Finite Group Databasebeta

← #13360570

Subgroups — #13360570

Order 1792.

998 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
1#11740367C211yesmaximal, characteristic
2#11740361C211yesmaximal, characteristic, complemented
3C22×C4×C7⋊C8C211yesmaximal, characteristic, complemented
4C2×#89596C211yesmaximal, characteristic, complemented
5#11736071C211yesmaximal, characteristic, complemented
6C7×#1896C211yesmaximal, characteristic, complemented
7#11729286C211yesmaximal, characteristic, complemented
8#11728127C211yesmaximal, characteristic, complemented
9#11728125C211yesmaximal, characteristic, complemented
10#11728123C211yesmaximal, characteristic, complemented
11#11727736C211yesmaximal, characteristic, complemented
12#11726501C211yesmaximal, characteristic, complemented
13#11726499C211yesmaximal, characteristic, complemented
14#11726495C211yesmaximal, characteristic, complemented
15#11726493C211yesmaximal, characteristic, complemented
16C7×#525C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C2×#6513C2211yescharacteristic
19C2×#6511C2211yescharacteristic
20#90482C2211yescharacteristic
21C23×C7⋊C8C2211yescharacteristic
22C23×C7⋊C8C2211yescharacteristic
23C2×#6470C2211yescharacteristic
24C2×C7×#104C2211yescharacteristic
25C2×C7×#104C2211yescharacteristic
26C7×#407C2211yescharacteristic
27#90006C2211yescharacteristic
28#90005C2211yescharacteristic
29#89979C2211yescharacteristic
30#89901C2211yescharacteristic
31C2×#6396C2211yescharacteristic
32C2×#6396C2211yescharacteristic
33#89894C2211yescharacteristic
34#89891C2211yescharacteristic
35#89823C412yescomplemented
36#89820C412yescomplemented
37#89813C412yescomplemented
38#89810C412yescomplemented
39#89783—22no—
40D4×C7⋊C8—22no—
41#89774C2211yescharacteristic
42#89771C2211yescharacteristic
43#89770C2211yescharacteristic
44#89769C2211yescharacteristic
45C2×#6379C2211yescharacteristic
46C2×#6379C2211yescharacteristic
47C2×C4×C7⋊C8—24no—
48C2×C4×C7⋊C8C2211yescharacteristic
49C2×C4×C7⋊C8C2211yescharacteristic
50C2×C4×C7⋊C8C2211yescharacteristic
51C2×C4×C7⋊C8C2211yescharacteristic
52#89596—24no—
53#89502—22no—
54(C22⋊D7)⋊C8—22no—
55C7×#339C2211yescharacteristic
56C7×#339C2211yescharacteristic
57#89353C2211yescharacteristic
58#89353C2211yescharacteristic
59#89318C2211yescharacteristic
60#89318C2211yescharacteristic
61#21544—71nomaximal, Sylow
62C2×C7×#41C2311yescharacteristic
63C23×C4×C7—21no—
64C23×C4×C7C2311yescharacteristic
65C2×#1157C2311yescharacteristic
66C2×C7×M16C2311yescharacteristic
67C2×C7×M16C2311yescharacteristic
68C7×#123—21no—
69C7×C22⋊Q8C2×C412yes—
70C7×#121C2×C412yes—
71C7×#120—21no—
72C4×C7×D4—22no—
73C7×#117C2311yescharacteristic
74C2×C42×C7—21no—
75C2×C42×C7—22no—
76C2×C42×C7—22no—
77C2×C42×C7C2311yescharacteristic
78C2×C42×C7C2311yescharacteristic
79#6516—21no—
80#6513—22no—
81#6513—22no—
82#6511—22no—
83#6511—22no—
84C2×#1144C2×C411yescharacteristic, complemented
85C2×#1143C2×C411yescharacteristic, complemented
86C2×#1142C2×C411yescharacteristic, complemented
87C2×#1141C2×C411yescharacteristic, complemented
88#6493C2×C412yes—
89#6492—21no—
90C4×C22⋊D7—22no—
91#6489C2311yescharacteristic
92#6487C2×C412yes—
93C2×#1136—21no—
94C2×#1136C2311yescharacteristic
95C2×#1136C2311yescharacteristic
96C22×C7⋊C8—22no—
97C22×C7⋊C8—22no—
98C22×C7⋊C8—22no—
99C22×C7⋊C8—22no—
100C22×C7⋊C8—21no—
