Finite Group Databasebeta

← C2×C4×#14556149 #32861473

Subgroups — C2×C4×#14556149 #32861473

Order 18176.

2894 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556149C211yesmaximal, characteristic
2C2×C4×#11765866C211yesmaximal, characteristic, complemented
3C2×C4×#11765864C211yesmaximal, characteristic, complemented
4C4×#14556149C2116yesmaximal, direct product factor
5C2×C4×#11765855C211yesmaximal, characteristic, complemented
6C2×#17986091C211yesmaximal, characteristic, complemented
7C2×C4×#11765854C211yesmaximal, characteristic, complemented
8C2×SD16×Dic71C211yesmaximal, characteristic, complemented
9C2×#17986086C211yesmaximal, characteristic, complemented
10C2×C4×#11765850C211yesmaximal, characteristic, complemented
11C2×#17986079C211yesmaximal, characteristic, complemented
12C2×#17986034C211yesmaximal, characteristic, complemented
13C2×#17985994C211yesmaximal, characteristic, complemented
14C2×#17985992C211yesmaximal, characteristic, complemented
15C2×C4×C8×D71C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765864C2211yescharacteristic
19C2×#14556149C4116yesdirect product factor
20C2×#14556149C2218yes—
21C22×#11765855C2211yescharacteristic
22C22×#11765854C2211yescharacteristic
23C22×#11765850C2211yescharacteristic
24C22×C8×D71C2211yescharacteristic
25C22×C8×D71C2211yescharacteristic
26C4×#11765866—24no—
27C4×#11765866C2218yescomplemented
28C4×#11765864—24no—
29C4×#11765864C2218yescomplemented
30C2×Q8×Dic71C2211yescharacteristic
31C2×C4×Dic142C2211yescharacteristic
32C2×#14556093C2211yescharacteristic
33C2×C4×D284—21no—
34C2×C4×D284C2211yescharacteristic
35C2×D4×Dic71C2211yescharacteristic
36C2×#14556090—21no—
37C2×#14556090C2211yescharacteristic
38C2×C4×C22⋊D71—21no—
39C2×(C22⋊D71)⋊C4—21no—
40C2×#14556086—21no—
41C2×#14556086C2211yescharacteristic
42C2×#14556086C2211yescharacteristic
43C2×#14556084—21no—
44C22×C4×Dic71—21no—
45C2×C42×D71—21no—
46C2×C42×D71C2211yescharacteristic
47C4×#11765855C2218yescomplemented
48#17986091C2218yescomplemented
49C4×#11765854C2218yescomplemented
50SD16×Dic71C2218yescomplemented
51#17986086C2218yescomplemented
52C4×#11765850C2218yescomplemented
53#17986079C2218yescomplemented
54#17986034C2218yescomplemented
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58#17985994C2218yescomplemented
59#17985992C2218yescomplemented
60C2×#14556053C2211yescharacteristic
61C2×#14556052C2211yescharacteristic
62C2×#14556051C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C4×C71⋊C8C2211yescharacteristic
67C2×C8×Dic71C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C4×C8×D71C2218yescomplemented
70C22×SD16×C71C2211yescharacteristic
71C2×C4×Q8×C71C2211yescharacteristic
72C2×C4×D4×C71C2211yescharacteristic
73C4×SD16×C71C2218yescomplemented
