Finite Group Databasebeta

← #385×Dic73 #33007154

Subgroups — #385×Dic73 #33007154

Order 18688.

2782 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic73C211yesmaximal, characteristic
2C2×#17988462C211yesmaximal, characteristic
3C2×C4⋊C4×Dic73C212yesmaximal, complemented
4C2×C22⋊C4×Dic73C211yesmaximal, characteristic
5C2×C22⋊C4×Dic73C211yesmaximal, characteristic
6#22608165C212yesmaximal, complemented
7#22608163C212yesmaximal, complemented
8#22608154C211yesmaximal, characteristic
9#22608153C211yesmaximal, characteristic
10#95×Dic73C212yesmaximal, complemented
11C2×#385×C73C211yesmaximal, characteristic
12C24×Dic73C2211yescharacteristic
13C24×Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2212yes—
15C22×C22⋊Dic73C2211yescharacteristic
16C22×C22⋊Dic73C2211yescharacteristic
17C22×C4×Dic73—24no—
18C22×C4×Dic73—28no—
19C22×C4×Dic73C2211yescharacteristic
20C22×C4×Dic73C2212yes—
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2212yes—
23C22×C4×Dic73C2212yes—
24#17988462C418yescomplemented
25C4⋊C4×Dic73—28no—
26C22⋊C4×Dic73—24no—
27C22⋊C4×Dic73C418yescomplemented
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C24×C4×C73C2211yescharacteristic
37C22×C4⋊C4×C73C2212yes—
38C22×C22⋊C4×C73C2211yescharacteristic
39C22×C22⋊C4×C73C2211yescharacteristic
40#385×C73C418yescomplemented
41C2×#95×C73C2212yes—
42C23×Dic73—24no—
43C23×Dic73—24no—
44C23×Dic73—24no—
45C23×Dic73—24no—
46C23×Dic73—22no—
47C23×Dic73—22no—
48C23×Dic73C2×C414yes—
49C23×Dic73C2×C414yes—
50C23×Dic73D414yes—
51C23×Dic73Q814yes—
52C23×Dic73C2312yes—
53C23×Dic73C2311yescharacteristic
54C23×Dic73C2311yescharacteristic
55C23×Dic73C2311yescharacteristic
56C23×Dic73C2312yes—
57C23×Dic73C2311yescharacteristic
58C2×C4⋊Dic73—24no—
59C2×C4⋊Dic73—24no—
60C2×C4⋊Dic73C2×C418yescomplemented
61C2×C22⋊Dic73—22no—
62C2×C22⋊Dic73—22no—
63C2×C22⋊Dic73—22no—
64C2×C22⋊Dic73—22no—
65C2×C22⋊Dic73C2×C414yes—
66C2×C22⋊Dic73C2×C414yes—
67C2×C4×Dic73—232no—
68C2×C4×Dic73—24no—
69C2×C4×Dic73—24no—
70C2×C4×Dic73—24no—
71C2×C4×Dic73—24no—
72C2×C4×Dic73—24no—
73C2×C4×Dic73—24no—
74C2×C4×Dic73—22no—
75C2×C4×Dic73—22no—
76C2×C4×Dic73—24no—
77C2×C4×Dic73—24no—
78C2×C4×Dic73—24no—
79C2×C4×Dic73C2×C418yescomplemented
80C2×C4×Dic73D418yes—
81#14556498—22no—
82#14556498—22no—
83#14556498—24no—
84#14556498—24no—
85#14556498—24no—
86#14556498—24no—
87#14556498C2×C418yescomplemented
88#14556498C2×C418yescomplemented
89C25×C73C2311yescharacteristic
90C23×C4×C73—22no—
91C23×C4×C73—22no—
92C23×C4×C73—24no—
93C23×C4×C73—24no—
94C23×C4×C73C2×C414yes—
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2312yes—
98C23×C4×C73C2312yes—
99C2×C4⋊C4×C73—24no—
100C2×C4⋊C4×C73—24no—
101C2×C4⋊C4×C73C2×C418yescomplemented
102C2×C22⋊C4×C73—22no—
103C2×C22⋊C4×C73—22no—
104C2×C22⋊C4×C73C2×C414yes—
105C2×C22⋊C4×C73C2×C414yes—
106C2×C22⋊C4×C73C2×C414yes—
107C2×C22⋊C4×C73C2×C414yes—
108#95×C73C2×C418yescomplemented
109C22×Dic73—28no—
110C22×Dic73—216no—
111C22×Dic73—28no—
112C22×Dic73—28no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—216no—
120C22×Dic73—216no—
121C22×Dic73—28no—
122C22×Dic73—216no—
123C22×Dic73—28no—
