Finite Group Databasebeta

← #32020592

Subgroups — #32020592

Order 18176.

774 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986296C211yesmaximal, characteristic
2#22591311C211yesmaximal, characteristic
3#22589306C211yesmaximal, characteristic, complemented
4#22589108C211yesmaximal, characteristic, complemented
5#22589022C211yesmaximal, characteristic
6#22589022C211yesmaximal, characteristic
7#22588967C211yesmaximal, characteristic
8#22588960C211yesmaximal, characteristic
9#22588929C211yesmaximal, characteristic, complemented
10#22588915C211yesmaximal, characteristic, complemented
11C4×#14556061C211yesmaximal, characteristic, complemented
12C4×#14556059C211yesmaximal, characteristic, complemented
13C4⋊C4×C71⋊C8C211yesmaximal, characteristic, complemented
14C4×#14556048C211yesmaximal, characteristic
15C71×#2370C211yesmaximal, characteristic, complemented
16C2×C4×D284C2211yescharacteristic
17#17986296C418yescomplemented
18C2×#14556061C2211yescharacteristic
19C2×#14556061C2211yescharacteristic
20C2×#14556059C2211yescharacteristic
21C2×#14556059C2211yescharacteristic
22C2×C4⋊(C71⋊C8)C2211yescharacteristic
23C2×#14556048C2211yescharacteristic
24C2×#14556048C2211yescharacteristic
25C2×#14556048C2211yescharacteristic
26C2×#14556048C2211yescharacteristic
27C2×C4×C71⋊C8C2211yescharacteristic
28C2×C4×C71⋊C8C2211yescharacteristic
29C2×C4×C71⋊C8C2211yescharacteristic
30#17985901C2211yescharacteristic
31#17985901C2211yescharacteristic
32#17985889—21no—
33#17985889—21no—
34#17985865C2211yescharacteristic
35#17985861—21no—
36C4×C4⋊Dic71C2211yescharacteristic
37C4×C4⋊Dic71C2211yescharacteristic
38#17985846—21no—
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985754C2211yescharacteristic
48#17985754C2211yescharacteristic
49C2×#125×C71C2211yescharacteristic
50#389×C71—21no—
51#389×C71C2211yescharacteristic
52#389×C71C2211yescharacteristic
53#387×C71—21no—
54#387×C71—21no—
55C4×C4⋊C4×C71—21no—
56C4×C4⋊C4×C71C2211yescharacteristic
57C4×C4⋊C4×C71C2211yescharacteristic
58C4×C4⋊C4×C71C2211yescharacteristic
59C4×C4⋊C4×C71C2211yescharacteristic
60C22×D284C2311yescharacteristic
61C22×C4×D71—21no—
62C22×C71⋊C8C2311yescharacteristic
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C4×D284—22no—
67C4×D284C2×C414yes—
68C2×C4⋊Dic71C2311yescharacteristic
69C2×C4⋊Dic71C2311yescharacteristic
70C2×C4⋊Dic71C2311yescharacteristic
71C2×(C2×D71)⋊C4—21no—
72C2×(C2×D71)⋊C4—21no—
73C2×(C2×D71)⋊C4—21no—
74C2×(C2×D71)⋊C4—21no—
75C2×(C2×D71)⋊C4—21no—
76C2×C4×Dic71—21no—
77C2×C4×Dic71—21no—
78#14556061—22no—
79#14556061C2×C414yes—
80#14556059—22no—
81#14556059C2×C414yes—
82C4⋊(C71⋊C8)C2×C414yes—
83#14556048—22no—
