Finite Group Databasebeta

← #32150196

Subgroups — #32150196

Order 18176.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985983C211yesmaximal, characteristic, complemented
2C2×#17985973C211yesmaximal, characteristic, complemented
3#22589994C212yesmaximal, complemented
4#22589990C212yesmaximal, complemented
5#22589986C214yesmaximal, complemented
6#22589981C214yesmaximal, complemented
7C71×#3449C211yesmaximal, characteristic
8C22×#11765849—21no—
9C2×#14556087—21no—
10#17985983—21no—
11#17985983—21no—
12#17985983C2212yes—
13#17985983C2212yes—
14C2×#14556047—21no—
15C2×#14556045C2212yes—
16#17985973—21no—
17#17985973—21no—
18#17985973C2212yes—
19#17985973C2212yes—
20C2×#14556043—21no—
21C2×#14556043C2212yes—
22#17985789C2218yescomplemented
23#17985786C2218yescomplemented
24C22×#41×C71C411yescharacteristic, complemented
25C22×#41×C71C2211yescharacteristic
26#537×C71—21no—
27#537×C71—21no—
28#536×C71—21no—
29#536×C71C411yescharacteristic, complemented
30#536×C71C2211yescharacteristic
31#535×C71—21no—
32#535×C71C411yescharacteristic, complemented
33#535×C71C2211yescharacteristic
34#534×C71C412yescomplemented
35#534×C71C2212yes—
36#532×C71—21no—
37#532×C71—21no—
38#525×C71—21no—
39#525×C71—21no—
40#525×C71C412yescomplemented
41#525×C71C2212yes—
42C2×#117×C71C411yescharacteristic, complemented
43C2×#11765849—22no—
44C2×#11765849—22no—
45C2×#11765849—22no—
46C2×#11765849—41no—
47C2×#11765849—41no—
48C2×#11765849—41no—
49C22×C71⋊C8—41no—
50#14556087—22no—
51#14556087—22no—
52#14556087—41no—
53#14556087—41no—
54C2×C4⋊Dic71—41no—
55C2×C22⋊Dic71—22no—
56C2×C4×Dic71—41no—
57#14556047—22no—
58#14556047—22no—
59#14556045—22no—
60#14556045C2314yes—
61#14556043—22no—
62#14556043—22no—
63#14556043—22no—
64#14556043C2314yes—
65C2×#41×C71—21no—
66C2×#41×C71—21no—
67C2×#41×C71—21no—
68C2×#41×C71—21no—
69C2×#41×C71—41no—
70C2×#41×C71—41no—
71C2×#41×C71—41no—
72C2×#41×C71—41no—
73C2×#41×C71—41no—
74C2×#41×C71—41no—
75C2×#41×C71—41no—
76C2×#41×C71—41no—
77C2×#41×C71C2×C411yescharacteristic
78C2×#41×C71C2×C411yescharacteristic
79C2×#41×C71D411yescharacteristic
80C2×#41×C71D411yescharacteristic
81C2×#41×C71D411yescharacteristic
82C2×#41×C71D411yescharacteristic
83C2×#41×C71C2311yescharacteristic
84C2×#41×C71C2311yescharacteristic
85C22×Q8×C71C2×C411yescharacteristic, complemented
86C22×Q8×C71D411yescharacteristic
87C22×D4×C71C2×C411yescharacteristic
88C22×D4×C71C2×C412yes—
89C22×D4×C71C2×C411yescharacteristic, complemented
90C22×D4×C71D411yescharacteristic
91C22×D4×C71C2311yescharacteristic
92C23×C4×C71C2×C411yescharacteristic
93C23×C4×C71C2×C412yescomplemented
94C23×C4×C71D411yescharacteristic
95C23×C4×C71D411yescharacteristic
96C4⋊Q8×C71—21no—
97C4⋊Q8×C71—21no—
98#127×C71—21no—
99#127×C71—21no—
100#124×C71—21no—
101#124×C71—21no—
102#124×C71—21no—
103#124×C71—21no—
104#123×C71—22no—
105#123×C71—22no—
