Finite Group Databasebeta

← C4×#17988741 #33091582

Subgroups — C4×#17988741 #33091582

Order 18688.

1448 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D73C211yesmaximal, characteristic
2C2×#17988741C211yesmaximal, characteristic
3C2×C4×#11924018C211yesmaximal, characteristic, complemented
4C4×#14556567C211yesmaximal, characteristic
5#22610274C211yesmaximal, characteristic, complemented
6#22610269C211yesmaximal, characteristic, complemented
7#22610235C211yesmaximal, characteristic
8#22610183C211yesmaximal, characteristic, complemented
9#22610182C211yesmaximal, characteristic, complemented
10#22610117C211yesmaximal, characteristic
11#22609864C211yesmaximal, characteristic
12C4×#14556516C211yesmaximal, characteristic, complemented
13C4×#14556515C211yesmaximal, characteristic, complemented
14C4×#14556503C211yesmaximal, characteristic
15C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
16C22×Q8×D73C2211yescharacteristic
17C22×#11924018C2211yescharacteristic
18C2×#14556567C2211yescharacteristic
19C2×Q8×Dic73C2211yescharacteristic
20C2×C4×Dic146—21no—
21C2×C4×Dic146C2211yescharacteristic
22C2×#14556556—21no—
23C2×#14556556C2211yescharacteristic
24C4×Q8×D73—24no—
25C4×Q8×D73—24no—
26C2×C4⋊C4×D73—21no—
27C2×C4⋊C4×D73C2211yescharacteristic
28C2×C42×D73—21no—
29C2×C42×D73C2211yescharacteristic
30#17988741C418yesdirect product factor
31C4×#11924018—24no—
32C2×#14556524C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556516C2211yescharacteristic
35C2×#14556515C2211yescharacteristic
36C2×#14556515C2211yescharacteristic
37C2×#14556515C2211yescharacteristic
38C2×#14556514C2211yescharacteristic
39C2×#14556503C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×C4×#10596831C2211yescharacteristic
42#17988494C2211yescharacteristic
43#17988483C2211yescharacteristic
44#17988468—21no—
45#17988458—21no—
46#17988444C2211yescharacteristic
47C4×#11924007—21no—
48C4×C4⋊Dic73C2211yescharacteristic
49C4×#11924005—21no—
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C22×Q16×C73C2211yescharacteristic
57C2×C4×Q8×C73C2211yescharacteristic
58C2×C4×Q8×C73C2211yescharacteristic
59C4×Q16×C73—24no—
60C2×#107×C73C2211yescharacteristic
61C2×#103×C73C2211yescharacteristic
62C2×#103×C73C2211yescharacteristic
63C2×C4×C8×C73C2211yescharacteristic
64C22×Dic146—21no—
65C22×Dic146C2311yescharacteristic
66C2×Q8×D73—22no—
67C2×Q8×D73—22no—
68C2×Q8×D73—22no—
69C2×Q8×D73—22no—
70C2×Q8×D73—22no—
71C2×Q8×D73C2×C414yes—
72C22×C4×D73—21no—
73C22×C4×D73—21no—
74C22×C4×D73D411yescharacteristic
75C22×C4×D73D411yescharacteristic
76C22×C4×D73C2311yescharacteristic
77C2×#11924018—22no—
78C2×#11924018—22no—
79C2×#11924018C2×C414yescomplemented
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82#14556567—22no—
83#14556567C2×C414yes—
84Q8×Dic73—22no—
85Q8×Dic73—22no—
86C4×Dic146—28no—
87C4×Dic146—22no—
88C4×Dic146D414yes—
89#14556556—28no—
90#14556556—22no—
91#14556556—22no—
92C2×C4⋊Dic73—21no—
93C2×C4⋊Dic73C2311yescharacteristic
94C2×C4⋊Dic73C2311yescharacteristic
95C2×C4⋊Dic73C2311yescharacteristic
96C2×#11924007—21no—
97C2×#11924007—21no—
98C2×#11924007—21no—
99C2×#11924007—21no—
100C2×#11924007—21no—
101C4⋊C4×D73—28no—
102C4⋊C4×D73—22no—
103C4⋊C4×D73—22no—
104C2×#11924005—21no—