84#14556048—22no—
85#14556048C2×C414yes—
86#14556048C2×C414yes—
87C4×C71⋊C8—22no—
88C4×C71⋊C8—22no—
89C4×C71⋊C8—22no—
90C71⋊#95—21no—
91C71⋊#95—21no—
92C71⋊#95—21no—
93C71⋊#95—21no—
94#125×C71—22no—
95#125×C71C2×C414yes—
96C2×C4⋊C4×C71—21no—
97C2×C4⋊C4×C71—21no—
98C2×C4⋊C4×C71—21no—
99C2×C4⋊C4×C71—21no—
100C2×C4⋊C4×C71D411yescharacteristic
101C2×C4⋊C4×C71D411yescharacteristic
102C2×C4⋊C4×C71C2311yescharacteristic
103C2×C4⋊C4×C71C2311yescharacteristic
104C2×C4⋊C4×C71C2311yescharacteristic
105C2×C4⋊C4×C71C2311yescharacteristic
106C2×C42×C71—21no—
107C2×C42×C71—21no—
108C2×C42×C71—21no—
109C2×C42×C71C2311yescharacteristic
110C2×C42×C71C2311yescharacteristic
111C2×C42×C71C2311yescharacteristic
112#95×C71—21no—
113#95×C71—21no—
114#95×C71—21no—
115#95×C71—21no—
116#95×C71—21no—
117#95×C71D411yescharacteristic
118#95×C71D411yescharacteristic
119C23×D71—21no—
120C2×D284—21no—
121C2×D284—21no—
122C2×D284—21no—
123C2×D284—21no—
124C2×D284—21no—
125C2×D284C22×C412yes—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C2×C4×D71—24no—
130C2×C4×D71—81no—
131C2×C4×D71—81no—
132C2×C71⋊C8—21no—
133C2×C71⋊C8—21no—
134C2×C71⋊C8—21no—
135C2×C71⋊C8—21no—
136C2×C71⋊C8—21no—
137C2×C71⋊C8—21no—
138C2×C71⋊C8—21no—
139C2×C71⋊C8—21no—
140C2×C71⋊C8—21no—
141C2×C71⋊C8C22×C412yes—
142C2×C71⋊C8C22×C412yes—
143C2×C71⋊C8#4112yes—
144C4⋊Dic71—21no—
145C4⋊Dic71—21no—
146C4⋊Dic71—21no—
147C4⋊Dic71—21no—
148C4⋊Dic71—21no—
149C4⋊Dic71C22×C412yes—
150(C2×D71)⋊C4—24no—
151(C2×D71)⋊C4—42no—
152(C2×D71)⋊C4—42no—
153(C2×D71)⋊C4—81no—
154(C2×D71)⋊C4—81no—
155C4×Dic71—81no—
156C4×Dic71—81no—
157C22×C4×C71—21no—
158C22×C4×C71—21no—
159C22×C4×C71—21no—
160C22×C4×C71—21no—
161C22×C4×C71C2×D411yescharacteristic
162C22×C4×C71C2×D411yescharacteristic
163C22×C4×C71C2×D411yescharacteristic
164C22×C4×C71C2×D411yescharacteristic
165C22×C4×C71C2×D411yescharacteristic
166C22×C4×C71C2×D411yescharacteristic
167C22×C4×C71C2411yescharacteristic
168C4⋊C4×C71—24no—
169C4⋊C4×C71—24no—
170C4⋊C4×C71—22no—
171C4⋊C4×C71—22no—
172C4⋊C4×C71—21no—
173C4⋊C4×C71—21no—
174C4⋊C4×C71—21no—
175C4⋊C4×C71—21no—
176C4⋊C4×C71—21no—
177C4⋊C4×C71—42no—
178C4⋊C4×C71—81no—
179C4⋊C4×C71C22×C412yes—
180C4⋊C4×C71C22×C412yes—
181C4⋊C4×C71#4112yes—
182C42×C71—21no—
183C42×C71—21no—
184C42×C71—21no—
185C42×C71—21no—
186C42×C71—42no—
187C42×C71—81no—
188C42×C71—81no—
189C42×C71C22×C412yes—
190C42×C71#4112yes—
191C23×C71C22×D411yescharacteristic
192C22×D71—22no—
193C22×D71—41no—
194C22×D71—41no—
195C22×D71—41no—
196C22×D71—41no—
197C22×D71—41no—
198C22×D71—41no—
199C2×C4×C71—21no—
200C2×C4×C71—21no—
201C2×C4×C71—21no—
202C2×C4×C71—21no—
203C2×C4×C71—21no—
204C2×C4×C71—21no—
