Finite Group Databasebeta

← #33009372

Subgroups — #33009372

Order 18688.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic73C211yesmaximal, characteristic
2C2×#17988494C211yesmaximal, characteristic
3C2×#17988486C211yesmaximal, characteristic
4C2×C4×C4⋊Dic73C211yesmaximal, characteristic
5#22608196C212yesmaximal
6#22608188C212yesmaximal
7#22608165C212yesmaximal
8#22608165C212yesmaximal
9#22608161C211yesmaximal, characteristic
10#22608160C211yesmaximal, characteristic
11C2×#391×C73C211yesmaximal, characteristic
12C2×Q8×Dic73—24no—
13C2×Q8×Dic73—24no—
14C2×Q8×Dic73—24no—
15C22×C4⋊Dic73C2211yescharacteristic
16C22×C4⋊Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2212yes—
18C22×C4⋊Dic73C2212yes—
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4×Dic73C2212yes—
22C22×C4×Dic73C2211yescharacteristic
23C22×C4×Dic73C2211yescharacteristic
24#17988494—24no—
25#17988486—24no—
26C4×C4⋊Dic73—24no—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C23×Q8×C73C2211yescharacteristic
37C22×C4⋊C4×C73C2211yescharacteristic
38C22×C42×C73C2211yescharacteristic
39#391×C73C418yescomplemented
40C2×#95×C73C2212yes—
41C2×#95×C73C2212yes—
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C23×Dic73C2311yescharacteristic
48Q8×Dic73—232no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—24no—
52C2×C4⋊Dic73—24no—
53C2×C4⋊Dic73—22no—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73—24no—
56C2×C4⋊Dic73—24no—
57C2×C4⋊Dic73—22no—
58C2×C4⋊Dic73—24no—
59C2×C4⋊Dic73—22no—
60C2×C4⋊Dic73—22no—
61C2×C4⋊Dic73—22no—
62C2×C4⋊Dic73—22no—
63C2×C4⋊Dic73—22no—
64C2×C4⋊Dic73—42no—
65C2×C4⋊Dic73D414yes—
66C2×C4⋊Dic73Q814yescomplemented
67C2×C4×Dic73—24no—
68C2×C4×Dic73—24no—
69C2×C4×Dic73—22no—
70C2×C4×Dic73—24no—
71C2×C4×Dic73—22no—
72C2×C4×Dic73—22no—
73C2×C4×Dic73—22no—
74C2×C4×Dic73—22no—
75C2×C4×Dic73D414yes—
76#14556498—22no—
77#14556498—22no—
78#14556498—24no—
79#14556498—24no—
80#14556498—24no—
81#14556498—24no—
82#14556498—24no—
83#14556498—42no—
84#14556498—42no—
85C22×Q8×C73—22no—
86C22×Q8×C73—22no—
87C22×Q8×C73—22no—
88C22×Q8×C73—22no—
89C22×Q8×C73C2×C414yes—
90C22×Q8×C73D414yes—
91C22×Q8×C73Q814yes—
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2312yes—
94C23×C4×C73C2312yes—
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73—22no—
99C2×C4⋊C4×C73C2×C414yes—
100C2×C42×C73—22no—
101C2×C42×C73—22no—
102C2×C42×C73C2×C414yes—
103#95×C73C2×C418yes—
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—22no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—22no—
118C22×Dic73—21no—
119C22×Dic73—22no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—22no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—22no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—22no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73C2×D414yes—
141C22×Dic73C2×D412yes—
142C22×Dic73C2×D412yes—
143C22×Dic73C2×Q812yes—
144C22×Dic73C2×Q812yes—
145C22×Dic73#4112yes—
146C22×Dic73#4112yes—
147C4⋊Dic73—28no—
148C4⋊Dic73—216no—
149C4⋊Dic73—28no—
150C4⋊Dic73—28no—
151C4⋊Dic73—48no—
152C4⋊Dic73—44no—
153C4×Dic73—216no—
154C4×Dic73—28no—
155C4×Dic73—44no—
