Finite Group Databasebeta

← #389×Dic73 #33007180

Subgroups — #389×Dic73 #33007180

Order 18688.

1918 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988486C211yesmaximal, characteristic
2C2×C4⋊C4×Dic73C212yesmaximal
3C2×C4⋊C4×Dic73C211yesmaximal, characteristic
4C2×C4⋊C4×Dic73C211yesmaximal, characteristic
5C2×C42×Dic73C211yesmaximal, characteristic
6#22608165C212yesmaximal
7#22608163C212yesmaximal
8#22608161C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10#95×Dic73C212yesmaximal
11C2×#389×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2212yes—
15C22×C4×Dic73C2212yes—
16C22×C4×Dic73C2211yescharacteristic
17C22×C4×Dic73C2211yescharacteristic
18C22×C4×Dic73C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20C22×C4×Dic73C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23#17988486C418yescomplemented
24C4⋊C4×Dic73—24no—
25C4⋊C4×Dic73—28no—
26C4⋊C4×Dic73C418yescomplemented
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C42×Dic73—24no—
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2212yes—
37C22×C4⋊C4×C73C2211yescharacteristic
38C22×C42×C73C2211yescharacteristic
39#389×C73C418yescomplemented
40C2×#95×C73C2212yes—
41C23×Dic73C2312yes—
42C23×Dic73C2312yes—
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C2×C4⋊Dic73—24no—
48C2×C4⋊Dic73—24no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—22no—
52C2×C4⋊Dic73—22no—
53C2×C4⋊Dic73C2×C414yes—
54C2×C4⋊Dic73C2×C418yes—
55C2×C4⋊Dic73C2×C414yes—
56C2×C4×Dic73—22no—
57C2×C4×Dic73—22no—
58C2×C4×Dic73—22no—
59C2×C4×Dic73—22no—
60C2×C4×Dic73—24no—
61C2×C4×Dic73—22no—
62C2×C4×Dic73—22no—
63C2×C4×Dic73—24no—
64C2×C4×Dic73—22no—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—24no—
67C2×C4×Dic73—24no—
68C2×C4×Dic73—24no—
69C2×C4×Dic73—22no—
70C2×C4×Dic73—22no—
71C2×C4×Dic73—22no—
72C2×C4×Dic73—22no—
73C2×C4×Dic73C2×C418yes—
74C2×C4×Dic73C2×C414yes—
75C2×C4×Dic73C2×C414yes—
76C2×C4×Dic73D414yes—
77C2×C4×Dic73D414yes—
78C2×C4×Dic73Q814yes—
79C2×C4×Dic73Q814yes—
80#14556498—24no—
81#14556498—24no—
82#14556498—24no—
83#14556498—24no—
84#14556498—24no—
85#14556498C2×C418yes—
86#14556498C2×C418yes—
87C23×C4×C73C2312yes—
88C23×C4×C73C2312yes—
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73—24no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—24no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73C2×C414yes—
97C2×C4⋊C4×C73C2×C418yes—
98C2×C4⋊C4×C73C2×C414yes—
99C2×C4⋊C4×C73C2×C414yes—
100C2×C4⋊C4×C73C2×C414yes—
101C2×C42×C73—22no—
102C2×C42×C73—22no—
103C2×C42×C73C2×C414yes—
104#95×C73C2×C418yes—
105C22×Dic73—21no—
106C22×Dic73—21no—
107C22×Dic73—21no—
108C22×Dic73—21no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—21no—
