C414yes—
69C4×C7×Q8—22no—
70C4×C7×Q8—22no—
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C22⋊C4—21no—
77C2×C7×C22⋊C4—21no—
78C2×C7×C22⋊C4—21no—
79C2×C7×C22⋊C4—21no—
80C2×C7×C22⋊C4—21no—
81C2×C42×C7—21no—
82C2×C42×C7D411yescharacteristic
83C2×C42×C7D411yescharacteristic
84C2×C42×C7D411yescharacteristic
85C2×C42×C7D411yescharacteristic
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×#1144—22no—
90C2×#1144—22no—
91C2×#1144C2×C414yescomplemented
92C2×#1142—22no—
93C2×#1142—22no—
94C2×#1142C2×C414yes—
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7—21no—
105C2×C4×Dic7—21no—
106C2×C4×Dic7—21no—
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C4×Dic14—22no—
112C4×Dic14—22no—
113C4×Dic14—22no—
114C4×Dic14—22no—
115C4×Dic14C2×C414yescomplemented
116C4×Dic14D414yes—
117C7×#95—21no—
118C7×#95—21no—
119C7×#95—21no—
120C7×#95—21no—
121#6409—22no—
122#6409—22no—
123#6409C2×C414yescomplemented
124#6406—22no—
125#6406—22no—
126#6406C2×C414yes—
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130#6384—22no—
131#6384—22no—
132#6382—22no—
133#6381—22no—
134C4⋊(C7⋊C8)—22no—
135C4⋊(C7⋊C8)C2×C414yescomplemented
136#6377—22no—
137#6377—22no—
138C2×#464—71no—
139C2×#441—71no—
140C2×#440—71no—
141C4×#124D711yescharacteristic
142C42×Q8—71no—
143#1983—71no—
144#1949—71no—
145#1928—71no—
146#1926—71no—
147#1880—71no—
148#1878—71no—
149#1805—71no—
150#1767—71no—
151#1763—71no—
152#1762—71no—
153C24×C7—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8C22×C412yes—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4C22×C412yes—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—42no—
170C22×C4×C7—42no—
171C22×C4×C7—42no—
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2411yescharacteristic
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C2×Dic14—21no—
184C2×Dic14—21no—
185C2×Dic14—21no—
186C2×Dic14C22×C412yes—
187C2×Dic14C2×D412yes—
188C2×Dic14#4112yes—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—42no—
194C7×C22⋊C4—24no—
195C7×C22⋊C4—24no—
196C7×C22⋊C4—42no—
197C7×C22⋊C4—42no—
198C7×C22⋊C4—42no—
199C42×C7—22no—
200C42×C7—21no—
201C42×C7—21no—
202C42×C7—41no—
203C42×C7—41no—
204C42×C7—41no—
205C42×C7—42no—
206C42×C7C22×C412yes—
207C42×C7C2×D412yes—
208C42×C7#4112yes—
209C42×C7#4112yes—
210#1144—28no—
211#1142—28no—
212C4⋊Dic7—21no—
213C4⋊Dic7—21no—
214C4⋊Dic7—21no—
215C4⋊Dic7C22×C412yes—
216C4⋊Dic7C2×D412yes—
217C4⋊Dic7#4112yes—
218Dic7⋊C4—24no—
219Dic7⋊C4—24no—
220Dic7⋊C4—24no—
221C4×Dic7—24no—
222C4×Dic7—24no—
223C4×Dic7—24no—
224C4×Dic7—42no—
225C4×Dic7—42no—
226C4×Dic7—42no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8C22×C412yes—
238C2×C7⋊C8C22×C412yes—
239C22×Q16—71no—
240C22×SD16—71no—
241C2×#124C2×D711yescharacteristic
242C2×C4×Q8—71no—
243C2×C4×Q8—71no—
244C2×C4×Q8—71no—
245C2×C4×Q8C2×D711yescharacteristic
246C2×C4×D4C2×D711yescharacteristic
247#464—78no—
248#441—144no—
249#440—144no—
250C2×#107—71no—
251C2×#106—71no—
252C2×C4⋊C8—71no—
253C2×C4⋊C8—71no—
254C2×#103—71no—
255C2×#103—71no—
256C2×#103—71no—
257C2×#103—71no—
258C2×#103—71no—
259C2×#102—71no—
260C2×#102—71no—
261C2×#102—71no—
262C2×#97—71no—
263C2×#97—71no—
264#391C2×D711yescharacteristic
265#390C2×D711yescharacteristic
266#388—21no—
267#388—21no—
268#382C2×D711yescharacteristic
269C4×C4⋊C4—71no—
270C4×C4⋊C4—71no—
271C4×C4⋊C4—71no—
272C4×C4⋊C4—141no—
273C4×C4⋊C4—141no—
274C4×C4⋊C4—141no—
275C4×C22⋊C4—21no—
276C4×C22⋊C4—21no—
277C43—141no—
278C43C2×D711yescharacteristic
279#340—71no—