156C24×C73C2411yescharacteristic
157C2×Q8×C73—28no—
158C2×Q8×C73—28no—
159C2×Q8×C73—28no—
160C2×Q8×C73—28no—
161C2×Q8×C73—28no—
162C2×Q8×C73—28no—
163C2×Q8×C73C4⋊C4116yescomplemented
164C22×C4×C73—21no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73—21no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—22no—
174C22×C4×C73—21no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—21no—
179C22×C4×C73—22no—
180C22×C4×C73—21no—
181C22×C4×C73—22no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73C22×C412yes—
185C22×C4×C73C22×C414yes—
186C22×C4×C73C22×C414yes—
187C22×C4×C73C22×C412yes—
188C22×C4×C73C22×C412yes—
189C22×C4×C73C2×D412yes—
190C22×C4×C73C2×D412yes—
191C22×C4×C73C2×D414yes—
192C22×C4×C73C2×D412yes—
193C22×C4×C73C2×Q812yes—
194C22×C4×C73C2×Q814yes—
195C22×C4×C73C2×Q812yes—
196C22×C4×C73#4112yes—
197C22×C4×C73#4112yes—
198C22×C4×C73#4112yes—
199C4⋊C4×C73—28no—
200C42×C73—28no—
201C23×C73C23×C411yescharacteristic
202C23×C73C22×D411yescharacteristic
203C23×C73C22×D411yescharacteristic
204C23×C73C22×D411yescharacteristic
205C23×C73C22×Q811yescharacteristic
206C23×C73C22×Q811yescharacteristic
207C23×C73C2×#4111yescharacteristic
208C23×C73C2×#4111yescharacteristic
209C23×C73C2×#4111yescharacteristic
210C23×C73C2×#4111yescharacteristic
211C23×C73C2×#4111yescharacteristic
212C23×C73H(5,𝔽2)11yescharacteristic
213C23×C732−1+411yescharacteristic
214C23×C732−1+411yescharacteristic
215C23×C732−1+411yescharacteristic
216Q8×C73—232no—
217C2×C4×C73—22no—
218C2×C4×C73—24no—
219C2×C4×C73—24no—
220C2×C4×C73—22no—
221C2×C4×C73—24no—
222C2×C4×C73—24no—
223C2×C4×C73—24no—
224C2×C4×C73—22no—
225C2×C4×C73—24no—
226C2×C4×C73—22no—
227C2×C4×C73—22no—
228C2×C4×C73—22no—
229C2×C4×C73—22no—
230C2×C4×C73—24no—
231C2×C4×C73—24no—
232C2×C4×C73—22no—
233C2×C4×C73—22no—
234C2×C4×C73—24no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—42no—
240C2×C4×C73—42no—
241C2×C4×C73—42no—
242C2×C4×C73—42no—
243C2×C4×C73C2×C4⋊C418yes—
244C2×C4×C73C2×C4⋊C414yes—
245C2×C4×C73C4×D414yes—
246C2×C4×C73C4×D414yes—
247C2×C4×C73C4×Q814yescomplemented
248C2×C4×C73#12014yes—
249C2×C4×C73C22⋊Q814yes—
250C2×C4×C73C22⋊Q814yes—
251C2×C4×C73#12314yes—
252C2×Dic73—22no—
253C2×Dic73—22no—
254C2×Dic73—22no—
255C2×Dic73—22no—
256C2×Dic73—22no—
257C2×Dic73—22no—
258C2×Dic73—24no—
259C2×Dic73—22no—
260C2×Dic73—22no—
261C2×Dic73—22no—
262C2×Dic73—22no—
263C2×Dic73—22no—
264C2×Dic73—22no—
265C2×Dic73—24no—
266C2×Dic73—24no—
267C2×Dic73—22no—
268C2×Dic73—22no—
269C2×Dic73—22no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—42no—
273C2×Dic73—41no—
274C2×Dic73—41no—
275C2×Dic73—42no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—41no—
280C2×Dic73—41no—
281C2×Dic73—42no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—42no—
285C2×Dic73—41no—
286C2×Dic73—42no—
287C2×Dic73—42no—
288C2×Dic73—42no—
289C2×Dic73—42no—
290C2×Dic73—42no—
291C2×Dic73—42no—
292C2×Dic73—42no—
293C2×Dic73C22⋊Q814yes—
294C22×C73C22×C4⋊C411yescharacteristic
295C22×C73C2×C4×D411yescharacteristic
296C22×C73C2×C4×D411yescharacteristic
297C22×C73C2×C4×Q811yescharacteristic
