Finite Group Databasebeta

← #13259145

Subgroups — #13259145

Order 1792.

1246 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×#90436C211yesmaximal, characteristic
2C2×#89904C211yesmaximal, characteristic
3#11739515C211yesmaximal, characteristic
4C7×#1728C211yesmaximal, characteristic, complemented
5C2×#89354C211yesmaximal, characteristic, complemented
6C2×#89351C211yesmaximal, characteristic, complemented
7#11729281C211yesmaximal, characteristic, complemented
8C22×#1157C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C22×C7×M16C2211yescharacteristic
11C22×C42×C7C2211yescharacteristic
12C2×#6489C2211yescharacteristic
13C22×#1136C2211yescharacteristic
14C22×#1136C2211yescharacteristic
15#90436—22no—
16#90436—22no—
17#90436—22no—
18#90436C414yescomplemented
19C2×#6470—22no—
20C2×D7×M16—22no—
21C2×#6464—22no—
22#89985C414yes—
23C2×#6398—21no—
24#89904—22no—
25#89904C414yescomplemented
26C2×#6397—21no—
27#89711—21no—
28C4×(C2×D7)⋊C4—22no—
29#89701—21no—
30C7×#336—22no—
31#89354—22no—
32#89351—22no—
33#89319—22no—
34#10746—71nomaximal, Sylow
35C23×C4×C7C2×C412yes—
36C23×C4×C7C2311yescharacteristic
37C22×C22⋊D7C2×C412yes—
38C2×#1157—21no—
39C2×#1157—21no—
40C2×#1157—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157—21no—
45C2×#1157—21no—
46C2×#1157C2×C412yes—
47C2×#1157C2×C412yes—
48C2×#1157D412yes—
49C2×#1157Q812yes—
50C22×D28D411yescharacteristic
51C22×C4×D7D412yes—
52C22×Dic14D411yescharacteristic
53C2×C7×M16—21no—
54C2×C7×M16—21no—
55C2×C7×M16—21no—
56C2×C7×M16—21no—
57C2×C7×M16—21no—
58C2×C7×M16—21no—
59C2×C7×M16—21no—
60C2×C7×M16—21no—
61C2×C7×M16—21no—
62C2×C7×M16C2×C412yes—
63C2×C7×M16C2×C412yes—
64C2×C7×M16D412yes—
65C22×C7×C8—21no—
66C22×C7×C8D412yes—
67C2×C42×C7—21no—
68C2×C42×C7—21no—
69C2×C42×C7—21no—
70C2×C42×C7—21no—
71C2×C42×C7—21no—
72C2×C42×C7—21no—
73C2×C22⋊Dic7C2×C412yes—
74C2×(C2×D7)⋊C4—24no—
75#6489—21no—
76#6489—21no—
77#6489—21no—
78#6489—21no—
79C2×C4⋊Dic7—21no—
80C2×C4×Dic7—21no—
81C2×#1136—21no—
82C2×#1136—21no—
83C2×#1136—21no—
84C2×#1136—21no—
85C2×#1136—21no—
86C2×#1136—21no—
87C2×#1136—21no—
88C2×#1136—21no—
89C2×#1136—21no—
90C2×#1136C2×C412yes—
91C2×#1136C2×C412yes—
92C2×#1136D412yes—
93C22×C7⋊C8—21no—
94C22×C7⋊C8D412yes—
95#6470—28no—
96#6470—28no—
97D7×M16—28no—
98D7×M16—28no—
99#6464—28no—
100#6464—28no—
101C2×#1131—24no—
102C2×C8×D7—24no—
103C7⋊#95—24no—
104#6398—24no—
105#6397—24no—
106C2×#568—71no—
107C2×#413—71no—
108#2297—71no—
109C2×#344—71no—
110C2×#344—71no—
111#1728—71no—
112#1728D711yescharacteristic, complemented
113C24×C7C22×C411yescharacteristic
114C23×D7C22⋊C412yes—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—44no—
119C22×C4×C7C22×C411yescharacteristic
120C22×C4×C7C22×C411yescharacteristic
