Finite Group Databasebeta

← #13324636

Subgroups — #13324636

Order 1792.

624 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737043C211yesmaximal, characteristic
2#11736992C211yesmaximal, characteristic, complemented
3#11736876C211yesmaximal, characteristic, complemented
4C7×#1586C211yesmaximal, characteristic, complemented
5#11728634C211yesmaximal, characteristic, complemented
6#11728616C211yesmaximal, characteristic, complemented
7#11728595C211yesmaximal, characteristic, complemented
8#11726284C211yesmaximal, characteristic, complemented
9#11726275C211yesmaximal, characteristic, complemented
10#11725933C211yesmaximal, characteristic, complemented
11#11725933C211yesmaximal, characteristic, complemented
12#11725907C211yesmaximal, characteristic, complemented
13#11725906C211yesmaximal, characteristic, complemented
14#11725835C211yesmaximal, characteristic, complemented
15#11725825C211yesmaximal, characteristic, complemented
16#90239C2211yescharacteristic
17#90239C2211yescharacteristic
18C4×C7×D8C2211yescharacteristic
19C7×#436C2211yescharacteristic
20C7×C8×D4C2211yescharacteristic
21#89929C411yescharacteristic
22#89923C411yescharacteristic
23#89901—21no—
24#89899—21no—
25#89883—21no—
26#89882—21no—
27C4×#1141C2211yescharacteristic
28C4×#1141C2211yescharacteristic
29#89784C2211yescharacteristic
30D4×C7⋊C8C2211yescharacteristic
31#89655C411yescharacteristic
32#89646C411yescharacteristic
33#89610C2211yescharacteristic
34#89607C2211yescharacteristic
35#89607C2211yescharacteristic
36#89606C2211yescharacteristic
37#89547C411yescharacteristic
38#89547C411yescharacteristic
39#89532C411yescharacteristic
40#89532C411yescharacteristic
41#89502—21no—
42#89500—21no—
43#89499—21no—
44#89499—21no—
45C4×D56C2211yescharacteristic
46#89460C2211yescharacteristic
47C8×D28C2211yescharacteristic
48#89457C2211yescharacteristic
49#89457C2211yescharacteristic
50C4×C8×D7C2211yescharacteristic
51C7×#334C2211yescharacteristic
52C7×D4⋊C8C2211yescharacteristic
53C7×D4⋊C8C2211yescharacteristic
54C7×#322C2211yescharacteristic
55D4⋊(C7⋊C8)C2211yescharacteristic
56D4⋊(C7⋊C8)C2211yescharacteristic
57#89278C2211yescharacteristic
58#89278C2211yescharacteristic
59#89274C2211yescharacteristic
60#89274C2211yescharacteristic
61#89254C2211yescharacteristic
62#89254C2211yescharacteristic
63#89252C2211yescharacteristic
64#89250C2211yescharacteristic
65#89249C2211yescharacteristic
66#89249C2211yescharacteristic
67#17989—71nomaximal, Sylow
68C2×#1157—21no—
69C2×#1157—21no—
70C2×C7×D8C2×C411yescharacteristic
71C2×C7×M16—21no—
72C22×C7×C8—21no—
73C4×C7×D4C2311yescharacteristic
74C4×C7×D4C2311yescharacteristic
75#6503C2×C411yescharacteristic
76#6503C2×C411yescharacteristic
77#6501C2×C411yescharacteristic
78#6501C2×C411yescharacteristic
79C2×#1141C2×C411yescharacteristic