298C22×C73C4×#4111yescharacteristic
299C22×C73#51911yescharacteristic
300C22×C73#52011yescharacteristic
301C22×C73C2×#12011yescharacteristic
302C22×C73C2×C22⋊Q811yescharacteristic
303C22×C73C2×C22⋊Q811yescharacteristic
304C22×C73C2×C22⋊Q811yescharacteristic
305C22×C73C2×#12311yescharacteristic
306C22×C73#52511yescharacteristic
307C22×C73#52911yescharacteristic
308C22×C73#53311yescharacteristic
309C22×C73#53611yescharacteristic
310C22×C73#53711yescharacteristic
311C22×C73#54111yescharacteristic
312C22×C73#54211yescharacteristic
313C22×C73#54611yescharacteristic
314C22×C73#54711yescharacteristic
315C22×C73#54811yescharacteristic
316C22×C73#54811yescharacteristic
317C22×C73#54811yescharacteristic
318C22×C73D4×Q811yescharacteristic
319C22×C73D4×Q811yescharacteristic
320C22×C73#55011yescharacteristic
321C22×C73#55611yescharacteristic
322C22×C73#55611yescharacteristic
323C22×C73#55711yescharacteristic
324C22×C73#55711yescharacteristic
325C22×C73#55711yescharacteristic
326C22×C73#55711yescharacteristic
327C22×C73Q8211yescharacteristic
328C22×C73#55911yescharacteristic
329C4×C73—28no—
330C4×C73—24no—
331C4×C73—42no—
332C4×C73—44no—
333C4×C73#38518yes—
334Dic73—24no—
335Dic73—42no—
336Dic73—44no—
337Dic73—42no—
338Dic73—42no—
339Dic73—82no—
340#14017—731nomaximal, Sylow
341C2×C73C2×#38511yescharacteristic
342C2×C73C4×C22⋊Q811yescharacteristic
343C2×C73#232311yescharacteristic
344C2×C73Q8×C4⋊C411yescharacteristic
345C2×C73#235111yescharacteristic
346C2×C73#236511yescharacteristic
347C2×C73#236711yescharacteristic
348C2×C73#240711yescharacteristic
349C2×C73#240911yescharacteristic
350C2×C73#244611yescharacteristic
351C2×C73#244811yescharacteristic
352C2×C73#245111yescharacteristic
353C2×C73#245311yescharacteristic
354C2×C73#258111yescharacteristic
355C2×C73#258211yescharacteristic
356C22×C4×Q8—731no—
357C2×#391—731no—
358C2×#391D7311yescharacteristic
359C2×#389—731no—
360C2×C4×C4⋊C4—731no—
361#1444—732no—
362#1442—732no—
363#1436—732no—
364#1436—732no—
365C4⋊#95—731no—
366C4⋊#95—731no—
367C73#1401711yescharacteristic, complemented, Sylow
368C23×Q8C2×D7311yescharacteristic
369C2×C4×Q8—1464no—
370C2×C4×Q8—1464no—
371C2×C4×Q8—1464no—
372C22×C4⋊C4—732no—
373C22×C4⋊C4—731no—
374C22×C4⋊C4—731no—
375C22×C4⋊C4—732no—
376C22×C4⋊C4—731no—
377C22×C4⋊C4—731no—
378C22×C4⋊C4C2×D7311yescharacteristic
379C22×C42—731no—
380C22×C42—732no—
381C22×C42—731no—
382C22×C42C2×D7311yescharacteristic
383#391—1464no—
384#391Dic7318yescomplemented
385#389—1464no—
386C4×C4⋊C4—1464no—
387C2×#95—732no—
388C2×#95—732no—
389C2×#95—732no—
390C2×#95—732no—
391C2×#95—731no—
392C2×#95—732no—
393C2×#95—732no—
394C2×#95—732no—
395C2×#95—731no—
396C2×#95C2×D7312yes—
397C2×#95C2×D7312yes—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8Dic14614yes—
403C22×Q8D29214yes—
404C22×Q8C2×Dic7314yes—
405C23×C4—731no—
406C23×C4—731no—
407C23×C4—732no—
408C23×C4—731no—
409C23×C4—731no—
410C23×C4—732no—
411C23×C4C22×D7312yes—
412C23×C4C22×D7311yescharacteristic
413C23×C4C22×D7312yes—
414C23×C4C22×D7311yescharacteristic
415C23×C4C22×D7311yescharacteristic
416C4×Q8—14632no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—2922no—
