Finite Group Databasebeta

← #13356201

Subgroups — #13356201

Order 1792.

1218 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#428C211yesmaximal, characteristic, complemented
2C2×#89905C211yesmaximal, characteristic
3#11739673C211yesmaximal, characteristic
4C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
5C2×#89738C211yesmaximal, characteristic
6#11729733C211yesmaximal, characteristic, complemented
7#11729335C211yesmaximal, characteristic, complemented
8#11728378C212yesmaximal, complemented
9#11728377C212yesmaximal, complemented
10#11728324C212yesmaximal, complemented
11#11728323C212yesmaximal, complemented
12C22×#1157C2211yescharacteristic
13C22×C7×M16C2211yescharacteristic
14C2×C7×#117C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4×Dic7—21no—
18C22×C4×Dic7C2211yescharacteristic
19C22×#1136C2211yescharacteristic
20C7×#428—24no—
21C2×C7×#107C2212yes—
22C2×C7×#106C2212yes—
23C2×C7⋊#95—21no—
24#89905C418yescomplemented
25C2×#6395C2212yes—
26C2×#6390C2212yes—
27#89760C2211yescharacteristic
28#89760C2211yescharacteristic
29C4⋊C4×Dic7—21no—
30C4⋊C4×Dic7—21no—
31C4⋊C4×Dic7C2212yes—
32C4⋊C4×Dic7C2212yes—
33#89746C2211yescharacteristic
34#89746C2211yescharacteristic
35C2×#6384C2212yes—
36#89738—24no—
37C2×#6383C2212yes—
38#89730—21no—
39#89730—21no—
40C4×(C2×D7)⋊C4—21no—
41C4×(C2×D7)⋊C4—21no—
42#89345C2212yes—
43#89345C2212yes—
44#89324C2212yes—
45#89324C2212yes—
46#21059—71nomaximal, Sylow
47C23×C4×C7—21no—
48C23×C4×C7C2311yescharacteristic
49C22×C22⋊D7—21no—
50C23×Dic7—21no—
51C23×Dic7D411yescharacteristic
52C23×Dic7D411yescharacteristic
53C2×#1157—22no—
54C2×#1157—22no—
55C2×#1157—22no—
56C2×#1157—22no—
57C2×#1157—22no—
58C2×#1157C2×C414yes—
59C22×D28C2311yescharacteristic
60C22×C4×D7—21no—
61C22×Dic14C2311yescharacteristic
62C2×C7×M16—22no—
63C2×C7×M16—22no—
64C2×C7×M16C2×C414yes—
65C22×C7×C8C2312yes—
66C7×#117—22no—
67C7×#117—22no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4D414yes—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2312yes—
74C2×C7×C22⋊C4—21no—
75C2×C42×C7—21no—
76C2×(C2×D7)⋊C4—21no—
77C2×(C2×D7)⋊C4—21no—
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80C2×C4⋊Dic7—21no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7C2×C414yes—
83C2×C4⋊Dic7C2312yes—
84C2×C4×Dic7—22no—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—44no—
89C2×C4×Dic7D411yescharacteristic
90C2×C4×Dic7D411yescharacteristic
91C2×C4×Dic7C2311yescharacteristic
92C2×C4×Dic7C2311yescharacteristic
93C2×#1136—22no—
94C2×#1136—22no—
95C2×#1136—22no—
96C22×C7⋊C8C2312yes—
97C7×#107—24no—
98C7×#106—24no—
99C7⋊#95—21no—
100C7⋊#95—21no—
101C7⋊#95—21no—
102C7⋊#95—21no—
103C7⋊#95—22no—
104C7⋊#95—22no—
105#6395C2×C418yescomplemented
106#6390C2×C418yescomplemented
107#6384—24no—
108#6383—24no—
109C2×#428D711yescharacteristic, complemented
110C2×#417—71no—
111C2×#417—71no—
112#2297—71no—
113C2×C4×C4⋊C4—71no—
114#1928—72no—
115#1927—72no—
116#1926—72no—
117#1925—72no—
118#1736—71no—
119#1728—71no—
120C24×C7C2×D411yescharacteristic
121C23×D7—21no—
122C22×C4×C7—24no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7C22×C412yes—
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2×D412yes—
131C22×C4×C7#4112yes—
132C22×C4×C7#4112yes—