74C2×#106×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C2×C4×C8×C71C2211yescharacteristic
78C2×#11765866—22no—
79C2×#11765866—24no—
80C2×#11765866C2×C418yescomplemented
81C2×#11765866C2314yes—
82C2×#11765864—22no—
83C2×#11765864—24no—
84C2×#11765864C2×C418yescomplemented
85C2×#11765864C2314yes—
86C22×Dic142C2311yescharacteristic
87C22×D284—21no—
88C22×D284C2311yescharacteristic
89C22×C22⋊D71—21no—
90C23×Dic71—21no—
91C23×Dic71—21no—
92C22×C4×D71—21no—
93C22×C4×D71—21no—
94C22×C4×D71—21no—
95C22×C4×D71D411yescharacteristic
96C22×C4×D71D411yescharacteristic
97C22×C4×D71C2311yescharacteristic
98#14556149C2×C4164yesdirect product factor
99C2×#11765855C2×C418yescomplemented
100C2×#11765855C2314yes—
101C2×#11765854C2×C418yescomplemented
102C2×#11765854C2314yes—
103C2×#11765850C2×C418yescomplemented
104C2×#11765850C2314yes—
105C22×C71⋊C8C2311yescharacteristic
106C22×C71⋊C8C2311yescharacteristic
107C2×C8×D71—24no—
108C2×C8×D71C2×C418yescomplemented
109C2×C8×D71C2314yes—
110C2×C8×D71C2314yes—
111Q8×Dic71—22no—
112Q8×Dic71C2314yes—
113C4×Dic142—22no—
114C4×Dic142C2314yes—
115#14556093—22no—
116#14556093C2314yes—
117C4×D284—28no—
118C4×D284—22no—
119C4×D284C2314yes—
120D4×Dic71—22no—
121D4×Dic71C2314yes—
122#14556090—28no—
123#14556090—22no—
124#14556090C2314yes—
125C4×C22⋊D71—28no—
126(C22⋊D71)⋊C4—28no—
127#14556086—22no—
128#14556086—22no—
129#14556086—28no—
130#14556086C2314yes—
131#14556086C2314yes—
132#14556084—28no—
133C2×C4⋊Dic71—21no—
134C2×C4⋊Dic71C2311yescharacteristic
135C2×C4⋊Dic71C2311yescharacteristic
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C2×C22⋊Dic71—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71—21no—
147C2×C4×Dic71—28no—
148C2×C4×Dic71—21no—
149C2×C4×Dic71D411yescharacteristic
150C2×C4×Dic71D411yescharacteristic
151C2×C4×Dic71C2311yescharacteristic
152C42×D71—28no—
153C42×D71D414yes—
154C42×D71C2314yes—
155#14556061C2314yes—
156#14556061C2314yes—
157#14556060C2314yes—
158#14556053C2314yes—
159#14556052C2314yes—
160#14556051C2314yes—
161#14556050C2314yes—
162#14556049C2314yes—
163#14556048C2314yes—
164C4×C71⋊C8C2314yes—
165C8×Dic71C2314yes—
166C8×Dic71C2314yes—
167C22×Q8×C71C2311yescharacteristic
168C22×D4×C71C2311yescharacteristic
169C23×C4×C71—21no—
170C2×SD16×C71C2×C418yescomplemented
171C2×SD16×C71C2314yes—
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C4×Q8×C71—22no—
175C4×Q8×C71C2314yes—
176C4×D4×C71—22no—
177C4×D4×C71C2314yes—
178C2×C4⋊C4×C71—21no—
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C4⋊C4×C71C2311yescharacteristic
181C2×C22⋊C4×C71—21no—
182C2×C42×C71—21no—
183C2×C42×C71C2311yescharacteristic
184#106×C71C2314yes—
185#103×C71C2314yes—
186#102×C71C2314yes—
187C4×C8×C71C2314yes—
188C23×D71—21no—
189C23×D71C2×D411yescharacteristic
190#11765866—216no—
191#11765866—28no—
192#11765866C22×C4116yescomplemented