112C22×Dic73—21no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—22no—
129C22×Dic73C22×C414yes—
130C22×Dic73C22×C414yes—
131C22×Dic73C22×C412yes—
132C22×Dic73C22×C412yes—
133C22×Dic73C22×C412yes—
134C22×Dic73C22×C412yes—
135C22×Dic73C2×D412yes—
136C22×Dic73C2×D412yes—
137C22×Dic73C2×D412yes—
138C22×Dic73C2×D412yes—
139C22×Dic73C2×Q812yes—
140C22×Dic73C2×Q812yes—
141C22×Dic73C2×Q812yes—
142C22×Dic73C2×Q812yes—
143C22×Dic73#4112yes—
144C22×Dic73#4112yes—
145C22×Dic73#4112yes—
146C22×Dic73#4112yes—
147C4⋊Dic73—28no—
148C4⋊Dic73—28no—
149C4⋊Dic73—216no—
150C4×Dic73—28no—
151C4×Dic73—28no—
152C4×Dic73—28no—
153C4×Dic73—216no—
154C4×Dic73—28no—
155C4×Dic73—28no—
156C4×Dic73—48no—
157C4×Dic73C4⋊C4116yescomplemented
158C24×C73C2411yescharacteristic
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—22no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73—22no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73C22×C414yes—
178C22×C4×C73C22×C414yes—
179C22×C4×C73C22×C412yes—
180C22×C4×C73C22×C412yes—
181C22×C4×C73C22×C414yes—
182C22×C4×C73C22×C414yes—
183C22×C4×C73C22×C412yes—
184C22×C4×C73C22×C412yes—
185C22×C4×C73C22×C412yes—
186C22×C4×C73C2×D412yes—
187C22×C4×C73C2×D412yes—
188C22×C4×C73C2×Q812yes—
189C22×C4×C73C2×Q812yes—
190C22×C4×C73#4112yes—
191C22×C4×C73#4112yes—
192C22×C4×C73#4112yes—
193C22×C4×C73#4112yes—
194C4⋊C4×C73—216no—
195C4⋊C4×C73—28no—
196C4⋊C4×C73C42116yescomplemented
197C42×C73—28no—
198C23×C73C23×C411yescharacteristic
199C23×C73C23×C411yescharacteristic
200C23×C73C23×C411yescharacteristic
201C23×C73C22×D411yescharacteristic
202C23×C73C22×D411yescharacteristic
203C23×C73C22×Q811yescharacteristic
204C23×C73C22×Q811yescharacteristic
205C23×C73C2×#4111yescharacteristic
206C23×C73C2×#4111yescharacteristic
207C23×C73C2×#4111yescharacteristic
208C23×C73C2×#4111yescharacteristic
209C23×C73C2×#4111yescharacteristic
210C23×C73C2×#4111yescharacteristic
211C23×C73C2×#4111yescharacteristic
212C23×C73C2×#4111yescharacteristic
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—24no—
216C2×C4×C73—24no—
217C2×C4×C73—24no—
218C2×C4×C73—24no—
219C2×C4×C73—24no—
220C2×C4×C73—24no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
225C2×C4×C73—22no—
226C2×C4×C73—22no—
227C2×C4×C73—22no—
228C2×C4×C73—22no—
229C2×C4×C73—22no—
230C2×C4×C73—22no—
231C2×C4×C73—24no—
232C2×C4×C73—24no—
233C2×C4×C73—24no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73—42no—
237C2×C4×C73—42no—
238C2×C4×C73C2×C4218yes—
239C2×C4×C73C2×C4214yes—
240C2×C4×C73C2×C4⋊C414yes—
241C2×C4×C73#11714yes—
242C2×C4×C73C4×D414yes—
243C2×C4×C73C4×D414yes—
244C2×C4×C73C4×D414yes—
245C2×C4×C73C4×Q814yes—
