Finite Group Databasebeta

← C4×#17986668 #32157303

Subgroups — C4×#17986668 #32157303

Order 18176.

3420 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986668C211yesmaximal, characteristic
2C2×C4×#11765866C211yesmaximal, characteristic, complemented
3#22591402C213yesmaximal, complemented
4#22591378C213yesmaximal, complemented
5#22591374C213yesmaximal, complemented
6#22591290C213yesmaximal, complemented
7Q8×Dic71⋊C4C211yesmaximal, characteristic, complemented
8#22591181C211yesmaximal, characteristic, complemented
9#22591178C211yesmaximal, characteristic, complemented
10C4×#14556124C213yesmaximal, complemented
11C4×#14556102C213yesmaximal, complemented
12C4×#14556099C213yesmaximal, complemented
13C4×Q8×Dic71C211yesmaximal, characteristic, complemented
14C42×C22⋊D71C213yesmaximal, complemented
15C2×C4×#41×C71C211yesmaximal, characteristic, complemented
16C22×#11765866C2211yescharacteristic
17#17986668C4116yesdirect product factor
18C2×#14556124C2213yes—
19C2×#14556102C2213yes—
20C2×#14556099C2213yes—
21C4×#11765866—28no—
22C2×Q8×Dic71C2211yescharacteristic
23C2×Q8×Dic71C2211yescharacteristic
24C2×Q8×Dic71C2211yescharacteristic
25C2×C4×D284C2213yes—
26C2×#14556090C2213yes—
27C2×C4×C22⋊D71C2213yes—
28C2×C4×C22⋊D71C2213yes—
29C2×C4×C22⋊D71C2216yes—
30C2×C4×C22⋊D71C2213yes—
31C2×#14556086C2213yes—
32C2×C42×D71C2213yes—
33#17985902C2213yes—
34#17985902C2213yes—
35#17985901C2213yes—
36#17985900C2213yes—
37#17985899C2216yes—
38#17985899C2216yes—
39#17985897C2213yes—
40#17985895C2213yes—
41#17985890C2216yes—
42#17985887C2216yes—
43#17985878C2216yes—
44#17985875C2216yes—
45#17985868C2213yes—
46#17985859C2213yes—
47#17985856C2213yes—
48C4⋊C4×Dic71C2213yes—
49C4⋊C4×Dic71C2213yes—
50C4×Dic71⋊C4C2213yes—
51C4×Dic71⋊C4C2213yes—
52C4×Dic71⋊C4C2211yescharacteristic
53C4×C4⋊Dic71C2213yes—
54C4×(C2×D71)⋊C4C2213yes—
55C4×(C2×D71)⋊C4C2213yes—
56C4×(C2×D71)⋊C4C2213yes—
57C4×C22⋊Dic71C2213yes—
58C4×C22⋊Dic71C2213yes—
59C4×C22⋊Dic71C2213yes—
60C42×Dic71C2213yes—
61C22×#41×C71C2211yescharacteristic
62C4×#41×C71—28no—
63C2×C4×Q8×C71C2211yescharacteristic
64C2×C4×Q8×C71C2211yescharacteristic
65C2×C4×D4×C71C2213yes—
66C2×C4×D4×C71C2213yes—
67C2×#117×C71C2213yes—
68C22×C42×C71C2213yes—
69C2×#11765866—24no—
70C2×#11765866—24no—
71C2×#11765866C2×C418yescomplemented
72C22×D284C2313yes—
73C22×C22⋊D71C2313yes—
74C22×C22⋊D71C2316yes—
75C22×C4×D71C2313yes—
76C22×C4×D71C2313yes—
77C22×C4×D71C2313yes—
78#14556124C2×C4124yescomplemented
79#14556102C2×C4124yescomplemented
80#14556099C2×C4124yescomplemented
81Q8×Dic71—24no—
82Q8×Dic71—24no—
83Q8×Dic71C2×C418yescomplemented
84C4×D284—212no—
85#14556090—212no—
86C4×C22⋊D71—212no—
87C4×C22⋊D71—212no—
