Finite Group Databasebeta

← #13413022

Subgroups — #13413022

Order 1792.

806 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic7⋊C4C211yesmaximal, characteristic
2#11731782C211yesmaximal, characteristic, complemented
3C7×#1802C211yesmaximal, characteristic
4#11729360C211yesmaximal, characteristic
5#11728216C211yesmaximal, characteristic, complemented
6#11728205C211yesmaximal, characteristic, complemented
7#11727922C211yesmaximal, characteristic
8#11727907C211yesmaximal, characteristic
9#11727907C211yesmaximal, characteristic
10Dic7×#102C211yesmaximal, characteristic
11#11727325C211yesmaximal, characteristic, complemented
12#11726601C211yesmaximal, characteristic, complemented
13#11726564C211yesmaximal, characteristic, complemented
14#11726561C211yesmaximal, characteristic, complemented
15#11726549C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×D4×Dic7C2211yescharacteristic
18C2×D4×Dic7C2211yescharacteristic
19C22×Dic7⋊C4—21no—
20C2×#6452—21no—
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×#102C2211yescharacteristic
23C2×C7×#102C2211yescharacteristic
24C7×#384C2211yescharacteristic
25C2×#6406C2211yescharacteristic
26C2×#6406C2211yescharacteristic
27#89982—21no—
28C2×#6392C2211yescharacteristic
29C2×Dic7⋊C8C2211yescharacteristic
30C2×Dic7⋊C8C2211yescharacteristic
31C2×C8×Dic7C2211yescharacteristic
32#89757C2211yescharacteristic
33#89756—21no—
34#89752—21no—
35#89748C2211yescharacteristic
36#89748C2211yescharacteristic
37#89748C2211yescharacteristic
38C4⋊C4×Dic7C2211yescharacteristic
39#89745C2211yescharacteristic
40#89744—21no—
41C2×#6381C2211yescharacteristic
42#89718—21no—
43#89714—21no—
44C4×Dic7⋊C4C2211yescharacteristic
45#89700C2211yescharacteristic
46#89700C2211yescharacteristic
47C7×#340C2211yescharacteristic
48C7×#340C2211yescharacteristic
49#89346C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89345C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#26106—71nomaximal, Sylow
60C22×C7×D4C2311yescharacteristic
61C23×C4×C7—21no—
62C23×Dic7—21no—
63C23×Dic7—21no—
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C4×C7×D4—22no—
67C4×C7×D4—41no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C22⋊C4—21no—
74C2×C42×C7C2311yescharacteristic
75C2×C22⋊Dic7—21no—
76C2×C22⋊Dic7—21no—
77D4×Dic7—22no—
78D4×Dic7—22no—
79D4×Dic7—41no—
80D4×Dic7Q814yes—
81C2×C4⋊Dic7—21no—
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—21no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—44no—
96C2×Dic7⋊C4D411yescharacteristic
97C2×Dic7⋊C4D411yescharacteristic
98C2×C4×Dic7—21no—
99C2×C4×Dic7C2311yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103#6452—44no—
104C7×C4⋊C8—41no—
105C7×#102—22no—
106C7×#102—22no—
107#6406—22no—
108#6406—22no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95D411yescharacteristic
115C7⋊#95D411yescharacteristic
116#6392—41no—
117Dic7⋊C8—22no—
118Dic7⋊C8—41no—
119C8×Dic7—22no—
120#6381—41no—
121#2552—71no—
122D4×C4⋊C4—71no—
123#2099—71no—
124#2099—71no—
125#2086—71no—
126#2086—71no—
127#1947—71no—
128#1939—71no—
129#1862—71no—
130#1862—71no—
131#1834—71no—
132#1802—71no—
133#1802—71no—
134#1802D711yescharacteristic
135C4×#102—71no—
136C24×C7—21no—
137C2×C7×D4—21no—
138C2×C7×D4—21no—
139C2×C7×D4—21no—
140C2×C7×D4C2×Q812yes—
141C2×C7×D4#4112yes—
142C2×C7×D4#4112yes—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—42no—
147C22×C4×C7—42no—
148C22×C4×C7—81no—
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2411yescharacteristic
152C22×Dic7—21no—
153C22×Dic7—24no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—42no—
158C22×Dic7—42no—
159C22×Dic7—42no—
160C22×Dic7—42no—
161C22×Dic7—81no—
162C22×Dic7C2×D411yescharacteristic
163C22×Dic7C2×D411yescharacteristic
164C22×Dic7C2×D411yescharacteristic
165C22×Dic7C2×D411yescharacteristic
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8—21no—
170C2×C7×C8—21no—