280#340—71no—
281#340—71no—
282#340—71no—
283#336—71no—
284#336—71no—
285C23×C7—22no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7C22×D411yescharacteristic
293C7×Q8—22no—
294C7×Q8—22no—
295C7×Q8—41no—
296C7×Q8—41no—
297C7×D4—22no—
298C7×D4—22no—
299C7×D4—41no—
300C7×D4—41no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—22no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—84no—
324C2×C4×C7C4×D412yes—
325C2×C4×C7C4×D412yes—
326C2×C4×C7#12112yes—
327C2×C4×C7#12112yes—
328C2×C4×C7#13712yes—
329C2×C4×C7C23×C411yescharacteristic
330C2×C4×C7C22×D411yescharacteristic
331C2×C4×C7C2×#4111yescharacteristic
332C2×C4×C7C2×#4111yescharacteristic
333C2×C4×C7C2×#4111yescharacteristic
334C2×C4×C7C2×#4111yescharacteristic
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—41no—
342C2×Dic7—41no—
343C2×Dic7—41no—
344C2×Dic7—41no—
345C2×Dic7—41no—
346C2×Dic7—41no—
347Dic14—22no—
348Dic14—22no—
349Dic14—22no—
350Dic14C4×D414yes—
351C7⋊C8—22no—
352C7⋊C8—22no—
353C7⋊C8—41no—
354C7⋊C8—41no—
355C22×Q8—71no—
356C22×Q8C22×D711yescharacteristic
357C22×D4C22×D711yescharacteristic
358C23×C4—21no—
359C2×Q16—74no—
360C2×Q16—142no—
361C2×Q16—142no—
362C2×SD16—74no—
363C2×SD16—142no—
364C2×SD16—142no—
365C22×C8—71no—
366C22×C8—71no—
367C22×C8—71no—
368C22×C8—71no—
369#124—22no—
370#124C4×D714yes—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—74no—
374C4×Q8—74no—
375C4×Q8—142no—
376C4×Q8—142no—
377C4×Q8—142no—
378C4×Q8—142no—
379C4×D4—22no—
380C4×D4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—71no—
383C2×C4⋊C4—71no—
384C2×C4⋊C4—71no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4C22×D711yescharacteristic
389C2×C4⋊C4C22×D711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—141no—
397C2×C42—141no—
398C2×C42—141no—
399C2×C42—141no—
400C2×C42—141no—
401C2×C42—141no—
402C2×C42C22⋊D711yescharacteristic
403C2×C42C22⋊D711yescharacteristic
404C2×C42C22⋊D711yescharacteristic
405C2×C42C22⋊D711yescharacteristic
406C2×C42C22×D711yescharacteristic
407C2×C42C22×D711yescharacteristic
408C2×C42C22×D711yescharacteristic
409#107—142no—
410#106—142no—
411C4⋊C8—74no—
412C4⋊C8—142no—
413#103—74no—
414#103—142no—
415#103—142no—
416#103—142no—
417#103—142no—
418#102—74no—
419#102—142no—
420#102—142no—
421#97—142no—
422#97—142no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—141no—
428#95—141no—
429#95—141no—
430C22×C7—42no—
431C22×C7—42no—
432C22×C7—42no—
433C22×C7—81no—
434C22×C7—81no—
435C22×C7—81no—
436C22×C7—81no—
437C22×C7C2×C4×D411yescharacteristic
438C22×C7C2×#12111yescharacteristic
439C22×C7#52511yescharacteristic
440C22×C7C2×#13711yescharacteristic
441C22×C7#57511yescharacteristic
442C22×C7#57511yescharacteristic
443C22×C7#57511yescharacteristic
444C4×C7—22no—
445C4×C7—22no—
446C4×C7—22no—
447C4×C7—22no—
448C4×C7—22no—
449C4×C7—41no—
450C4×C7—42no—
451C4×C7—81no—
452C4×C7—81no—
453C4×C7C2×C4×D411yescharacteristic
454C4×C7C4×#4111yescharacteristic
455C4×C7#52911yescharacteristic
456C4×C7#53211yescharacteristic
457Dic7—24no—
458Dic7—42no—
459Dic7—42no—
460Dic7—42no—
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—72no—
468C2×Q8—72no—
469C2×Q8—72no—
470C2×Q8—141no—
471C2×Q8—141no—
472C2×Q8—141no—
473C2×Q8C2×C4×D712yes—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4C2×C4×D712yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—141no—
487C22×C4—141no—
488C22×C4—141no—
489C22×C4—141no—
490C22×C4C2×C22⋊D711yescharacteristic
491C22×C4C2×C22⋊D711yescharacteristic