88C4×C22⋊D71—412no—
89C4×C22⋊D71C2×C4124yescomplemented
90#14556086—212no—
91C2×C4⋊Dic71C2313yes—
92C2×C4⋊Dic71C2313yes—
93C2×C4⋊Dic71C2313yes—
94C2×Dic71⋊C4C2313yes—
95C2×Dic71⋊C4C2316yes—
96C2×Dic71⋊C4C2311yescharacteristic
97C2×Dic71⋊C4C2311yescharacteristic
98C2×C22⋊Dic71C2313yes—
99C2×C22⋊Dic71C2313yes—
100C2×C22⋊Dic71C2316yes—
101C2×C22⋊Dic71C2313yes—
102C2×(C2×D71)⋊C4C2313yes—
103C2×(C2×D71)⋊C4C2313yes—
104C2×(C2×D71)⋊C4C2316yes—
105C2×(C2×D71)⋊C4C2316yes—
106C2×(C2×D71)⋊C4C2313yes—
107C2×C4×Dic71C2313yes—
108C2×C4×Dic71C2313yes—
109C2×C4×Dic71C2313yes—
110C2×C4×Dic71C2311yescharacteristic
111C2×C4×Dic71C2313yes—
112C2×C4×Dic71C2313yes—
113C2×C4×Dic71C2313yes—
114C2×C4×Dic71C2313yes—
115C2×C4×Dic71C2311yescharacteristic
116C42×D71—212no—
117C71⋊#95C2311yescharacteristic
118C71⋊#95C2311yescharacteristic
119C71⋊#95C2313yes—
120C71⋊#95C2313yes—
121C71⋊#95C2313yes—
122C71⋊#95C2313yes—
123C71⋊#95C2316yes—
124C2×#41×C71—24no—
125C2×#41×C71—24no—
126C2×#41×C71C2×C418yescomplemented
127C22×Q8×C71C2311yescharacteristic
128C22×D4×C71C2313yes—
129C23×C4×C71C2313yes—
130C23×C4×C71C2313yes—
131C23×C4×C71C2313yes—
132C4×Q8×C71—24no—
133C4×Q8×C71D418yescomplemented
134C4×D4×C71—212no—
135C4×D4×C71—212no—
136#117×C71—212no—
137C2×C4⋊C4×C71C2313yes—
138C2×C4⋊C4×C71C2313yes—
139C2×C22⋊C4×C71C2316yes—
140C2×C42×C71—212no—
141C2×C42×C71C2311yescharacteristic
142C2×C42×C71C2313yes—
143C2×C42×C71C2313yes—
144C2×C42×C71C2313yes—
145C23×D71C2413yes—
146#11765866—232no—
147C2×D284—26no—
148C2×D284—26no—
149C2×D284C22×C4112yes—
150C2×C22⋊D71—26no—
151C2×C22⋊D71—26no—
152C2×C22⋊D71—46no—
153C2×C22⋊D71—46no—
154C2×C22⋊D71C22×C4112yes—
155C2×C22⋊D71C22×C4124yes—
156C22×Dic71C2413yes—
157C22×Dic71C2413yes—
158C22×Dic71C2411yescharacteristic
159C22×Dic71C2413yes—
160C22×Dic71C2411yescharacteristic
161C22×Dic71C2411yescharacteristic
162C22×Dic71C2411yescharacteristic
163C2×C4×D71—26no—
164C2×C4×D71—26no—
165C2×C4×D71—26no—
166C2×C4×D71—26no—
167C2×C4×D71—26no—
168C2×C4×D71—26no—
169C2×C4×D71—26no—
170C2×C4×D71—43no—
171C2×C4×D71C22×C4112yes—
172C4⋊Dic71—26no—
173C4⋊Dic71—26no—
174C4⋊Dic71C22×C4112yes—
175Dic71⋊C4—26no—
176Dic71⋊C4—46no—
177Dic71⋊C4C22×C414yes—
178Dic71⋊C4#4114yescomplemented
179C22⋊Dic71—26no—
180C22⋊Dic71—26no—
181C22⋊Dic71—46no—
182C22⋊Dic71C22×C4112yes—
183(C2×D71)⋊C4—212no—
184(C2×D71)⋊C4—26no—
185(C2×D71)⋊C4—26no—
186(C2×D71)⋊C4—46no—
187(C2×D71)⋊C4C22×C4112yes—
188C4×Dic71—22no—
189C4×Dic71—26no—
190C4×Dic71—26no—
191C4×Dic71—26no—
192C4×Dic71—26no—
193C4×Dic71—26no—
194C4×Dic71—43no—
195C4×Dic71C22×C4112yes—
196C4×Dic71#4114yescomplemented
197C24×C71C2413yes—
198#41×C71—232no—
199C2×Q8×C71C22×C414yes—
200C2×Q8×C71C2×D414yes—