124C22×Dic73—22no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—22no—
128C22×Dic73—22no—
129C22×Dic73—22no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—22no—
138C22×Dic73C4⋊C4116yescomplemented
139C22×Dic73C22×C412yes—
140C22×Dic73C22×C414yes—
141C22×Dic73C22×C412yes—
142C22×Dic73C22×C412yes—
143C22×Dic73C22×C414yes—
144C22×Dic73C22×C412yes—
145C22×Dic73C2×D412yes—
146C22×Dic73C2×D414yes—
147C22×Dic73C2×D412yes—
148C22×Dic73C2×D414yes—
149C22×Dic73C2×Q812yes—
150C22×Dic73C2×Q812yes—
151C22×Dic73#4114yes—
152C22×Dic73#4114yes—
153C4⋊Dic73—216no—
154C22⋊Dic73—28no—
155C22⋊Dic73—28no—
156C4×Dic73—216no—
157C4×Dic73—216no—
158C4×Dic73—216no—
159C4×Dic73—44no—
160C4×Dic73—44no—
161C24×C73—22no—
162C24×C73—22no—
163C24×C73—22no—
164C24×C73—22no—
165C24×C73C22×C412yes—
166C24×C73C22×C412yes—
167C24×C73C22×C412yes—
168C24×C73C2×D412yes—
169C24×C73C2×Q812yes—
170C24×C73#4112yes—
171C24×C73#4112yes—
172C24×C73C2411yescharacteristic
173C22×C4×C73—216no—
174C22×C4×C73—28no—
175C22×C4×C73—28no—
176C22×C4×C73—28no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—216no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—22no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—22no—
192C22×C4×C73—22no—
193C22×C4×C73—22no—
194C22×C4×C73C22×C414yes—
195C22×C4×C73C22×C414yes—
196C22×C4×C73C22×C412yes—
197C22×C4×C73C22×C412yes—
198C22×C4×C73C22×C414yes—
199C22×C4×C73C22×C414yes—
200C22×C4×C73C2×D414yes—
201C22×C4×C73#4114yes—
202C4⋊C4×C73—216no—
203C22⋊C4×C73—28no—
204C22⋊C4×C73C42116yescomplemented
205C23×C73—24no—
206C23×C73—24no—
207C23×C73—24no—
208C23×C73—24no—
209C23×C73—24no—
210C23×C73—24no—
211C23×C73—22no—
212C23×C73—24no—
213C23×C73—22no—
214C23×C73—22no—
215C23×C73—24no—
216C23×C73—22no—
217C23×C73—24no—
218C23×C73—24no—
219C23×C73—24no—
220C23×C73—24no—
221C23×C73C2×C4214yes—
222C23×C73C2×C4⋊C414yes—
223C23×C73#11714yes—
224C23×C73C4×D414yes—
225C23×C73C4×D414yes—
226C23×C73C4×Q814yes—
227C23×C73C4×Q814yes—
228C23×C73C23×C411yescharacteristic
229C23×C73C23×C411yescharacteristic
230C23×C73C23×C411yescharacteristic
231C23×C73C22×D411yescharacteristic
232C23×C73C22×D412yes—
233C23×C73C22×Q811yescharacteristic
234C23×C73C2×#4112yes—
235C23×C73C2×#4112yes—
236C23×C73C2×#4111yescharacteristic
237C23×C73C2×#4112yes—
238C23×C73C2×#4111yescharacteristic
239C2×C4×C73—232no—
240C2×C4×C73—24no—
241C2×C4×C73—24no—
242C2×C4×C73—24no—
243C2×C4×C73—24no—
244C2×C4×C73—24no—
245C2×C4×C73—24no—
246C2×C4×C73—24no—
247C2×C4×C73—24no—
248C2×C4×C73—24no—
249C2×C4×C73—24no—
250C2×C4×C73—24no—
251C2×C4×C73—24no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—24no—
255C2×C4×C73—24no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—42no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—42no—
262C2×C4×C73C2×C4218yescomplemented
263C2×C4×C73C4×D418yes—
264C2×Dic73—232no—
265C2×Dic73—24no—
266C2×Dic73—24no—
267C2×Dic73—24no—
268C2×Dic73—22no—
269C2×Dic73—24no—
270C2×Dic73—24no—
271C2×Dic73—22no—
272C2×Dic73—24no—
273C2×Dic73—24no—
274C2×Dic73—24no—
275C2×Dic73—232no—
276C2×Dic73—24no—
277C2×Dic73—24no—
278C2×Dic73—22no—
279C2×Dic73—22no—
280C2×Dic73—24no—