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×Q811yescharacteristic
129C22×C4×C7#4111yescharacteristic
130C22×C4×C7#4111yescharacteristic
131C22×C4×C7#4111yescharacteristic
132C22×C4×C7#4111yescharacteristic
133C2×C22⋊D7—22no—
134C2×C22⋊D7—22no—
135C2×C22⋊D7—22no—
136C2×C22⋊D7—22no—
137C2×C22⋊D7C4214yes—
138C2×C22⋊D7C4⋊C414yes—
139C22×Dic7—22no—
140C22×Dic7C22⋊C412yes—
141#1157—22no—
142#1157—22no—
143#1157—22no—
144#1157—22no—
145#1157—22no—
146#1157—22no—
147#1157—22no—
148#1157—22no—
149#1157—22no—
150#1157—22no—
151#1157—22no—
152#1157—22no—
153#1157—22no—
154#1157—22no—
155#1157—22no—
156#1157—22no—
157C2×D28—21no—
158C2×D28—21no—
159C2×D28—21no—
160C2×D28—21no—
161C2×D28C22⋊C412yes—
162C2×D28C4⋊C412yes—
163C2×C4×D7—22no—
164C2×C4×D7—22no—
165C2×C4×D7—22no—
166C2×C4×D7—22no—
167C2×C4×D7C22⋊C414yes—
168C2×C4×D7C4⋊C414yes—
169C2×Dic14—21no—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14—21no—
173C2×Dic14C22⋊C412yes—
174C2×Dic14C4⋊C412yes—
175C7×M16—22no—
176C7×M16—22no—
177C7×M16—22no—
178C7×M16—22no—
179C7×M16—22no—
180C7×M16—22no—
181C7×M16—41no—
182C7×M16—41no—
183C2×C7×C8—22no—
184C2×C7×C8—22no—
185C2×C7×C8—22no—
186C2×C7×C8—41no—
187C2×C7×C8—41no—
188C2×C7×C8C22⋊C414yescomplemented
189C42×C7—41no—
190C42×C7—41no—
191C42×C7—41no—
192C42×C7—41no—
193C22⋊Dic7—22no—
194C22⋊Dic7—22no—
195(C2×D7)⋊C4—48no—
196C4⋊Dic7—41no—
197C4⋊Dic7—41no—
198C4×Dic7—41no—
199C4×Dic7—41no—
200#1136—22no—
201#1136—22no—
202#1136—22no—
203#1136—22no—
204#1136—22no—
205#1136—22no—
206#1136—41no—
207#1136—41no—
208C2×C7⋊C8—22no—
209C2×C7⋊C8—22no—
210C2×C7⋊C8—22no—
211C2×C7⋊C8—41no—
212C2×C7⋊C8—41no—
213C2×C7⋊C8C22⋊C414yescomplemented
214#1131—216no—
215C8×D7—216no—
216C22×#41—71no—
217#568—74no—
218#568—142no—
219#568—142no—
220#568—142no—
221C2×#131—142no—
222C2×#131—142no—
223C22×M16—71no—
224C22×M16—71no—
225C22×M16—142no—
226C22×M16C2×D711yescharacteristic
227C22×M16C2×D711yescharacteristic
228C2×#117—71no—
229C22×C42C2×D711yescharacteristic
230#413—74no—
231#413—142no—
232C2×#101—141no—
233C2×#100—141no—
234#391—141no—
235#390—141no—
236#386—74no—
237C4×C22⋊C4—142no—
238#344—142no—
239#344—142no—
240#336—22no—
241#336—142no—
242C23×C7—42no—
243C23×C7C2×C4211yescharacteristic
244C23×C7C2×C22⋊C411yescharacteristic
245C23×C7C2×C4⋊C411yescharacteristic
246C23×C7C4×D411yescharacteristic
247C23×C7C4×D411yescharacteristic
248C23×C7C4×D411yescharacteristic
249C23×C7C4×D411yescharacteristic
250C22×D7—22no—
251C22×D7—22no—
252C22×D7—44no—
253C22×D7#9514yes—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7C2×C22⋊C411yescharacteristic
262C2×C4×C7C2×C22⋊C411yescharacteristic
263C2×C4×C7C2×C22⋊C411yescharacteristic
264C2×C4×C7C2×C22⋊C411yescharacteristic