201C2×Q8×C71#4114yes—
202C2×D4×C71—26no—
203C2×D4×C71—26no—
204C2×D4×C71C22×C4112yes—
205C22×C4×C71—26no—
206C22×C4×C71—26no—
207C22×C4×C71—26no—
208C22×C4×C71—26no—
209C22×C4×C71—26no—
210C22×C4×C71—26no—
211C22×C4×C71—26no—
212C22×C4×C71—43no—
213C22×C4×C71C22×C4112yes—
214C22×C4×C71C2413yes—
215C22×C4×C71C2411yescharacteristic
216C22×C4×C71C2413yes—
217C22×C4×C71C2411yescharacteristic
218C22×C4×C71C2413yes—
219C22×C4×C71C2411yescharacteristic
220C4⋊C4×C71—26no—
221C4⋊C4×C71C2×D4112yes—
222C22⋊C4×C71—212no—
223C42×C71—22no—
224C42×C71—26no—
225C42×C71—26no—
226C42×C71C2×D4112yes—
227C23×C71—23no—
228C23×C71—23no—
229C23×C71—23no—
230C23×C71—23no—
231C23×C71—23no—
232C23×C71—23no—
233C23×C71C23×C416yes—
234C23×C71C2511yescharacteristic
235C22×D71—23no—
236C22×D71—23no—
237C22×D71—23no—
238C22×D71—23no—
239C22×D71—23no—
240C22×D71—23no—
241C22×D71C23×C416yes—
242Q8×C71C4×D4116yescomplemented
243D4×C71—224no—
244C2×C4×C71—21no—
245C2×C4×C71—21no—
246C2×C4×C71—21no—
247C2×C4×C71—23no—
248C2×C4×C71—21no—
249C2×C4×C71—23no—
250C2×C4×C71—224no—
251C2×C4×C71—23no—
252C2×C4×C71—23no—
253C2×C4×C71—23no—
254C2×C4×C71—412no—
255C2×C4×C71—412no—
256C2×C4×C71C23×C412yes—
257C2×C4×C71C23×C416yes—
258C2×C4×C71C22×D416yes—
259C2×C4×C71C22×D416yes—
260C2×C4×C71C22×D412yes—
261C2×C4×C71C2×#4112yes—
262C2×C4×C71C2×#4112yes—
263C2×C4×C71C2×#4116yes—
264C2×C4×C71H(5,𝔽2)12yes—
265C22⋊D71—224no—
266C22⋊D71—424no—
267C2×Dic71—21no—
268C2×Dic71—21no—
269C2×Dic71—21no—
270C2×Dic71—21no—
271C2×Dic71—23no—
272C2×Dic71—21no—
273C2×Dic71—23no—
274C2×Dic71—21no—
275C2×Dic71—23no—
276C2×Dic71—23no—
277C2×Dic71—23no—
278C2×Dic71—23no—
279C2×Dic71—23no—
280C2×Dic71—23no—
281C2×Dic71C23×C416yes—
282C2×Dic71C23×C412yes—
283C2×Dic71C23×C412yes—
284C2×Dic71C2×#4112yes—
285C2×Dic71C2×#4112yes—
286C2×Dic71C2×#4112yes—
287C2×Dic71C2×#4112yes—
288D284—224no—
289C4×D71—224no—
290C4×D71—412no—
291C4×D71—412no—
292C22×C71—26no—
293C22×C71—26no—
294C22×C71—26no—
295C22×C71—43no—
296C22×C71—43no—
297C22×C71—43no—
298C22×C71—43no—
299C22×C71C24×C411yescharacteristic
300C22×C71C23×D411yescharacteristic
301C22×C71C22×#4111yescharacteristic
302C22×C71C22×#4111yescharacteristic
303C22×C71C22×#4111yescharacteristic
304C22×C71C2×H(5,𝔽2)11yescharacteristic
305C22×C71#58511yescharacteristic
306C2×D71—26no—
307C2×D71—26no—
308C2×D71—26no—
309C2×D71—43no—
310C2×D71—43no—
311C2×D71—43no—
312C2×D71—43no—
313C4×C71—22no—
314C4×C71—26no—
315C4×C71—22no—
316C4×C71—43no—
317C4×C71C2×C4×D4112yes—
318C4×C71#55014yescomplemented
319Dic71—22no—
320Dic71—26no—
321Dic71—22no—
322Dic71—22no—
323Dic71—43no—
324Dic71—43no—
325Dic71C4×#4114yescomplemented
326C4×#550—711nomaximal, Sylow
327C2×C71—46no—