171C2×C7×C8—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—42no—
179C7×C4⋊C4—81no—
180C7×C22⋊C4—42no—
181C42×C7—21no—
182C42×C7—21no—
183C22⋊Dic7—24no—
184C22⋊Dic7—42no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—21no—
190C4⋊Dic7—21no—
191C4⋊Dic7—21no—
192C4⋊Dic7—42no—
193C4⋊Dic7C2×Q812yes—
194Dic7⋊C4—22no—
195Dic7⋊C4—42no—
196Dic7⋊C4—42no—
197Dic7⋊C4—42no—
198Dic7⋊C4—42no—
199Dic7⋊C4—42no—
200Dic7⋊C4—42no—
201Dic7⋊C4—81no—
202Dic7⋊C4—81no—
203Dic7⋊C4—81no—
204Dic7⋊C4D814yes—
205C4×Dic7—21no—
206C4×Dic7—21no—
207C4×Dic7—42no—
208C4×Dic7C2×Q812yes—
209C4×Dic7#4112yes—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×#125—141no—
217C2×C4×D4—71no—
218C2×C4×D4—71no—
219C2×C4×D4C2×D711yescharacteristic
220C22×C4⋊C4—141no—
221C2×#107—71no—
222C2×#107—71no—
223C2×C4⋊C8—71no—
224C2×C4⋊C8—71no—
225C2×C4⋊C8C2×D711yescharacteristic
226C2×#102—71no—
227C2×#102—71no—
228C2×#102C2×D711yescharacteristic
229C2×#102C2×D711yescharacteristic
230C2×C4×C8—71no—
231#398—141no—
232#398—141no—
233#389—71no—
234#389—71no—
235#389—71no—
236#389—71no—
237#389—141no—
238#385—141no—
239#385—141no—
240#384—71no—
241#384—71no—
242#384—71no—
243#384C2×D711yescharacteristic
244#380—141no—
245C4×C4⋊C4—71no—
246C4×C4⋊C4—71no—
247#340—71no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#340C2×D711yescharacteristic
256#340C2×D711yescharacteristic
257#336—71no—
258#336—71no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—41no—
263C23×C7—41no—
264C23×C7—41no—
265C23×C7—41no—
266C23×C7C22×D411yescharacteristic
267C7×D4—22no—
268C7×D4—22no—
269C7×D4—22no—
270C7×D4#12514yescomplemented
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—84no—
286C2×C4×C7C2×D812yes—
287C2×C4×C7C22×Q811yescharacteristic
288C2×C4×C7C2×#4111yescharacteristic
289C2×C4×C7C2×#4111yescharacteristic
290C2×C4×C7C2×#4111yescharacteristic
291C2×C4×C7H(5,𝔽2)11yescharacteristic
292C2×C4×C72−1+411yescharacteristic
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—22no—
298C2×Dic7—21no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—48no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—84no—
314C2×Dic7C22⋊Q812yes—
315C2×Dic7C22⋊Q812yes—
316C2×Dic7C2×D812yes—
317C2×Dic7C2×D812yes—
318C2×Dic7#13712yes—
319C7×C8—41no—
320C7×C8—41no—
321C7⋊C8—41no—
322C7⋊C8—41no—
323C22×D4C22×D711yescharacteristic
324C23×C4—21no—
325C23×C4—141no—
326C23×C4—141no—
327C22×C8—71no—
328C22×C8—71no—
329C22×C8C22×D711yescharacteristic
330C22×C8C22×D711yescharacteristic
331#125—284no—
332C4×D4—22no—
333C4×D4—41no—
334C4×D4—74no—
335C4×D4—142no—
336C4×D4—142no—
337C4×D4—281no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—71no—
341C2×C4⋊C4—71no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4—141no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4—284no—
357C2×C4⋊C4C22×D711yescharacteristic
358C2×C4⋊C4C22×D711yescharacteristic
359C2×C4⋊C4C22×D711yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—141no—
362C2×C22⋊C4—141no—
363C2×C42—71no—
364C2×C42—71no—
365C2×C42—141no—
366C2×C42C22×D711yescharacteristic
367#107—281no—
368#107—281no—
369C4⋊C8—41no—
370C4⋊C8—142no—
371C4⋊C8—281no—
372#102—22no—
373#102—22no—
374#102—142no—
375#102—142no—
376C4×C8—142no—
377#95—71no—
378#95—71no—
379#95—141no—
380#95—141no—
381#95—141no—
382#95—141no—
383#95—141no—
384C22×C7—24no—
385C22×C7—42no—
386C22×C7—42no—
387C22×C7—42no—
388C22×C7—42no—
389C22×C7—42no—
390C22×C7—42no—
391C22×C7C2×C22⋊Q811yescharacteristic
392C22×C7#54611yescharacteristic
393C22×C7#54811yescharacteristic
394C22×C7C22×D811yescharacteristic
395C22×C7C2×#13711yescharacteristic
396C22×C7#57711yescharacteristic
397C22×C7#57711yescharacteristic
398C4×C7—22no—
399C4×C7—41no—
400C4×C7—81no—
401C4×C7—81no—
402C4×C7—81no—
403C4×C7C2×#12511yescharacteristic
404C4×C7#54411yescharacteristic
405C4×C7#55211yescharacteristic
406C4×C7#55311yescharacteristic
407Dic7—22no—
408Dic7—22no—
409Dic7—41no—
410Dic7—42no—