246C2×C4×C73C4×Q814yes—
247C2×C4×C73C4×Q814yes—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—22no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—22no—
254C2×Dic73—22no—
255C2×Dic73—22no—
256C2×Dic73—22no—
257C2×Dic73—22no—
258C2×Dic73—22no—
259C2×Dic73—22no—
260C2×Dic73—22no—
261C2×Dic73—22no—
262C2×Dic73—22no—
263C2×Dic73—22no—
264C2×Dic73—22no—
265C2×Dic73—22no—
266C2×Dic73—24no—
267C2×Dic73—24no—
268C2×Dic73—24no—
269C2×Dic73—24no—
270C2×Dic73—24no—
271C2×Dic73—24no—
272C2×Dic73—42no—
273C2×Dic73—42no—
274C2×Dic73—42no—
275C2×Dic73—42no—
276C2×Dic73—42no—
277C2×Dic73—42no—
278C2×Dic73—42no—
279C2×Dic73—42no—
280C2×Dic73C2×C4⋊C414yes—
281C2×Dic73C2×C4⋊C414yes—
282C2×Dic73C4×D414yes—
283C2×Dic73C4×D414yes—
284C2×Dic73C4×Q814yes—
285C2×Dic73C4×Q814yes—
286C2×Dic73#12114yes—
287C2×Dic73C22⋊Q814yes—
288C2×Dic73#12514yes—
289C2×Dic73C4⋊Q814yes—
290C22×C73C22×C4211yescharacteristic
291C22×C73C22×C4⋊C411yescharacteristic
292C22×C73C2×#11711yescharacteristic
293C22×C73C2×C4×D411yescharacteristic
294C22×C73C2×C4×D411yescharacteristic
295C22×C73C2×C4×D411yescharacteristic
296C22×C73C2×C4×D411yescharacteristic
297C22×C73C2×C4×D411yescharacteristic
298C22×C73C2×C4×Q811yescharacteristic
299C22×C73C2×C4×Q811yescharacteristic
300C22×C73C2×C4×Q811yescharacteristic
301C22×C73C2×C4×Q811yescharacteristic
302C22×C73C2×C4×Q811yescharacteristic
303C22×C73C4×#4111yescharacteristic
304C22×C73C4×#4111yescharacteristic
305C22×C73C4×#4111yescharacteristic
306C22×C73C4×#4111yescharacteristic
307C22×C73C4×#4111yescharacteristic
308C22×C73C4×#4111yescharacteristic
309C22×C73C2×#12111yescharacteristic
310C22×C73C2×C22⋊Q811yescharacteristic
311C22×C73#52511yescharacteristic
312C22×C73#52511yescharacteristic
313C22×C73C2×#12511yescharacteristic
314C22×C73#52911yescharacteristic
315C22×C73#52911yescharacteristic
316C22×C73#52911yescharacteristic
317C22×C73#52911yescharacteristic
318C22×C73C2×C4⋊Q811yescharacteristic
319C22×C73#53211yescharacteristic
320C22×C73#53211yescharacteristic
321C22×C73#53311yescharacteristic
322C22×C73#53311yescharacteristic
323C22×C73#53311yescharacteristic
324C22×C73#53311yescharacteristic
325C4×C73—28no—
326C4×C73—24no—
327C4×C73—24no—
328C4×C73—44no—
329C4×C73C4×C4⋊C418yescomplemented
330Dic73—24no—
331Dic73—24no—
332Dic73—24no—
333Dic73—44no—
334Dic73—44no—
335Dic73#38918yesdirect product factor
336C4×#389—731nomaximal, Sylow
337C2×C73C2×C4×C4⋊C411yescharacteristic
338C2×C73C42×D411yescharacteristic
339C2×C73C42×Q811yescharacteristic
340C2×C73C2×#38911yescharacteristic
341C2×C73#229311yescharacteristic
342C2×C73#229511yescharacteristic
343C2×C73#229611yescharacteristic
344C2×C73C4×#12111yescharacteristic