193#11765864—216no—
194#11765864—28no—
195#11765864C22×C4116yescomplemented
196C2×Dic142—21no—
197C2×Dic142—22no—
198C2×Dic142C22×C414yes—
199C2×Dic142C2412yes—
200C2×D284—28no—
201C2×D284—24no—
202C2×D284—21no—
203C2×D284—22no—
204C2×D284C22×C414yes—
205C2×D284C2412yes—
206C2×C22⋊D71—28no—
207C2×C22⋊D71—24no—
208C22×Dic71—21no—
209C22×Dic71—28no—
210C22×Dic71—24no—
211C22×Dic71—21no—
212C22×Dic71—21no—
213C22×Dic71—24no—
214C22×Dic71—44no—
215C22×Dic71C2×D411yescharacteristic
216C22×Dic71C2×D411yescharacteristic
217C22×Dic71C2×D411yescharacteristic
218C2×C4×D71—24no—
219C2×C4×D71—28no—
220C2×C4×D71—24no—
221C2×C4×D71—24no—
222C2×C4×D71—24no—
223C2×C4×D71—24no—
224C2×C4×D71—44no—
225C2×C4×D71—44no—
226C2×C4×D71C22×C414yes—
227C2×C4×D71C2×D414yes—
228C2×C4×D71C2×D414yes—
229C2×C4×D71C2×D412yes—
230C2×C4×D71#4114yes—
231C2×C4×D71C2412yes—
232#11765855C22×C4116yescomplemented
233#11765854C22×C4116yescomplemented
234#11765850C22×C4116yescomplemented
235C2×C71⋊C8—22no—
236C2×C71⋊C8C22×C414yes—
237C2×C71⋊C8C2412yes—
238C2×C71⋊C8C2412yes—
239C8×D71—28no—
240C8×D71C22×C4116yescomplemented
241C4⋊Dic71—21no—
242C4⋊Dic71—21no—
243C4⋊Dic71—24no—
244C4⋊Dic71C2412yes—
245C4⋊Dic71C2412yes—
246Dic71⋊C4—24no—
247Dic71⋊C4—24no—
248C22⋊Dic71—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253C4×Dic71—24no—
254C4×Dic71—24no—
255C4×Dic71—24no—
256C4×Dic71—24no—
257C4×Dic71—24no—
258C4×Dic71C2×D414yes—
259C4×Dic71C2×D412yes—
260C4×Dic71C2×D414yes—
261C4×Dic71C2412yes—
262C24×C71—21no—
263C2×Q8×C71—21no—
264C2×Q8×C71—22no—
265C2×Q8×C71C22×C414yes—
266C2×Q8×C71C2412yes—
267C2×D4×C71—21no—
268C2×D4×C71—22no—
269C2×D4×C71C22×C414yes—
270C2×D4×C71C2412yes—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—24no—
275C22×C4×C71—44no—
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2411yescharacteristic
279SD16×C71C22×C4116yescomplemented
280C2×C8×C71—22no—
281C2×C8×C71C22×C414yes—
282C2×C8×C71C2412yes—
283C2×C8×C71C2412yes—
284C4⋊C4×C71—24no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71C2412yes—
288C4⋊C4×C71C2412yes—
289C22⋊C4×C71—24no—
290C42×C71—24no—
291C42×C71C2×D412yes—
292C42×C71C2412yes—
293C23×C71—24no—
294C23×C71—22no—
295C23×C71—42no—
296C23×C71—42no—
297C23×C71C22×D411yescharacteristic
298C22×D71—22no—
299C22×D71—22no—
300C22×D71—24no—
301C22×D71—22no—
302C22×D71—42no—
303C22×D71—42no—
304C22×D71C4×D414yes—
305C22×D71C22×D412yes—
306Q8×C71—24no—
307Q8×C71—22no—
308Q8×C71C23×C414yes—
309D4×C71—24no—
310D4×C71—22no—
311D4×C71C23×C414yes—
312C2×C4×C71—24no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—48no—
320C2×C4×C71#13514yescomplemented
321C2×C4×C71C23×C412yes—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D411yescharacteristic
324C2×C4×C71C22×D412yes—
325C2×C4×C71C2×#4112yes—
326C2×C4×C71C2511yescharacteristic