411Dic7—81no—
412Dic7—81no—
413Dic7—81no—
414Dic7#47414yes—
415C24—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4#115712yes—
420C2×D4#115912yes—
421C2×D4Q8×D712yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—71no—
428C22×C4—71no—
429C22×C4—71no—
430C22×C4—71no—
431C22×C4—81no—
432C22×C4—144no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—282no—
438C22×C4—282no—
439C22×C4—282no—
440C22×C4—282no—
441C22×C4—561no—
442C22×C4D4×D711yescharacteristic
443C22×C4D4×D711yescharacteristic
444C22×C4C23×D711yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—141no—
452C2×C8—141no—
453C2×C8—141no—
454C2×C8—141no—
455C2×C8—141no—
456C2×C8—141no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—74no—
465C4⋊C4—72no—
466C4⋊C4—81no—
467C4⋊C4—142no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—282no—
476C4⋊C4—282no—
477C4⋊C4—282no—
478C4⋊C4—282no—
479C4⋊C4—282no—
480C4⋊C4—282no—
481C4⋊C4—282no—
482C4⋊C4—561no—
483C4⋊C4—561no—
484C4⋊C4—561no—
485C22⋊C4—42no—
486C22⋊C4—144no—
487C22⋊C4—282no—
488C42—21no—
489C42—21no—
490C42—72no—
491C42—72no—
492C42—141no—
493C42—141no—
494C42—282no—
495C2×C7—44no—
496C2×C7#244211yescharacteristic
497C2×C7C2×#47411yescharacteristic
498C2×C7#308411yescharacteristic
499C2×C7#329411yescharacteristic
500C2×C7#333111yescharacteristic
501C2×C7#335811yescharacteristic
502C2×C7#337211yescharacteristic
503C23—22no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C2×D4×D711yescharacteristic
511D4—22no—
512D4—22no—
513D4—22no—
514D4#645214yescomplemented
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—72no—
530C2×C4—72no—
531C2×C4—72no—
532C2×C4—72no—
533C2×C4—72no—
534C2×C4—84no—
535C2×C4—141no—
536C2×C4—141no—
537C2×C4—141no—
538C2×C4—141no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—142no—
543C2×C4—288no—
544C2×C4—281no—
545C2×C4—281no—
546C2×C4—281no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—281no—
550C2×C4—281no—
551C2×C4—281no—
552C2×C4—281no—
553C2×C4—281no—
554C2×C4—281no—
555C2×C4—564no—
556C2×C4D7×D812yes—
557C2×C4C2×#115711yescharacteristic
558C2×C4C2×#115911yescharacteristic
559C2×C4#654811yescharacteristic
560C2×C4C2×Q8×D711yescharacteristic
561C2×C4D7×#4111yescharacteristic
562C2×C4#655411yescharacteristic
563C8—41no—
564C8—41no—
565C8—281no—
566C8—281no—
567C7#2610611yescharacteristic, complemented, Sylow
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22#9018111yescharacteristic
576C22#9028911yescharacteristic
577C22D7×C22⋊Q811yescharacteristic
578C22C2×D7×D811yescharacteristic
579C22#9045311yescharacteristic
580C22#9046611yescharacteristic
581C22D7×#13711yescharacteristic
582C4—22no—
583C4—41no—
584C4—74no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—142no—
589C4—142no—
590C4—281no—
591C4—282no—
592C4—561no—
593C4—561no—
594C4—561no—
595C4C2×#645211yescharacteristic
596C4#9022211yescharacteristic
597C4#9029211yescharacteristic
598C4#9031411yescharacteristic
599C2—44no—
600C2#1173134711yescharacteristic
601C2#1173620211yescharacteristic
602C2#1173635211yescharacteristic
603C2#1173776311yescharacteristic
604C2#1173786311yescharacteristic
605C2D7×#47411yescharacteristic
606C2#1173850811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#1802C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenter#1802D7
hypocenterC7#26106
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #11731782C2semidirect
5. #11728216C2semidirect
6. #11728205C2semidirect
11. #11727325C2semidirect
12. #11726601C2semidirect
13. #11726564C2semidirect
14. #11726561C2semidirect
15. #11726549C2semidirect
270. C7×D4#125semidirect
514. D4#6452semidirect
567. C7#26106semidirect

Maximal subgroups

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

subgroupindex
D4×Dic7⋊C42
#117317822
C7×#18022
#117293602
#117282162
#117282052
#117279222
#117279072
Dic7×#1022
#117273252
#117266012
#117265642
#117265612
#117265492
#261067