106#123×C71C2×C412yes—
107#123×C71C2×C412yescomplemented
108#123×C71C2×C412yescomplemented
109#123×C71C2312yes—
110C22⋊Q8×C71—22no—
111C22⋊Q8×C71—22no—
112C22⋊Q8×C71—21no—
113C22⋊Q8×C71—21no—
114C22⋊Q8×C71—21no—
115C22⋊Q8×C71—21no—
116#121×C71—22no—
117#121×C71—22no—
118#121×C71—22no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—21no—
123#121×C71—21no—
124#121×C71—21no—
125#121×C71—21no—
126#120×C71—22no—
127#120×C71—22no—
128#120×C71C2×C412yes—
129#120×C71C2×C412yescomplemented
130#120×C71C2×C412yescomplemented
131#120×C71C2312yes—
132C4×D4×C71—22no—
133C4×D4×C71—22no—
134C4×D4×C71—22no—
135C4×D4×C71—22no—
136#117×C71—21no—
137#117×C71—21no—
138#117×C71C2×C412yescomplemented
139#117×C71C2×C411yescharacteristic, complemented
140#117×C71C2×C411yescharacteristic, complemented
141C2×C4⋊C4×C71—21no—
142C2×C22⋊C4×C71C2×C412yes—
143C2×C42×C71—21no—
144C22×Dic71—42no—
145#11765849—24no—
146#11765849—42no—
147#11765849—42no—
148#11765849—42no—
149C2×C71⋊C8—42no—
150C2×C71⋊C8—42no—
151C2×C71⋊C8—42no—
152C4⋊Dic71—42no—
153C4⋊Dic71—42no—
154C22⋊Dic71—24no—
155C22⋊Dic71—42no—
156C4×Dic71—42no—
157C4×Dic71—42no—
158C24×C71C22⋊C411yescharacteristic
159C24×C71C22×C411yescharacteristic
160C24×C71C22×C412yes—
161C24×C71C2×D411yescharacteristic
162#41×C71—41no—
163#41×C71—41no—
164#41×C71—41no—
165#41×C71—41no—
166#41×C71—41no—
167#41×C71—41no—
168#41×C71—41no—
169#41×C71—41no—
170#41×C71—41no—
171#41×C71—41no—
172#41×C71—41no—
173#41×C71—41no—
174#41×C71—41no—
175#41×C71—41no—
176#41×C71—41no—
177#41×C71—41no—
178#41×C71—42no—
179#41×C71—42no—
180#41×C71—42no—
181#41×C71—42no—
182#41×C71—42no—
183#41×C71—42no—
184#41×C71—41no—
185#41×C71—41no—
186#41×C71—41no—
187#41×C71—41no—
188C2×Q8×C71—21no—
189C2×Q8×C71—21no—
190C2×Q8×C71—41no—
191C2×Q8×C71—41no—
192C2×Q8×C71—41no—
193C2×Q8×C71—41no—
194C2×Q8×C71C22⋊C411yescharacteristic
195C2×Q8×C71C22⋊C411yescharacteristic
196C2×Q8×C71C2×D411yescharacteristic
197C2×Q8×C71C2×D411yescharacteristic
198C2×D4×C71—22no—
199C2×D4×C71—22no—
200C2×D4×C71—22no—
201C2×D4×C71—22no—
202C2×D4×C71—22no—
203C2×D4×C71—22no—
204C2×D4×C71—21no—
205C2×D4×C71—21no—
206C2×D4×C71—41no—
207C2×D4×C71—41no—
208C2×D4×C71—41no—
209C2×D4×C71—41no—
210C2×D4×C71—41no—
211C2×D4×C71—41no—
212C2×D4×C71—41no—
213C2×D4×C71—41no—
214C2×D4×C71—42no—
215C2×D4×C71—42no—
216C2×D4×C71C22⋊C411yescharacteristic
217C2×D4×C71C22⋊C411yescharacteristic
218C2×D4×C71C22⋊C411yescharacteristic
219C2×D4×C71C22⋊C411yescharacteristic
220C2×D4×C71C22×C411yescharacteristic
221C2×D4×C71C22×C411yescharacteristic
222C2×D4×C71C22×C411yescharacteristic
223C2×D4×C71C2×D411yescharacteristic
224C2×D4×C71C2×D411yescharacteristic
225C2×D4×C71C2×D411yescharacteristic
226C2×D4×C71C2×D411yescharacteristic
227C2×D4×C71C2411yescharacteristic
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—42no—
244C22×C4×C71—42no—