327C22⋊D71—216no—
328C2×Dic71—24no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—216no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—42no—
335C2×Dic71—42no—
336C2×Dic71—48no—
337C2×Dic71C4×D414yes—
338C2×Dic71#13514yescomplemented
339C2×Dic71C22×D412yes—
340C2×Dic71C22×D412yes—
341C2×Dic71C22×D412yes—
342D284—216no—
343D284—24no—
344D284—22no—
345D284C23×C414yes—
346C4×D71—28no—
347C4×D71—216no—
348C4×D71—28no—
349C4×D71—48no—
350C4×D71—48no—
351C4×D71C4×D418yes—
352C4×D71C23×C414yes—
353C4×D71C2×#4114yes—
354Dic142—24no—
355Dic142—22no—
356Dic142C23×C414yes—
357C8×C71—22no—
358C8×C71C23×C414yes—
359C71⋊C8—22no—
360C71⋊C8C23×C414yes—
361C22×C71—24no—
362C22×C71—48no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71C2×C4×D412yes—
366C22×C71C2×#13512yes—
367C22×C71C2×#13512yes—
368C22×C71C23×D411yescharacteristic
369C2×D71—28no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—24no—
373C2×D71—48no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71C2×C4×D414yes—
377C4×C71—24no—
378C4×C71—22no—
379C4×C71—42no—
380C4×C71—42no—
381C4×C71C2×C4×D412yes—
382C4×C71C2×#13514yescomplemented
383C4×C71C24×C411yescharacteristic
384C4×C71C22×#4111yescharacteristic
385Dic71—24no—
386Dic71—22no—
387Dic71—42no—
388Dic71—42no—
389Dic71C2×C4×D414yes—
390Dic71C2×#13514yescomplemented
391C2×C4×#135—711nomaximal, Sylow
392C2×C71—44no—
393C2×C71C4×#13514yescomplemented
394C2×C71C22×C4×D411yescharacteristic
395C2×C71C22×#13511yescharacteristic
396C2×C71C22×#13511yescharacteristic
397D71—24no—
398D71—44no—
399C22×#135—711no—
400C2×C4×#41—711no—
401C2×C4×#41—711no—
402C4×#135—7116no—
403C2×C4×Q16—711no—
404C2×C4×Q16—711no—
405C2×C4×SD16—711no—
406C2×C4×SD16—711no—
407C2×C4×SD16—711no—
408C2×C4×SD16D7111yescharacteristic, complemented
409C2×C4×D8—711no—
410C2×C4×D8—711no—
411C2×#427—711no—
412C2×#416—711no—
413C2×#416—711no—
414C22×C4×C8—711no—
415C71C2×C4×#13511yescharacteristic, complemented, Sylow
416C22×#41—711no—
417C22×#41—711no—
418C2×#135—7116no—
419C2×#135—718no—
420C22×Q16—711no—
421C22×SD16—711no—
422C22×SD16C2×D7111yescharacteristic
423C22×D8—711no—
424C23×C8—711no—
425C23×C8—711no—
426C4×#41—718no—
427C4×#41—718no—
428C4×#41—1424no—
429C4×#41—1424no—
430C2×C4×Q8—711no—
431C2×C4×Q8—711no—
432C2×C4×Q8—711no—
433C2×C4×Q8C2×D7111yescharacteristic
434C2×C4×D4—711no—
435C2×C4×D4—711no—
436C2×C4×D4—711no—
437C2×C4×D4—1421no—
438C2×C4×D4—1421no—
439C2×C4×D4—1421no—
440C2×C4×D4—1421no—
441C2×C4×D4C2×D7111yescharacteristic
442C2×#117—711no—
443C2×#117—711no—
444C2×#117—1421no—
445C2×#117—1421no—
446C22×C42—711no—
447C22×C42—1421no—
448C22×C42—1421no—
449C4×Q16—718no—
450C4×Q16—718no—
451C4×SD16—718no—
452C4×SD16—718no—
453C4×SD16—718no—
454C4×SD16C2×D7118yescomplemented
455C4×D8—718no—
456C4×D8—718no—
457#427—718no—
458C2×#107—711no—