105C2×#11924005—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73—21no—
108C2×C4×Dic73—21no—
109C2×C4×Dic73—21no—
110C2×C4×Dic73D411yescharacteristic
111C2×C4×Dic73D411yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—28no—
114C42×D73—22no—
115C42×D73—22no—
116#14556524—22no—
117#14556516—22no—
118#14556516C2×C414yescomplemented
119#14556515—22no—
120#14556515—22no—
121#14556515C2×C414yescomplemented
122#14556514—22no—
123#14556503—22no—
124#14556503C2×C414yes—
125C4×#10596831—22no—
126#14556498—21no—
127#14556498—21no—
128#14556498—21no—
129#14556498—21no—
130#14556498—21no—
131C22×Q8×C73C2311yescharacteristic
132C22×Q8×C73C2311yescharacteristic
133C2×Q16×C73—22no—
134C2×Q16×C73—22no—
135C2×Q16×C73C2×C414yescomplemented
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C4×Q8×C73—22no—
139C4×Q8×C73—22no—
140C4×Q8×C73—22no—
141C4×Q8×C73D414yes—
142C2×C4⋊C4×C73—21no—
143C2×C4⋊C4×C73—21no—
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C4⋊C4×C73C2311yescharacteristic
146C2×C42×C73—21no—
147C2×C42×C73—21no—
148C2×C42×C73C2311yescharacteristic
149#107×C73—22no—
150#103×C73—22no—
151#103×C73—22no—
152C4×C8×C73—22no—
153C23×D73C2×D411yescharacteristic
154C2×Dic146—24no—
155C2×Dic146—24no—
156C2×Dic146—21no—
157C2×Dic146—21no—
158C2×Dic146—21no—
159C2×Dic146—24no—
160C2×Dic146C22×C412yes—
161C2×Dic146C2×D412yes—
162C2×Dic146#4112yes—
163Q8×D73—28no—
164Q8×D73—28no—
165Q8×D73—28no—
166Q8×D73—28no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73C2×D411yescharacteristic
172C22×Dic73C2×D411yescharacteristic
173C22×Dic73C2×D411yescharacteristic
174C2×C4×D73—24no—
175C2×C4×D73—24no—
176C2×C4×D73—24no—
177C2×C4×D73—22no—
178C2×C4×D73—22no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—24no—
184C2×C4×D73—22no—
185C2×C4×D73—22no—
186C2×C4×D73—41no—
187C2×C4×D73—42no—
188C2×C4×D73—42no—
189C2×C4×D73Q1614yescomplemented
190C2×C4×D73C22×C412yes—
191C2×C4×D73#4112yes—
192#11924018—28no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831C22×C412yes—
199C4⋊Dic73—24no—
200C4⋊Dic73—21no—
201C4⋊Dic73—21no—
202C4⋊Dic73—21no—
203C4⋊Dic73—21no—
204C4⋊Dic73C22×C412yes—
205C4⋊Dic73C2×D412yes—
206#11924007—24no—
207#11924007—24no—
208#11924007—24no—
209#11924007—24no—
210#11924007—42no—
211#11924005—24no—
212#11924005—42no—
213C4×Dic73—24no—
214C4×Dic73—24no—
215C4×Dic73—24no—
216C4×Dic73—22no—
217C4×Dic73—22no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73—42no—
221C2×Q8×C73—21no—
222C2×Q8×C73—21no—
223C2×Q8×C73—21no—
224C2×Q8×C73—21no—
225C2×Q8×C73—21no—
226C2×Q8×C73—21no—
227C2×Q8×C73—21no—
228C2×Q8×C73—21no—
229C2×Q8×C73C22×C412yes—
230C2×Q8×C73C22×C412yes—
231C2×Q8×C73C2×D412yes—
232C2×Q8×C73#4112yes—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2411yescharacteristic
240Q16×C73—28no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73C22×C412yes—
247C4⋊C4×C73—24no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—42no—
252C4⋊C4×C73C2×D412yes—
253C42×C73—24no—
254C42×C73—42no—
255C42×C73C2×D412yes—
256C42×C73C2×D412yes—
257C23×C73C22×D411yescharacteristic
258C22×D73—21no—
259C22×D73—21no—
260C22×D73—21no—
261C22×D73—21no—
262C22×D73C4×D412yes—
263C22×D73C2×Q1612yes—
264C22×D73#13512yes—
265Q8×C73—22no—
266Q8×C73—22no—
267Q8×C73—22no—
268Q8×C73—22no—
269Q8×C73—22no—