328C2×C71C22×C4×D411yescharacteristic
329C2×C71C2×C4×#4111yescharacteristic
330C2×C71C4×H(5,𝔽2)11yescharacteristic
331C2×C71C2×#55011yescharacteristic
332C2×C71D4×#4111yescharacteristic
333C2×C71#348011yescharacteristic
334C2×C71#348311yescharacteristic
335D71—46no—
336C2×#550—711no—
337C2×C4×#41—711no—
338C2×C4×#41D7111yescharacteristic, complemented
339#2366—713no—
340#2363—713no—
341#2363—713no—
342#2354—713no—
343Q8×C4⋊C4—711no—
344#2341—711no—
345#2341—711no—
346C4×#127—713no—
347C4×#121—713no—
348C4×#121—713no—
349C42×Q8—711no—
350C42×D4—713no—
351C71C4×#55011yescharacteristic, complemented, Sylow
352C22×#41—711no—
353C22×#41C2×D7111yescharacteristic
354#550—7116no—
355C2×#127—713no—
356C2×#121—713no—
357C2×#121—713no—
358C4×#41—28no—
359C4×#41—1428no—
360C2×C4×Q8—711no—
361C2×C4×Q8—711no—
362C2×C4×Q8—711no—
363C2×C4×Q8C2×D7111yescharacteristic
364C2×C4×Q8C2×D7111yescharacteristic
365C2×C4×D4—716no—
366C2×C4×D4—713no—
367C2×C4×D4—713no—
368C2×C4×D4—713no—
369C2×C4×D4—713no—
370C2×C4×D4—713no—
371C2×C4×D4C2×D7113yes—
372C2×C4×D4C2×D7113yes—
373C2×#117—713no—
374C2×#117C2×D7113yes—
375C22×C42—713no—
376C22×C42C2×D7113yes—
377#390—713no—
378#390—713no—
379#390—713no—
380#390—716no—
381#390—716no—
382#390—713no—
383#389—713no—
384#389—713no—
385#388—716no—
386#388—716no—
387#386—716no—
388#386—716no—
389#384—713no—
390#380—713no—
391#380—713no—
392C4×C4⋊C4—713no—
393C4×C4⋊C4—713no—
394C4×C4⋊C4—713no—
395C4×C4⋊C4—713no—
396C4×C4⋊C4—713no—
397C4×C4⋊C4—711no—
398C4×C22⋊C4—713no—
399C4×C22⋊C4—713no—
400C4×C22⋊C4—713no—
401C4×C22⋊C4—713no—
402C4×C22⋊C4—713no—
403C4×C22⋊C4—713no—
404C43—713no—
405C2×#41—24no—
406C2×#41—24no—
407C2×#41—718no—
408C2×#41—1424no—
409C2×#41—1424no—
410C2×#41C4×D7118yescomplemented
411C22×Q8C22×D7111yescharacteristic
412C22×D4—716no—
413C22×D4—713no—
414C22×D4—713no—
415C22×D4C22×D7113yes—
416C23×C4—713no—
417C23×C4—713no—
418C23×C4—713no—
419C23×C4C22×D7113yes—
420C23×C4C22×D7113yes—
421C23×C4C22×D7113yes—
422#127—7124no—
423#121—7124no—
424#121—7124no—
425C4×Q8—24no—
426C4×Q8—718no—
427C4×Q8—1424no—
428C4×Q8—1424no—
429C4×Q8C22⋊D7118yescomplemented
430C4×D4—212no—
431C4×D4—212no—
432C4×D4—28412no—
433C4×D4—7124no—
434C4×D4—14212no—
435C4×D4—14212no—
436C4×D4—14212no—
437C4×D4—14212no—
438#117—212no—
439#117—14212no—
440C2×C4⋊C4—716no—
441C2×C4⋊C4—711no—
442C2×C4⋊C4—711no—
443C2×C4⋊C4—713no—
444C2×C4⋊C4—713no—
445C2×C4⋊C4—713no—
446C2×C4⋊C4—713no—
447C2×C4⋊C4C22×D7113yes—
448C2×C4⋊C4C22×D7113yes—
449C2×C22⋊C4—716no—
450C2×C22⋊C4—716no—
451C2×C22⋊C4—713no—
452C2×C22⋊C4—713no—
453C2×C22⋊C4—713no—
454C2×C22⋊C4—713no—
455C2×C22⋊C4—716no—
456C2×C22⋊C4—713no—
457C2×C22⋊C4—713no—
458C2×C22⋊C4C22×D7116yes—