80C2×#1141C2×C411yescharacteristic
81C4×C22⋊D7—21no—
82C4×C22⋊D7—21no—
83C2×#1136—21no—
84C22×C7⋊C8—21no—
85C2×D56C2×C411yescharacteristic
86C2×#1131—21no—
87C2×#1131—21no—
88C2×C8×D7—21no—
89C2×C8×D7—21no—
90C2×C8×D7C2×C411yescharacteristic
91C2×C8×D7C2×C411yescharacteristic
92#6458C2×C411yescharacteristic
93#6458C2×C411yescharacteristic
94#6451C2×C411yescharacteristic
95#6451C2×C411yescharacteristic
96#6448—21no—
97#6448—21no—
98#6447—21no—
99#6447—21no—
100C4×D28C2311yescharacteristic
101C4×D28C2311yescharacteristic
102C42×D7C2311yescharacteristic
103C7×#107C2×C411yescharacteristic
104C7×C4⋊C8C2311yescharacteristic
105C7×C4⋊C8C2311yescharacteristic
106C7×#102C2×C411yescharacteristic
107C7×#102C2×C411yescharacteristic
108C7×C22⋊C8—21no—
109C7×C22⋊C8—21no—
110C4×C7×C8C2311yescharacteristic
111C4×C7×C8C2311yescharacteristic
112C4×C7×C8C2311yescharacteristic
113#6406C2×C411yescharacteristic
114#6406C2×C411yescharacteristic
115C22⋊(C7⋊C8)—21no—
116C22⋊(C7⋊C8)—21no—
117#6395C2×C411yescharacteristic
118#6395C2×C411yescharacteristic
119(C2×D7)⋊C8—21no—
120(C2×D7)⋊C8—21no—
121(C2×D7)⋊C8—21no—
122(C2×D7)⋊C8—21no—
123(C2×D7)⋊C8—21no—
124(C2×D7)⋊C8—21no—
125(C2×D7)⋊C8—21no—
126(C2×D7)⋊C8D411yescharacteristic
127(C2×D7)⋊C8D411yescharacteristic
128#6392C2×C411yescharacteristic
129#6389—21no—
130#6389—21no—
131Dic7⋊C8—21no—
132Dic7⋊C8D411yescharacteristic
133Dic7⋊C8D411yescharacteristic
134C8×Dic7C2×C411yescharacteristic
135C8×Dic7C2×C411yescharacteristic
136#6383C2×C411yescharacteristic
137#6383C2×C411yescharacteristic
138#6381C2×C411yescharacteristic
139#6381C2×C411yescharacteristic
140C4⋊(C7⋊C8)C2311yescharacteristic
141C4⋊(C7⋊C8)C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3169—71no—
146#2981—71no—
147#2981—71no—
148#1586—71no—
149#1586—71no—
150#1586—71no—
151#1586D711yescharacteristic, complemented
152#1581—71no—
153#1581—71no—
154#1581—71no—
155#1581—71no—
156#1568—71no—
157#1496—71no—
158#1496—71no—
159#1452—71no—
160C2×C7×D4C22×C411yescharacteristic
161C2×C7×D4C22×C411yescharacteristic
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C2×C22⋊D7—21no—
165C2×C22⋊D7—21no—
166C2×C22⋊D7—21no—
167C2×C22⋊D7—21no—
168C2×C22⋊D7—21no—
169C2×C22⋊D7—21no—
170#1157—81no—
171#1157—81no—
172#1157—81no—
173#1157—81no—
174C2×D28—21no—
175C2×D28—21no—
176C2×D28C22×C411yescharacteristic
177C2×D28C22×C411yescharacteristic
178C2×C4×D7—21no—
179C2×C4×D7—21no—
180C2×C4×D7C22×C411yescharacteristic
181C2×C4×D7C2×D411yescharacteristic
182C2×C4×D7#4111yescharacteristic
183C2×Dic14—21no—
184C2×Dic14—21no—
185C7×D8—41no—
186C7×M16—81no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—81no—
191C2×C7×C8C22×C411yescharacteristic
192C2×C7×C8C22×C411yescharacteristic
193C2×C7×C8C2×D411yescharacteristic
194C2×C7×C8C2×D411yescharacteristic