133C22×C4×C7#4112yes—
134C22×C4×C7#4112yes—
135C22×C4×C7C2411yescharacteristic
136C2×C22⋊D7—24no—
137C2×C22⋊D7—42no—
138C2×C22⋊D7—42no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—24no—
143C22×Dic7—22no—
144C22×Dic7—21no—
145C22×Dic7—22no—
146C22×Dic7—41no—
147C22×Dic7—41no—
148C22×Dic7—42no—
149C22×Dic7—42no—
150C22×Dic7C2×D411yescharacteristic
151C22×Dic7C2×D411yescharacteristic
152C22×Dic7C2×D411yescharacteristic
153C22×Dic7C2×D411yescharacteristic
154#1157—28no—
155#1157—28no—
156#1157—44no—
157#1157—44no—
158C2×D28—21no—
159C2×D28—21no—
160C2×D28—21no—
161C2×D28—21no—
162C2×D28—21no—
163C2×D28C22×C412yes—
164C2×C4×D7—24no—
165C2×C4×D7—42no—
166C2×C4×D7—42no—
167C2×Dic14—21no—
168C2×Dic14—21no—
169C2×Dic14—21no—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14C22×C412yes—
173C7×M16—28no—
174C2×C7×C8—22no—
175C2×C7×C8—22no—
176C2×C7×C8C22×C414yes—
177C7×C4⋊C4—24no—
178C7×C4⋊C4—22no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4C2×D414yes—
184C7×C22⋊C4—42no—
185C42×C7—42no—
186(C2×D7)⋊C4—42no—
187(C2×D7)⋊C4—42no—
188(C2×D7)⋊C4—42no—
189(C2×D7)⋊C4—42no—
190C4⋊Dic7—24no—
191C4⋊Dic7—22no—
192C4⋊Dic7C22×C414yes—
193C4×Dic7—22no—
194C4×Dic7—22no—
195C4×Dic7—21no—
196C4×Dic7—21no—
197C4×Dic7—21no—
198C4×Dic7—21no—
199C4×Dic7—44no—
200C4×Dic7—44no—
201#1136—44no—
202C2×C7⋊C8—22no—
203C2×C7⋊C8—22no—
204C2×C7⋊C8—22no—
205C22×#41—71no—
206C22×M16—71no—
207C22×M16C2×D711yescharacteristic
208C2×#117C2×D711yescharacteristic
209C22×C4⋊C4—71no—
210C22×C4⋊C4C2×D711yescharacteristic
211C22×C42—71no—
212C22×C42—141no—
213#428—24no—
214C2×#107C2×D712yes—
215C2×#106C2×D712yes—
216#417—78no—
217#417—144no—
218C2×#103—72no—
219C2×#103—72no—
220C2×#102—72no—
221C2×#102—72no—
222#391—71no—
223#391—71no—
224#390—71no—
225#390—71no—
226#386—141no—
227#386—141no—
228C4×C4⋊C4—72no—
229C4×C4⋊C4—72no—
230C4×C4⋊C4—141no—
231C4×C4⋊C4—141no—
232C4×C22⋊C4—141no—
233C4×C22⋊C4—141no—
234C2×#95—141no—
235#340—72no—
236#340—72no—
237#336—72no—
238#336—72no—
239C23×C7—21no—
240C23×C7—21no—
241C23×C7—21no—
242C23×C7—21no—
243C23×C7C4×D412yes—
244C23×C7#12112yes—
245C23×C7#12312yes—
246C23×C7C22×D411yescharacteristic
247C22×D7—22no—
248C22×D7—41no—
249C22×D7—41no—
250C22×D7—41no—
251C22×D7—41no—
252C22×D7—41no—
253C22×D7—41no—
254C2×C4×C7—24no—
255C2×C4×C7—48no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—41no—
263C2×C4×C7—41no—
264C2×C4×C7#11714yes—
265C2×C4×C7C4×D412yes—
266C2×C4×C7C4×D414yes—
267C2×C4×C7#12112yes—
268C2×C4×C7#12312yes—
269C2×C4×C7#12414yes—
270C2×C4×C7#12614yes—
271C2×C4×C7C23×C411yescharacteristic
272C2×C4×C7C22×D411yescharacteristic
273C2×C4×C7C2×#4111yescharacteristic
274C2×C4×C7C2×#4111yescharacteristic
275C2×C4×C7C2×#4111yescharacteristic
276C2×C4×C7C2×#4111yescharacteristic
277C22⋊D7—48no—
278C2×Dic7—28no—
279C2×Dic7—21no—
280C2×Dic7—21no—
281C2×Dic7—21no—
282C2×Dic7—21no—
283C2×Dic7—24no—
284C2×Dic7—22no—
285C2×Dic7—21no—
286C2×Dic7—21no—
287C2×Dic7—21no—
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—44no—
292C2×Dic7—48no—
293C2×Dic7—41no—
294C2×Dic7—41no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7AGL(1,ℤ/8)12yes—
298C2×Dic7#13712yes—
299D28—22no—
300D28—22no—
301D28—41no—
302D28—41no—
303C4×D7—48no—
304Dic14—22no—
305Dic14—22no—