101C22×C7⋊C8C2×C412yes—
102C22×C7⋊C8C2×C412yes—
103C22×C7⋊C8D412yes—
104C22×C7⋊C8D412yes—
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109#6470—22no—
110#6470—22no—
111C2×#1131—21no—
112C2×C8×D7—21no—
113C7×#104—22no—
114C7×#104—22no—
115C7×C22⋊C8—22no—
116#6409C2×C412yescomplemented
117#6406C2×C412yescomplemented
118C22⋊(C7⋊C8)—22no—
119C22⋊(C7⋊C8)—22no—
120#6396—22no—
121#6396—22no—
122(C2×D7)⋊C8—22no—
123#6389—21no—
124Dic7⋊C8—22no—
125C8×Dic7—21no—
126#6384C2×C412yescomplemented
127#6383C2×C412yescomplemented
128#6382C2×C412yescomplemented
129#6381C2×C412yescomplemented
130#6379—22no—
131#6379—22no—
132C4⋊(C7⋊C8)—22no—
133#6377—21no—
134C4×C7⋊C8—22no—
135C4×C7⋊C8—22no—
136C4×C7⋊C8—22no—
137C4×C7⋊C8—21no—
138C4×C7⋊C8D414yescomplemented
139#3050—71no—
140C2×#443—71no—
141#2929—71no—
142#2929—71no—
143C22×C4×C8—71no—
144#1974—71no—
145#1945—71no—
146#1937—71no—
147#1937—71no—
148#1896—71no—
149#1896D711yescharacteristic, complemented
150#1810—71no—
151#1772—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—22no—
161C2×C7×D4—21no—
162C2×C7×D4C22×C411yescharacteristic
163C22×C4×C7—24no—
164C22×C4×C7—28no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7C22×C412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7#4111yescharacteristic
175C22×C4×C7C2411yescharacteristic
176C2×C22⋊D7—22no—
177C2×C22⋊D7—21no—
178#1157—21no—
179#1157—21no—
180#1157—21no—
181#1157—21no—
182C2×D28C22×C411yescharacteristic
183C2×C4×D7—21no—
184C2×Dic14C22×C411yescharacteristic
185C7×M16—21no—
186C7×M16—21no—
187C7×M16—21no—
188C7×M16—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4C22×C412yes—
193C7×C22⋊C4—22no—
194C7×C22⋊C4—21no—
195C7×C22⋊C4—22no—
196C42×C7—24no—
197C42×C7—21no—
198C42×C7—21no—
199C42×C7—21no—
200C42×C7C2×D412yes—
201C42×C7#4112yes—
202C22⋊Dic7—22no—
203C22⋊Dic7—21no—
204#1144—22no—
205#1143—22no—
206#1142—22no—
207#1141—22no—
208(C2×D7)⋊C4—22no—
209C4⋊Dic7C22×C412yes—
210Dic7⋊C4—22no—
211C4×Dic7—21no—
212#1136—21no—
213#1136—21no—
214#1136—21no—
215#1136—21no—
216#1136—42no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—24no—
222C2×C7⋊C8—24no—
223C2×C7⋊C8—24no—
224C2×C7⋊C8—24no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—42no—
228C2×C7⋊C8C22×C412yes—
229C2×C7⋊C8C22×C411yescharacteristic
230C2×C7⋊C8C22×C411yescharacteristic
231C2×C7⋊C8C2×D412yes—
232C2×C7⋊C8C2×D412yes—
233C2×C7⋊C8C2×D411yescharacteristic
234C2×C7⋊C8C2×D411yescharacteristic
235C2×C7⋊C8C2×D412yes—
236C2×C7⋊C8#4112yes—
237C2×C7⋊C8#4112yes—
238#1131—42no—
239C8×D7—42no—
240C2×#135—71no—
241C2×#131—71no—
242C2×#131—71no—
243C23×C8—71no—
244C23×C8—71no—
245#525—71no—
246#525C2×D711yescharacteristic
247C22×C42C2×D711yescharacteristic
248#467—72no—
249#466—72no—
250#465—72no—
251#465—72no—
252#443—144no—
253#435—142no—
254#435—142no—
255C8×D4—142no—
256C8×D4—142no—
257C2×#108—71no—
258C2×#108—71no—
259#427—71no—
260#424—71no—
261#424—71no—
262C2×#104—71no—
263C2×#104—71no—
264C2×#104C2×D711yescharacteristic
265C2×#104C2×D711yescharacteristic
266#416—71no—
267#416—71no—
268#408—71no—
269#408—71no—
270#407—71no—
271#407C2×D711yescharacteristic
272#405—71no—
273#405—71no—
274C2×C4×C8—71no—
275C2×C4×C8—71no—
276C2×C4×C8—71no—
277C2×C4×C8—71no—
278C2×C4×C8—144no—
279#341—71no—
280#341—71no—
281#339—71no—
282#339—71no—
283#339C2×D711yescharacteristic
284#339C2×D711yescharacteristic