270Q8×C73—41no—
271Q8×C73—41no—
272Q8×C73C4×D414yes—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73#12012yes—
288C2×C4×C73#12012yes—
289C2×C4×C73C2×Q1612yes—
290C2×C4×C73#13712yes—
291C2×C4×C73C23×C411yescharacteristic
292C2×C4×C73C22×D411yescharacteristic
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×Dic73—22no—
298C2×Dic73—21no—
299C2×Dic73—22no—
300C2×Dic73—21no—
301C2×Dic73—22no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—22no—
305C2×Dic73—21no—
306C2×Dic73—22no—
307C2×Dic73—21no—
308C2×Dic73—21no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73C4×D412yes—
317C2×Dic73C2×Q1612yes—
318C4×D73—216no—
319C4×D73—22no—
320C4×D73—22no—
321C4×D73—22no—
322C4×D73—22no—
323C4×D73—28no—
324C4×D73—44no—
325C4×D73—48no—
326Dic146—216no—
327Dic146—22no—
328Dic146—22no—
329Dic146—22no—
330Dic146C4×D414yes—
331C8×C73—22no—
332C8×C73—41no—
333#10596831—22no—
334#10596831—41no—
335C22×C73C2×C4×D411yescharacteristic
336C22×C73C2×#12011yescharacteristic
337C22×C73#52511yescharacteristic
338C22×C73C22×Q1611yescharacteristic
339C22×C73C2×#13511yescharacteristic
340C22×C73C2×#13711yescharacteristic
341C22×C73#57511yescharacteristic
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73—22no—
346C2×D73—22no—
347C2×D73—22no—
348C2×D73C4×Q1614yescomplemented
349C4×C73—22no—
350C4×C73—24no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—81no—
354C4×C73#45114yescomplemented
355C4×C73C2×C4×D411yescharacteristic
356C4×C73C2×C4×D411yescharacteristic
357C4×C73#52511yescharacteristic
358C4×C73#52511yescharacteristic
359Dic73—22no—
360Dic73—22no—
361Dic73—24no—
362Dic73—42no—
363Dic73—41no—
364Dic73—42no—
365Dic73—81no—
366C4×#451—731nomaximal, Sylow
367C2×C73C4×#12011yescharacteristic
368C2×C73C2×C4×Q1611yescharacteristic
369C2×C73C4×#13711yescharacteristic
370C2×C73C2×#45111yescharacteristic
371C2×C73#300211yescharacteristic
372C2×C73#310411yescharacteristic
373C2×C73#310811yescharacteristic
374D73—24no—
375C22×C4×Q8—731no—
376C2×#451—731no—
377C2×C4×Q16—731no—
378C2×C4×Q16D7311yescharacteristic, complemented
379C4×C22⋊Q8—731no—
380#1878—731no—
381#1878—731no—
382#1872—731no—
383#1863—731no—
384#1863—731no—
385#1852—731no—
386#1787—731no—
387C4×#103—731no—
388C4×#103—731no—
389C4×C22⋊C8—731no—
390C73C4×#45111yescharacteristic, complemented, Sylow
391C23×Q8—731no—
392C22×Q16—731no—
393C22×Q16C2×D7311yescharacteristic
394C2×C22⋊Q8—731no—
395C2×C4×Q8—731no—
396C2×C4×Q8—731no—
397C2×C4×Q8—731no—
398C2×C4×Q8—1461no—
399C2×C4×Q8—1461no—
400C2×C4×Q8—1464no—
401C2×C4×Q8—1464no—
402C2×C4×Q8C2×D7311yescharacteristic
403C2×C4×Q8C2×D7311yescharacteristic
404C22×C4⋊C4—731no—
405C22×C4⋊C4—1461no—
406C22×C42—731no—
407C22×C42—1461no—
408#451—738no—
409C4×Q16—24no—
410C4×Q16—1464no—
411C2×#107—731no—
412C2×#107C2×D7311yescharacteristic
413C2×#103—731no—
414C2×#103—731no—
415C2×#103—731no—
416C2×#103—731no—
417C2×#103—731no—
418C2×#103—731no—
419C2×#103C2×D7311yescharacteristic
420C2×#103C2×D7311yescharacteristic
421C2×C22⋊C8—731no—
422C2×C22⋊C8—731no—
423C2×C4×C8—731no—
424C2×C4×C8C2×D7311yescharacteristic
425#391—731no—
426#389—731no—
427#387—1461no—
428#385—1461no—
429#380—731no—
430C4×C4⋊C4—731no—
431C4×C4⋊C4—1461no—
432C4×C22⋊C4—1461no—
433#340—731no—
434#340—731no—
435#340—731no—