281C2×Dic73—24no—
282C2×Dic73—24no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—42no—
286C2×Dic73—41no—
287C2×Dic73—41no—
288C2×Dic73—42no—
289C2×Dic73—42no—
290C2×Dic73—42no—
291C2×Dic73—42no—
292C2×Dic73—42no—
293C2×Dic73C2×C4⋊C414yes—
294C2×Dic73C2×C4⋊C414yes—
295C2×Dic73C4×D418yes—
296C2×Dic73C4×D418yes—
297C2×Dic73#12014yes—
298C2×Dic73C22⋊Q818yes—
299C2×Dic73#12314yes—
300C22×C73—28no—
301C22×C73—24no—
302C22×C73—28no—
303C22×C73—24no—
304C22×C73—24no—
305C22×C73—24no—
306C22×C73—24no—
307C22×C73—24no—
308C22×C73—28no—
309C22×C73—28no—
310C22×C73C4×C4⋊C418yescomplemented
311C22×C73C22×C4211yescharacteristic
312C22×C73C22×C4⋊C411yescharacteristic
313C22×C73C2×#11711yescharacteristic
314C22×C73C2×C4×D412yes—
315C22×C73C2×C4×D412yes—
316C22×C73C2×C4×D411yescharacteristic
317C22×C73C2×C4×D411yescharacteristic
318C22×C73C2×C4×D412yes—
319C22×C73C2×C4×Q811yescharacteristic
320C22×C73C2×C4×Q811yescharacteristic
321C22×C73C4×#4112yes—
322C22×C73C4×#4112yes—
323C22×C73C4×#4112yes—
324C22×C73C2×#12011yescharacteristic
325C22×C73C2×C22⋊Q812yes—
326C22×C73C2×#12311yescharacteristic
327C22×C73#52512yes—
328C22×C73#52511yescharacteristic
329C22×C73#52511yescharacteristic
330C22×C73#52512yes—
331C22×C73#52912yes—
332C22×C73#52912yes—
333C22×C73#53312yes—
334C4×C73—28no—
335C4×C73—28no—
336C4×C73—42no—
337C4×C73—42no—
338Dic73—24no—
339Dic73—28no—
340Dic73—44no—
341Dic73—42no—
342Dic73—42no—
343Dic73#38518yesdirect product factor
344C4×#385—731nomaximal, Sylow
345C2×C73—28no—
346C2×C73C2×C4×C4⋊C411yescharacteristic
347C2×C73C42×D412yes—
348C2×C73C2×#38511yescharacteristic
349C2×C73#229012yes—
350C2×C73#229611yescharacteristic
351C2×C73C4×#12011yescharacteristic
352C2×C73C4×#12011yescharacteristic
353C2×C73C4×#12311yescharacteristic
354C2×C73C4×#12311yescharacteristic
355C2×C73C4×C22⋊Q812yes—
356C2×C73C4×C22⋊Q812yes—
357C23×C42—731no—
358C2×#385—731no—
359C2×#385D7311yescharacteristic
360C2×C4×C4⋊C4—732no—
361C2×C4×C22⋊C4—731no—
362C2×C4×C22⋊C4—731no—
363#1436—732no—
364#1436—732no—
365C22⋊#95—731no—
366C22⋊#95—731no—
367C4×#95—732no—
368C73C4×#38511yescharacteristic, complemented, Sylow
369C24×C4—731no—
370C24×C4—731no—
371C24×C4C2×D7311yescharacteristic
372C22×C4⋊C4—732no—
373C22×C4⋊C4C2×D7312yes—
374C22×C22⋊C4—731no—
375C22×C22⋊C4—731no—
376C22×C22⋊C4C2×D7311yescharacteristic
377C22×C22⋊C4C2×D7311yescharacteristic
378C22×C42—732no—
379C22×C42—732no—
380C22×C42—732no—
381C22×C42—731no—
382C22×C42—731no—
383C22×C42—1468no—
384C22×C42—1464no—
385#385—738no—
386#385Dic7318yesdirect product factor
387C4×C4⋊C4—1468no—
388C4×C22⋊C4—738no—
389C4×C22⋊C4—1464no—
390C2×#95—732no—
391C2×#95—732no—
392C2×#95—732no—
393C2×#95—732no—
394C2×#95—732no—
395C2×#95—732no—
396C2×#95—731no—
397C2×#95—731no—
398C2×#95C2×D7312yes—
399C25C22×D7311yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—731no—
405C23×C4—734no—
406C23×C4—734no—
407C23×C4—734no—
408C23×C4—732no—
409C23×C4—731no—
410C23×C4—734no—
411C23×C4—731no—
412C23×C4—731no—
413C23×C4—732no—
414C23×C4—1464no—
415C23×C4—1464no—
416C23×C4—1464no—
417C23×C4—1464no—
418C23×C4—1462no—
419C23×C4—1462no—