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—24no—
288C23×C7—21no—
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—44no—
299C2×C4×C7—216no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—21no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—21no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—21no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7C4×D412yes—
315C2×C4×C7C23×C411yescharacteristic
316C2×C4×C7C22×D411yescharacteristic
317C2×C4×C7C22×D411yescharacteristic
318C2×C4×C7C2×#4111yescharacteristic
319C2×C4×C7C2×#4111yescharacteristic
320C2×C4×C7C2×#4111yescharacteristic
321C22⋊D7—41no—
322C22⋊D7—41no—
323C22⋊D7—44no—
324C2×Dic7—22no—
325C2×Dic7—21no—
326D28—21no—
327D28—21no—
328C4×D7—41no—
329C4×D7—41no—
330Dic14—21no—
331Dic14—21no—
332C7×C8—41no—
333C7×C8—41no—
334C7⋊C8—22no—
335C7⋊C8—22no—
336C7⋊C8—41no—
337C7⋊C8—41no—
338C7⋊C8C4×D412yes—
339C7⋊C8C4×D412yes—
340C7⋊C8#12112yes—
341C7⋊C8#12112yes—
342C2×#41—71no—
343C2×#41C22×D711yescharacteristic
344C23×C4—21no—
345C23×C4C22×D711yescharacteristic
346#135—142no—
347#135—142no—
348C2×Q16—71no—
349C2×SD16—71no—
350C2×SD16—71no—
351C2×D8—71no—
352#131—142no—
353#131—142no—
354#131—142no—
355#131—142no—
356C2×M16—71no—
357C2×M16—71no—
358C2×M16—141no—
359C2×M16—141no—
360C2×M16C22×D711yescharacteristic
361C2×M16C22×D711yescharacteristic
362C22×C8—71no—
363C22×C8—71no—
364C22×C8—72no—
365C22×C8—72no—
366C22×C8—72no—
367C22×C8—72no—
368C22×C8—71no—
369C22×C8—71no—
370C22×C8—141no—
371C22×C8—142no—
372C22×C8—142no—
373C22×C8—142no—
374C22×C8—142no—
375C22×C8—141no—
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—21no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42C22×D711yescharacteristic
392C2×C42C22×D711yescharacteristic
393#108—142no—
394#108—142no—
395#107—72no—
396#106—72no—
397C4⋊C8—142no—
398C4⋊C8—142no—
399#104—22no—
400#104—22no—
401#104—142no—
402#104—142no—
403#103—72no—
404#103—72no—
405#102—72no—
406#102—72no—
407C22⋊C8—22no—
408C22⋊C8—142no—
409C22⋊C8—142no—
410C22⋊C8—142no—
411#97—141no—
412#97—141no—
413C4×C8—74no—
414C4×C8—142no—
415C4×C8—142no—
416C4×C8—141no—
417C4×C8—141no—
418C4×C8—142no—
419C22×C7—24no—
420C22×C7—24no—
421C22×C7—22no—
422C22×C7—22no—
423C22×C7—22no—
424C22×C7—42no—
425C22×C7—41no—
426C22×C7#44314yescomplemented
427C22×C7C2×C4×D411yescharacteristic
428C22×C7#52511yescharacteristic
429C22×C7#52911yescharacteristic
430C2×D7—42no—
431C2×D7—41no—
432C4×C7—24no—
433C4×C7—24no—
434C4×C7—22no—
435C4×C7—42no—
436C4×C7—41no—
437C4×C7C2×C4×D411yescharacteristic
438C4×C7C4×#4111yescharacteristic
439C4×C7C2×#12111yescharacteristic
440C4×C7#53211yescharacteristic
441Dic7—42no—
442Dic7—41no—
443C24#115911yescharacteristic
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—22no—
455C2×D4—21no—
456C2×D4—71no—
457C2×D4—142no—
458C2×D4—141no—
459C2×D4C2×C4×D711yescharacteristic
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—141no—
470C22×C4C2×C4×D712yes—
471C22×C4D4×D712yes—
472C22×C4#115911yescharacteristic
473C22×C4C23×D711yescharacteristic
474Q16—142no—
475SD16—142no—
476SD16—142no—
477D8—142no—
478M16—21no—
479M16—21no—
480M16—21no—
481M16—21no—
482M16—141no—
483M16—141no—
484M16—141no—
485M16—141no—
486M16—282no—
487M16—282no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—71no—
491C2×C8—71no—
492C2×C8—72no—