205C2×C4×C71—21no—
206C2×C4×C71—21no—
207C2×C4×C71—22no—
208C2×C4×C71—22no—
209C2×C4×C71—21no—
210C2×C4×C71—21no—
211C2×C4×C71—22no—
212C2×C4×C71—21no—
213C2×C4×C71—21no—
214C2×C4×C71—21no—
215C2×C4×C71—21no—
216C2×C4×C71—41no—
217C2×C4×C71—41no—
218C2×C4×C71—41no—
219C2×C4×C71—41no—
220C2×C4×C71—41no—
221C2×C4×C71—41no—
222C2×C4×C71—41no—
223C2×C4×C71—41no—
224C2×C4×C71—41no—
225C2×C4×C71C4×D412yes—
226C2×C4×C71C4×D412yes—
227C2×C4×C71#13512yes—
228C2×C4×C71#13512yes—
229C2×C4×C71C23×C411yescharacteristic
230C2×C4×C71C2×#4111yescharacteristic
231C2×C4×C71C2×#4111yescharacteristic
232C2×C4×C71C2×#4111yescharacteristic
233C2×C4×C712−1+411yescharacteristic
234C2×C4×C712−1+411yescharacteristic
235C2×Dic71—22no—
236C2×Dic71—41no—
237C2×Dic71—41no—
238C2×Dic71—41no—
239C2×Dic71—41no—
240C2×Dic71—41no—
241C2×Dic71—41no—
242C2×Dic71—41no—
243C2×Dic71—41no—
244D284—22no—
245D284—22no—
246D284—41no—
247D284—41no—
248C4×D71—84no—
249C71⋊C8—22no—
250C71⋊C8—22no—
251C71⋊C8—22no—
252C71⋊C8—41no—
253C22×C71C2×C4×D411yescharacteristic
254C22×C71#54711yescharacteristic
255C22×C71#54811yescharacteristic
256C22×C71C2×#13511yescharacteristic
257C22×C71C2×#13511yescharacteristic
258C22×C71#57611yescharacteristic
259C22×C71#57711yescharacteristic
260C2×D71—42no—
261C2×D71—42no—
262C2×D71—42no—
263C2×D71—81no—
264C2×D71—81no—
265C2×D71—81no—
266C2×D71—81no—
267C4×C71—22no—
268C4×C71—22no—
269C4×C71—22no—
270C4×C71—22no—
271C4×C71—41no—
272C4×C71—41no—
273C4×C71—42no—
274C4×C71—42no—
275C4×C71—42no—
276C4×C71—81no—
277C4×C71C4×#4111yescharacteristic
278C4×C71#51911yescharacteristic
279C4×C71#55211yescharacteristic
280C4×C71#55611yescharacteristic
281Dic71—42no—
282Dic71—81no—
283Dic71—81no—
284#23065—711nomaximal, Sylow
285C2×C71#236211yescharacteristic
286C2×C71C4×#13511yescharacteristic
287C2×C71#294611yescharacteristic
288C2×C71#333711yescharacteristic
289C2×C71#333911yescharacteristic
290C2×C71#336111yescharacteristic
291C2×C71#336511yescharacteristic
292D71—82no—
293C2×#478—711no—
294#2370D7111yescharacteristic, complemented
295#2357—711no—
296#1991—711no—
297#1949—711no—
298#1934—711no—
299#1934—711no—
300#1926—711no—
301#1925—711no—
302#1921—711no—
303#1919—711no—
304C4×#107—711no—
305C4×#106—711no—
306C8×C4⋊C4—711no—
307C4×#102—711no—
308C71#2306511yescharacteristic, complemented, Sylow
309C2×#125C2×D7111yescharacteristic
310C2×C4×D4—711no—
311#478—718no—
312C2×#107—711no—
313C2×#107—711no—
314C2×#106—711no—
315C2×#106—711no—
316C2×C4⋊C8—711no—
317C2×#102—711no—
318C2×#102—711no—
319C2×#102—711no—
320C2×#102—711no—
321C2×C4×C8—711no—
322C2×C4×C8—711no—
323C2×C4×C8—711no—
324#390—711no—
325#390—711no—
