Finite Group Databasebeta

← #13360646

Subgroups — #13360646

Order 1792.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2930C211yesmaximal, characteristic, complemented
2C2×#89917C211yesmaximal, characteristic, complemented
3#11741201C211yesmaximal, characteristic, complemented
4C2×M16×Dic7C211yesmaximal, characteristic, complemented
5#11740368C211yesmaximal, characteristic
6#11729762C211yesmaximal, characteristic, complemented
7#11729465C211yesmaximal, characteristic, complemented
8#11728291C211yesmaximal, characteristic, complemented
9#11728290C211yesmaximal, characteristic, complemented
10#11727753C211yesmaximal, characteristic, complemented
11#11727752C211yesmaximal, characteristic, complemented
12#11727737C211yesmaximal, characteristic, complemented
13#11727719C211yesmaximal, characteristic, complemented
14#11727644C211yesmaximal, characteristic, complemented
15#11727641C211yesmaximal, characteristic, complemented
16C2×C7×#131C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C7×#525C2211yescharacteristic
19C2×#6513C2211yescharacteristic
20#90482C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C22×#1136C2211yescharacteristic
23C2×#6464C2211yescharacteristic
24C7×#436—22no—
25C7×#435—22no—
26C7×#424C2211yescharacteristic
27C7×#408C2211yescharacteristic
28C7×#407C2211yescharacteristic
29C7×#405C2211yescharacteristic
30C2×#6411C2211yescharacteristic
31C2×#6411C2211yescharacteristic
32#90005C2211yescharacteristic
33#89979C2211yescharacteristic
34#89917—24no—
35C2×#6399C2211yescharacteristic
36C2×#6399C2211yescharacteristic
37#89900—22no—
38#89899—22no—
39C2×#6396C2211yescharacteristic
40C2×#6396C2211yescharacteristic
41M16×Dic7—24no—
42#89882C2211yescharacteristic
43#89874C2211yescharacteristic
44#89873C2211yescharacteristic
45C2×#6389C2211yescharacteristic
46C2×#6389C2211yescharacteristic
47C2×C8×Dic7C2211yescharacteristic
48C2×C8×Dic7C2211yescharacteristic
49#89824C412yescomplemented
50#89821C412yescomplemented
51#89814C412yescomplemented
52#89811C412yescomplemented
53#89774C2211yescharacteristic
54#89770C2211yescharacteristic
55#89353C2211yescharacteristic
56#89353C2211yescharacteristic
57#89350C2211yescharacteristic
58#89350C2211yescharacteristic
59#89327C2211yescharacteristic
60#89327C2211yescharacteristic
61#21551—71nomaximal, Sylow
62C2×C7×#41C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—21no—
65C2×#1157C2311yescharacteristic
66C7×#131—22no—
67C7×#131—22no—
68C2×C7×M16—22no—
69C2×C7×M16—21no—
70C2×C7×M16—22no—
71C2×C7×M16D412yes—
72C2×C7×M16D412yes—
73C2×C7×M16C2311yescharacteristic
74C2×C7×M16C2311yescharacteristic
75C22×C7×C8—21no—
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C7×#123—21no—
79C7×C22⋊Q8C2×C412yes—
80C7×#121C2×C412yes—
81C7×#120—21no—
82C4×C7×D4—22no—
83C7×#117C2311yescharacteristic
84#6516—21no—
85#6513—22no—
86#6513—22no—
87C2×#1144C2×C411yescharacteristic, complemented
88C2×#1143C2×C411yescharacteristic, complemented
89C2×#1142C2×C411yescharacteristic, complemented
90C2×#1141C2×C411yescharacteristic, complemented
91#6493C2×C412yes—
92#6492—21no—
93C4×C22⋊D7—22no—
94#6489C2311yescharacteristic
95#6487C2×C412yes—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7C2311yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C2×#1136—22no—
102C2×#1136—22no—
103C2×#1136C2×C412yes—
104C2×#1136C2×C412yes—
105C2×#1136C2311yescharacteristic
106C2×#1136C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109#6464—22no—
110#6464—22no—