245C22×C4×C71C22⋊C411yescharacteristic
246C22×C4×C71C22⋊C411yescharacteristic
247C22×C4×C71C22⋊C411yescharacteristic
248C22×C4×C71C22⋊C411yescharacteristic
249C22×C4×C71C22⋊C411yescharacteristic
250C22×C4×C71C22⋊C411yescharacteristic
251C22×C4×C71C22⋊C411yescharacteristic
252C22×C4×C71C22⋊C411yescharacteristic
253C22×C4×C71C22⋊C411yescharacteristic
254C22×C4×C71C22×C411yescharacteristic
255C22×C4×C71C22×C411yescharacteristic
256C22×C4×C71C22×C412yes—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C4⋊C4×C71—22no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—22no—
266C4⋊C4×C71—22no—
267C4⋊C4×C71—22no—
268C4⋊C4×C71—22no—
269C22⋊C4×C71—22no—
270C22⋊C4×C71—22no—
271C22⋊C4×C71—22no—
272C22⋊C4×C71—22no—
273C22⋊C4×C71—22no—
274C22⋊C4×C71—22no—
275C22⋊C4×C71—22no—
276C22⋊C4×C71—22no—
277C22⋊C4×C71—22no—
278C22⋊C4×C71C22×C412yes—
279C22⋊C4×C71C22×C412yes—
280C42×C71—22no—
281C42×C71—21no—
282C42×C71—21no—
283C23×C71—21no—
284C23×C71—21no—
285C23×C71—21no—
286C23×C71—21no—
287C23×C71—21no—
288C23×C71—21no—
289C23×C71—22no—
290C23×C71—42no—
291C23×C71—81no—
292C23×C71—81no—
293C23×C71—81no—
294C23×C71—82no—
295C23×C71C2×C22⋊C411yescharacteristic
296C23×C71C2×C22⋊C411yescharacteristic
297C23×C71C2×C22⋊C411yescharacteristic
298C23×C71C2×C22⋊C411yescharacteristic
299C23×C71C2×C22⋊C411yescharacteristic
300C23×C71C23×C411yescharacteristic
301C23×C71C22×D411yescharacteristic
302Q8×C71—41no—
303Q8×C71—41no—
304Q8×C71—41no—
305Q8×C71—41no—
306Q8×C71—42no—
307Q8×C71—41no—
308Q8×C71—41no—
309D4×C71—41no—
310D4×C71—41no—
311D4×C71—41no—
312D4×C71—41no—
313D4×C71—41no—
314D4×C71—41no—
315D4×C71—41no—
316D4×C71—41no—
317D4×C71—41no—
318D4×C71—41no—
319D4×C71—41no—
320D4×C71—41no—
321D4×C71—42no—
322D4×C71—44no—
323D4×C71—42no—
324D4×C71—42no—
325D4×C71—41no—
326D4×C71—41no—
327D4×C71—82no—
328D4×C71—82no—
329D4×C71—82no—
330D4×C71—82no—
331C2×C4×C71—21no—
332C2×C4×C71—21no—
333C2×C4×C71—21no—
334C2×C4×C71—21no—
335C2×C4×C71—21no—
336C2×C4×C71—21no—
337C2×C4×C71—21no—
338C2×C4×C71—21no—
339C2×C4×C71—21no—
340C2×C4×C71—21no—
341C2×C4×C71—21no—
342C2×C4×C71—21no—
343C2×C4×C71—21no—
344C2×C4×C71—21no—
345C2×C4×C71—21no—
346C2×C4×C71—21no—
347C2×C4×C71—21no—
348C2×C4×C71—21no—
349C2×C4×C71—21no—
350C2×C4×C71—21no—
351C2×C4×C71—21no—
352C2×C4×C71—21no—
353C2×C4×C71—21no—
354C2×C4×C71—21no—
355C2×C4×C71—21no—
356C2×C4×C71—21no—
357C2×C4×C71—21no—
358C2×C4×C71—21no—
359C2×C4×C71—21no—
360C2×C4×C71—21no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—44no—
365C2×C4×C71—42no—
366C2×C4×C71—42no—
367C2×C4×C71—42no—
368C2×C4×C71—82no—
369C2×C4×C71#9911yescharacteristic
370C2×C4×C71#9911yescharacteristic
371C2×C4×C71#9911yescharacteristic
372C2×C4×C71#9911yescharacteristic
373C2×C4×C71C2×C22⋊C411yescharacteristic
374C2×C4×C71C2×C22⋊C411yescharacteristic
375C2×C4×C71C2×C22⋊C411yescharacteristic