459C2×C42—212no—
460C2×C42—713no—
461C2×C42—713no—
462C2×C42—711no—
463C2×C42—713no—
464C2×C42—713no—
465C2×C42—713no—
466C2×C42—713no—
467C2×C42—713no—
468C2×C42—711no—
469C2×C42—14212no—
470C2×C42C22×D7113yes—
471C2×C42C22×D7113yes—
472C2×C42C22×D7111yescharacteristic
473C2×C42C22×D7113yes—
474#95—711no—
475#95—711no—
476#95—713no—
477#95—713no—
478#95—713no—
479#95—713no—
480#95—716no—
481C24—713no—
482C24C23×D7113yes—
483#41—232no—
484#41—14232no—
485C2×Q8C2×C4×D7114yes—
486C2×Q8C2×C22⋊D7114yes—
487C2×Q8#1176586514yes—
488C2×D4—26no—
489C2×D4—26no—
490C2×D4—2846no—
491C2×D4—2846no—
492C2×D4—7124no—
493C2×D4—7112no—
494C2×D4—7112no—
495C2×D4—1426no—
496C2×D4—1426no—
497C2×D4—1426no—
498C2×D4—1426no—
499C2×D4C2×C4×D71112yes—
500C22×C4—26no—
501C22×C4—26no—
502C22×C4—26no—
503C22×C4—26no—
504C22×C4—26no—
505C22×C4—26no—
506C22×C4—26no—
507C22×C4—43no—
508C22×C4—2843no—
509C22×C4—711no—
510C22×C4—711no—
511C22×C4—711no—
512C22×C4—713no—
513C22×C4—711no—
514C22×C4—7112no—
515C22×C4—713no—
516C22×C4—713no—
517C22×C4—1426no—
518C22×C4—1426no—
519C22×C4—1426no—
520C22×C4—1426no—
521C22×C4—1426no—
522C22×C4—1426no—
523C22×C4—1426no—
524C22×C4C2×C4×D71112yes—
525C22×C4C23×D7113yes—
526C22×C4C23×D7111yescharacteristic
527C22×C4C23×D7113yes—
528C22×C4C23×D7111yescharacteristic
529C22×C4C23×D7113yes—
530C22×C4C23×D7111yescharacteristic
531C4⋊C4—26no—
532C4⋊C4—2846no—
533C4⋊C4—714no—
534C4⋊C4—7112no—
535C4⋊C4—714no—
536C4⋊C4—1426no—
537C4⋊C4—1426no—
538C4⋊C4—1426no—
539C4⋊C4C2×C22⋊D71112yes—
540C22⋊C4—212no—
541C22⋊C4—2846no—
542C22⋊C4—2846no—
543C22⋊C4—7112no—
544C22⋊C4—7112no—
545C22⋊C4—1426no—
546C22⋊C4—1426no—
547C22⋊C4—1426no—
548C22⋊C4—14212no—
549C22⋊C4—1426no—
550C42—22no—
551C42—26no—
552C42—26no—
553C42—2843no—
554C42—7112no—
555C42—714no—
556C42—1426no—
557C42—1422no—
558C42—1426no—
559C42—1426no—
560C42—1426no—
561C42—1426no—
562C42C2×C22⋊D71112yes—
563C23—23no—
564C23—23no—
565C23—23no—
566C23—23no—
567C23—23no—
568C23—23no—
569C23—716no—
570C23—1423no—
571C23—1423no—
572C23—1423no—
573C23—1423no—
574C23—1423no—
575C23—1423no—
576C23C22×C4×D7116yes—
577C23C24×D7111yescharacteristic
578Q8C4×C22⋊D71116yescomplemented
579D4—224no—
580D4—28424no—
581D4—14224no—
582D4—14224no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—21no—
587C2×C4—23no—
588C2×C4—21no—
589C2×C4—224no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—412no—
594C2×C4—412no—
595C2×C4—28412no—
596C2×C4—28412no—
597C2×C4—712no—
598C2×C4—712no—
599C2×C4—712no—
600C2×C4—716no—
601C2×C4—712no—
602C2×C4—712no—
603C2×C4—712no—
604C2×C4—1423no—
605C2×C4—1423no—
606C2×C4—1423no—
607C2×C4—1423no—
608C2×C4—1423no—
609C2×C4—1423no—
610C2×C4—1421no—
