Finite Group Databasebeta

← #13358166

Subgroups — #13358166

Order 1792.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2320C211yesmaximal, characteristic, complemented
2C2×#89798C211yesmaximal, characteristic
3#11730860C211yesmaximal, characteristic
4C4×#6409C211yesmaximal, characteristic, complemented
5#11727433C211yesmaximal, characteristic
6#11727430C211yesmaximal, characteristic
7#11727429C211yesmaximal, characteristic, complemented
8#11727428C211yesmaximal, characteristic, complemented
9#11727374C211yesmaximal, characteristic, complemented
10#11727373C211yesmaximal, characteristic, complemented
11#11727371C211yesmaximal, characteristic
12#11727369C211yesmaximal, characteristic
13#11727235C211yesmaximal, characteristic, complemented
14C4×#6383C211yesmaximal, characteristic
15#11727188C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17C22×#1143C2211yescharacteristic
18C2×C4×D28C2211yescharacteristic
19C7×#391C2211yescharacteristic
20C7×#391C2211yescharacteristic
21C7×#389C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#387—21no—
24C7×#387—21no—
25C7×#383—21no—
26C7×#382—21no—
27C4×C7×C4⋊C4C2211yescharacteristic
28C7×#376C2211yescharacteristic
29C2×#6409C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32#89798C418yescomplemented
33C2×#6383C2211yescharacteristic
34C2×#6383C2211yescharacteristic
35C2×#6383C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6381C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39#89711C2211yescharacteristic
40#89711C2211yescharacteristic
41C4×C4⋊Dic7C2211yescharacteristic
42#89700C2211yescharacteristic
43#89700C2211yescharacteristic
44C2×#6377C2211yescharacteristic
45C2×#6377C2211yescharacteristic
46C2×#6377C2211yescharacteristic
47C2×C4×C7⋊C8C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49C2×C4×C7⋊C8C2211yescharacteristic
50#89441—21no—
51#89441—21no—
52#89439—21no—
53#89436—21no—
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#21291—71nomaximal, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C4×C7×Q8—22no—
65C4×C7×Q8C2×C414yes—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C42×C7—21no—
73C2×C42×C7—21no—
74C2×C42×C7C2311yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×#1143—22no—
78C2×#1143—22no—
79C2×#1143C2×C414yes—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×C4×Dic7—21no—
91C22×C7⋊C8C2311yescharacteristic
92C22×C7⋊C8C2311yescharacteristic
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C4×D28—22no—
96C4×D28C2×C414yes—
97C7×#95—21no—
98C7×#95—21no—
99C7×#95—21no—
100C7×#95—21no—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95D411yescharacteristic
105C7×#95D411yescharacteristic
106C7×#95D411yescharacteristic
107C7×#95D411yescharacteristic
108#6409—22no—
109#6409—22no—
110#6409C2×C414yes—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114#6383—22no—
115#6383—22no—
116#6383C2×C414yes—
117#6382—22no—
118#6381—22no—
119#6381C2×C414yes—
120#6377—22no—
121#6377—22no—
122#6377C2×C414yes—
123C4×C7⋊C8—22no—
124C4×C7⋊C8—22no—
125C4×C7⋊C8—22no—
126C2×#440—71no—
127#2320D711yescharacteristic, complemented
128#2319—71no—
129#1973—71no—
130#1968—71no—
131#1943—71no—
132#1942—71no—
133#1936—71no—
134#1935—71no—
135#1934—71no—
136#1933—71no—
137#1776—71no—
138C4×#103—71no—
139C4×#102—71no—
140#1726—71no—
141C23×D7—21no—
142C2×C7×Q8—21no—
143C2×C7×Q8—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8—21no—
146C2×C7×Q8—21no—
147C2×C7×Q8C22×C412yes—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2411yescharacteristic
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C2×D28—21no—
163C2×D28—21no—
164C2×D28—21no—
165C2×D28—21no—
166C2×D28—21no—
167C2×D28C22×C412yes—
168C2×C4×D7—24no—
169C2×C4×D7—81no—
170C2×C4×D7—81no—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—81no—
178C7×C4⋊C4—81no—
179C7×C4⋊C4C22×C412yes—
180C42×C7—24no—
