Finite Group Databasebeta

← #417×Dic73 #33083778

Subgroups — #417×Dic73 #33083778

Order 18688.

1706 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic73C211yesmaximal, characteristic
2C2×#17988588C211yesmaximal, characteristic
3C2×M16×Dic73C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
5#22609763C212yesmaximal, complemented
6#22609758C212yesmaximal, complemented
7#103×Dic73C212yesmaximal, complemented
8#102×Dic73C212yesmaximal, complemented
9#22609651C211yesmaximal, characteristic, complemented
10#22609650C211yesmaximal, characteristic, complemented
11C2×#417×C73C211yesmaximal, characteristic
12C22×#11924012C2211yescharacteristic
13#41×Dic73—24no—
14#41×Dic73C418yescomplemented
15C2×Q8×Dic73C2211yescharacteristic
16C2×Q8×Dic73C2211yescharacteristic
17C2×D4×Dic73—21no—
18C2×D4×Dic73—21no—
19C2×D4×Dic73C2211yescharacteristic
20C2×D4×Dic73C2211yescharacteristic
21C2×#14556550—21no—
22C2×#14556550C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C4×Dic73—21no—
25C22×C4×Dic73—21no—
26C22×C4×Dic73C2211yescharacteristic
27#17988588C418yescomplemented
28C2×#14556515C2212yes—
29C2×#14556512C2212yes—
30M16×Dic73—24no—
31C2×#14556501C2212yes—
32C2×C8×Dic73C2212yes—
33C4⋊C4×Dic73—21no—
34C4⋊C4×Dic73—21no—
35C4⋊C4×Dic73C2212yes—
36C4⋊C4×Dic73C2212yes—
37C2×#14556498—21no—
38#17988350C2212yes—
39#17988350C2212yes—
40#17988349C2212yes—
41#17988349C2212yes—
42C22×#41×C73C2211yescharacteristic
43C22×M16×C73C2211yescharacteristic
44C22×C4⋊C4×C73C2211yescharacteristic
45#417×C73C418yescomplemented
46C2×#103×C73C2212yes—
47C2×#102×C73C2212yes—
48C23×Dic73—21no—
49C23×Dic73—21no—
50C23×Dic73—21no—
51C23×Dic73D411yescharacteristic
52C23×Dic73D411yescharacteristic
53C2×#11924012—22no—
54C2×#11924012—22no—
55C2×#11924012C2×C414yescomplemented
56C22×#10596831C2312yes—
57Q8×Dic73—22no—
58Q8×Dic73—22no—
59Q8×Dic73C2×C414yescomplemented
60Q8×Dic73C2×C414yescomplemented
61D4×Dic73—28no—
62D4×Dic73—28no—
63D4×Dic73—22no—
64D4×Dic73—22no—
65D4×Dic73C2×C414yescomplemented
66D4×Dic73C2×C414yescomplemented
67#14556550—28no—
68#14556550—22no—
69#14556550C2×C414yes—
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73C2×C414yescomplemented
75C2×C4⋊Dic73C2312yes—
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C22⋊Dic73—21no—
79C2×C22⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C4×Dic73—21no—
82C2×C4×Dic73—21no—
83C2×C4×Dic73—28no—
84C2×C4×Dic73—22no—
85C2×C4×Dic73—22no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—44no—
88C2×C4×Dic73C2×C414yes—
89C2×C4×Dic73D411yescharacteristic
90C2×C4×Dic73D411yescharacteristic
91C2×C4×Dic73D414yes—
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94#14556515C2×C418yescomplemented
95#14556512C2×C418yescomplemented
96#14556501—24no—
97C8×Dic73—24no—
98#14556498—22no—
99#14556498—22no—
100C2×#41×C73—22no—
101C2×#41×C73—22no—
102C2×#41×C73—22no—
103C2×#41×C73C2×C414yes—
104C2×#41×C73C2×C414yes—
105C2×#41×C73C2×C414yes—
106C22×Q8×C73C2311yescharacteristic
107C22×D4×C73—21no—
108C22×D4×C73C2311yescharacteristic
109C23×C4×C73—21no—
110C23×C4×C73—21no—
111C23×C4×C73C2311yescharacteristic
112C2×M16×C73—22no—
113C2×M16×C73—22no—