111C2×#1131—21no—
112C2×C8×D7—21no—
113C7×C4⋊C8—22no—
114C7×C22⋊C8—22no—
115C7×C22⋊C8—22no—
116C7×#97—21no—
117C4×C7×C8—21no—
118#6411—22no—
119#6411—22no—
120#6409C2×C412yescomplemented
121#6406C2×C412yescomplemented
122C22⋊(C7⋊C8)—22no—
123#6399—22no—
124#6399—22no—
125#6396—22no—
126#6396—22no—
127(C2×D7)⋊C8—22no—
128#6389—21no—
129#6389—22no—
130#6389D414yescomplemented
131Dic7⋊C8—22no—
132C8×Dic7—22no—
133C8×Dic7—21no—
134C8×Dic7—22no—
135#6384C2×C412yescomplemented
136#6383C2×C412yescomplemented
137#6382C2×C412yescomplemented
138#6381C2×C412yescomplemented
139#3054—71no—
140C2×#444—71no—
141#2930—71no—
142#2930D711yescharacteristic, complemented
143C2×C4×M16—71no—
144#1974—71no—
145#1945—71no—
146#1938—71no—
147#1938—71no—
148#1896—71no—
149#1896—71no—
150#1811—71no—
151#1773—71no—
152#1764—71no—
153#1764—71no—
154C24×C7#4111yescharacteristic
155C7×#41—21no—
156C7×#41—21no—
157C7×#41—21no—
158C7×#41—21no—
159C2×C7×Q8C22×C411yescharacteristic
160C2×C7×D4—21no—
161C2×C7×D4—22no—
162C2×C7×D4C22×C411yescharacteristic
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7#4111yescharacteristic
171C22×C4×C7C2411yescharacteristic
172C2×C22⋊D7—21no—
173C2×C22⋊D7—22no—
174C22×Dic7—21no—
175C22×Dic7—24no—
176C22×Dic7—21no—
177C22×Dic7—44no—
178#1157—21no—
179#1157—21no—
180#1157—21no—
181#1157—21no—
182C2×D28C22×C411yescharacteristic
183C2×C4×D7—21no—
184C2×Dic14C22×C411yescharacteristic
185C7×M16—24no—
186C7×M16—24no—
187C7×M16—21no—
188C7×M16—21no—
189C7×M16—21no—
190C7×M16—21no—
191C7×M16—42no—
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8—21no—
195C2×C7×C8—21no—
196C2×C7×C8—42no—
197C2×C7×C8C2×D412yes—
198C2×C7×C8C2×D412yes—
199C2×C7×C8C2×D411yescharacteristic
200C2×C7×C8C2×D411yescharacteristic
201C2×C7×C8#4112yes—
202C7×C4⋊C4—22no—
203C7×C4⋊C4C22×C412yes—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—21no—
206C7×C22⋊C4—22no—
207C42×C7—21no—
208C22⋊Dic7—22no—
209C22⋊Dic7—21no—
210#1144—22no—
211#1143—22no—
212#1142—22no—
213#1141—22no—
214(C2×D7)⋊C4—22no—
215C4⋊Dic7C22×C412yes—
216Dic7⋊C4—22no—
217C4×Dic7—24no—
218C4×Dic7—21no—
219C4×Dic7—21no—
220C4×Dic7—21no—
221C4×Dic7C2×D412yes—
222C4×Dic7#4112yes—
223#1136—24no—
224#1136—24no—
225#1136—21no—
226#1136—21no—
227#1136—21no—
228#1136—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8C22×C412yes—
234C2×C7⋊C8C22×C411yescharacteristic
235C2×C7⋊C8C22×C411yescharacteristic
236C2×C7⋊C8C2×D412yes—
237C2×C7⋊C8#4112yes—
238#1131—42no—
239C8×D7—42no—
240C2×#135—71no—
241C2×#131—71no—
242C2×#131C2×D711yescharacteristic
243C22×M16—71no—
244C22×M16C2×D711yescharacteristic
245#525—71no—
246#525C2×D711yescharacteristic
247C22×C42—71no—
248#470—72no—
249#469—72no—
250#468—72no—
251#468—72no—
252#444—144no—
253#436—22no—
254#436—142no—
255#435—22no—
256#435—142no—
257C2×#108—71no—
258C2×#108—71no—
259#427—71no—
260#424—71no—
261#424C2×D711yescharacteristic
262C2×#104—71no—
263C2×#104—71no—
264C2×#104—71no—
265C2×#104—71no—
266#416—71no—
267#416—71no—
268#408—71no—
269#408C2×D711yescharacteristic
270#407—71no—
271#407C2×D711yescharacteristic
272#405—71no—
273#405C2×D711yescharacteristic
274C4×M16—144no—
275C2×#97—71no—
276C2×#97—71no—
277C2×C4×C8—71no—
278C2×C4×C8—71no—
279#341—71no—
280#341—71no—
281#339—71no—
282#339—71no—
283#339—71no—
284#339—71no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—42no—
289C23×C7C4×D412yes—
290C23×C7C2×#4111yescharacteristic
291C22×D7—21no—
292C7×Q8—21no—
293C7×Q8—21no—
294C7×D4—21no—
295C7×D4—21no—