459C2×#107—711no—
460C2×#106—711no—
461C2×#106C2×D7111yescharacteristic
462#416—718no—
463#416—718no—
464C2×#103—711no—
465C2×#103—711no—
466C2×#103—711no—
467C2×#103C2×D7111yescharacteristic
468C2×#102—711no—
469C2×#102—711no—
470C2×#102—711no—
471C2×#102C2×D7111yescharacteristic
472C2×C4×C8—711no—
473C2×C4×C8—711no—
474C2×C4×C8—711no—
475C2×C4×C8—718no—
476C2×C4×C8C2×D7111yescharacteristic
477C2×#41—718no—
478C2×#41—714no—
479C2×#41—718no—
480C2×#41—714no—
481C2×#41—1422no—
482C2×#41—1424no—
483C2×#41—1422no—
484C2×#41—1424no—
485C22×Q8—711no—
486C22×Q8C22×D7111yescharacteristic
487C22×D4—711no—
488C22×D4—1421no—
489C22×D4—1421no—
490C22×D4C22×D7111yescharacteristic
491C23×C4—21no—
492C23×C4—711no—
493C23×C4—711no—
494C23×C4—711no—
495C23×C4—1421no—
496C23×C4—1421no—
497C23×C4—1421no—
498C23×C4—1421no—
499C23×C4—1421no—
500#135—7164no—
501C2×Q16—718no—
502C2×Q16—714no—
503C2×SD16—718no—
504C2×SD16—714no—
505C2×SD16C4×D7118yescomplemented
506C2×SD16C22×D7114yes—
507C2×D8—718no—
508C2×D8—714no—
509C22×C8—711no—
510C22×C8—718no—
511C22×C8—714no—
512C22×C8—711no—
513C22×C8—714no—
514C22×C8—1424no—
515C22×C8C22×D7111yescharacteristic
516C22×C8C22×D7111yescharacteristic
517C4×Q8—22no—
518C4×Q8—714no—
519C4×Q8—714no—
520C4×Q8—714no—
521C4×Q8—1422no—
522C4×Q8—1422no—
523C4×Q8—1422no—
524C4×Q8C22×D7114yes—
525C4×D4—22no—
526C4×D4—714no—
527C4×D4—714no—
528C4×D4—714no—
529C4×D4—1428no—
530C4×D4—1422no—
531C4×D4—1422no—
532C4×D4—1428no—
533C4×D4—1428no—
534C4×D4—1428no—
535C4×D4—1422no—
536C4×D4C22×D7114yes—
537#117—714no—
538#117—714no—
539#117—1428no—
540#117—1428no—
541#117—1422no—
542#117—1422no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—711no—
545C2×C4⋊C4—711no—
546C2×C4⋊C4—1421no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4C22×D7111yescharacteristic
550C2×C4⋊C4C22×D7111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C42—21no—
558C2×C42—711no—
559C2×C42—711no—
560C2×C42—711no—
561C2×C42—714no—
562C2×C42—714no—
563C2×C42—1428no—
564C2×C42—1428no—
565C2×C42—1421no—
566C2×C42—1421no—
567C2×C42—1421no—
568C2×C42—1421no—
569C2×C42—1421no—
570C2×C42C22×D7111yescharacteristic
571#107—714no—
572#107—714no—
573#106—714no—
574#106C22×D7114yes—
575#103—714no—
576#103—714no—
577#103—714no—
578#103C22×D7114yes—
579#102—714no—
580#102—714no—
581#102—714no—
582#102C22×D7114yes—
583C4×C8—714no—
584C4×C8—714no—
585C4×C8—714no—
586C4×C8C22×D7114yes—
587C24—21no—
588C24—711no—
589C24—1421no—
590#41—7116no—
591#41—7116no—
592#41—1428no—
593#41—14216no—
594#41—1428no—
595#41—14216no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—714no—
599C2×Q8—712no—
600C2×Q8—1421no—
601C2×Q8—1422no—
602C2×Q8C2×C4×D7114yes—
603C2×Q8C23×D7112yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—714no—
607C2×D4—712no—
608C2×D4—1424no—
