Finite Group Databasebeta

← #33009796

Subgroups — #33009796

Order 18688.

1838 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
1C22×#14556590C211yesmaximal, characteristic
2C2×#17988491C212yesmaximal
3C2×#17988485C211yesmaximal, characteristic
4C2×C4⋊C4×Dic73C211yesmaximal, characteristic
5#22608201C212yesmaximal
6#22608182C212yesmaximal
7#22608162C212yesmaximal
8#22608160C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10C4×#14556498C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C23×Dic146C2212yes—
13C2×#14556590—24no—
14C2×#14556590—24no—
15C2×#14556590C418yescomplemented
16C22×C4⋊Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×#11924007C2212yes—
19C22×#11924007C2212yes—
20C22×C4×Dic73C2212yes—
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23#17988491—28no—
24#17988485—24no—
25C4⋊C4×Dic73—24no—
26C2×#14556498C2211yescharacteristic
27C2×#14556498C2211yescharacteristic
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C4⋊C4×C73C2211yescharacteristic
38C22×C42×C73C2211yescharacteristic
39C2×#95×C73C2212yes—
40C2×#95×C73C2212yes—
41C22×Dic146—24no—
42C22×Dic146—24no—
43C22×Dic146—24no—
44C22×Dic146—24no—
45C22×Dic146—42no—
46C22×Dic146—42no—
47C22×Dic146C2×C418yes—
48C23×Dic73C2312yes—
49C23×Dic73C2311yescharacteristic
50C23×Dic73C2312yes—
51C23×Dic73C2311yescharacteristic
52C23×Dic73C2311yescharacteristic
53C23×Dic73C2311yescharacteristic
54#14556590—232no—
55C2×C4⋊Dic73—22no—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73—22no—
58C2×C4⋊Dic73C2×C414yes—
59C2×C4⋊Dic73D414yes—
60C2×C4⋊Dic73D414yes—
61C2×#11924007—24no—
62C2×#11924007—24no—
63C2×#11924007—24no—
64C2×#11924007—24no—
65C2×#11924007—42no—
66C2×#11924007C2×C418yes—
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×Dic73—42no—
74C2×C4×Dic73C2×C414yes—
75C2×C4×Dic73Q814yescomplemented
76#14556498—24no—
77#14556498—24no—
78#14556498—24no—
79#14556498—24no—
80#14556498—22no—
81#14556498—22no—
82#14556498—24no—
83#14556498—42no—
84#14556498D414yes—
85#14556498Q814yescomplemented
86C23×C4×C73C2312yes—
87C23×C4×C73C2311yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2312yes—
90C23×C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73C2×C414yes—
96C2×C4⋊C4×C73Q814yescomplemented
97C2×C42×C73—22no—
98C2×C42×C73—22no—
99C2×C42×C73—22no—
100#95×C73—24no—
101#95×C73—42no—
102C2×Dic146—216no—
103C2×Dic146—216no—
104C2×Dic146—48no—
105C2×Dic146—48no—
106C2×Dic146—48no—
107C2×Dic146—48no—
108C2×Dic146—48no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—21no—
112C22×Dic73—22no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—22no—
117C22×Dic73—21no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—22no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73C22×C414yes—
139C22×Dic73C22×C412yes—
140C22×Dic73C22×C412yes—
141C22×Dic73C2×D414yes—
142C22×Dic73C2×D414yes—
143C22×Dic73C2×D412yes—
144C22×Dic73C2×D412yes—
145C22×Dic73C2×Q812yes—
146C22×Dic73C2×Q812yes—