306Dic14—41no—
307Dic14—41no—
308C7×C8—24no—
309C7⋊C8—42no—
310C2×#41—74no—
311C2×#41—142no—
312C2×#41—142no—
313C2×#41—142no—
314C2×#41—142no—
315C2×#41—142no—
316C22×Q8—71no—
317C22×D4—71no—
318C22×D4—141no—
319C23×C4—21no—
320C23×C4—71no—
321C23×C4—71no—
322C23×C4—141no—
323C23×C4—141no—
324C23×C4C22×D711yescharacteristic
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—142no—
328C2×M16—142no—
329C2×M16—142no—
330C2×M16C4×D714yes—
331C22×C8—72no—
332C22×C8C22×D712yes—
333#117—22no—
334#117—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—74no—
338C2×C4⋊C4—72no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4C22⋊D714yes—
342C2×C4⋊C4C22×D711yescharacteristic
343C2×C4⋊C4C22×D711yescharacteristic
344C2×C4⋊C4C22×D712yes—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—141no—
347C2×C22⋊C4—141no—
348C2×C22⋊C4—141no—
349C2×C22⋊C4—141no—
350C2×C42—21no—
351C2×C42—71no—
352C2×C42—71no—
353C2×C42—71no—
354C2×C42—71no—
355C2×C42—142no—
356C2×C42—142no—
357C2×C42—142no—
358C2×C42—142no—
359C2×C42—284no—
360#107—24no—
361#106—24no—
362#103—78no—
363#103—144no—
364#102—78no—
365#102—144no—
366#95—142no—
367#95—142no—
368#95—141no—
369#95—141no—
370#95—141no—
371#95—141no—
372C22×C7—22no—
373C22×C7—22no—
374C22×C7—22no—
375C22×C7—22no—
376C22×C7—22no—
377C22×C7—22no—
378C22×C7#38814yes—
379C22×C7C2×C4×D411yescharacteristic
380C22×C7C2×#12111yescharacteristic
381C22×C7C2×#12311yescharacteristic
382C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C7C2×#13711yescharacteristic
384C22×C7#57511yescharacteristic
385C22×C7#57511yescharacteristic
386C2×D7—42no—
387C2×D7—42no—
388C2×D7—42no—
389C2×D7—81no—
390C2×D7—81no—
391C2×D7—81no—
392C2×D7—81no—
393C4×C7—44no—
394C4×C7—81no—
395C4×C7—81no—
396C4×C7#38814yes—
397C4×C7C2×#11711yescharacteristic
398C4×C7C2×C4×D411yescharacteristic
399C4×C7C2×#12411yescharacteristic
400C4×C7C2×#12611yescharacteristic
401Dic7—22no—
402Dic7—22no—
403Dic7—41no—
404Dic7—41no—
405Dic7—44no—
406Dic7—42no—
407C24—141no—
408C24D4×D711yescharacteristic
409#41—148no—
410#41—148no—
411#41—284no—
412#41—284no—
413C2×Q8—72no—
414C2×Q8—141no—
415C2×Q8—141no—
416C2×Q8—141no—
417C2×Q8—141no—
418C2×Q8—141no—
419C2×D4—72no—
420C2×D4—144no—
421C2×D4—141no—
422C2×D4—141no—
423C2×D4—141no—
424C2×D4—141no—
425C2×D4—141no—
426C2×D4—282no—
427C2×D4—282no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—71no—
435C22×C4—71no—
436C22×C4—71no—
437C22×C4—71no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—144no—
442C22×C4—142no—
443C22×C4—141no—
444C22×C4—142no—
445C22×C4—144no—
446C22×C4—281no—
447C22×C4—281no—
448C22×C4—282no—
449C22×C4—282no—
450C22×C4—282no—
451C22×C4—282no—
452C22×C4C2×C4×D712yes—
453C22×C4#115712yes—
454C22×C4D4×D711yescharacteristic
455C22×C4#115912yes—
456C22×C4#116112yes—
457C22×C4#116112yes—
458C22×C4C2×C22⋊D712yes—
459C22×C4C23×D711yescharacteristic
460M16—28no—
461M16—284no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—142no—
465C2×C8—142no—
466C2×C8—142no—
467C2×C8C2×C4×D714yes—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—74no—
475C4⋊C4—144no—
476C4⋊C4—142no—
477C4⋊C4C2×C22⋊D714yes—
478C22⋊C4—42no—
479C22⋊C4—282no—
480C22⋊C4—282no—
481C22⋊C4—282no—
482C22⋊C4—282no—
483C42—42no—