114C2×M16×C73C2×C414yescomplemented
115C22×C8×C73C2312yes—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—22no—
118C2×C4⋊C4×C73C2×C414yescomplemented
119C2×C4⋊C4×C73C2312yes—
120#103×C73C2×C418yescomplemented
121#102×C73C2×C418yescomplemented
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—24no—
125C22×Dic73—22no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—24no—
129C22×Dic73—24no—
130C22×Dic73—41no—
131C22×Dic73—41no—
132C22×Dic73—42no—
133C22×Dic73—42no—
134C22×Dic73—42no—
135C22×Dic73—42no—
136C22×Dic73—42no—
137C22×Dic73—42no—
138C22×Dic73C22⋊C414yes—
139C22×Dic73C22⋊C414yes—
140C22×Dic73C2×D411yescharacteristic
141C22×Dic73C2×D411yescharacteristic
142C22×Dic73C2×D411yescharacteristic
143C22×Dic73C2×D411yescharacteristic
144#11924012—28no—
145C2×#10596831—22no—
146C2×#10596831—22no—
147C2×#10596831C22×C414yes—
148C4⋊Dic73—24no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—22no—
152C4⋊Dic73—24no—
153C4⋊Dic73—24no—
154C4⋊Dic73C22×C414yes—
155C4⋊Dic73C22×C412yes—
156C4⋊Dic73C22×C412yes—
157C22⋊Dic73—24no—
158C22⋊Dic73—24no—
159C22⋊Dic73—24no—
160C4×Dic73—24no—
161C4×Dic73—24no—
162C4×Dic73—24no—
163C4×Dic73—44no—
164C4×Dic73—44no—
165C4×Dic73C22⋊C414yes—
166C4×Dic73C22⋊C414yes—
167C4×Dic73C22×C412yes—
168C4×Dic73C22×C412yes—
169C4×Dic73C2×D412yes—
170C4×Dic73C2×D412yes—
171C24×C73—21no—
172C24×C73C2×D411yescharacteristic
173#41×C73—28no—
174#41×C73—28no—
175#41×C73—28no—
176#41×C73C42116yescomplemented
177C2×Q8×C73—21no—
178C2×Q8×C73—21no—
179C2×Q8×C73—21no—
180C2×Q8×C73C22×C412yes—
181C2×Q8×C73C22×C412yes—
182C2×Q8×C73C22×C412yes—
183C2×D4×C73—24no—
184C2×D4×C73—24no—
185C2×D4×C73—24no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73C22×C412yes—
190C2×D4×C73C22×C412yes—
191C2×D4×C73C22×C412yes—
192C22×C4×C73—21no—
193C22×C4×C73—24no—
194C22×C4×C73—24no—
195C22×C4×C73—24no—
196C22×C4×C73—24no—
197C22×C4×C73—22no—
198C22×C4×C73—42no—
199C22×C4×C73—42no—
200C22×C4×C73C22×C412yes—
201C22×C4×C73C22×C412yes—
202C22×C4×C73C22×C412yes—
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D412yes—
205C22×C4×C73#4112yes—
206C22×C4×C73#4112yes—
207C22×C4×C73C2411yescharacteristic
208M16×C73—28no—
209C2×C8×C73—22no—
210C2×C8×C73—22no—
211C2×C8×C73C22×C414yes—
212C4⋊C4×C73—24no—
213C4⋊C4×C73—22no—
214C4⋊C4×C73C22×C414yes—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—22no—
220C23×C73—22no—
221C23×C73—22no—
222C23×C73—41no—
223C23×C73—41no—
224C23×C73—41no—
225C23×C73—41no—
226C23×C73C2×C22⋊C412yes—
227C23×C73C4×D412yes—
228C23×C73C4×D412yes—
229C23×C73C22×D411yescharacteristic
230Q8×C73—22no—
231Q8×C73—22no—
232Q8×C73—22no—
233Q8×C73C2×C4214yescomplemented
234D4×C73—216no—
235D4×C73—22no—
236D4×C73—22no—
237D4×C73—22no—
238D4×C73C2×C4214yescomplemented
239C2×C4×C73—22no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—216no—
243C2×C4×C73—24no—
244C2×C4×C73—48no—
245C2×C4×C73—42no—
246C2×C4×C73—42no—
247C2×C4×C73C2×C4214yes—
248C2×C4×C73C2×C22⋊C412yes—
249C2×C4×C73#11714yes—
250C2×C4×C73C4×D414yes—
251C2×C4×C73C4×D412yes—
252C2×C4×C73C4×D414yes—
253C2×C4×C73C4×D412yes—
254C2×C4×C73C23×C411yescharacteristic
255C2×C4×C73C23×C411yescharacteristic