326#389—21no—
327#389C2×D7111yescharacteristic
328#389C2×D7111yescharacteristic
329#388—1421no—
330#388—1421no—
331#387—21no—
332#387—21no—
333#382—711no—
334#381—1421no—
335C4×C4⋊C4—21no—
336C4×C4⋊C4—711no—
337C4×C4⋊C4—711no—
338C4×C4⋊C4C2×D7111yescharacteristic
339C4×C4⋊C4C2×D7111yescharacteristic
340C4×C4⋊C4C2×D7111yescharacteristic
341C4×C4⋊C4C2×D7111yescharacteristic
342C4×C22⋊C4—1421no—
343#340—711no—
344#340—711no—
345#340—711no—
346#340—711no—
347#340—711no—
348#340—711no—
349#340—711no—
350#340—711no—
351#336—711no—
352#336—711no—
353C22×D4—711no—
354C23×C4—1421no—
355C22×C8—711no—
356C22×C8—711no—
357C22×C8—711no—
358C22×C8—711no—
359#125—22no—
360#125C4×D7114yes—
361C4×D4—714no—
362C4×D4—1422no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—711no—
368C2×C4⋊C4—711no—
369C2×C4⋊C4—711no—
370C2×C4⋊C4C22⋊D7111yescharacteristic
371C2×C4⋊C4C22⋊D7111yescharacteristic
372C2×C4⋊C4C22×D7111yescharacteristic
373C2×C4⋊C4C22×D7111yescharacteristic
374C2×C4⋊C4C22×D7111yescharacteristic
375C2×C4⋊C4C22×D7111yescharacteristic
376C2×C22⋊C4—1421no—
377C2×C22⋊C4—1421no—
378C2×C22⋊C4—1421no—
379C2×C22⋊C4—1421no—
380C2×C22⋊C4—1421no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—1421no—
385C2×C42—1421no—
386C2×C42C22×D7111yescharacteristic
387C2×C42C22×D7111yescharacteristic
388C2×C42C22×D7111yescharacteristic
389#107—714no—
390#107—1422no—
391#106—714no—
392#106—1422no—
393C4⋊C8—714no—
394#102—714no—
395#102—714no—
396#102—1422no—
397#102—1422no—
398C4×C8—1422no—
399C4×C8—1422no—
400C4×C8—1422no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—1421no—
407#95—1421no—
408#95—1421no—
409#95—1421no—
410#95C22⋊D7111yescharacteristic
411#95C22⋊D7111yescharacteristic
412C24—1421no—
413C2×D4—712no—
414C2×D4—1421no—
415C2×D4—1421no—
416C2×D4—1421no—
417C2×D4—1421no—
418C2×D4—1421no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—5681no—
424C22×C4—5681no—
425C22×C4—1421no—
426C22×C4—1421no—
427C22×C4—1421no—
428C22×C4—1424no—
429C22×C4C2×C22⋊D7111yescharacteristic
430C22×C4C2×C22⋊D7111yescharacteristic
431C22×C4C2×C22⋊D7111yescharacteristic
432C22×C4C2×C22⋊D7111yescharacteristic
433C22×C4C2×C22⋊D7111yescharacteristic
434C22×C4C2×C22⋊D7111yescharacteristic
435C22×C4C23×D7111yescharacteristic
436C2×C8—712no—
437C2×C8—712no—
438C2×C8—712no—
439C2×C8—1421no—
440C2×C8—1421no—
441C2×C8—1421no—
442C2×C8—1421no—
443C2×C8—1421no—
444C2×C8—1421no—
445C2×C8—1421no—
446C2×C8—1421no—
447C2×C8—1421no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—81no—
459C4⋊C4—712no—
460C4⋊C4—1421no—
461C4⋊C4—1421no—
462C4⋊C4—1421no—
463C4⋊C4—1421no—
464C4⋊C4—1421no—
465C4⋊C4C2×C4×D7112yes—
466C4⋊C4C2×C4×D7112yes—