181C42×C7—21no—
182C42×C7—21no—
183C42×C7—21no—
184C42×C7—21no—
185C42×C7—81no—
186C42×C7C22×C412yes—
187C42×C7#4112yes—
188#1143—28no—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—81no—
191(C2×D7)⋊C4—81no—
192(C2×D7)⋊C4—81no—
193(C2×D7)⋊C4—81no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7C22×C412yes—
200Dic7⋊C4—81no—
201Dic7⋊C4—81no—
202C4×Dic7—81no—
203C2×C7⋊C8—21no—
204C2×C7⋊C8—21no—
205C2×C7⋊C8—21no—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8—21no—
209C2×C7⋊C8C22×C412yes—
210C2×C7⋊C8C22×C412yes—
211C2×C7⋊C8#4112yes—
212C2×C7⋊C8#4112yes—
213C2×C7⋊C8#4112yes—
214C2×C7⋊C8#4112yes—
215C22×SD16—71no—
216C2×C4×Q8C2×D711yescharacteristic
217C2×C4×D4—71no—
218#440—78no—
219C2×#107—71no—
220C2×#107—71no—
221C2×#106—71no—
222C2×#103—71no—
223C2×#103—71no—
224C2×#103—71no—
225C2×#102—71no—
226C2×#102—71no—
227C2×#102—71no—
228C2×#97—71no—
229C2×#97—71no—
230C2×#97—71no—
231C2×C4×C8—71no—
232C2×C4×C8—71no—
233C2×C4×C8—71no—
234#391C2×D711yescharacteristic
235#391C2×D711yescharacteristic
236#390—71no—
237#390—71no—
238#389—71no—
239#389—71no—
240#389C2×D711yescharacteristic
241#389C2×D711yescharacteristic
242#388—141no—
243#388—141no—
244#387—21no—
245#387—21no—
246#383—21no—
247#382—21no—
248#381—141no—
249#380—141no—
250C4×C4⋊C4—71no—
251C4×C4⋊C4C2×D711yescharacteristic
252#376C2×D711yescharacteristic
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259C23×C7C22×D411yescharacteristic
260C22×D7—22no—
261C22×D7—41no—
262C22×D7—41no—
263C22×D7—41no—
264C22×D7—41no—
265C22×D7—41no—
266C22×D7—41no—
267C7×Q8—22no—
268C7×Q8—22no—
269C7×Q8—41no—
270C7×Q8—41no—
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7C4×D412yes—
300C2×C4×C7C4×D412yes—
301C2×C4×C7C23×C411yescharacteristic
302C2×C4×C7C2×#4111yescharacteristic
303C2×C4×C7C2×#4111yescharacteristic
304C2×C4×C7C2×#4111yescharacteristic
305C2×C4×C7C2×#4111yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×Dic7—22no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316D28—22no—
317D28—22no—
318D28—41no—
319D28—41no—
320C4×D7—84no—
321C7⋊C8—22no—
322C7⋊C8—22no—
323C7⋊C8—22no—
324C7⋊C8#11714yes—
325C22×Q8C22×D711yescharacteristic
326C22×D4—71no—
327C23×C4—141no—
328C2×SD16—74no—
329C2×SD16—142no—
330C2×SD16—142no—
331C22×C8—71no—
332C22×C8—71no—
333C22×C8—71no—
334C22×C8—71no—
335C4×Q8—22no—
336C4×Q8C4×D714yes—
337C4×D4—74no—
338C4×D4—142no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—141no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C4⋊C4C22×D711yescharacteristic
349C2×C4⋊C4C22×D711yescharacteristic
350C2×C22⋊C4—141no—
351C2×C22⋊C4—141no—
352C2×C22⋊C4—141no—
353C2×C22⋊C4—141no—
354C2×C22⋊C4—141no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—141no—
358C2×C42C22×D711yescharacteristic
359C2×C42C22×D711yescharacteristic
360C2×C42C22×D711yescharacteristic
361#107—74no—
362#107—142no—
363#106—142no—
364#103—74no—
365#103—142no—
366#103—142no—
367#102—74no—
368#102—142no—
369#102—142no—
370#97—74no—
371#97—142no—
372#97—142no—
373C4×C8—142no—
374C4×C8—142no—
375C4×C8—142no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—141no—
384#95—141no—
385#95—141no—
386#95C22⋊D711yescharacteristic
387#95C22⋊D711yescharacteristic
388#95C22⋊D711yescharacteristic
389#95C22⋊D711yescharacteristic
390C22×C7C2×C4×D411yescharacteristic
391C22×C7#53211yescharacteristic
392C22×C7#53211yescharacteristic
393C22×C7#57611yescharacteristic
394C22×C7#57711yescharacteristic
395C22×C7#57711yescharacteristic
396C22×C7#57811yescharacteristic
397C2×D7—42no—
398C2×D7—42no—
399C2×D7—42no—
400C2×D7—81no—
401C2×D7—81no—
402C2×D7—81no—
403C2×D7—81no—
404C4×C7—22no—
405C4×C7—22no—
406C4×C7—41no—
407C4×C7—41no—
408C4×C7—41no—
409C4×C7—41no—
410C4×C7—42no—
411C4×C7—42no—
412C4×C7—81no—
413C4×C7—81no—
414C4×C7C2×#11711yescharacteristic
415C4×C7C4×#4111yescharacteristic