609C2×D4—1428no—
610C2×D4—1424no—
611C2×D4—1428no—
612C2×D4—1421no—
613C2×D4—1422no—
614C2×D4C2×C4×D7114yes—
615C2×D4C23×D7112yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—2844no—
622C22×C4—2844no—
623C22×C4—2844no—
624C22×C4—711no—
625C22×C4—711no—
626C22×C4—714no—
627C22×C4—712no—
628C22×C4—714no—
629C22×C4—712no—
630C22×C4—711no—
631C22×C4—714no—
632C22×C4—714no—
633C22×C4—1424no—
634C22×C4—1424no—
635C22×C4—1424no—
636C22×C4—1428no—
637C22×C4—1424no—
638C22×C4—1421no—
639C22×C4—1421no—
640C22×C4—1424no—
641C22×C4—1424no—
642C22×C4—1428no—
643C22×C4—1421no—
644C22×C4—1424no—
645C22×C4D4×D7111yescharacteristic
646C22×C4D4×D7111yescharacteristic
647C22×C4C23×D7111yescharacteristic
648Q16—7116no—
649SD16—7116no—
650SD16C2×C4×D71116yescomplemented
651D8—7116no—
652C2×C8—22no—
653C2×C8—714no—
654C2×C8—712no—
655C2×C8—7116no—
656C2×C8—712no—
657C2×C8—1428no—
658C2×C8—1422no—
659C2×C8C2×C4×D7114yes—
660C2×C8C23×D7112yes—
661C2×C8C23×D7112yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—712no—
666C4⋊C4—712no—
667C4⋊C4—1424no—
668C4⋊C4—1424no—
669C4⋊C4—1424no—
670C4⋊C4—1421no—
671C4⋊C4—1421no—
672C4⋊C4C23×D7112yes—
673C4⋊C4C23×D7112yes—
674C22⋊C4—24no—
675C22⋊C4—1424no—
676C22⋊C4—1424no—
677C22⋊C4—1424no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C42—24no—
681C42—714no—
682C42—714no—
683C42—712no—
684C42—712no—
685C42—1424no—
686C42—1424no—
687C42—1424no—
688C42—1424no—
689C42—1424no—
690C42D4×D7112yes—
691C42C23×D7112yes—
692C23—22no—
693C23—24no—
694C23—42no—
695C23—42no—
696C23—2842no—
697C23—2842no—
698C23—712no—
699C23—714no—
700C23—1422no—
701C23—1424no—
702C23—1422no—
703C23—1422no—
704C23C2×D4×D7111yescharacteristic
705Q8—22no—
706Q8—24no—
707Q8—714no—
708Q8—1422no—
709Q8—1424no—
710Q8C22×C4×D7114yes—
711D4—22no—
712D4—24no—
713D4—714no—
714D4—14216no—
715D4—14216no—
716D4—1422no—
717D4—1424no—
718D4C22×C4×D7114yes—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—48no—
727C2×C4—2848no—
728C2×C4—2842no—
729C2×C4—2842no—
730C2×C4—2848no—
731C2×C4—2848no—
732C2×C4—712no—
733C2×C4—712no—
734C2×C4—714no—
735C2×C4—714no—
736C2×C4—714no—
737C2×C4—714no—
738C2×C4—718no—
739C2×C4—712no—
740C2×C4—1428no—
741C2×C4—14216no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—14216no—
745C2×C4—1422no—
746C2×C4—1424no—
747C2×C4—1422no—
748C2×C4—1428no—
749C2×C4#1455614914yesdirect product factor
750C2×C4C22×C4×D7112yes—
751C2×C4C2×D4×D7112yes—
752C2×C4C2×D4×D7111yescharacteristic
753C2×C4C2×D4×D7112yes—
754C2×C4#41×D7112yes—
755C2×C4C24×D7111yescharacteristic
756C8—22no—
757C8—714no—
758C8—1422no—
759C8C22×C4×D7114yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—2842no—
765C22—2842no—
766C22—2848no—
767C22—714no—
768C22—1424no—
769C22—1422no—
770C22—1422no—
771C22—1428no—
772C22C4×D4×D7112yes—
773C22#135×D7112yes—