467C4⋊C4#1176586612yes—
468C22⋊C4—2842no—
469C22⋊C4—2842no—
470C22⋊C4—5681no—
471C22⋊C4—5681no—
472C22⋊C4—1424no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—81no—
479C42—81no—
480C42—5681no—
481C42—5681no—
482C42C2×C4×D7112yes—
483C42#1176586512yes—
484C23—2841no—
485C23—2841no—
486C23—2841no—
487C23—2841no—
488C23—2841no—
489C23—2841no—
490C23—1422no—
491C23C22×C22⋊D7111yescharacteristic
492D4—2841no—
493D4—2841no—
494D4—1422no—
495D4—1422no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—2841no—
523C2×C4—2841no—
524C2×C4—2841no—
525C2×C4—2841no—
526C2×C4—2841no—
527C2×C4—2841no—
528C2×C4—2841no—
529C2×C4—2841no—
530C2×C4—5684no—
531C2×C4—1422no—
532C2×C4C4×C22⋊D7112yes—
533C2×C4C4×C22⋊D7112yes—
534C2×C4#1455614812yes—
535C2×C4#1455614812yes—
536C2×C4C22×C4×D7111yescharacteristic
537C2×C4#41×D7111yescharacteristic
538C2×C4C2×#1176586511yescharacteristic
539C2×C4C2×#1176586611yescharacteristic
540C2×C4#1455617511yescharacteristic
541C2×C4#1455617611yescharacteristic
542C8—2841no—
543C8—1422no—
544C8—1422no—
545C8—1422no—
546C22—2842no—
547C22—2842no—
548C22—2842no—
549C22—5681no—
550C22—5681no—
551C22—5681no—
552C22—5681no—
553C22C2×C4×C22⋊D7111yescharacteristic
554C22#1798664811yescharacteristic
555C22#1798666011yescharacteristic
556C22C2×#1455614811yescharacteristic
557C22C2×#1455614811yescharacteristic
558C22#1798680211yescharacteristic
559C22#1798680711yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—2842no—
571C4—5681no—
572C4—5681no—
573C4C4×#1176586611yescharacteristic
574C4#1798647511yescharacteristic
575C4#1798669011yescharacteristic
576C4#1798672211yescharacteristic
577C2—5682no—
578C2#2259136311yescharacteristic
579C2C4×#1455614811yescharacteristic
580C2#2259716811yescharacteristic
581C2#2260071911yescharacteristic
582C2#2260073611yescharacteristic
583C2#2260100011yescharacteristic
584C2#2260103611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2370C2
socleC23×C71C22×D4
prime radicalC22×D284C23
cosocleC22×C4×C71C24
hypercenter#2370D71
hypocenterC71#23065
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #22589306C2semidirect
4. #22589108C2semidirect
9. #22588929C2semidirect
10. #22588915C2semidirect
11. C4×#14556061C2semidirect
12. C4×#14556059C2semidirect
13. C4⋊C4×C71⋊C8C2semidirect
15. C71×#2370C2semidirect
17. #17986296C4semidirect
294. #2370D71semidirect
308. C71#23065semidirect

Maximal subgroups

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

subgroupindex
C2×#179862962
#225913112
#225893062
#225891082
#225890222
#225889672
#225889602
#225889292
#225889152
C4×#145560612
C4×#145560592
C4⋊C4×C71⋊C82
C4×#145560482
C71×#23702
#2306571