345C2×C73C4×#12111yescharacteristic
346C2×C73C4×C22⋊Q811yescharacteristic
347C2×C73C4×C22⋊Q811yescharacteristic
348C2×C73C4×#12511yescharacteristic
349C2×C73C4×#12511yescharacteristic
350C2×C73C4×C4⋊Q811yescharacteristic
351C2×C73C4×C4⋊Q811yescharacteristic
352C2×#389—731no—
353C2×#389D7311yescharacteristic
354C2×C4×C4⋊C4—731no—
355C2×C4×C4⋊C4—731no—
356C2×C4×C4⋊C4—732no—
357C2×C43—731no—
358#1436—732no—
359#1436—732no—
360C4⋊#95—731no—
361C4⋊#95—731no—
362C4×#95—732no—
363C73C4×#38911yescharacteristic, complemented, Sylow
364C22×C4⋊C4—731no—
365C22×C4⋊C4—731no—
366C22×C4⋊C4—732no—
367C22×C4⋊C4C2×D7311yescharacteristic
368C22×C4⋊C4C2×D7312yes—
369C22×C4⋊C4C2×D7311yescharacteristic
370C22×C42—731no—
371C22×C42—731no—
372C22×C42—732no—
373C22×C42—731no—
374C22×C42—731no—
375C22×C42—732no—
376C22×C42—731no—
377C22×C42—731no—
378C22×C42C2×D7311yescharacteristic
379#389—738no—
380#389Dic7318yesdirect product factor
381C4×C4⋊C4—738no—
382C4×C4⋊C4—1464no—
383C4×C4⋊C4—1468no—
384C2×#95—732no—
385C2×#95—732no—
386C2×#95—732no—
387C2×#95—732no—
388C2×#95—732no—
389C2×#95—732no—
390C2×#95—732no—
391C2×#95C2×D7312yes—
392C43—1464no—
393C23×C4—731no—
394C23×C4—731no—
395C23×C4—731no—
396C23×C4—731no—
397C23×C4—732no—
398C23×C4—732no—
399C23×C4C22×D7312yes—
400C23×C4C22×D7312yes—
401C23×C4C22×D7311yescharacteristic
402C23×C4C22×D7311yescharacteristic
403C23×C4C22×D7311yescharacteristic
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—734no—
409C2×C4⋊C4—738no—
410C2×C4⋊C4—734no—
411C2×C4⋊C4—1464no—
412C2×C4⋊C4—1464no—
413C2×C4⋊C4—1462no—
414C2×C4⋊C4—1462no—
415C2×C4⋊C4—1462no—
416C2×C4⋊C4—1462no—
417C2×C4⋊C4C4×D7314yes—
418C2×C4⋊C4C4×D7314yes—
419C2×C4⋊C4C2×Dic7314yes—
420C2×C4⋊C4C2×Dic7318yes—
421C2×C4⋊C4C2×Dic7314yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—734no—
425C2×C42—734no—
426C2×C42—734no—
427C2×C42—738no—
428C2×C42—734no—
429C2×C42—734no—
430C2×C42—734no—
431C2×C42—1464no—
432C2×C42—1464no—
433C2×C42—1464no—
434C2×C42—1462no—
435C2×C42—1462no—
436C2×C42—1462no—
437C2×C42—1462no—
438C2×C42—1464no—
439C2×C42—1464no—
440C2×C42—1462no—
441C2×C42—1462no—
442C2×C42—1462no—
443C2×C42—1462no—
444C2×C42—1462no—
445C2×C42—1462no—
446C2×C42—1462no—
447C2×C42—1462no—
448C2×C42C2×Dic7314yes—
449#95—738no—
450#95—738no—
451#95—1464no—
452#95—1464no—
453#95—1464no—
454#95—1464no—
455#95—1464no—
456#95C2×Dic7318yes—
457C24C23×D7311yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—732no—
477C22×C4—732no—
478C22×C4—732no—
479C22×C4—732no—
480C22×C4—732no—
481C22×C4—732no—
482C22×C4—732no—
483C22×C4—732no—
484C22×C4—732no—
485C22×C4—732no—
486C22×C4—732no—
487C22×C4—732no—
488C22×C4—732no—