774C22C2×#1455614912yes—
775C22C22×D4×D7111yescharacteristic
776C4—24no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—2842no—
781C4—2842no—
782C4—714no—
783C4—714no—
784C4—1424no—
785C4—1422no—
786C4C4×D4×D7112yes—
787C4C2×#1455614914yesdirect product factor
788C4C23×C4×D7111yescharacteristic
789C4C2×#41×D7111yescharacteristic
790C2—44no—
791C2—2844no—
792C2—1424no—
793C2C4×#1455614914yesdirect product factor
794C2C2×C4×D4×D7111yescharacteristic
795C2C2×#135×D7111yescharacteristic
796C2C22×#1455614911yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×C4×SD16×C71C2
socleC23×C71C22×D4
prime radicalC22×#14556149C2
cosocleC2×C4×C71C25
hypercenterC2×C4×SD16D71
hypocenterC71C2×C4×#135
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11765866C2semidirect
3. C2×C4×#11765864C2semidirect
4. C4×#14556149C2direct (N × H)
5. C2×C4×#11765855C2semidirect
6. C2×#17986091C2semidirect
7. C2×C4×#11765854C2semidirect
8. C2×SD16×Dic71C2semidirect
9. C2×#17986086C2semidirect
10. C2×C4×#11765850C2semidirect
11. C2×#17986079C2semidirect
12. C2×#17986034C2semidirect
13. C2×#17985994C2semidirect
14. C2×#17985992C2semidirect
15. C2×C4×C8×D71C2semidirect
16. C2×C4×SD16×C71C2semidirect
19. C2×#14556149C4direct (N × H)
27. C4×#11765866C22semidirect
29. C4×#11765864C22semidirect
47. C4×#11765855C22semidirect
48. #17986091C22semidirect
49. C4×#11765854C22semidirect
50. SD16×Dic71C22semidirect
51. #17986086C22semidirect
52. C4×#11765850C22semidirect
53. #17986079C22semidirect
54. #17986034C22semidirect
58. #17985994C22semidirect
59. #17985992C22semidirect
69. C4×C8×D71C22semidirect
73. C4×SD16×C71C22semidirect
80. C2×#11765866C2×C4semidirect
84. C2×#11765864C2×C4semidirect
98. #14556149C2×C4direct (N × H)
99. C2×#11765855C2×C4semidirect
101. C2×#11765854C2×C4semidirect
103. C2×#11765850C2×C4semidirect
108. C2×C8×D71C2×C4semidirect
170. C2×SD16×C71C2×C4semidirect
192. #11765866C22×C4semidirect
195. #11765864C22×C4semidirect
232. #11765855C22×C4semidirect
233. #11765854C22×C4semidirect
234. #11765850C22×C4semidirect
240. C8×D71C22×C4semidirect
279. SD16×C71C22×C4semidirect
320. C2×C4×C71#135semidirect
338. C2×Dic71#135semidirect
382. C4×C71C2×#135semidirect
390. Dic71C2×#135semidirect
393. C2×C71C4×#135semidirect
408. C2×C4×SD16D71semidirect
415. C71C2×C4×#135semidirect
454. C4×SD16C2×D71semidirect
505. C2×SD16C4×D71semidirect
650. SD16C2×C4×D71semidirect
749. C2×C4#14556149direct (N × H)
787. C4C2×#14556149direct (N × H)
793. C2C4×#14556149direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561492
C2×C4×#117658662
C2×C4×#117658642
C4×#145561492
C2×C4×#117658552
C2×#179860912
C2×C4×#117658542
C2×SD16×Dic712
C2×#179860862
C2×C4×#117658502
C2×#179860792
C2×#179860342
C2×#179859942
C2×#179859922
C2×C4×C8×D712
C2×C4×SD16×C712
C2×C4×#13571