492C22×C4C2×C22⋊D711yescharacteristic
493C22×C4C2×C22⋊D711yescharacteristic
494C22×C4C2×C22⋊D711yescharacteristic
495C22×C4C2×C22⋊D711yescharacteristic
496C22×C4C23×D711yescharacteristic
497Q16—148no—
498SD16—148no—
499C2×C8—72no—
500C2×C8—72no—
501C2×C8—141no—
502C2×C8—141no—
503C2×C8—141no—
504C2×C8—141no—
505C2×C8—141no—
506C2×C8—141no—
507C2×C8—141no—
508C2×C8—141no—
509C2×C8—141no—
510C2×C8—141no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—72no—
517C4⋊C4—72no—
518C4⋊C4—72no—
519C4⋊C4—144no—
520C4⋊C4—144no—
521C4⋊C4—144no—
522C4⋊C4—141no—
523C4⋊C4—141no—
524C4⋊C4—141no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C42—22no—
531C42—21no—
532C42—21no—
533C42—41no—
534C42—41no—
535C42—41no—
536C42—42no—
537C42—144no—
538C42—144no—
539C42—144no—
540C42—282no—
541C42—282no—
542C42—282no—
543C42C2×C4×D712yes—
544C42#115712yes—
545C42D4×D712yes—
546C42#115912yes—
547C2×C7—82no—
548C2×C7C4×#12111yescharacteristic
549C2×C7#294311yescharacteristic
550C2×C7C4×#13711yescharacteristic
551C2×C7#303711yescharacteristic
552C2×C7#304011yescharacteristic
553C2×C7#311111yescharacteristic
554C2×C7#311711yescharacteristic
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23C22×C22⋊D711yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—74no—
568Q8—142no—
569Q8—142no—
570Q8—142no—
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—142no—
601C2×C4—142no—
602C2×C4—142no—
603C2×C4—142no—
604C2×C4—281no—
605C2×C4—281no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4C4×C22⋊D712yes—
611C2×C4C4×C22⋊D712yes—
612C2×C4#650112yes—
613C2×C4#650112yes—
614C2×C4#651412yes—
615C2×C4C22×C4×D711yescharacteristic
616C2×C4C2×#115711yescharacteristic
617C2×C4C2×D4×D711yescharacteristic
618C2×C4C2×#115911yescharacteristic
619C2×C4D7×#4111yescharacteristic
620C2×C4D7×#4111yescharacteristic
621C8—142no—
622C8—142no—
623C8—281no—
624C8—281no—
625C7#2150811yescharacteristic, complemented, Sylow
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×C4×C22⋊D711yescharacteristic
634C22C2×#650111yescharacteristic
635C22#9051311yescharacteristic
636C22#9051311yescharacteristic
637C22#9051311yescharacteristic
638C22C2×#651411yescharacteristic
639C22#9051911yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4—144no—
650C4—282no—
651C4—282no—
652C4—282no—
653C4C4×#115911yescharacteristic
654C4C4×D4×D711yescharacteristic
655C4#9023911yescharacteristic
656C4#9024811yescharacteristic
657C2—82no—
658C2C4×#650111yescharacteristic
659C2#1173995111yescharacteristic
660C2C4×#651411yescharacteristic
661C2#1174039011yescharacteristic
662C2#1174058711yescharacteristic
663C2#1174059811yescharacteristic
664C2#1174075911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#124C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenterC4×#124D7
hypocenterC7#21508
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
3. C2×#89802C2semidirect
5. C42×Dic14C2semidirect
7. #11729385C2semidirect
9. #11727444C2semidirect
10. #11727421C2semidirect
13. #11727313C2semidirect
14. #11727294C2semidirect
15. #11727145C2semidirect
38. #89826C4semidirect
91. C2×#1144C2×C4semidirect
115. C4×Dic14C2×C4semidirect
123. #6409C2×C4semidirect
135. C4⋊(C7⋊C8)C2×C4semidirect
625. C7#21508semidirect

Maximal subgroups

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

subgroupindex
C4×C7×#1242
C2×#898262
C2×#898022
C2×#897902
C42×Dic142
#117294752
#117293852
#117293632
#117274442
#117274212
#117274142
#117273912
#117273132
#117272942
#117271452
#215087