489C22×C4—732no—
490C22×C4—732no—
491C22×C4—732no—
492C22×C4—734no—
493C22×C4—734no—
494C22×C4—1462no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4—1462no—
498C22×C4—1462no—
499C22×C4—1462no—
500C22×C4—1462no—
501C22×C4—1462no—
502C22×C4—1462no—
503C22×C4—1462no—
504C22×C4—1462no—
505C22×C4—1462no—
506C22×C4—1461no—
507C22×C4—1461no—
508C22×C4—1461no—
509C22×C4—1461no—
510C22×C4—1461no—
511C22×C4—1461no—
512C22×C4—1461no—
513C22×C4—1461no—
514C22×C4—1461no—
515C22×C4—1461no—
516C22×C4—1461no—
517C22×C4—1461no—
518C22×C4C2×C4×D7314yes—
519C22×C4C2×C4×D7314yes—
520C22×C4C2×C4×D7312yes—
521C22×C4C2×C4×D7312yes—
522C22×C4C22×Dic7314yes—
523C22×C4C22×Dic7314yes—
524C22×C4C22×Dic7312yes—
525C22×C4C22×Dic7312yes—
526C22×C4C22×Dic7312yes—
527C22×C4D4×D7312yes—
528C22×C4D4×D7312yes—
529C22×C4Q8×D7312yes—
530C22×C4Q8×D7312yes—
531C22×C4#1192402712yes—
532C22×C4#1192402712yes—
533C22×C4#1192402912yes—
534C22×C4#1192402912yes—
535C4⋊C4—216no—
536C4⋊C4—28no—
537C4⋊C4—14616no—
538C4⋊C4—1468no—
539C4⋊C4—1468no—
540C4⋊C4C4×Dic73116yescomplemented
541C42—28no—
542C42—2928no—
543C42—7316no—
544C42—14616no—
545C42—1468no—
546C42—1468no—
547C42—1468no—
548C42—1468no—
549C42—1468no—
550C23C22×C4×D7311yescharacteristic
551C23C22×C4×D7311yescharacteristic
552C23C23×Dic7311yescharacteristic
553C23C2×D4×D7311yescharacteristic
554C23C2×D4×D7311yescharacteristic
555C23C2×Q8×D7311yescharacteristic
556C23C2×Q8×D7311yescharacteristic
557C23#41×D7311yescharacteristic
558C23#41×D7311yescharacteristic
559C23#41×D7311yescharacteristic
560C23#41×D7311yescharacteristic
561C23C2×#1192402711yescharacteristic
562C23C2×#1192402711yescharacteristic
563C23C2×#1192402911yescharacteristic
564C23C2×#1192402911yescharacteristic
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—2922no—
591C2×C4—2922no—
592C2×C4—2922no—
593C2×C4—2922no—
594C2×C4—2922no—
595C2×C4—2922no—
596C2×C4—2922no—
597C2×C4—2922no—
598C2×C4—734no—
599C2×C4—734no—
600C2×C4—734no—
601C2×C4—734no—
602C2×C4—734no—
603C2×C4—734no—
604C2×C4—734no—
605C2×C4—734no—
606C2×C4—734no—
607C2×C4—734no—
608C2×C4—1464no—
609C2×C4—1464no—
610C2×C4—1464no—
611C2×C4—1464no—
612C2×C4—1464no—
613C2×C4—1464no—
614C2×C4—1462no—
615C2×C4—1462no—
616C2×C4—1462no—
617C2×C4—1462no—
618C2×C4—1462no—
619C2×C4—1462no—
620C2×C4—1462no—
621C2×C4—1462no—
622C2×C4—1462no—
623C2×C4—1462no—
624C2×C4—1462no—
625C2×C4—1462no—
626C2×C4—1462no—
627C2×C4—1462no—
628C2×C4—1462no—
629C2×C4—1462no—
630C2×C4—1462no—
631C2×C4—1462no—
632C2×C4C2×C4×Dic7318yes—
633C2×C4C2×C4×Dic7314yes—
634C2×C4C4⋊C4×D7314yes—
635C2×C4#1455654914yes—
636C2×C4#1455655314yes—
637C2×C4D4×Dic7314yes—
638C2×C4D4×Dic7314yes—
639C2×C4#1455655614yes—