376C2×C4×C71C2×C22⋊C411yescharacteristic
377C2×C4×C71C2×C22⋊C411yescharacteristic
378C2×C4×C71C2×C22⋊C411yescharacteristic
379C2×C4×C71C2×C22⋊C411yescharacteristic
380C2×C4×C71C22×D411yescharacteristic
381C2×Dic71—44no—
382C2×Dic71—84no—
383C71⋊C8—44no—
384C22×C71—21no—
385C22×C71—21no—
386C22×C71—21no—
387C22×C71—21no—
388C22×C71—21no—
389C22×C71—21no—
390C22×C71—41no—
391C22×C71—41no—
392C22×C71—41no—
393C22×C71—41no—
394C22×C71—41no—
395C22×C71—41no—
396C22×C71—41no—
397C22×C71—42no—
398C22×C71—42no—
399C22×C71—42no—
400C22×C71—42no—
401C22×C71—42no—
402C22×C71—81no—
403C22×C71—81no—
404C22×C71—81no—
405C22×C71—81no—
406C22×C71—84no—
407C22×C71C2×#9911yescharacteristic
408C22×C71C2×#9911yescharacteristic
409C22×C71C22×C22⋊C411yescharacteristic
410C4×C71—21no—
411C4×C71—21no—
412C4×C71—21no—
413C4×C71—21no—
414C4×C71—21no—
415C4×C71—21no—
416C4×C71—42no—
417C4×C71—42no—
418C4×C71—42no—
419C4×C71C2×#9911yescharacteristic
420C4×C71C2×#9911yescharacteristic
421C4×C71C2×#9911yescharacteristic
422C4×C71C2×#9911yescharacteristic
423Dic71—84no—
424#33347—711nomaximal, Sylow
425C2×C71—21no—
426C2×C71—21no—
427C2×C71—21no—
428C2×C71—41no—
429C2×C71—41no—
430C2×C71—41no—
431C2×C71—41no—
432C2×C71—41no—
433C2×C71—41no—
434C2×C71—82no—
435C2×C71C22×#9911yescharacteristic
436#3449D7111yescharacteristic
437C2×#413—711no—
438C2×#410—711no—
439#2123—712no—
440#2122—712no—
441#2121—714no—
442#2120—714no—
443C71#3334711yescharacteristic, complemented, Sylow
444C22×#41Dic7111yescharacteristic, complemented
445C22×#41C2×D7111yescharacteristic
446C22×M16—1421no—
447#537—21no—
448#537—21no—
449#536—21no—
450#536Dic7111yescharacteristic, complemented
451#536C2×D7111yescharacteristic
452#535—21no—
453#535Dic7111yescharacteristic, complemented
454#535C2×D7111yescharacteristic
455#534Dic7112yescomplemented
456#534C2×D7112yes—
457#532—21no—
458#532—21no—
459#525—21no—
460#525—21no—
461#525Dic7112yescomplemented
462#525C2×D7112yes—
463C2×#117—1421no—
464C2×#117Dic7111yescharacteristic, complemented
465#413—712no—
466#413—712no—
467#413—1421no—
468#413—1421no—
469C2×#101—1421no—
470C2×#100—712no—
471#410—712no—
472#410—712no—
473#410—1421no—
474#410—1421no—
475C2×#99—712no—
476C2×#99—1421no—
477#352—718no—
478AΣL(1,𝔽16)—718no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×Dic7111yescharacteristic
492C2×#41C2×Dic7111yescharacteristic
493C2×#41C22⋊D7111yescharacteristic
494C2×#41C22⋊D7111yescharacteristic
495C2×#41C22⋊D7111yescharacteristic
496C2×#41C22⋊D7111yescharacteristic
497C2×#41C22×D7111yescharacteristic
498C2×#41C22×D7111yescharacteristic
499C22×Q8C2×Dic7111yescharacteristic, complemented
500C22×Q8C22⋊D7111yescharacteristic
501C22×D4C2×Dic7111yescharacteristic
502C22×D4C2×Dic7112yes—
503C22×D4C2×Dic7111yescharacteristic, complemented
504C22×D4C22⋊D7111yescharacteristic
505C22×D4C22×D7111yescharacteristic