493C2×C8—72no—
494C2×C8—71no—
495C2×C8—71no—
496C2×C8—72no—
497C2×C8—72no—
498C2×C8—72no—
499C2×C8—72no—
500C2×C8—144no—
501C2×C8—144no—
502C2×C8—144no—
503C2×C8—144no—
504C2×C8—141no—
505C2×C8—141no—
506C2×C8—141no—
507C2×C8—141no—
508C2×C8—141no—
509C2×C8—141no—
510C2×C8—282no—
511C2×C8—282no—
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—24no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—141no—
527C42D4×D712yes—
528C42#115912yes—
529C2×C7—21no—
530C2×C7—21no—
531C2×C7—24no—
532C2×C7—81no—
533C2×C7C4×#12111yescharacteristic
534C2×C7C2×#44312yes—
535D7—81no—
536C23—21no—
537C23—21no—
538C23—24no—
539C23—21no—
540C23—141no—
541C23(C22⋊D7)⋊C412yes—
542C23C2×#115911yescharacteristic
543Q8—21no—
544Q8—21no—
545Q8—141no—
546Q8—141no—
547D4—21no—
548D4—21no—
549D4—41no—
550D4—41no—
551D4—44no—
552D4—141no—
553D4—141no—
554D4—281no—
555D4—281no—
556D4—284no—
557C2×C4—216no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—142no—
573C2×C4—141no—
574C2×C4—281no—
575C2×C4—281no—
576C2×C4(C22⋊D7)⋊C412yes—
577C2×C4C22×C4×D711yescharacteristic
578C2×C4C2×D4×D711yescharacteristic
579C2×C4C2×D4×D711yescharacteristic
580C2×C4C2×#115911yescharacteristic
581C2×C4D7×#4111yescharacteristic
582C2×C4D7×#4111yescharacteristic
583C8—41no—
584C8—41no—
585C8—72no—
586C8—72no—
587C8—72no—
588C8—72no—
589C8—142no—
590C8—142no—
591C8—281no—
592C8—281no—
593C7#2154411yescharacteristic, complemented, Sylow
594C22—24no—
595C22—24no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—41no—
601C22—282no—
602C22—281no—
603C22#8959614yescomplemented
604C22C2×(C22⋊D7)⋊C411yescharacteristic
605C22#9027711yescharacteristic
606C22#9034011yescharacteristic
607C4—24no—
608C4—24no—
609C4—22no—
610C4—42no—
611C4—41no—
612C4—282no—
613C4—281no—
614C4C4×#115911yescharacteristic
615C4C4×D4×D711yescharacteristic
616C4#9028711yescharacteristic
617C4D7×#12111yescharacteristic
618C2—21no—
619C2—21no—
620C2—24no—
621C2—81no—
622C2—561no—
623C2#1173210511yescharacteristic
624C2C2×#8959612yes—
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1896C2
socleC22×C7C2×C4×D4
prime radical#11740367C2
cosocleC22×C4×C7C24
hypercenter#1896D7
hypocenterC7#21544
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #11740361C2semidirect
3. C22×C4×C7⋊C8C2semidirect
4. C2×#89596C2semidirect
5. #11736071C2semidirect
6. C7×#1896C2semidirect
7. #11729286C2semidirect
8. #11728127C2semidirect
9. #11728125C2semidirect
10. #11728123C2semidirect
11. #11727736C2semidirect
12. #11726501C2semidirect
13. #11726499C2semidirect
14. #11726495C2semidirect
15. #11726493C2semidirect
35. #89823C4semidirect
36. #89820C4semidirect
37. #89813C4semidirect
38. #89810C4semidirect
84. C2×#1144C2×C4semidirect
85. C2×#1143C2×C4semidirect
86. C2×#1142C2×C4semidirect
87. C2×#1141C2×C4semidirect
116. #6409C2×C4semidirect
117. #6406C2×C4semidirect
126. #6384C2×C4semidirect
127. #6383C2×C4semidirect
128. #6382C2×C4semidirect
129. #6381C2×C4semidirect
138. C4×C7⋊C8D4semidirect
149. #1896D7semidirect
426. C22×C7#443semidirect
593. C7#21544semidirect
603. C22#89596semidirect

Maximal subgroups

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

subgroupindex
#117403672
#117403612
C22×C4×C7⋊C82
C2×#895962
#117360712
C7×#18962
#117292862
#117281272
#117281252
#117281232
#117277362
#117265012
#117264992
#117264952
#117264932
#215447