484C42—142no—
485C42—142no—
486C42—141no—
487C42—141no—
488C42—141no—
489C42—141no—
490C42—284no—
491C42—284no—
492C2×C7—24no—
493C2×C7C2×#38811yescharacteristic
494C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
495C2×C7C4×#13711yescharacteristic
496C2×C7#303611yescharacteristic
497C2×C7#303711yescharacteristic
498C2×C7#309211yescharacteristic
499C2×C7#309311yescharacteristic
500D7—82no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—142no—
506C23—281no—
507C23—281no—
508C23—281no—
509C23—281no—
510C23—281no—
511C23—281no—
512C23#645612yes—
513C23#645712yes—
514C23#650212yes—
515C23C2×D4×D711yescharacteristic
516Q8—142no—
517Q8—142no—
518Q8—281no—
519Q8—281no—
520D4—142no—
521D4—142no—
522D4—288no—
523D4—281no—
524D4—281no—
525C2×C4—24no—
526C2×C4—48no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—72no—
536C2×C4—72no—
537C2×C4—148no—
538C2×C4—141no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—144no—
543C2×C4—142no—
544C2×C4—141no—
545C2×C4—141no—
546C2×C4—141no—
547C2×C4—141no—
548C2×C4—141no—
549C2×C4—141no—
550C2×C4—288no—
551C2×C4—284no—
552C2×C4—281no—
553C2×C4—282no—
554C2×C4—282no—
555C2×C4—281no—
556C2×C4—288no—
557C2×C4#645514yes—
558C2×C4#645612yes—
559C2×C4#645712yes—
560C2×C4#646114yes—
561C2×C4C4×C22⋊D714yes—
562C2×C4#650212yes—
563C2×C4#651014yes—
564C2×C4C22×C4×D711yescharacteristic
565C2×C4C2×#115711yescharacteristic
566C2×C4C2×#115911yescharacteristic
567C2×C4C2×#116111yescharacteristic
568C2×C4C2×#116111yescharacteristic
569C2×C4C22×C22⋊D711yescharacteristic
570C8—24no—
571C8—282no—
572C7#2105911yescharacteristic, complemented, Sylow
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—282no—
580C22—282no—
581C22—282no—
582C22—561no—
583C22—561no—
584C22—561no—
585C22—561no—
586C22#8976214yes—
587C22C2×#645611yescharacteristic
588C22C2×#645711yescharacteristic
589C22D7×AGL(1,ℤ/8)11yescharacteristic
590C22#9046411yescharacteristic
591C22D7×#13711yescharacteristic
592C22#9046811yescharacteristic
593C22C2×#650211yescharacteristic
594C4—44no—
595C4—81no—
596C4—81no—
597C4—142no—
598C4—142no—
599C4—284no—
600C4—281no—
601C4—281no—
602C4—282no—
603C4#8976214yes—
604C4C2×#645511yescharacteristic
605C4C2×#646111yescharacteristic
606C4C2×C4×C22⋊D711yescharacteristic
607C4C2×#651011yescharacteristic
608C2—24no—
609C2—562no—
610C2#1173664411yescharacteristic
611C2#1173664511yescharacteristic
612C2#1173666011yescharacteristic
613C2#1173666111yescharacteristic
614C2C2×#8976211yescharacteristic
615C2#1174137611yescharacteristic
616C2#1174141111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#428C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenterC2×#428D7
hypocenterC7#21059
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×C7×#428C2semidirect
4. C2×C4⋊C4×Dic7C2semidirect
6. #11729733C2semidirect
7. #11729335C2semidirect
8. #11728378C2semidirect
9. #11728377C2semidirect
10. #11728324C2semidirect
11. #11728323C2semidirect
24. #89905C4semidirect
105. #6395C2×C4semidirect
106. #6390C2×C4semidirect
109. C2×#428D7semidirect
572. C7#21059semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4282
C2×#899052
#117396732
C2×C4⋊C4×Dic72
C2×#897382
#117297332
#117293352
#117283782
#117283772
#117283242
#117283232
#210597