416C4×C7#52911yescharacteristic
417C4×C7#52911yescharacteristic
418Dic7—42no—
419Dic7—81no—
420Dic7—81no—
421C24—141no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×C4×D712yes—
428C2×D4—72no—
429C2×D4—141no—
430C2×D4—141no—
431C2×D4—141no—
432C2×D4—141no—
433C2×D4—141no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—141no—
439C22×C4—144no—
440C22×C4—141no—
441C22×C4—141no—
442C22×C4—561no—
443C22×C4—561no—
444C22×C4C2×C22⋊D711yescharacteristic
445C22×C4C2×C22⋊D711yescharacteristic
446C22×C4C2×C22⋊D711yescharacteristic
447C22×C4C2×C22⋊D711yescharacteristic
448C22×C4C2×C22⋊D711yescharacteristic
449C22×C4C2×C22⋊D711yescharacteristic
450C22×C4C23×D711yescharacteristic
451SD16—148no—
452C2×C8—72no—
453C2×C8—72no—
454C2×C8—72no—
455C2×C8—72no—
456C2×C8—72no—
457C2×C8—72no—
458C2×C8—141no—
459C2×C8—141no—
460C2×C8—141no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—141no—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—72no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—561no—
479C4⋊C4—561no—
480C4⋊C4C2×C4×D712yes—
481C22⋊C4—144no—
482C22⋊C4—561no—
483C22⋊C4—561no—
484C22⋊C4—561no—
485C22⋊C4—561no—
486C42—24no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—81no—
492C42—561no—
493C42C2×C4×D712yes—
494C42#115712yes—
495C2×C7#229311yescharacteristic
496C2×C7#294611yescharacteristic
497C2×C7#294711yescharacteristic
498C2×C7#317411yescharacteristic
499C2×C7#317511yescharacteristic
500C2×C7#317811yescharacteristic
501C2×C7#317911yescharacteristic
502D7—82no—
503C23—142no—
504C23—281no—
505C23—281no—
506C23—281no—
507C23—281no—
508C23—281no—
509C23—281no—
510C23C22×C22⋊D711yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—41no—
514Q8—41no—
515D4—142no—
516D4—142no—
517D4—281no—
518D4—281no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—142no—
548C2×C4—281no—
549C2×C4—281no—
550C2×C4—281no—
551C2×C4—281no—
552C2×C4—281no—
553C2×C4—281no—
554C2×C4—281no—
555C2×C4—281no—
556C2×C4—564no—
557C2×C4C4×C22⋊D712yes—
558C2×C4C4×C22⋊D712yes—
559C2×C4C22×C4×D711yescharacteristic
560C2×C4C2×#115711yescharacteristic
561C2×C4D7×#4111yescharacteristic
562C2×C4D7×#4111yescharacteristic
563C2×C4D7×#4111yescharacteristic
564C2×C4D7×#4111yescharacteristic
565C8—74no—
566C8—142no—
567C8—142no—
568C8—142no—
569C7#2129111yescharacteristic, complemented, Sylow
570C22—282no—
571C22—282no—
572C22—282no—
573C22—561no—
574C22—561no—
575C22—561no—
576C22—561no—
577C22C2×C4×C22⋊D711yescharacteristic
578C22#9052311yescharacteristic
579C22#9052311yescharacteristic
580C22#9052611yescharacteristic
581C22#9052811yescharacteristic
582C22#9052811yescharacteristic
583C22#9052911yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—282no—
595C4—561no—
596C4—561no—
597C4D7×#11711yescharacteristic
598C4#9021311yescharacteristic
599C4#9021911yescharacteristic
600C4#9021911yescharacteristic
601C2—562no—
602C2#1173967011yescharacteristic
603C2#1173999211yescharacteristic
604C2#1174000911yescharacteristic
605C2#1174088811yescharacteristic
606C2#1174089011yescharacteristic
607C2#1174090211yescharacteristic
608C2#1174090411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2320C2
socleC23×C7C22×D4
prime radicalC22×D28C23
cosocleC22×C4×C7C24
hypercenter#2320D7
hypocenterC7#21291
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
1. C7×#2320C2semidirect
4. C4×#6409C2semidirect
7. #11727429C2semidirect
8. #11727428C2semidirect
9. #11727374C2semidirect
10. #11727373C2semidirect
13. #11727235C2semidirect
15. #11727188C2semidirect
32. #89798C4semidirect
127. #2320D7semidirect
569. C7#21291semidirect

Maximal subgroups

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

subgroupindex
C7×#23202
C2×#897982
#117308602
C4×#64092
#117274332
#117274302
#117274292
#117274282
#117273742
#117273732
#117273712
#117273692
#117272352
C4×#63832
#117271882
#212917