420C2×C4⋊C4—734no—
421C2×C4⋊C4—734no—
422C2×C4⋊C4—1464no—
423C2×C4⋊C4—1464no—
424C2×C4⋊C4—1462no—
425C2×C4⋊C4—1462no—
426C2×C4⋊C4—1462no—
427C2×C4⋊C4—1464no—
428C2×C4⋊C4—1464no—
429C2×C4⋊C4—1462no—
430C2×C4⋊C4—1462no—
431C2×C4⋊C4—1462no—
432C2×C4⋊C4—1462no—
433C2×C4⋊C4—1462no—
434C2×C4⋊C4—1464no—
435C2×C4⋊C4—1462no—
436C2×C4⋊C4—1462no—
437C2×C4⋊C4C2×Dic7314yes—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—734no—
441C2×C42—1462no—
442C2×C42—1462no—
443C2×C42—1462no—
444C2×C42—1464no—
445C2×C42—1464no—
446C2×C42—1462no—
447C2×C42—1464no—
448C2×C42—1462no—
449C2×C42C2×Dic7314yes—
450#95—2922no—
451#95—2922no—
452#95—1464no—
453#95—1462no—
454#95—1462no—
455#95—1464no—
456#95—1464no—
457#95—1464no—
458#95—1464no—
459#95C2×Dic7318yes—
460#95C2×Dic7318yes—
461C24C23×D7311yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8C4⋊Dic73116yescomplemented
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—732no—
490C22×C4—732no—
491C22×C4—732no—
492C22×C4—732no—
493C22×C4—734no—
494C22×C4—732no—
495C22×C4—732no—
496C22×C4—1462no—
497C22×C4—1462no—
498C22×C4—1462no—
499C22×C4—1462no—
500C22×C4—1462no—
501C22×C4—1462no—
502C22×C4—1462no—
503C22×C4—1461no—
504C22×C4—1461no—
505C22×C4—1461no—
506C22×C4—1462no—
507C22×C4—1461no—
508C22×C4—1461no—
509C22×C4—1461no—
510C22×C4—1461no—
511C22×C4—1462no—
512C22×C4—1461no—
513C22×C4—1461no—
514C22×C4—1461no—
515C22×C4—1462no—
516C22×C4—1462no—
517C22×C4—1461no—
518C22×C4—1461no—
519C22×C4—1461no—
520C22×C4—1462no—
521C22×C4—1461no—
522C22×C4—1461no—
523C22×C4—1461no—
524C22×C4—1461no—
525C22×C4—1462no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4C22×Dic7312yes—
532C22×C4C22×Dic7314yes—
533C22×C4C22×Dic7314yes—
534C22×C4C22×Dic7312yes—
535C22×C4C22×Dic7312yes—
536C22×C4D4×D7312yes—
537C22×C4D4×D7312yes—
538C22×C4C2×D29214yes—
539C22×C4C2×D29212yes—
540C22×C4Q8×D7312yes—
541C22×C4C2×Dic14614yes—
542C22×C4C2×Dic14612yes—
543C22×C4#1192402712yes—
544C22×C4#1192402712yes—
545C22×C4#1192402912yes—
546C4⋊C4—28no—
547C4⋊C4—2928no—
548C4⋊C4—2924no—
549C4⋊C4—1468no—
550C4⋊C4—1468no—
551C4⋊C4—14616no—
552C4⋊C4—1468no—
553C42—28no—
554C42—2924no—
555C42—14616no—
556C42—1468no—
557C23C23×Dic7311yescharacteristic
558C23C2×D4×D7311yescharacteristic
559C23C2×D4×D7311yescharacteristic
560C23C22×D29211yescharacteristic
561C23C2×Q8×D7311yescharacteristic
562C23C22×Dic14611yescharacteristic
563C23#41×D7311yescharacteristic
564C23#41×D7311yescharacteristic
565C23C2×#1192402711yescharacteristic
566C23C2×#1192402711yescharacteristic
567C23C2×#1192402911yescharacteristic
568C23#1455663711yescharacteristic
569C23#1455663811yescharacteristic
570C23#1455663911yescharacteristic
571C23#1455663911yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—2921no—
600C2×C4—2921no—
601C2×C4—2922no—
602C2×C4—2921no—
603C2×C4—2921no—
604C2×C4—2921no—
605C2×C4—2921no—
606C2×C4—2922no—
607C2×C4—2921no—
608C2×C4—2921no—
609C2×C4—2921no—
610C2×C4—2922no—
611C2×C4—2921no—
612C2×C4—2921no—
613C2×C4—2921no—
614C2×C4—2922no—
615C2×C4—2922no—
616C2×C4—2922no—
617C2×C4—2922no—
618C2×C4—2922no—