265C2×C4×C7C2×C4⋊C411yescharacteristic
266C2×C4×C7C2×C4⋊C411yescharacteristic
267C2×C4×C7#11711yescharacteristic
268C2×C4×C7#11711yescharacteristic
269C2×C4×C7C4×D411yescharacteristic
270C2×C4×C7C4×D411yescharacteristic
271C2×C4×C7C4×D411yescharacteristic
272C2×C4×C7C4×D411yescharacteristic
273C2×C4×C7#12011yescharacteristic
274C2×C4×C7#12011yescharacteristic
275C2×C4×C7#12011yescharacteristic
276C2×C4×C7#12011yescharacteristic
277C2×C4×C7#12111yescharacteristic
278C2×C4×C7#12111yescharacteristic
279C2×C4×C7#12111yescharacteristic
280C2×C4×C7#12111yescharacteristic
281C2×C4×C7C22⋊Q811yescharacteristic
282C2×C4×C7C22⋊Q811yescharacteristic
283C2×C4×C7C22⋊Q811yescharacteristic
284C2×C4×C7C22⋊Q811yescharacteristic
285C2×C4×C7#12311yescharacteristic
286C2×C4×C7#12311yescharacteristic
287C2×C4×C7#12311yescharacteristic
288C2×C4×C7#12311yescharacteristic
289C22⋊D7—24no—
290C22⋊D7—24no—
291C22⋊D7—24no—
292C22⋊D7—24no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—44no—
296C2×Dic7—42no—
297C2×Dic7#9514yes—
298D28—22no—
299D28—22no—
300D28—22no—
301D28—22no—
302C4×D7—24no—
303C4×D7—24no—
304C4×D7—24no—
305C4×D7—24no—
306Dic14—22no—
307Dic14—22no—
308Dic14—22no—
309Dic14—22no—
310C7×C8—24no—
311C7×C8—42no—
312C7⋊C8—24no—
313C7⋊C8—42no—
314C2×#41—72no—
315C2×#41—72no—
316C2×#41—72no—
317C2×#41—72no—
318C2×#41—141no—
319C2×#41—141no—
320C2×#41—141no—
321C2×#41—141no—
322C2×#41—141no—
323C2×#41—141no—
324C2×#41—141no—
325C2×#41—141no—
326C22×Q8—71no—
327C22×D4—72no—
328C22×D4—71no—
329C23×C4—72no—
330C23×C4C4×D712yes—
331C23×C4C22×D711yescharacteristic
332#131—148no—
333#131—148no—
334#131—148no—
335#131—148no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—72no—
346C2×M16—72no—
347C2×M16—72no—
348C2×M16—144no—
349C2×M16—148no—
350C2×M16—148no—
351C2×M16—141no—
352C2×M16—141no—
353C2×M16—141no—
354C2×M16—141no—
355C2×M16—141no—
356C2×M16—141no—
357C2×M16—141no—
358C2×M16—141no—
359C2×M16—141no—
360C2×M16C4×D712yes—
361C2×M16C4×D712yes—
362C2×M16D2812yes—
363C22×C8—21no—
364C22×C8—72no—
365C22×C8—144no—
366C22×C8—141no—
367C22×C8C22⋊D712yes—
368#117—141no—
369#117—141no—
370#117—141no—
371#117—141no—
372C2×C4⋊C4—141no—
373C2×C22⋊C4—72no—
374C2×C22⋊C4—144no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—141no—
382#101—144no—
383#100—144no—
384#95—144no—
385C22×C7—22no—
386C22×C7—22no—
387C22×C7—22no—
388C22×C7—41no—
389C22×C7—41no—
390C22×C7—41no—
391C22×C7—41no—
392C22×C7C2×#9511yescharacteristic
393C22×C7C4×C22⋊C411yescharacteristic
394C22×C7C4×C22⋊C411yescharacteristic
395C22×C7#38511yescharacteristic
396C22×C7#38511yescharacteristic
397C22×C7#38611yescharacteristic
398C22×C7#38611yescharacteristic
399C2×D7—24no—
400C2×D7—44no—
401C2×D7—44no—
402C2×D7—82no—