296C7×D4—41no—
297C7×D4—41no—
298C7×D4—82no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—21no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7C4×D412yes—
310C2×C4×C7C23×C411yescharacteristic
311C2×C4×C7C22×D411yescharacteristic
312C2×C4×C7C22×D411yescharacteristic
313C2×C4×C7C2×#4111yescharacteristic
314C2×C4×C7C2×#4111yescharacteristic
315C2×C4×C7C2×#4111yescharacteristic
316C22⋊D7—41no—
317C22⋊D7—41no—
318C22⋊D7—82no—
319C2×Dic7—24no—
320C2×Dic7—22no—
321C2×Dic7—22no—
322C2×Dic7—21no—
323C2×Dic7—22no—
324C2×Dic7—48no—
325C2×Dic7—42no—
326D28—21no—
327D28—21no—
328C4×D7—41no—
329C4×D7—41no—
330Dic14—21no—
331Dic14—21no—
332C7×C8—22no—
333C7×C8—41no—
334C7×C8—41no—
335C7×C8#12112yes—
336C7×C8#12112yes—
337C7⋊C8—22no—
338C7⋊C8—41no—
339C7⋊C8—41no—
340C7⋊C8C4×D412yes—
341C7⋊C8C4×D412yes—
342C2×#41—71no—
343C2×#41C22×D711yescharacteristic
344C23×C4—141no—
345C23×C4C22×D711yescharacteristic
346#135—142no—
347#135—142no—
348C2×Q16—71no—
349C2×SD16—71no—
350C2×SD16—71no—
351C2×D8—71no—
352#131—22no—
353#131—22no—
354#131—142no—
355#131—142no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—21no—
359C2×M16—72no—
360C2×M16—72no—
361C2×M16—71no—
362C2×M16—71no—
363C2×M16—142no—
364C2×M16—142no—
365C2×M16—141no—
366C2×M16C22⋊D712yes—
367C2×M16C22⋊D712yes—
368C2×M16C22×D711yescharacteristic
369C2×M16C22×D711yescharacteristic
370C22×C8—21no—
371C22×C8—71no—
372C22×C8—71no—
373C22×C8—141no—
374C22×C8C22×D711yescharacteristic
375C22×C8C22×D711yescharacteristic
376#123—21no—
377#123—141no—
378C22⋊Q8—72no—
379C22⋊Q8C4×D712yes—
380#121—72no—
381#121C4×D712yes—
382#120—21no—
383#120—141no—
384C4×D4—22no—
385C4×D4—142no—
386#117—71no—
387#117C22×D711yescharacteristic
388C2×C42—71no—
389C2×C42—71no—
390C2×C42—142no—
391C2×C42—142no—
392C2×C42—141no—
393#108—142no—
394#108—142no—
395#107—72no—
396#106—72no—
397C4⋊C8—22no—
398C4⋊C8—142no—
399#104—142no—
400#104—142no—
401#104—142no—
402#104—142no—
403#103—72no—
404#103—72no—
405#102—72no—
406#102—72no—
407C22⋊C8—22no—
408C22⋊C8—22no—
409C22⋊C8—142no—
410C22⋊C8—142no—
411#97—21no—
412#97—74no—
413#97—142no—
414#97—141no—
415C4×C8—21no—
416C4×C8—142no—
417C4×C8—142no—
418C4×C8—141no—
419C22×C7—22no—
420C22×C7—22no—
421C22×C7—22no—
422C22×C7—22no—
423C22×C7—42no—
424C22×C7—42no—
425C22×C7—42no—
426C22×C7—41no—
427C22×C7C2×C4×D411yescharacteristic
428C22×C7#52511yescharacteristic
429C22×C7#52911yescharacteristic
430C2×D7—42no—
431C2×D7—41no—
432C4×C7—22no—
433C4×C7—42no—
434C4×C7—41no—
435C4×C7C2×C4×D411yescharacteristic
436C4×C7C4×#4111yescharacteristic
437C4×C7C2×#12111yescharacteristic
438C4×C7#53211yescharacteristic
439Dic7—24no—
440Dic7—42no—
441Dic7—42no—
442Dic7—41no—
443C24#115711yescharacteristic
444#41—21no—
445#41—21no—
446#41—21no—
447#41—21no—
448#41—141no—
449#41—141no—
450#41—141no—
451#41—141no—
452C2×Q8—71no—
453C2×Q8C2×C4×D711yescharacteristic
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—71no—
457C2×D4—141no—
458C2×D4—142no—
459C2×D4C2×C4×D711yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—141no—
466C22×C4—144no—
467C22×C4—141no—
468C22×C4—141no—
469C22×C4—284no—
470C22×C4C2×C4×D712yes—
471C22×C4#115711yescharacteristic
472C22×C4C2×C22⋊D712yes—
473C22×C4C23×D711yescharacteristic
474Q16—142no—
475SD16—142no—
476SD16—142no—
477D8—142no—
478M16—24no—
479M16—24no—
480M16—21no—
481M16—21no—
482M16—21no—
483M16—21no—
484M16—42no—
485M16—144no—
486M16—144no—
487M16—141no—
488M16—141no—
489M16—141no—
490M16—141no—