195C7×C4⋊C4C22×C411yescharacteristic
196C7×C4⋊C4C22×C411yescharacteristic
197C7×C22⋊C4—21no—
198C7×C22⋊C4—21no—
199C42×C7C2411yescharacteristic
200C22⋊Dic7—21no—
201C22⋊Dic7—21no—
202#1141—41no—
203#1141—41no—
204(C2×D7)⋊C4—21no—
205(C2×D7)⋊C4—21no—
206(C2×D7)⋊C4—21no—
207(C2×D7)⋊C4—21no—
208C4⋊Dic7C22×C411yescharacteristic
209C4⋊Dic7C22×C411yescharacteristic
210Dic7⋊C4—21no—
211Dic7⋊C4—21no—
212C4×Dic7C22×C411yescharacteristic
213C4×Dic7C2×D411yescharacteristic
214C4×Dic7#4111yescharacteristic
215#1136—81no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—81no—
220C2×C7⋊C8C22×C411yescharacteristic
221C2×C7⋊C8C22×C411yescharacteristic
222C2×C7⋊C8C2×D411yescharacteristic
223C2×C7⋊C8C2×D411yescharacteristic
224D56—41no—
225#1131—81no—
226#1131—81no—
227C8×D7—41no—
228C8×D7—41no—
229C8×D7—81no—
230C8×D7—81no—
231#532—71no—
232#532—71no—
233#500—71no—
234#493—71no—
235#486—71no—
236#486—71no—
237#466—71no—
238#466—71no—
239#466—71no—
240#466—71no—
241C4×D8—71no—
242C4×D8—71no—
243C4×D8—71no—
244C4×D8C2×D711yescharacteristic
245#436—71no—
246#436—71no—
247#436—71no—
248#436C2×D711yescharacteristic
249#435—141no—
250#435—141no—
251#435—141no—
252#435—141no—
253C8×D4—71no—
254C8×D4—71no—
255C8×D4—71no—
256C8×D4C2×D711yescharacteristic
257#432—71no—
258#432—71no—
259#431—71no—
260#431—71no—
261#408—141no—
262#408—141no—
263#408—141no—
264#408—141no—
265C2×C4×C8—71no—
266#335—71no—
267#335—71no—
268#334—71no—
269#334C2×D711yescharacteristic
270D4⋊C8—71no—
271D4⋊C8—71no—
272D4⋊C8—71no—
273D4⋊C8—71no—
274D4⋊C8—71no—
275D4⋊C8—71no—
276D4⋊C8C2×D711yescharacteristic
277D4⋊C8C2×D711yescharacteristic
278#322—71no—
279#322—71no—
280#322—71no—
281#322C2×D711yescharacteristic
282C23×C7—21no—
283C23×C7—21no—
284C22×D7—21no—
285C22×D7—21no—
286C22×D7C4×D411yescharacteristic
287C7×D4—21no—
288C7×D4—21no—
289C7×D4—21no—
290C7×D4—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7C23×C411yescharacteristic
298C2×C4×C7C22×D411yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C22⋊D7—81no—
301C22⋊D7—81no—
302C22⋊D7—81no—
303C22⋊D7—81no—
304C22⋊D7—81no—
305C22⋊D7—81no—
306C2×Dic7—21no—
307C2×Dic7—21no—
308C2×Dic7C4×D411yescharacteristic
309C2×Dic7C4×D411yescharacteristic
310C2×Dic7C4×D411yescharacteristic
311D28—21no—
312D28—21no—
313D28—21no—
314D28—21no—
315D28—81no—
316D28—81no—
317C4×D7—21no—
318C4×D7—21no—
319C4×D7—21no—
320C4×D7—21no—
321C4×D7—41no—
322C4×D7—41no—
323C4×D7—41no—
324C4×D7—41no—
325C4×D7—41no—
326Dic14—81no—
327Dic14—81no—
328C7×C8—21no—
329C7×C8—21no—
330C7×C8—21no—
331C7×C8—21no—
332C7×C8—41no—
333C7×C8—41no—
334C7×C8—41no—
335C7⋊C8—21no—
336C7⋊C8—21no—
337C7⋊C8—21no—
338C7⋊C8—21no—
339C7⋊C8—41no—
340C7⋊C8—41no—
341C7⋊C8—41no—
342C2×#41—141no—
343C2×#41—141no—
344C2×D8—71no—
345C2×D8—71no—
346C2×D8—71no—