147C22×Dic73C2×Q812yes—
148C22×Dic73C2×Q812yes—
149C22×Dic73#4112yes—
150C22×Dic73#4112yes—
151C4⋊Dic73—44no—
152C4⋊Dic73C22⋊C4116yes—
153#11924007—216no—
154#11924007—48no—
155C4×Dic73—28no—
156C4×Dic73—28no—
157C4×Dic73—48no—
158C24×C73C2411yescharacteristic
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—22no—
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—21no—
172C22×C4×C73—21no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—21no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—21no—
180C22×C4×C73—22no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73C22×C414yes—
184C22×C4×C73C22×C412yes—
185C22×C4×C73C2×D412yes—
186C22×C4×C73C2×D412yes—
187C22×C4×C73C2×D412yes—
188C22×C4×C73C2×Q812yes—
189C22×C4×C73C2×Q812yes—
190C22×C4×C73C2×Q814yes—
191C22×C4×C73C2×Q812yes—
192C22×C4×C73#4112yes—
193C22×C4×C73#4112yes—
194C4⋊C4×C73—28no—
195C4⋊C4×C73—28no—
196C42×C73—44no—
197C23×C73C23×C411yescharacteristic
198C23×C73C22×D411yescharacteristic
199C23×C73C22×D411yescharacteristic
200C23×C73C22×D411yescharacteristic
201C23×C73C22×Q811yescharacteristic
202C23×C73C22×Q811yescharacteristic
203C23×C73C22×Q811yescharacteristic
204C23×C73C2×#4111yescharacteristic
205C23×C73C2×#4111yescharacteristic
206C23×C73C2×#4111yescharacteristic
207C23×C73C2×#4111yescharacteristic
208C23×C73H(5,𝔽2)11yescharacteristic
209C23×C73H(5,𝔽2)11yescharacteristic
210C23×C732−1+411yescharacteristic
211C23×C732−1+411yescharacteristic
212C2×C4×C73—24no—
213C2×C4×C73—24no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—24no—
222C2×C4×C73—22no—
223C2×C4×C73—24no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—42no—
231C2×C4×C73—42no—
232C2×C4×C73—42no—
233C2×C4×C73—41no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73—42no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73C2×C22⋊C414yes—
241C2×C4×C73C4×Q814yes—
242C2×C4×C73C4×Q814yes—
243C2×C4×C73C22⋊Q814yes—
244C2×C4×C73C22⋊Q814yes—
245C2×C4×C73#12414yes—
246C2×C4×C73C4⋊Q814yes—
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—24no—
250C2×Dic73—24no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—22no—
254C2×Dic73—22no—
255C2×Dic73—22no—
256C2×Dic73—24no—
257C2×Dic73—24no—
258C2×Dic73—22no—
259C2×Dic73—22no—
260C2×Dic73—24no—
261C2×Dic73—24no—
262C2×Dic73—22no—
263C2×Dic73—22no—
264C2×Dic73—22no—
265C2×Dic73—22no—
266C2×Dic73—22no—
267C2×Dic73—22no—
268C2×Dic73—22no—
269C2×Dic73—22no—
270C2×Dic73—22no—
271C2×Dic73—22no—
272C2×Dic73—22no—
273C2×Dic73—22no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—42no—
279C2×Dic73—42no—
280C2×Dic73—42no—
281C2×Dic73—42no—
282C2×Dic73—42no—
283C2×Dic73—42no—
284C2×Dic73—42no—
285C2×Dic73C2×C22⋊C418yes—
286C2×Dic73C4×D414yes—
287C2×Dic73C4×Q814yes—
288C2×Dic73C4⋊Q814yescomplemented
289Dic146—432no—
290C22×C73C22×C22⋊C411yescharacteristic
291C22×C73C2×C4×D411yescharacteristic
292C22×C73C2×C4×Q811yescharacteristic
293C22×C73C2×C4×Q811yescharacteristic
294C22×C73C2×C4×Q811yescharacteristic