436#340—731no—
437#336—731no—
438#336—731no—
439C22×Q8—734no—
440C22×Q8—731no—
441C22×Q8—1461no—
442C22×Q8—1462no—
443C22×Q8—1462no—
444C22×Q8—1462no—
445C22×Q8—1462no—
446C22×Q8—1462no—
447C22×Q8C22×D7311yescharacteristic
448C22×Q8C22×D7311yescharacteristic
449C23×C4—731no—
450C23×C4—731no—
451C23×C4—731no—
452C23×C4—1461no—
453C23×C4—1461no—
454C2×Q16—22no—
455C2×Q16—22no—
456C2×Q16—734no—
457C2×Q16—1462no—
458C2×Q16—1462no—
459C2×Q16C4×D7314yescomplemented
460C22×C8—731no—
461C22×C8—731no—
462C22×C8C22×D7311yescharacteristic
463C22×C8C22×D7311yescharacteristic
464C22⋊Q8—734no—
465C22⋊Q8—1462no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—734no—
470C4×Q8—1468no—
471C4×Q8—1462no—
472C4×Q8—1468no—
473C4×Q8—1462no—
474C4×Q8—1462no—
475C4×Q8—1462no—
476C4×Q8—1462no—
477C4×Q8C22⋊D7314yes—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—731no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—731no—
483C2×C4⋊C4—1462no—
484C2×C4⋊C4—1468no—
485C2×C4⋊C4—1461no—
486C2×C4⋊C4—1461no—
487C2×C4⋊C4—1461no—
488C2×C4⋊C4—1461no—
489C2×C4⋊C4—1461no—
490C2×C4⋊C4—1461no—
491C2×C4⋊C4—1462no—
492C2×C4⋊C4C22×D7311yescharacteristic
493C2×C4⋊C4C22×D7311yescharacteristic
494C2×C22⋊C4—1461no—
495C2×C22⋊C4—1461no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—731no—
499C2×C42—731no—
500C2×C42—731no—
501C2×C42—1468no—
502C2×C42—1461no—
503C2×C42—1461no—
504C2×C42—1461no—
505C2×C42—1461no—
506C2×C42—1462no—
507C2×C42—1462no—
508C2×C42C22×D7311yescharacteristic
509#107—22no—
510#107—1462no—
511#103—22no—
512#103—22no—
513#103—734no—
514#103—734no—
515#103—1462no—
516#103—1462no—
517#103—1462no—
518#103—1462no—
519C22⋊C8—734no—
520C22⋊C8—1462no—
521C4×C8—22no—
522C4×C8—1462no—
523#95—1461no—
524#95—1461no—
525#95—1461no—
526#95—1461no—
527#95—1461no—
528C24—731no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—732no—
538C2×Q8—732no—
539C2×Q8—732no—
540C2×Q8—1464no—
541C2×Q8—1464no—
542C2×Q8—1464no—
543C2×Q8—1468no—
544C2×Q8—1468no—
545C2×Q8—1468no—
546C2×Q8—1468no—
547C2×Q8—1461no—
548C2×Q8—1461no—
549C2×Q8—1461no—
550C2×Q8C2×C4×D7312yes—
551C2×Q8C2×C4×D7312yes—
552C2×Q8C2×C22⋊D7312yes—
553C2×Q8#1192402812yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—2921no—
559C22×C4—2922no—
560C22×C4—2922no—
561C22×C4—731no—
562C22×C4—731no—
563C22×C4—734no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—731no—
567C22×C4—1462no—
568C22×C4—1464no—
569C22×C4—1464no—
570C22×C4—1464no—
571C22×C4—1464no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1462no—
576C22×C4—1461no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1461no—
580C22×C4—1461no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4D4×D7311yescharacteristic
584C22×C4D4×D7311yescharacteristic
585C22×C4C23×D7311yescharacteristic
586Q16—28no—
587Q16—1468no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—732no—
594C2×C8—1461no—
595C2×C8—1461no—
596C2×C8—1461no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8C2×C4×D7312yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—2922no—
606C4⋊C4—732no—
607C4⋊C4—732no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1461no—
613C4⋊C4—1461no—
614C4⋊C4—1464no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4C2×C22⋊D7312yes—
618C22⋊C4—2922no—
619C22⋊C4—1464no—