347C2×D8C4×D711yescharacteristic
348C2×M16—21no—
349C2×M16—141no—
350C2×M16—141no—
351C2×M16—141no—
352C22×C8—21no—
353C22×C8—71no—
354C22×C8—71no—
355C22×C8—141no—
356C22×C8—141no—
357C22×C8—141no—
358C4⋊Q8—71no—
359C4⋊Q8—71no—
360#127—71no—
361#127—71no—
362#124—141no—
363#124—141no—
364#121—71no—
365#121—71no—
366#121—71no—
367#121—71no—
368#121—141no—
369#121—141no—
370C4×D4—71no—
371C4×D4—71no—
372C4×D4—141no—
373C4×D4—141no—
374C4×D4C22×D711yescharacteristic
375C4×D4C22×D711yescharacteristic
376C2×C42—71no—
377#107—71no—
378#107—71no—
379#107—71no—
380#107C4×D711yescharacteristic
381C4⋊C8—71no—
382C4⋊C8—71no—
383C4⋊C8—71no—
384C4⋊C8—71no—
385C4⋊C8—141no—
386C4⋊C8C22×D711yescharacteristic
387C4⋊C8C22×D711yescharacteristic
388#102—71no—
389#102—71no—
390#102—71no—
391#102—71no—
392#102—71no—
393#102—71no—
394#102C4×D711yescharacteristic
395#102C4×D711yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—71no—
399C22⋊C8—71no—
400C22⋊C8—141no—
401C22⋊C8—141no—
402C22⋊C8—141no—
403C22⋊C8—141no—
404C22⋊C8—141no—
405C22⋊C8—141no—
406C22⋊C8—141no—
407C22⋊C8—141no—
408C22⋊C8—141no—
409#97—141no—
410#97—141no—
411C4×C8—71no—
412C4×C8—71no—
413C4×C8—71no—
414C4×C8—71no—
415C4×C8—71no—
416C4×C8C22×D711yescharacteristic
417C4×C8C22×D711yescharacteristic
418C4×C8C22×D711yescharacteristic
419C22×C7—41no—
420C22×C7—41no—
421C22×C7—41no—
422C22×C7—41no—
423C22×C7—41no—
424C22×C7—41no—
425C22×C7C2×C4×D411yescharacteristic
426C2×D7—21no—
427C2×D7—21no—
428C2×D7—21no—
429C2×D7—41no—
430C2×D7—41no—
431C2×D7—41no—
432C2×D7—41no—
433C2×D7—41no—
434C2×D7—41no—
435C4×C7—21no—
436C4×C7—41no—
437C4×C7—41no—
438C4×C7#56811yescharacteristic
439C4×C7#56811yescharacteristic
440C4×C7#57611yescharacteristic
441C4×C7#57611yescharacteristic
442Dic7—21no—
443Dic7—21no—
444Dic7—21no—
445Dic7—41no—
446Dic7—41no—
447#41—561no—
448#41—561no—
449#41—561no—
450#41—561no—
451C2×Q8—141no—
452C2×Q8—141no—
453C2×D4—71no—
454C2×D4—71no—
455C2×D4—141no—
456C2×D4—141no—
457C2×D4—141no—
458C2×D4—141no—
459C2×D4—141no—
460C2×D4—141no—
461C2×D4—141no—
462C2×D4—141no—
463C2×D4C2×C4×D711yescharacteristic
464C2×D4C2×C4×D711yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—71no—
468C22×C4—71no—
469C22×C4—71no—
470C22×C4—141no—
471C22×C4—141no—
472D8—41no—
473D8—281no—
474D8—281no—
475D8—281no—
476M16—81no—
477M16—561no—
478M16—561no—
479M16—561no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—71no—
484C2×C8—71no—
485C2×C8—71no—
486C2×C8—71no—
487C2×C8—81no—
488C2×C8—141no—
489C2×C8—141no—
490C2×C8—141no—
491C2×C8—281no—
492C2×C8—281no—
493C2×C8—561no—
494C2×C8—561no—
495C2×C8—561no—
496C2×C8C2×C4×D711yescharacteristic
497C2×C8C2×C4×D711yescharacteristic
498C2×C8D4×D711yescharacteristic
499C2×C8D4×D711yescharacteristic
500C4⋊C4—71no—
501C4⋊C4—71no—