295C22×C73#51811yescharacteristic
296C22×C73#51911yescharacteristic
297C22×C73C2×C22⋊Q811yescharacteristic
298C22×C73C2×C22⋊Q811yescharacteristic
299C22×C73C2×#12411yescharacteristic
300C22×C73C2×C4⋊Q811yescharacteristic
301C22×C73C2×C4⋊Q811yescharacteristic
302C22×C73#53211yescharacteristic
303C22×C73#53311yescharacteristic
304C22×C73#53311yescharacteristic
305C22×C73#54211yescharacteristic
306C22×C73#54211yescharacteristic
307C22×C73#54411yescharacteristic
308C22×C73#54411yescharacteristic
309C22×C73D4211yescharacteristic
310C22×C73D4211yescharacteristic
311C22×C73#54611yescharacteristic
312C22×C73#54611yescharacteristic
313C22×C73#54711yescharacteristic
314C22×C73#54811yescharacteristic
315C22×C73#54811yescharacteristic
316C22×C73D4×Q811yescharacteristic
317C22×C73D4×Q811yescharacteristic
318C22×C73D4×Q811yescharacteristic
319C22×C73#55411yescharacteristic
320C22×C73#55411yescharacteristic
321C22×C73#55511yescharacteristic
322C22×C73#55611yescharacteristic
323C22×C73#55711yescharacteristic
324C22×C73Q8211yescharacteristic
325C4×C73—44no—
326C4×C73—44no—
327C4×C73—42no—
328C4×C73—42no—
329C4×C73#39118yescomplemented
330Dic73—24no—
331Dic73—28no—
332Dic73—24no—
333Dic73—24no—
334Dic73—42no—
335Dic73—82no—
336#14053—731nomaximal, Sylow
337C2×C73C2×#39111yescharacteristic
338C2×C73C4×C4⋊Q811yescharacteristic
339C2×C73#233111yescharacteristic
340C2×C73D4×C22⋊C411yescharacteristic
341C2×C73Q8×C22⋊C411yescharacteristic
342C2×C73#236511yescharacteristic
343C2×C73#236911yescharacteristic
344C2×C73#243911yescharacteristic
345C2×C73#244011yescharacteristic
346C2×C73#245111yescharacteristic
347C2×C73#245211yescharacteristic
348C2×C73#249111yescharacteristic
349C2×C73#249211yescharacteristic
350C2×C73#255011yescharacteristic
351C2×C73#255111yescharacteristic
352C22×C4⋊Q8—731no—
353C2×#391—732no—
354C2×#389—731no—
355C2×C4×C4⋊C4—731no—
356#1446—732no—
357#1441—732no—
358#1436—732no—
359C4⋊#95—731no—
360C4⋊#95—731no—
361C4⋊#95D7311yescharacteristic
362C4×#95—731no—
363C73#1405311yescharacteristic, complemented, Sylow
364C23×Q8—732no—
365C2×C4⋊Q8—738no—
366C2×C4⋊Q8—1464no—
367C2×C4⋊Q8—1464no—
368C22×C4⋊C4—732no—
369C22×C4⋊C4—731no—
370C22×C4⋊C4—732no—
371C22×C4⋊C4—731no—
372C22×C4⋊C4C2×D7311yescharacteristic
373C22×C4⋊C4C2×D7311yescharacteristic
374C22×C42—732no—
375C22×C42—731no—
376C22×C42—731no—
377C22×C42C2×D7311yescharacteristic
378#391—1468no—
379#389—1464no—
380C4×C4⋊C4—1464no—
381C2×#95—732no—
382C2×#95—731no—
383C2×#95—731no—
384C2×#95—731no—
385C2×#95—731no—
386C2×#95—732no—
387C2×#95—732no—
388C2×#95—732no—
389C2×#95—732no—
390C2×#95—732no—
391C2×#95C2×D7312yes—
392C2×#95C2×D7312yes—
393C22×Q8—2922no—
394C22×Q8—2922no—
395C22×Q8—738no—
396C22×Q8—1464no—
397C22×Q8—1464no—
398C22×Q8—1464no—
399C22×Q8—1464no—
400C23×C4—732no—
401C23×C4—731no—
402C23×C4—731no—
403C23×C4—731no—
404C23×C4—731no—
405C23×C4—732no—
406C23×C4C22×D7312yes—
407C23×C4C22×D7311yescharacteristic