420C23×C4C2×Dic7314yes—
421C23×C4C22×D7311yescharacteristic
422C23×C4C22×D7311yescharacteristic
423C23×C4C22×D7312yes—
424C23×C4C22×D7312yes—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—738no—
428C2×C4⋊C4—1464no—
429C2×C4⋊C4—1464no—
430C2×C4⋊C4C2×Dic7318yescomplemented
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—734no—
434C2×C22⋊C4—734no—
435C2×C22⋊C4—1462no—
436C2×C22⋊C4—1462no—
437C2×C22⋊C4—1462no—
438C2×C22⋊C4—1462no—
439C2×C22⋊C4C4×D7314yes—
440C2×C22⋊C4C4×D7314yes—
441C2×C22⋊C4C2×Dic7314yes—
442C2×C22⋊C4C2×Dic7314yes—
443C2×C42—738no—
444C2×C42—738no—
445C2×C42—1462no—
446C2×C42—1462no—
447C2×C42—1464no—
448C2×C42—1464no—
449C2×C42—1464no—
450C2×C42—1464no—
451C2×C42—1464no—
452C2×C42—1464no—
453C2×C42—1464no—
454C2×C42—1464no—
455C2×C42—14632no—
456C2×C42—1464no—
457#95—738no—
458#95—738no—
459#95—1464no—
460#95—1462no—
461#95—1462no—
462#95—1464no—
463#95—1464no—
464#95—1464no—
465#95C2×Dic7318yescomplemented
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×C4×D7312yes—
471C24C2×C4×D7312yes—
472C24C22×Dic7312yes—
473C24D4×D7312yes—
474C24Q8×D7312yes—
475C24#1192402712yes—
476C24#1192402912yes—
477C24C23×D7311yescharacteristic
478C22×C4—28no—
479C22×C4—216no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—216no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—732no—
500C22×C4—734no—
501C22×C4—732no—
502C22×C4—732no—
503C22×C4—734no—
504C22×C4—7316no—
505C22×C4—732no—
506C22×C4—734no—
507C22×C4—732no—
508C22×C4—734no—
509C22×C4—732no—
510C22×C4—734no—
511C22×C4—732no—
512C22×C4—734no—
513C22×C4—732no—
514C22×C4—1462no—
515C22×C4—1461no—
516C22×C4—1461no—
517C22×C4—1462no—
518C22×C4—1462no—
519C22×C4—1462no—
520C22×C4—1462no—
521C22×C4—1462no—
522C22×C4—1462no—
523C22×C4—1462no—
524C22×C4—1462no—
525C22×C4—1461no—
526C22×C4—1462no—
527C22×C4—1461no—
528C22×C4—1468no—
529C22×C4—14616no—
530C22×C4—14616no—
531C22×C4—1468no—
532C22×C4—14616no—
533C22×C4—1468no—
534C22×C4—1468no—
535C22×C4—14616no—
536C22×C4—1468no—
537C22×C4—1462no—
538C22×C4—1462no—
539C22×C4—1462no—
540C22×C4—1462no—
541C22×C4—1462no—
542C22×C4—1462no—
543C22×C4C2×C4×D7314yes—
544C22×C4C2×C4×D7314yes—
545C22×C4C22×Dic7312yes—
546C22×C4C22×Dic7312yes—
547C22×C4C22×Dic7314yes—
548C22×C4C22×Dic7314yes—
549C22×C4D4×D7314yes—
550C22×C4#1192402714yes—
551C4⋊C4—216no—
552C4⋊C4—14616no—
553C22⋊C4—28no—
554C22⋊C4—1468no—
555C22⋊C4—1468no—
556C22⋊C4C4×Dic73116yescomplemented
557C42—2924no—
558C42—2924no—
559C42—14616no—
560C42—14616no—
561C42—14616no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—22no—
571C23—24no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—24no—
577C23—24no—
578C23C2×C4×Dic7314yes—
579C23C4⋊C4×D7314yes—
580C23#1455654914yes—
581C23#1455655314yes—
582C23D4×Dic7314yes—
583C23#1455655614yes—
584C23Q8×Dic7314yes—
585C23C22×C4×D7311yescharacteristic
586C23C22×C4×D7311yescharacteristic
587C23C23×Dic7311yescharacteristic
588C23C2×D4×D7311yescharacteristic
589C23C2×D4×D7312yes—
590C23C2×Q8×D7311yescharacteristic
591C23#41×D7312yes—
592C23#41×D7312yes—
593C23C2×#1192402712yes—
594C23C2×#1192402711yescharacteristic