403C4×C7—44no—
404C4×C7#37911yescharacteristic
405C4×C7#38011yescharacteristic
406C4×C7#38011yescharacteristic
407C4×C7#38111yescharacteristic
408C4×C7#38511yescharacteristic
409C4×C7#38511yescharacteristic
410C4×C7#38611yescharacteristic
411C4×C7#38611yescharacteristic
412Dic7—24no—
413Dic7—82no—
414C24—72no—
415C24C2×C4×D711yescharacteristic
416#41—142no—
417#41—142no—
418#41—142no—
419#41—142no—
420#41—142no—
421#41—142no—
422#41—142no—
423#41—142no—
424#41—142no—
425#41—142no—
426#41—142no—
427#41—142no—
428#41—142no—
429#41—142no—
430#41—142no—
431#41—142no—
432C2×Q8—72no—
433C2×Q8—72no—
434C2×Q8—141no—
435C2×Q8—141no—
436C2×Q8—141no—
437C2×Q8—141no—
438C2×D4—74no—
439C2×D4—74no—
440C2×D4—72no—
441C2×D4—72no—
442C2×D4—142no—
443C2×D4—142no—
444C2×D4—142no—
445C2×D4—142no—
446C2×D4—141no—
447C2×D4—141no—
448C2×D4—141no—
449C2×D4—141no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—44no—
454C22×C4—72no—
455C22×C4—74no—
456C22×C4—74no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4C2×C4×D711yescharacteristic
463C22×C4C2×C4×D711yescharacteristic
464C22×C4C2×D2811yescharacteristic
465C22×C4#115711yescharacteristic
466C22×C4#115711yescharacteristic
467C22×C4D4×D711yescharacteristic
468C22×C4D4×D711yescharacteristic
469C22×C4D4×D711yescharacteristic
470C22×C4D4×D711yescharacteristic
471C22×C4D4×D711yescharacteristic
472C22×C4#115911yescharacteristic
473C22×C4Q8×D711yescharacteristic
474C22×C4#116111yescharacteristic
475C22×C4C2×C22⋊D711yescharacteristic
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—22no—
482M16—41no—
483M16—41no—
484M16—1416no—
485M16—142no—
486M16—142no—
487M16—142no—
488M16—142no—
489M16—142no—
490M16—142no—
491M16—281no—
492M16—281no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—74no—
499C2×C8—1416no—
500C2×C8—142no—
501C2×C8—142no—
502C2×C8—142no—
503C2×C8—281no—
504C2×C8—281no—
505C2×C8(C2×D7)⋊C414yescomplemented
506C4⋊C4—281no—
507C4⋊C4—281no—
508C22⋊C4—142no—
509C22⋊C4—142no—
510C22⋊C4—288no—
511C42—41no—
512C42—41no—
513C42—41no—
514C42—41no—
515C42—281no—
516C42—281no—
517C2×C7—21no—
518C2×C7—21no—
519C2×C7—21no—
520C2×C7—21no—
521C2×C7—21no—
522C2×C7—21no—
523C2×C7C22⋊#9511yescharacteristic
524C2×C7#189112yes—
525D7—44no—
526C23—42no—
527C23—74no—
528C23—142no—
529C23—142no—
530C23—284no—
531C23C42×D711yescharacteristic
532C23C4×D2811yescharacteristic
533C23D7×C22⋊C411yescharacteristic
534C23(C22⋊D7)⋊C411yescharacteristic
535C23D7×C4⋊C411yescharacteristic
536C23#645611yescharacteristic
537C23C4×C22⋊D711yescharacteristic
538Q8—142no—
539Q8—142no—
540Q8—142no—
541Q8—142no—
542D4—144no—
543D4—144no—
544D4—144no—
545D4—144no—
546D4—142no—
547D4—142no—
548D4—142no—