619C2×C4—2922no—
620C2×C4—2922no—
621C2×C4—2922no—
622C2×C4—734no—
623C2×C4—1462no—
624C2×C4—1462no—
625C2×C4—1464no—
626C2×C4—1464no—
627C2×C4—1462no—
628C2×C4—1462no—
629C2×C4—1462no—
630C2×C4—1464no—
631C2×C4—1462no—
632C2×C4—1462no—
633C2×C4—1462no—
634C2×C4—1462no—
635C2×C4—1462no—
636C2×C4—1462no—
637C2×C4—1462no—
638C2×C4—1462no—
639C2×C4—1462no—
640C2×C4—1462no—
641C2×C4C2×C4⋊Dic7318yes—
642C2×C4C2×C4⋊Dic7314yes—
643C2×C4D4×Dic7314yes—
644C2×C4D4×Dic7314yes—
645C2×C4Q8×Dic7314yescomplemented
646C2×C4#1455656114yes—
647C2×C4#1455656814yes—
648C2×C4#1455656814yes—
649C2×C4#1455657514yes—
650C22C22×C4⋊Dic7311yescharacteristic
651C22C2×D4×Dic7311yescharacteristic
652C22C2×D4×Dic7311yescharacteristic
653C22C2×Q8×Dic7311yescharacteristic
654C22#41×Dic7311yescharacteristic
655C22#1798906511yescharacteristic
656C22#1798907011yescharacteristic
657C22C2×#1455656111yescharacteristic
658C22C22⋊Q8×D7311yescharacteristic
659C22C2×#1455656811yescharacteristic
660C22C2×#1455656811yescharacteristic
661C22C2×#1455657511yescharacteristic
662C22#1798910011yescharacteristic
663C22#1798912311yescharacteristic
664C22#1798913911yescharacteristic
665C22#1798916011yescharacteristic
666C22#1798916711yescharacteristic
667C22#1798919711yescharacteristic
668C22#1798921011yescharacteristic
669C22#1798923011yescharacteristic
670C22#1798924011yescharacteristic
671C22#1798924511yescharacteristic
672C22#1798924911yescharacteristic
673C22#1798924911yescharacteristic
674C22#1798925211yescharacteristic
675C22Q8×D29211yescharacteristic
676C22#1798925911yescharacteristic
677C22#1798930611yescharacteristic
678C22#1798931111yescharacteristic
679C22#1798931211yescharacteristic
680C22#1798931311yescharacteristic
681C22#1798931311yescharacteristic
682C22#1798931611yescharacteristic
683C22Q8×Dic14611yescharacteristic
684C22#1798931911yescharacteristic
685C4—28no—
686C4—24no—
687C4—44no—
688C4—42no—
689C4—2922no—
690C4—2924no—
691C4—2922no—
692C4—2922no—
693C4—5842no—
694C4—1464no—
695C4#1798846218yes—
696C2C2×#1798846211yescharacteristic
697C2C22⋊Q8×Dic7311yescharacteristic
698C2#2261261511yescharacteristic
699C2Q8×C4⋊Dic7311yescharacteristic
700C2#2261285211yescharacteristic
701C2#2261299111yescharacteristic
702C2#2261300611yescharacteristic
703C2#2261327911yescharacteristic
704C2#2261329411yescharacteristic
705C2#2261370511yescharacteristic
706C2#2261372711yescharacteristic
707C2#2261377311yescharacteristic
708C2#2261379511yescharacteristic
709C2#2261529511yescharacteristic
710C2#2261530211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#391×C73C2
socle, prime radical, cosocleC24×C73C24
hypercenterC2×#391D73
hypocenterC73#14017
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
39. #391×C73C4semidirect
66. C2×C4⋊Dic73Q8semidirect
163. C2×Q8×C73C4⋊C4semidirect
247. C2×C4×C73C4×Q8semidirect
367. C73#14017semidirect
384. #391Dic73semidirect
468. C2×Q8C4⋊Dic73semidirect
645. C2×C4Q8×Dic73semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic732
C2×#179884942
C2×#179884862
C2×C4×C4⋊Dic732
#226081962
#226081882
#226081652
#226081612
#226081602
C2×#391×C732
#1401773