502C4⋊C4—141no—
503C4⋊C4—141no—
504C4⋊C4C2×C4×D711yescharacteristic
505C4⋊C4C2×C4×D711yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—141no—
509C22⋊C4—141no—
510C22⋊C4—141no—
511C22⋊C4—141no—
512C22⋊C4—141no—
513C22⋊C4—141no—
514C42—71no—
515C42—71no—
516C42—71no—
517C42C23×D711yescharacteristic
518C2×C7—81no—
519C2×C7—81no—
520C2×C7#293211yescharacteristic
521C2×C7#294811yescharacteristic
522C2×C7#295711yescharacteristic
523D7—41no—
524D7—81no—
525D7—81no—
526C23—21no—
527C23—21no—
528C23—71no—
529C23—141no—
530C23—141no—
531Q8—561no—
532Q8—561no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—141no—
538D4—141no—
539D4—141no—
540D4—141no—
541D4—561no—
542D4—561no—
543D4—561no—
544D4—561no—
545D4—561no—
546D4—561no—
547D4—561no—
548D4—561no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—71no—
556C2×C4—71no—
557C2×C4—71no—
558C2×C4—141no—
559C2×C4—141no—
560C2×C4—141no—
561C2×C4—141no—
562C2×C4—141no—
563C2×C4—141no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4C22×C4×D711yescharacteristic
570C2×C4C2×D4×D711yescharacteristic
571C2×C4D7×#4111yescharacteristic
572C8—21no—
573C8—21no—
574C8—21no—
575C8—21no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—141no—
580C8—141no—
581C8—141no—
582C8—141no—
583C8—281no—
584C8—281no—
585C8—281no—
586C7#1798911yescharacteristic, complemented, Sylow
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—141no—
594C22—141no—
595C22—141no—
596C22—281no—
597C22—281no—
598C22—281no—
599C22—281no—
600C22—281no—
601C22—281no—
602C22C4×D4×D711yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—141no—
607C4—141no—
608C4—141no—
609C4—281no—
610C4—281no—
611C4#9043611yescharacteristic
612C4#9044111yescharacteristic
613C4#9046511yescharacteristic
614C4#9046511yescharacteristic
615C2—81no—
616C2—81no—
617C2—281no—
618C2—561no—
619C2—561no—
620C2#1173692511yescharacteristic
621C2#1173731211yescharacteristic
622C2#1173733511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1586C2
socleC22×C7C2×C4×D4
prime radical#11737043C2
cosocleC42×C7C24
hypercenter#1586D7
hypocenterC7#17989
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #11736992C2semidirect
3. #11736876C2semidirect
4. C7×#1586C2semidirect
5. #11728634C2semidirect
6. #11728616C2semidirect
7. #11728595C2semidirect
8. #11726284C2semidirect
9. #11726275C2semidirect
10. #11725933C2semidirect
11. #11725933C2semidirect
12. #11725907C2semidirect
13. #11725906C2semidirect
14. #11725835C2semidirect
15. #11725825C2semidirect
151. #1586D7semidirect
586. C7#17989semidirect

Maximal subgroups

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

subgroupindex
#117370432
#117369922
#117368762
C7×#15862
#117286342
#117286162
#117285952
#117262842
#117262752
#117259332
#117259072
#117259062
#117258352
#117258252
#179897