595C23C2×#1192402911yescharacteristic
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—2922no—
620C2×C4—2922no—
621C2×C4—2921no—
622C2×C4—2921no—
623C2×C4—2922no—
624C2×C4—2921no—
625C2×C4—2921no—
626C2×C4—2922no—
627C2×C4—2922no—
628C2×C4—2922no—
629C2×C4—734no—
630C2×C4—738no—
631C2×C4—734no—
632C2×C4—738no—
633C2×C4—734no—
634C2×C4—734no—
635C2×C4—738no—
636C2×C4—1464no—
637C2×C4—1464no—
638C2×C4—1464no—
639C2×C4—1462no—
640C2×C4—1462no—
641C2×C4—1464no—
642C2×C4—1464no—
643C2×C4—14632no—
644C2×C4—14632no—
645C2×C4—1464no—
646C2×C4—1464no—
647C2×C4—1464no—
648C2×C4—1462no—
649C2×C4—1464no—
650C2×C4—1464no—
651C2×C4—1462no—
652C2×C4—1464no—
653C2×C4—1464no—
654C2×C4—1464no—
655C2×C4C2×C4×Dic7318yescomplemented
656C2×C4D4×Dic7318yes—
657C22—28no—
658C22—24no—
659C22—28no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22C4⋊C4×Dic7318yescomplemented
668C22C22×C4×Dic7311yescharacteristic
669C22C2×C4⋊C4×D7311yescharacteristic
670C22C2×#1455654911yescharacteristic
671C22C4×D4×D7312yes—
672C22C4×D4×D7312yes—
673C22C2×#1455655311yescharacteristic
674C22C2×D4×Dic7311yescharacteristic
675C22C2×D4×Dic7312yes—
676C22C2×#1455655611yescharacteristic
677C22C2×Q8×Dic7311yescharacteristic
678C22C4×#1192402712yes—
679C22C4×#1192402712yes—
680C22#41×Dic7312yes—
681C22#120×D7311yescharacteristic
682C22C22⋊Q8×D7312yes—
683C22#123×D7311yescharacteristic
684C22#1798909312yes—
685C22#1798909311yescharacteristic
686C22#1798909511yescharacteristic
687C22#1798910012yes—
688C22#1798911412yes—
689C22#1798912312yes—
690C22#1798913912yes—
691C4—28no—
692C4—28no—
693C4—42no—
694C4—42no—
695C4—2924no—
696C4—2922no—
697C4—2922no—
698C4—738no—
699C4—1464no—
700C4—1468no—
701C2—28no—
702C2C2×C4⋊C4×Dic7311yescharacteristic
703C2C4×D4×Dic7312yes—
704C2#385×D7311yescharacteristic
705C2#2261236712yes—
706C2#2261241011yescharacteristic
707C2#2261243211yescharacteristic
708C2#120×Dic7311yescharacteristic
709C2#2261245011yescharacteristic
710C2#123×Dic7311yescharacteristic
711C2#2261246312yes—
712C2C22⋊Q8×Dic7312yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC2×#385×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#385D73
hypocenterC73C4×#385
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic73C2semidirect
6. #22608165C2semidirect
7. #22608163C2semidirect
10. #95×Dic73C2semidirect
24. #17988462C4semidirect
27. C22⋊C4×Dic73C4semidirect
40. #385×C73C4semidirect
60. C2×C4⋊Dic73C2×C4semidirect
79. C2×C4×Dic73C2×C4semidirect
87. #14556498C2×C4semidirect
88. #14556498C2×C4semidirect
101. C2×C4⋊C4×C73C2×C4semidirect
108. #95×C73C2×C4semidirect
138. C22×Dic73C4⋊C4semidirect
204. C22⋊C4×C73C42semidirect
262. C2×C4×C73C2×C42semidirect
310. C22×C73C4×C4⋊C4semidirect
343. Dic73#385direct (N × H)
368. C73C4×#385semidirect
386. #385Dic73direct (N × H)
430. C2×C4⋊C4C2×Dic73semidirect
465. #95C2×Dic73semidirect
556. C22⋊C4C4×Dic73semidirect
655. C2×C4C2×C4×Dic73semidirect
667. C22C4⋊C4×Dic73semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic732
C2×#179884622
C2×C4⋊C4×Dic732
C2×C22⋊C4×Dic732
#226081652
#226081632
#226081542
#226081532
#95×Dic732
C2×#385×C732
C4×#38573