256C2×C4×C73C23×C411yescharacteristic
257C2×C4×C73C22×D411yescharacteristic
258C2×C4×C73C2×#4111yescharacteristic
259C2×C4×C73C2×#4111yescharacteristic
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—28no—
267C2×Dic73—22no—
268C2×Dic73—22no—
269C2×Dic73—24no—
270C2×Dic73—44no—
271C2×Dic73—48no—
272C2×Dic73—48no—
273C2×Dic73—42no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—42no—
279C2×Dic73—48no—
280C2×Dic73C2×C22⋊C412yes—
281C2×Dic73C2×C22⋊C412yes—
282C2×Dic73C2×C22⋊C412yes—
283C2×Dic73C2×C22⋊C412yes—
284C2×Dic73AGL(1,ℤ/8)12yes—
285C2×Dic73#13712yes—
286C8×C73—24no—
287#10596831—24no—
288C22×C73—22no—
289C22×C73—22no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—24no—
295C22×C73—42no—
296C22×C73—42no—
297C22×C73—42no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—42no—
301C22×C73C4×C22⋊C414yes—
302C22×C73C22×C22⋊C411yescharacteristic
303C22×C73C2×C4×D411yescharacteristic
304C22×C73C2×C4×D411yescharacteristic
305C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C73C2×#13711yescharacteristic
307C22×C73#57511yescharacteristic
308C22×C73#57511yescharacteristic
309C4×C73—24no—
310C4×C73—44no—
311C4×C73C4×C22⋊C414yes—
312C4×C73C22×C4211yescharacteristic
313C4×C73C2×#11711yescharacteristic
314C4×C73C2×C4×D411yescharacteristic
315C4×C73C2×C4×D411yescharacteristic
316Dic73—22no—
317Dic73—22no—
318Dic73—22no—
319Dic73—42no—
320Dic73—42no—
321Dic73—44no—
322Dic73#41714yesdirect product factor
323C4×#417—731nomaximal, Sylow
324C2×C73—24no—
325C2×C73—44no—
326C2×C73C2×C4×C22⋊C411yescharacteristic
327C2×C73C2×#41711yescharacteristic
328C2×C73#289611yescharacteristic
329C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
330C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
331C2×C73C4×#13711yescharacteristic
332C2×C73C4×#13711yescharacteristic
333C2×C4×#41—731no—
334C2×#417—731no—
335C2×#417D7311yescharacteristic
336C2×C4×M16—731no—
337C2×C4×C4⋊C4—731no—
338#1763—732no—
339#1762—732no—
340C4×#103—732no—
341C4×#102—732no—
342#1736—731no—
343#1736—731no—
344C73C4×#41711yescharacteristic, complemented, Sylow
345C22×#41C2×D7311yescharacteristic
346C22×M16—731no—
347C22×M16C2×D7311yescharacteristic
348C4×#41—738no—
349C4×#41—1464no—
350C2×C4×Q8—731no—
351C2×C4×Q8—731no—
352C2×C4×D4—731no—
353C2×C4×D4—731no—
354C2×C4×D4—1461no—
355C2×C4×D4—1461no—
356C2×#117—731no—
357C2×#117—1461no—
358C22×C4⋊C4—731no—
359C22×C4⋊C4C2×D7311yescharacteristic
360C22×C42—731no—
361C22×C42—1461no—
362C22×C42—1461no—
363#417—738no—
364#417Dic7318yesdirect product factor
365C2×#103—732no—
366C2×#103C2×D7312yes—
367C2×#102—732no—
368C2×#102C2×D7312yes—
369C4×M16—1464no—
370C2×#97—732no—
371C2×C4×C8—732no—
372C4×C4⋊C4—732no—
373C4×C4⋊C4—732no—
374C4×C4⋊C4—1461no—
375C4×C4⋊C4—1461no—
376C2×#95—1461no—
377#340—732no—
378#340—732no—
379#340—732no—
380#340—732no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41C4×D7314yes—
385C2×#41C4×D7314yes—
386C2×#41C2×Dic7314yes—
387C22×Q8C22×D7311yescharacteristic
388C22×D4—21no—
389C22×D4C22×D7311yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—731no—
393C23×C4—731no—
394C23×C4—1461no—
395C23×C4—1461no—
396C23×C4—1461no—
397C23×C4C22×D7311yescharacteristic