408C23×C4C22×D7311yescharacteristic
409C23×C4C22×D7312yes—
410C23×C4C22×D7311yescharacteristic
411C4⋊Q8—14632no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—2922no—
417C2×C4⋊C4—734no—
418C2×C4⋊C4—734no—
419C2×C4⋊C4—734no—
420C2×C4⋊C4—738no—
421C2×C4⋊C4—1464no—
422C2×C4⋊C4—1464no—
423C2×C4⋊C4—1462no—
424C2×C4⋊C4—1462no—
425C2×C4⋊C4—1462no—
426C2×C4⋊C4—1464no—
427C2×C4⋊C4—1464no—
428C2×C4⋊C4Dic14614yescomplemented
429C2×C4⋊C4C4×D7314yes—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—2922no—
434C2×C42—734no—
435C2×C42—734no—
436C2×C42—1464no—
437C2×C42—1464no—
438C2×C42—1462no—
439C2×C42—1462no—
440C2×C42—1462no—
441C2×C42—1462no—
442#95—24no—
443#95—42no—
444#95—2922no—
445#95—734no—
446#95—734no—
447#95—1464no—
448#95—1462no—
449#95—1462no—
450#95—1464no—
451#95—1464no—
452#95—1464no—
453#95—1464no—
454C24C23×D7311yescharacteristic
455C2×Q8—2928no—
456C2×Q8—2928no—
457C2×Q8—2928no—
458C2×Q8—2928no—
459C2×Q8—2928no—
460C2×Q8—14616no—
461C2×Q8—14616no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—732no—
487C22×C4—732no—
488C22×C4—734no—
489C22×C4—732no—
490C22×C4—732no—
491C22×C4—734no—
492C22×C4—734no—
493C22×C4—732no—
494C22×C4—732no—
495C22×C4—732no—
496C22×C4—732no—
497C22×C4—732no—
498C22×C4—732no—
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—1462no—
516C22×C4—1461no—
517C22×C4—1461no—
518C22×C4—1462no—
519C22×C4—1461no—
520C22×C4—1461no—
521C22×C4—1462no—
522C22×C4—1461no—
523C22×C4—1462no—
524C22×C4—1461no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4C2×C4×D7314yes—
529C22×C4C2×C4×D7312yes—
530C22×C4D4×D7312yes—
531C22×C4D4×D7312yes—
532C22×C4D4×D7312yes—
533C22×C4Q8×D7312yes—
534C22×C4Q8×D7312yes—
535C22×C4C2×Dic14614yes—
536C22×C4C2×Dic14612yes—
537C22×C4#1192402712yes—
538C22×C4#1192402812yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—2928no—
542C4⋊C4—2924no—
543C4⋊C4—7316no—
544C4⋊C4—14616no—
545C42—44no—
546C42—2928no—
547C42—1468no—
548C42—1468no—
549C23C22×C4×D7311yescharacteristic
550C23C2×D4×D7311yescharacteristic
551C23C2×D4×D7311yescharacteristic
552C23C2×D4×D7311yescharacteristic
553C23C2×Q8×D7311yescharacteristic
554C23C2×Q8×D7311yescharacteristic
555C23C22×Dic14611yescharacteristic
556C23#41×D7311yescharacteristic
557C23#41×D7311yescharacteristic
558C23C2×#1192402711yescharacteristic
559C23C2×#1192402811yescharacteristic
560C23#1455663611yescharacteristic
561C23#1455663711yescharacteristic
562C23#1455663811yescharacteristic
563C23#1455663911yescharacteristic
564Q8—29232no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—2921no—
594C2×C4—2921no—
595C2×C4—2921no—
596C2×C4—2921no—
597C2×C4—2922no—
598C2×C4—2922no—
599C2×C4—2922no—
600C2×C4—2922no—
601C2×C4—2922no—
602C2×C4—2922no—
603C2×C4—2922no—
604C2×C4—734no—
605C2×C4—738no—
606C2×C4—734no—
607C2×C4—734no—
608C2×C4—1462no—
609C2×C4—1462no—
610C2×C4—1462no—
611C2×C4—1462no—
612C2×C4—1464no—
613C2×C4—1462no—
614C2×C4—1462no—
615C2×C4—1464no—
616C2×C4—1462no—
617C2×C4—1462no—