506C23×C4C2×Dic7111yescharacteristic
507C23×C4C2×Dic7112yescomplemented
508C23×C4C22⋊D7111yescharacteristic
509C23×C4C22⋊D7111yescharacteristic
510C2×M16—2841no—
511C2×M16—2841no—
512C2×M16—2841no—
513C2×M16—1422no—
514C2×M16—1422no—
515C2×M16—1422no—
516C22×C8—2841no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×Dic7112yes—
528#123C2×Dic7112yescomplemented
529#123C2×Dic7112yescomplemented
530#123C22×D7112yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×Dic7112yes—
550#120C2×Dic7112yescomplemented
551#120C2×Dic7112yescomplemented
552#120C22×D7112yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—2841no—
560#117—2841no—
561#117—1422no—
562#117—1422no—
563#117C2×Dic7112yescomplemented
564#117C2×Dic7111yescharacteristic, complemented
565#117C2×Dic7111yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—2841no—
568C2×C22⋊C4—1422no—
569C2×C22⋊C4C2×Dic7112yes—
570C2×C42—21no—
571C2×C42—2841no—
572#101—1422no—
573#101—1422no—
574#100—714no—
575#100—1422no—
576#99—714no—
577#99—1422no—
578#99—1422no—
579#99—1422no—
580C24C22⋊Dic7111yescharacteristic
581C24C22×Dic7111yescharacteristic
582C24C22×Dic7112yes—
583C24C2×C22⋊D7111yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊Dic7111yescharacteristic
617C2×Q8C22⋊Dic7111yescharacteristic
618C2×Q8C2×C22⋊D7111yescharacteristic
619C2×Q8C2×C22⋊D7111yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊Dic7111yescharacteristic
639C2×D4C22⋊Dic7111yescharacteristic
640C2×D4C22⋊Dic7111yescharacteristic
641C2×D4C22⋊Dic7111yescharacteristic
642C2×D4C22×Dic7111yescharacteristic
643C2×D4C22×Dic7111yescharacteristic
644C2×D4C22×Dic7111yescharacteristic
645C2×D4C2×C22⋊D7111yescharacteristic
646C2×D4C2×C22⋊D7111yescharacteristic
647C2×D4C2×C22⋊D7111yescharacteristic
648C2×D4C2×C22⋊D7111yescharacteristic
649C2×D4C23×D7111yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—2842no—
668C22×C4C22⋊Dic7111yescharacteristic
669C22×C4C22⋊Dic7111yescharacteristic
670C22×C4C22⋊Dic7111yescharacteristic
671C22×C4C22⋊Dic7111yescharacteristic
672C22×C4C22⋊Dic7111yescharacteristic
673C22×C4C22⋊Dic7111yescharacteristic
674C22×C4C22⋊Dic7111yescharacteristic
675C22×C4C22⋊Dic7111yescharacteristic
676C22×C4C22⋊Dic7111yescharacteristic
677C22×C4C22×Dic7111yescharacteristic
678C22×C4C22×Dic7111yescharacteristic
679C22×C4C22×Dic7112yes—
680C22×C4C2×C22⋊D7111yescharacteristic
681C22×C4C2×C22⋊D7111yescharacteristic
682C22×C4C2×C22⋊D7111yescharacteristic
683C22×C4C2×C22⋊D7111yescharacteristic
684C22×C4C2×C22⋊D7111yescharacteristic
685M16—2842no—
686M16—2842no—
687M16—2842no—
688M16—1424no—
689C2×C8—2842no—
690C2×C8—2842no—
691C2×C8—2842no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—2842no—
700C4⋊C4—2842no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—2842no—
711C22⋊C4—1424no—
712C22⋊C4C22×Dic7112yes—