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—734no—
401C2×M16—1462no—
402C2×M16—1462no—
403C2×M16C2×Dic7314yescomplemented
404C22×C8—732no—
405C22×C8C22×D7312yes—
406C4×Q8—734no—
407C4×Q8—734no—
408C4×Q8—1462no—
409C4×Q8—1462no—
410C4×D4—734no—
411C4×D4—734no—
412C4×D4—1462no—
413C4×D4—1462no—
414C4×D4—1468no—
415C4×D4—1468no—
416#117—734no—
417#117—1468no—
418#117—1462no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—734no—
422C2×C4⋊C4—732no—
423C2×C4⋊C4—731no—
424C2×C4⋊C4—731no—
425C2×C4⋊C4—1461no—
426C2×C4⋊C4—1461no—
427C2×C4⋊C4—1461no—
428C2×C4⋊C4—1462no—
429C2×C4⋊C4C2×Dic7314yescomplemented
430C2×C4⋊C4C22×D7312yes—
431C2×C22⋊C4—1461no—
432C2×C22⋊C4—1461no—
433C2×C22⋊C4—1461no—
434C2×C42—2924no—
435C2×C42—734no—
436C2×C42—731no—
437C2×C42—734no—
438C2×C42—731no—
439C2×C42—731no—
440C2×C42—731no—
441C2×C42—1462no—
442C2×C42—1462no—
443C2×C42—1468no—
444C2×C42—1461no—
445C2×C42—1461no—
446C2×C42—1461no—
447#103—738no—
448#103C2×Dic7318yescomplemented
449#102—738no—
450#102C2×Dic7318yescomplemented
451#97—1464no—
452C4×C8—1464no—
453#95—1462no—
454#95—1462no—
455C24—21no—
456C24D4×D7311yescharacteristic
457#41—28no—
458#41—28no—
459#41—28no—
460#41C4×Dic73116yescomplemented
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8C2×C4×D7312yes—
465C2×Q8C2×C4×D7312yes—
466C2×Q8C22×Dic7312yes—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×C4×D7312yes—
474C2×D4C2×C4×D7312yes—
475C2×D4C22×Dic7312yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—2922no—
485C22×C4—2922no—
486C22×C4—2922no—
487C22×C4—2922no—
488C22×C4—2922no—
489C22×C4—2922no—
490C22×C4—2921no—
491C22×C4—2921no—
492C22×C4—734no—
493C22×C4—731no—
494C22×C4—734no—
495C22×C4—731no—
496C22×C4—731no—
497C22×C4—731no—
498C22×C4—1464no—
499C22×C4—1464no—
500C22×C4—1464no—
501C22×C4—1462no—
502C22×C4—1461no—
503C22×C4—1461no—
504C22×C4—1462no—
505C22×C4—1462no—
506C22×C4C2×C4×D7312yes—
507C22×C4C2×C4×D7312yes—
508C22×C4C22×Dic7312yes—
509C22×C4D4×D7311yescharacteristic
510C22×C4D4×D7312yes—
511C22×C4#1192402712yes—
512C22×C4#1192402712yes—
513C22×C4C23×D7311yescharacteristic
514M16—28no—
515M16—1468no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—734no—
519C2×C8—1462no—
520C2×C8—1462no—
521C2×C8C22×Dic7314yes—
522C4⋊C4—24no—
523C4⋊C4—22no—
524C4⋊C4—734no—
525C4⋊C4—732no—
526C4⋊C4—732no—
527C4⋊C4—1464no—
528C4⋊C4—1464no—
529C4⋊C4—1464no—
530C4⋊C4—1461no—
531C4⋊C4—1461no—
532C4⋊C4—1462no—
533C4⋊C4C22×Dic7314yes—
534C22⋊C4—1464no—
535C22⋊C4—1464no—
536C22⋊C4—1464no—
537C42—2924no—
538C42—2924no—
539C42—734no—
540C42—734no—
541C42—732no—
542C42—732no—
543C42—732no—
544C42—732no—
545C42—1464no—
546C42—1464no—
547C42—1464no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C22⋊C4×D7312yes—
560C23#1455655112yes—
561C23D4×Dic7312yes—
562C23C2×D4×D7311yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8C2×C4×Dic7314yescomplemented
567D4—216no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4C2×C4×Dic7314yescomplemented
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—216no—
576C2×C4—24no—
577C2×C4—48no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—2928no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2922no—