549D4—142no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—74no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—144no—
561C2×C4—144no—
562C2×C4—144no—
563C2×C4—144no—
564C2×C4—284no—
565C2×C4—282no—
566C2×C4#643511yescharacteristic
567C2×C4C4×D2811yescharacteristic
568C2×C4D7×C22⋊C411yescharacteristic
569C2×C4D7×C22⋊C411yescharacteristic
570C2×C4D7×C22⋊C411yescharacteristic
571C2×C4(C22⋊D7)⋊C411yescharacteristic
572C2×C4#644511yescharacteristic
573C2×C4#644511yescharacteristic
574C2×C4#644611yescharacteristic
575C2×C4#644611yescharacteristic
576C2×C4#644711yescharacteristic
577C2×C4#644711yescharacteristic
578C2×C4D7×C4⋊C411yescharacteristic
579C2×C4D7×C4⋊C411yescharacteristic
580C2×C4#645511yescharacteristic
581C2×C4#645611yescharacteristic
582C2×C4#645711yescharacteristic
583C2×C4#645711yescharacteristic
584C2×C4#645811yescharacteristic
585C2×C4#645911yescharacteristic
586C2×C4#645911yescharacteristic
587C2×C4#646011yescharacteristic
588C2×C4C2×(C2×D7)⋊C411yescharacteristic
589C2×C4C4×C22⋊D711yescharacteristic
590C2×C4#650011yescharacteristic
591C2×C4#650011yescharacteristic
592C2×C4#650111yescharacteristic
593C2×C4#650911yescharacteristic
594C8—24no—
595C8—42no—
596C8—144no—
597C8—282no—
598C7#1074611yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—144no—
607C22—284no—
608C22—284no—
609C22—562no—
610C22D7×#9511yescharacteristic
611C22#8943711yescharacteristic
612C22#8943811yescharacteristic
613C22#8944011yescharacteristic
614C22C4×(C2×D7)⋊C411yescharacteristic
615C22#8972811yescharacteristic
616C22#8976111yescharacteristic
617C4—44no—
618C4—144no—
619C4—562no—
620C4#8943611yescharacteristic
621C4#8943711yescharacteristic
622C4#8943911yescharacteristic
623C4#8944011yescharacteristic
624C4#8972711yescharacteristic
625C4#8972811yescharacteristic
626C4#8975911yescharacteristic
627C4#8976111yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—284no—
635C2(C2×D7)⋊#9511yescharacteristic
636C2#1172774612yes—
subgroupG/H
centerC2×C4#6500
commutatorC23×C7C2×C42
FrattiniC23×C4C22×D7
FittingC7×#1728C2
socleC22×C7#386
prime radicalC22×#1157C22
cosocleC23×C4×C7C23
hypercenter#1728D7
hypocenterC7#10746
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1728

Complements

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

NH ≅ G/Ntype
4. C7×#1728C2semidirect
5. C2×#89354C2semidirect
6. C2×#89351C2semidirect
7. #11729281C2semidirect
18. #90436C4semidirect
25. #89904C4semidirect
112. #1728D7semidirect
188. C2×C7×C8C22⋊C4semidirect
213. C2×C7⋊C8C22⋊C4semidirect
505. C2×C8(C2×D7)⋊C4semidirect
598. C7#10746semidirect

Maximal subgroups

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

subgroupindex
C2×#904362
C2×#899042
#117395152
C7×#17282
C2×#893542
C2×#893512
#117292812
#107467