640C2×C4Q8×Dic7314yes—
641C2×C4Q8×Dic7314yes—
642C22C22×C4×Dic7311yescharacteristic
643C22C2×C4⋊C4×D7311yescharacteristic
644C22C2×#1455654911yescharacteristic
645C22C4×D4×D7311yescharacteristic
646C22C4×D4×D7311yescharacteristic
647C22C2×#1455655311yescharacteristic
648C22C2×D4×Dic7311yescharacteristic
649C22C2×D4×Dic7311yescharacteristic
650C22C4×Q8×D7311yescharacteristic
651C22C4×Q8×D7311yescharacteristic
652C22C2×#1455655611yescharacteristic
653C22C2×Q8×Dic7311yescharacteristic
654C22C2×Q8×Dic7311yescharacteristic
655C22C4×#1192402711yescharacteristic
656C22C4×#1192402711yescharacteristic
657C22C4×#1192402911yescharacteristic
658C22C4×#1192402911yescharacteristic
659C22#41×Dic7311yescharacteristic
660C22#41×Dic7311yescharacteristic
661C22#121×D7311yescharacteristic
662C22C22⋊Q8×D7311yescharacteristic
663C22#1798909711yescharacteristic
664C22#1798910011yescharacteristic
665C22#125×D7311yescharacteristic
666C22#1798911811yescharacteristic
667C22#1798912211yescharacteristic
668C22#1798912211yescharacteristic
669C22#1798912311yescharacteristic
670C22C4⋊Q8×D7311yescharacteristic
671C22#1798913211yescharacteristic
672C22#1798913811yescharacteristic
673C22#1798913911yescharacteristic
674C22#1798914211yescharacteristic
675C22#1798914211yescharacteristic
676C22#1798914311yescharacteristic
677C4—28no—
678C4—24no—
679C4—24no—
680C4—44no—
681C4—2924no—
682C4—2924no—
683C4—738no—
684C4—1464no—
685C4—1464no—
686C4—1464no—
687C4C4⋊C4×Dic7318yescomplemented
688C2C2×C4⋊C4×Dic7311yescharacteristic
689C2C4×D4×Dic7311yescharacteristic
690C2C4×Q8×Dic7311yescharacteristic
691C2#389×D7311yescharacteristic
692C2#2261238911yescharacteristic
693C2#2261240211yescharacteristic
694C2#2261241211yescharacteristic
695C2#2261243911yescharacteristic
696C2#121×Dic7311yescharacteristic
697C2#2261246111yescharacteristic
698C2C22⋊Q8×Dic7311yescharacteristic
699C2#2261249011yescharacteristic
700C2#125×Dic7311yescharacteristic
701C2#2261250211yescharacteristic
702C2C4⋊Q8×Dic7311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC2×#389×C73C2
socle, prime radical, cosocleC24×C73C24
hypercenterC2×#389D73
hypocenterC73C4×#389
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
23. #17988486C4semidirect
26. C4⋊C4×Dic73C4semidirect
39. #389×C73C4semidirect
157. C4×Dic73C4⋊C4semidirect
196. C4⋊C4×C73C42semidirect
329. C4×C73C4×C4⋊C4semidirect
335. Dic73#389direct (N × H)
363. C73C4×#389semidirect
380. #389Dic73direct (N × H)
540. C4⋊C4C4×Dic73semidirect
687. C4C4⋊C4×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884862
C2×C4⋊C4×Dic732
C2×C42×Dic732
#226081652
#226081632
#226081612
#226081602
#95×Dic732
C2×#389×C732
C4×#38973