713C22⋊C4C22×Dic7112yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—2842no—
718C42—2842no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊Dic7111yescharacteristic
732C23C2×C22⋊Dic7111yescharacteristic
733C23C2×C22⋊Dic7111yescharacteristic
734C23C2×C22⋊Dic7111yescharacteristic
735C23C2×C22⋊Dic7111yescharacteristic
736C23C23×Dic7111yescharacteristic
737C23C22×C22⋊D7111yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—82no—
805C2×C4—2844no—
806C2×C4—5684no—
807C2×C4#1455604311yescharacteristic
808C2×C4#1455604311yescharacteristic
809C2×C4#1455604311yescharacteristic
810C2×C4#1455604311yescharacteristic
811C2×C4C2×C22⋊Dic7111yescharacteristic
812C2×C4C2×C22⋊Dic7111yescharacteristic
813C2×C4C2×C22⋊Dic7111yescharacteristic
814C2×C4C2×C22⋊Dic7111yescharacteristic
815C2×C4C2×C22⋊Dic7111yescharacteristic
816C2×C4C2×C22⋊Dic7111yescharacteristic
817C2×C4C2×C22⋊Dic7111yescharacteristic
818C2×C4C22×C22⋊D7111yescharacteristic
819C8—2844no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#1455604311yescharacteristic
844C22C2×#1455604311yescharacteristic
845C22C22×C22⋊Dic7111yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—5684no—
856C4C2×#1455604311yescharacteristic
857C4C2×#1455604311yescharacteristic
858C4C2×#1455604311yescharacteristic
859C4C2×#1455604311yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#1455604311yescharacteristic
subgroupG/H
centerC4C2×#14556043
commutatorC23×C71C23×C4
FrattiniC2×D4C23×D71
Fitting, prime radicalC71×#3449C2
socleC2×C71C22×#99
cosocleC2×D4×C71C24
hypercenter#3449D71
hypocenterC71#33347
LCSG ▷ C23×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#17985983C2semidirect
2. C2×#17985973C2semidirect
3. #22589994C2semidirect
4. #22589990C2semidirect
5. #22589986C2semidirect
6. #22589981C2semidirect
22. #17985789C22semidirect
23. #17985786C22semidirect
24. C22×#41×C71C4semidirect
29. #536×C71C4semidirect
32. #535×C71C4semidirect
34. #534×C71C4semidirect
40. #525×C71C4semidirect
42. C2×#117×C71C4semidirect
85. C22×Q8×C71C2×C4semidirect
89. C22×D4×C71C2×C4semidirect
93. C23×C4×C71C2×C4semidirect
107. #123×C71C2×C4semidirect
108. #123×C71C2×C4semidirect
129. #120×C71C2×C4semidirect
130. #120×C71C2×C4semidirect
138. #117×C71C2×C4semidirect
139. #117×C71C2×C4semidirect
140. #117×C71C2×C4semidirect
443. C71#33347semidirect
444. C22×#41Dic71semidirect
450. #536Dic71semidirect
453. #535Dic71semidirect
455. #534Dic71semidirect
461. #525Dic71semidirect
464. C2×#117Dic71semidirect
499. C22×Q8C2×Dic71semidirect
503. C22×D4C2×Dic71semidirect
507. C23×C4C2×Dic71semidirect
528. #123C2×Dic71semidirect
529. #123C2×Dic71semidirect
550. #120C2×Dic71semidirect
551. #120C2×Dic71semidirect
563. #117C2×Dic71semidirect
564. #117C2×Dic71semidirect
565. #117C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179859832
C2×#179859732
#225899942
#225899902
#225899862
#225899812
C71×#34492
#3334771