585C2×C4—2922no—
586C2×C4—2921no—
587C2×C4—2928no—
588C2×C4—2928no—
589C2×C4—2924no—
590C2×C4—732no—
591C2×C4—732no—
592C2×C4—732no—
593C2×C4—732no—
594C2×C4—732no—
595C2×C4—732no—
596C2×C4—1462no—
597C2×C4—1462no—
598C2×C4—1464no—
599C2×C4—1468no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4C2×C4×Dic7314yes—
607C2×C4C22⋊C4×D7312yes—
608C2×C4#1455654714yes—
609C2×C4#1455655112yes—
610C2×C4#1455655114yes—
611C2×C4D4×Dic7312yes—
612C2×C4D4×Dic7314yes—
613C2×C4C22×C4×D7311yescharacteristic
614C2×C4C22×C4×D7311yescharacteristic
615C2×C4C23×Dic7311yescharacteristic
616C2×C4C2×D4×D7311yescharacteristic
617C2×C4C2×#1192402711yescharacteristic
618C2×C4C2×#1192402711yescharacteristic
619C8—24no—
620C8—1464no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—24no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22C22⋊C4×Dic7314yes—
635C22C2×C22⋊C4×D7311yescharacteristic
636C22C2×#1455655111yescharacteristic
637C22C2×D4×Dic7311yescharacteristic
638C22AGL(1,ℤ/8)×D7311yescharacteristic
639C22#137×D7311yescharacteristic
640C22#1798938311yescharacteristic
641C22#1798938611yescharacteristic
642C4—24no—
643C4—44no—
644C4—2922no—
645C4—2922no—
646C4—2924no—
647C4—734no—
648C4—1462no—
649C4—1462no—
650C4—1462no—
651C4C22⋊C4×Dic7314yes—
652C4C22×C4×Dic7311yescharacteristic
653C4C2×#1455654711yescharacteristic
654C4C2×#1455655111yescharacteristic
655C4C2×D4×Dic7311yescharacteristic
656C2—24no—
657C2—44no—
658C2C2×C22⋊C4×Dic7311yescharacteristic
659C2#417×D7311yescharacteristic
660C2#2261844711yescharacteristic
661C2AGL(1,ℤ/8)×Dic7311yescharacteristic
662C2#2261874411yescharacteristic
663C2#137×Dic7311yescharacteristic
664C2#2261875511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC4×C73C22×C42
FrattiniC22×C4C23×D73
FittingC2×#417×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#417D73
hypocenterC73C4×#417
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
3. C2×M16×Dic73C2semidirect
4. C2×C4⋊C4×Dic73C2semidirect
5. #22609763C2semidirect
6. #22609758C2semidirect
7. #103×Dic73C2semidirect
8. #102×Dic73C2semidirect
9. #22609651C2semidirect
10. #22609650C2semidirect
14. #41×Dic73C4semidirect
27. #17988588C4semidirect
45. #417×C73C4semidirect
55. C2×#11924012C2×C4semidirect
59. Q8×Dic73C2×C4semidirect
60. Q8×Dic73C2×C4semidirect
65. D4×Dic73C2×C4semidirect
66. D4×Dic73C2×C4semidirect
74. C2×C4⋊Dic73C2×C4semidirect
94. #14556515C2×C4semidirect
95. #14556512C2×C4semidirect
114. C2×M16×C73C2×C4semidirect
118. C2×C4⋊C4×C73C2×C4semidirect
120. #103×C73C2×C4semidirect
121. #102×C73C2×C4semidirect
176. #41×C73C42semidirect
233. Q8×C73C2×C42semidirect
238. D4×C73C2×C42semidirect
322. Dic73#417direct (N × H)
344. C73C4×#417semidirect
364. #417Dic73direct (N × H)
403. C2×M16C2×Dic73semidirect
429. C2×C4⋊C4C2×Dic73semidirect
448. #103C2×Dic73semidirect
450. #102C2×Dic73semidirect
460. #41C4×Dic73semidirect
566. Q8C2×C4×Dic73semidirect
571. D4C2×C4×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic732
C2×#179885882
C2×M16×Dic732
C2×C4⋊C4×Dic732
#226097632
#226097582
#103×Dic732
#102×Dic732
#226096512
#226096502
C2×#417×C732
C4×#41773