611C2×C4—1421no—
612C2×C4—1421no—
613C2×C4—1421no—
614C2×C4—1423no—
615C2×C4—1421no—
616C2×C4—1423no—
617C2×C4—1421no—
618C2×C4—14224no—
619C2×C4C22×C4×D7112yes—
620C2×C4C22×C4×D7116yes—
621C2×C4C22×C22⋊D7116yes—
622C2×C4C22×C22⋊D7112yes—
623C2×C4C22×C22⋊D7116yes—
624C2×C4#41×D7112yes—
625C2×C4#41×D7112yes—
626C2×C4C2×#1176586516yes—
627C2×C4#1455617412yes—
628C22—26no—
629C22—26no—
630C22—26no—
631C22—43no—
632C22—43no—
633C22—43no—
634C22—43no—
635C22—2843no—
636C22—2843no—
637C22—2843no—
638C22—2843no—
639C22—1426no—
640C22—1426no—
641C22—1426no—
642C22C23×C4×D7111yescharacteristic
643C22C23×C22⋊D7111yescharacteristic
644C22C2×#41×D7111yescharacteristic
645C22C2×#41×D7111yescharacteristic
646C22C22×#1176586511yescharacteristic
647C22C2×#1455617411yescharacteristic
648C22#1798683511yescharacteristic
649C4—22no—
650C4—22no—
651C4—26no—
652C4—43no—
653C4—2843no—
654C4—2843no—
655C4—714no—
656C4—1422no—
657C4—1426no—
658C4—1422no—
659C4—1422no—
660C4C2×C4×C22⋊D71112yes—
661C4#1798666814yesdirect product factor
662C2—46no—
663C2—2846no—
664C2C22×C4×C22⋊D7111yescharacteristic
665C2C4×#41×D7111yescharacteristic
666C2C4×#1455617411yescharacteristic
667C2C2×#1798666811yescharacteristic
668C2#41×C22⋊D7111yescharacteristic
669C2#2260193811yescharacteristic
670C2#2260196611yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×C4×#41×C71C2
socle, cosocleC23×C71C25
prime radicalC2×#17986668C2
hypercenterC2×C4×#41D71
hypocenterC71C4×#550
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11765866C2semidirect
3. #22591402C2semidirect
4. #22591378C2semidirect
5. #22591374C2semidirect
6. #22591290C2semidirect
7. Q8×Dic71⋊C4C2semidirect
8. #22591181C2semidirect
9. #22591178C2semidirect
10. C4×#14556124C2semidirect
11. C4×#14556102C2semidirect
12. C4×#14556099C2semidirect
13. C4×Q8×Dic71C2semidirect
14. C42×C22⋊D71C2semidirect
15. C2×C4×#41×C71C2semidirect
17. #17986668C4direct (N × H)
71. C2×#11765866C2×C4semidirect
78. #14556124C2×C4semidirect
79. #14556102C2×C4semidirect
80. #14556099C2×C4semidirect
83. Q8×Dic71C2×C4semidirect
89. C4×C22⋊D71C2×C4semidirect
126. C2×#41×C71C2×C4semidirect
133. C4×Q8×C71D4semidirect
178. Dic71⋊C4#41semidirect
196. C4×Dic71#41semidirect
242. Q8×C71C4×D4semidirect
318. C4×C71#550semidirect
325. Dic71C4×#41semidirect
338. C2×C4×#41D71semidirect
351. C71C4×#550semidirect
410. C2×#41C4×D71semidirect
429. C4×Q8C22⋊D71semidirect
578. Q8C4×C22⋊D71semidirect
661. C4#17986668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866682
C2×C4×#117658662
#225914022
#225913782
#225913742
#225912902
Q8×Dic71⋊C42
#225911812
#225911782
C4×#145561242
C4×#145561022
C4×#145560992
C4×Q8×Dic712
C42×C22⋊D712
C2×C4×#41×C712
C4×#55071