620C42—24no—
621C42—42no—
622C42—2922no—
623C42—1464no—
624C42—1464no—
625C42—1462no—
626C42—1462no—
627C42—1464no—
628C42—1461no—
629C42—1461no—
630C42D4×D7312yes—
631C42C2×C22⋊D7312yes—
632C23—732no—
633C23—732no—
634C23—732no—
635C23—1461no—
636C23—1461no—
637C23—1461no—
638C23—1461no—
639C23C2×D4×D7311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—41no—
646Q8—41no—
647Q8—734no—
648Q8—14616no—
649Q8—1462no—
650Q8—1462no—
651Q8—1462no—
652Q8C4×C22⋊D7314yes—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—2924no—
668C2×C4—2928no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—732no—
677C2×C4—732no—
678C2×C4—14616no—
679C2×C4—1461no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1461no—
683C2×C4—1461no—
684C2×C4—1461no—
685C2×C4—1462no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1462no—
689C2×C4—1461no—
690C2×C4—1462no—
691C2×C4—1468no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4#1455655912yes—
697C2×C4#1455655912yes—
698C2×C4Q16×D7312yes—
699C2×C4#1455662312yes—
700C2×C4C22×C4×D7311yescharacteristic
701C2×C4C2×D4×D7311yescharacteristic
702C2×C4C22×C22⋊D7311yescharacteristic
703C2×C4#41×D7311yescharacteristic
704C2×C4#41×D7311yescharacteristic
705C2×C4C2×#1192402811yescharacteristic
706C8—22no—
707C8—41no—
708C8—2921no—
709C8—1462no—
710C22—734no—
711C22—1462no—
712C22—1462no—
713C22—1462no—
714C22—1462no—
715C22—1462no—
716C22—1462no—
717C22C4×D4×D7311yescharacteristic
718C22C2×#1455655911yescharacteristic
719C22#1798909611yescharacteristic
720C22C2×Q16×D7311yescharacteristic
721C22#135×D7311yescharacteristic
722C22C2×#1455662311yescharacteristic
723C22#1798938411yescharacteristic
724C4—22no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—81no—
729C4—2922no—
730C4—2921no—
731C4—2922no—
732C4—5841no—
733C4—1462no—
734C4—1464no—
735C4—1462no—
736C4#1798874114yesdirect product factor
737C4C4×D4×D7311yescharacteristic
738C4C2×C4×C22⋊D7311yescharacteristic
739C4#1798909411yescharacteristic
740C4#1798909611yescharacteristic
741C2—1464no—
742C2C4×#1455655911yescharacteristic
743C2C4×Q16×D7311yescharacteristic
744C2C4×#1455662311yescharacteristic
745C2C2×#1798874111yescharacteristic
746C2#2261914511yescharacteristic
747C2#2261996811yescharacteristic
748C2#2262001511yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×Q16×C73C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenterC2×C4×Q16D73
hypocenterC73C4×#451
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11924018C2semidirect
5. #22610274C2semidirect
6. #22610269C2semidirect
8. #22610183C2semidirect
9. #22610182C2semidirect
12. C4×#14556516C2semidirect
13. C4×#14556515C2semidirect
15. C2×C4×Q16×C73C2semidirect
30. #17988741C4direct (N × H)
79. C2×#11924018C2×C4semidirect
118. #14556516C2×C4semidirect
121. #14556515C2×C4semidirect
135. C2×Q16×C73C2×C4semidirect
189. C2×C4×D73Q16semidirect
348. C2×D73C4×Q16semidirect
354. C4×C73#451semidirect
378. C2×C4×Q16D73semidirect
390. C73C4×#451semidirect
459. C2×Q16C4×D73semidirect
736. C4#17988741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D732
C2×#179887412
C2×C4×#119240182
C4×#145565672
#226102742
#226102692
#226102352
#226101832
#226101822
#226101172
#226098642
C4×#145565162
C4×#145565152
C4×#145565032
C2×C4×Q16×C732
C4×#45173