618C2×C4—1464no—
619C2×C4—1462no—
620C2×C4—1464no—
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—1464no—
631C2×C4—1462no—
632C2×C4—1464no—
633C2×C4—1462no—
634C2×C4—1462no—
635C2×C4C22⋊C4×D7314yes—
636C2×C4#1455655614yes—
637C2×C4C4×Dic14614yes—
638C2×C4#1455656814yes—
639C2×C4#1455656914yes—
640C2×C4#1455657714yes—
641C2×C4#1455659014yes—
642C22C2×C22⋊C4×D7311yescharacteristic
643C22C4×D4×D7311yescharacteristic
644C22C4×Q8×D7311yescharacteristic
645C22C2×#1455655611yescharacteristic
646C22C2×C4×Dic14611yescharacteristic
647C22#1798905911yescharacteristic
648C22#1798906311yescharacteristic
649C22C2×#1455656811yescharacteristic
650C22C2×#1455656911yescharacteristic
651C22C2×#1455657711yescharacteristic
652C22C4⋊Q8×D7311yescharacteristic
653C22C2×#1455659011yescharacteristic
654C22#1798913211yescharacteristic
655C22#1798913911yescharacteristic
656C22#1798914311yescharacteristic
657C22#1798920411yescharacteristic
658C22#1798921011yescharacteristic
659C22#1798921411yescharacteristic
660C22#1798921711yescharacteristic
661C22#1798922111yescharacteristic
662C22#1798922211yescharacteristic
663C22#1798923011yescharacteristic
664C22#1798923411yescharacteristic
665C22#1798923811yescharacteristic
666C22#1798924511yescharacteristic
667C22#1798924711yescharacteristic
668C22#1798925011yescharacteristic
669C22#1798925211yescharacteristic
670C22D4×Dic14611yescharacteristic
671C22#1798929211yescharacteristic
672C22#1798929611yescharacteristic
673C22#1798930011yescharacteristic
674C22#1798930511yescharacteristic
675C22#1798931311yescharacteristic
676C22Q8×Dic14611yescharacteristic
677C4—44no—
678C4—42no—
679C4—44no—
680C4—42no—
681C4—2922no—
682C4—5842no—
683C4—1464no—
684C4—1468no—
685C4—1464no—
686C4—1464no—
687C4#1798849118yescomplemented
688C2C2×#1798849111yescharacteristic
689C2#2261250211yescharacteristic
690C2#2261267811yescharacteristic
691C2#2261275211yescharacteristic
692C2#2261276511yescharacteristic
693C2#2261299011yescharacteristic
694C2#2261301811yescharacteristic
695C2#2261362511yescharacteristic
696C2#2261363611yescharacteristic
697C2#2261377311yescharacteristic
698C2#2261378411yescharacteristic
699C2#2261429011yescharacteristic
700C2#2261430111yescharacteristic
701C2#2261495511yescharacteristic
702C2#2261495911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×C4⋊#95C2
socle, prime radical, cosocleC24×C73C24
hypercenterC4⋊#95D73
hypocenterC73#14053
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×#14556590C4semidirect
75. C2×C4×Dic73Q8semidirect
85. #14556498Q8semidirect
96. C2×C4⋊C4×C73Q8semidirect
288. C2×Dic73C4⋊Q8semidirect
329. C4×C73#391semidirect
363. C73#14053semidirect
428. C2×C4⋊C4Dic146semidirect
687. C4#17988491semidirect

Maximal subgroups

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

subgroupindex
C22×#145565902
C2×#179884912
C2×#179884852
C2×C4⋊C4×Dic732
#226082012
#226081822
#226081622
#226081602
C4×#145564982
C73×C4⋊#952
#1405373