491M16—282no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—42no—
497C2×C8—71no—
498C2×C8—71no—
499C2×C8—72no—
500C2×C8—72no—
501C2×C8—72no—
502C2×C8—141no—
503C2×C8—141no—
504C2×C8—141no—
505C2×C8—141no—
506C2×C8—282no—
507C2×C8D4×D712yes—
508C2×C8#115912yes—
509C2×C8C2×C22⋊D712yes—
510C2×C8C2×C22⋊D711yescharacteristic
511C2×C8C2×C22⋊D711yescharacteristic
512C4⋊C4—22no—
513C4⋊C4—72no—
514C4⋊C4—142no—
515C4⋊C4C2×C4×D712yes—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—22no—
519C22⋊C4—142no—
520C22⋊C4—141no—
521C22⋊C4—142no—
522C42—21no—
523C42—72no—
524C42—72no—
525C42—144no—
526C42—141no—
527C42—141no—
528C42—141no—
529C2×C7—21no—
530C2×C7—21no—
531C2×C7—42no—
532C2×C7—81no—
533C2×C7C4×#12111yescharacteristic
534C2×C7#295612yes—
535D7—81no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—42no—
540C23—141no—
541C23C4×C22⋊D712yes—
542C23C2×#115711yescharacteristic
543Q8—21no—
544Q8—21no—
545Q8—141no—
546Q8—141no—
547D4—21no—
548D4—21no—
549D4—41no—
550D4—41no—
551D4—82no—
552D4—141no—
553D4—141no—
554D4—281no—
555D4—281no—
556D4—562no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—144no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—141no—
571C2×C4—142no—
572C2×C4—288no—
573C2×C4—282no—
574C2×C4—281no—
575C2×C4—281no—
576C2×C4C4×C22⋊D712yes—
577C2×C4C22×C4×D711yescharacteristic
578C2×C4C2×D4×D711yescharacteristic
579C2×C4C2×#115911yescharacteristic
580C2×C4D7×#4111yescharacteristic
581C2×C4D7×#4111yescharacteristic
582C2×C4C22×C22⋊D711yescharacteristic
583C8—22no—
584C8—41no—
585C8—41no—
586C8—72no—
587C8—72no—
588C8—142no—
589C8—281no—
590C8—281no—
591C8#650212yes—
592C8#650212yes—
593C7#2155111yescharacteristic, complemented, Sylow
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—282no—
603C22—281no—
604C22#9022911yescharacteristic
605C22#9023811yescharacteristic
606C22C2×C4×C22⋊D711yescharacteristic
607C4—22no—
608C4—42no—
609C4—41no—
610C4—144no—
611C4—282no—
612C4—282no—
613C4—281no—
614C4C4×#115911yescharacteristic
615C4C4×D4×D711yescharacteristic
616C4C2×#650211yescharacteristic
617C4#9052311yescharacteristic
618C2—21no—
619C2—21no—
620C2—42no—
621C2—81no—
622C2—561no—
623C2C4×#650211yescharacteristic
624C2#1174125612yes—
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2930C2
socleC22×C7C2×C4×D4
prime radical#11740368C2
cosocleC22×C4×C7C24
hypercenter#2930D7
hypocenterC7#21551
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
1. C7×#2930C2semidirect
2. C2×#89917C2semidirect
3. #11741201C2semidirect
4. C2×M16×Dic7C2semidirect
6. #11729762C2semidirect
7. #11729465C2semidirect
8. #11728291C2semidirect
9. #11728290C2semidirect
10. #11727753C2semidirect
11. #11727752C2semidirect
12. #11727737C2semidirect
13. #11727719C2semidirect
14. #11727644C2semidirect
15. #11727641C2semidirect
49. #89824C4semidirect
50. #89821C4semidirect
51. #89814C4semidirect
52. #89811C4semidirect
87. C2×#1144C2×C4semidirect
88. C2×#1143C2×C4semidirect
89. C2×#1142C2×C4semidirect
90. C2×#1141C2×C4semidirect
120. #6409C2×C4semidirect
121. #6406C2×C4semidirect
130. #6389D4semidirect
135. #6384C2×C4semidirect
136. #6383C2×C4semidirect
137. #6382C2×C4semidirect
138. #6381C2×C4semidirect
142. #2930D7semidirect
593. C7#21551semidirect

Maximal subgroups

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

subgroupindex
C7×#29302
C2×#899172
#117412012
C2×M16×Dic72
#117403682
#117297622
#117294652
#117282912
#117282902
#117277532
#117277522
#117277372
#117277192
#117276442
#117276412
#215517