Finite Group Databasebeta

← #33009202

Subgroups — #33009202

Order 18688.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988485C211yesmaximal, characteristic
2C2×#17988483C211yesmaximal, characteristic
3C2×#17988483C211yesmaximal, characteristic
4C2×#17988482C212yesmaximal
5C2×C4⋊C4×Dic73C211yesmaximal, characteristic
6#22608194C212yesmaximal
7#22608181C212yesmaximal
8#22608163C212yesmaximal
9#22608160C211yesmaximal, characteristic
10C4×#14556498C211yesmaximal, characteristic
11C2×#384×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×#11924007C2212yes—
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×C4×Dic73C2211yescharacteristic
18C22×C4×Dic73C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20#17988485C418yescomplemented
21#17988483—24no—
22#17988483—24no—
23#17988482—28no—
24C4⋊C4×Dic73—24no—
25C2×#14556498C2211yescharacteristic
26C2×#14556498C2211yescharacteristic
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2212yes—
37C22×C4⋊C4×C73C2212yes—
38C22×C4⋊C4×C73C2211yescharacteristic
39C22×C42×C73C2211yescharacteristic
40#384×C73—24no—
41C23×Dic73C2312yes—
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2312yes—
46C23×Dic73C2311yescharacteristic
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73C2×C414yes—
50C2×C4⋊Dic73C2×C414yes—
51C2×C4⋊Dic73D414yes—
52C2×C4⋊Dic73Q814yes—
53C2×#11924007—24no—
54C2×#11924007—24no—
55C2×#11924007—24no—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×#11924007—42no—
60C2×#11924007—42no—
61C2×#11924007C2×C418yes—
62C2×C4×Dic73—24no—
63C2×C4×Dic73—24no—
64C2×C4×Dic73—22no—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—22no—
67C2×C4×Dic73—22no—
68C2×C4×Dic73—22no—
69C2×C4×Dic73—42no—
70C2×C4×Dic73Q814yes—
71#14556498—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—24no—
75#14556498—22no—
76#14556498—22no—
77#14556498—42no—
78#14556498C2×C418yes—
79#14556498D414yes—
80#14556498Q814yes—
81C23×C4×C73C2312yes—
82C23×C4×C73C2312yes—
83C23×C4×C73C2311yescharacteristic
84C23×C4×C73C2311yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—24no—
89C2×C4⋊C4×C73—24no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—24no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—24no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—42no—
96C2×C4⋊C4×C73—42no—
97C2×C4⋊C4×C73D414yes—
98C2×C42×C73—22no—
99C2×C42×C73—22no—
100C2×C42×C73C2×C414yes—
101C22×Dic73—21no—
102C22×Dic73—22no—
103C22×Dic73—21no—
104C22×Dic73—22no—
105C22×Dic73—21no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—21no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—21no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—21no—
126C22×Dic73—22no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—22no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73C22×C414yes—
134C22×Dic73C22×C414yes—
135C22×Dic73C2×D412yes—
136C22×Dic73C2×D414yes—
137C22×Dic73C2×D412yes—
138C22×Dic73C2×Q812yes—
139C22×Dic73C2×Q812yes—
140C22×Dic73C2×Q814yes—
141C22×Dic73C2×Q812yes—
142C22×Dic73C2×Q812yes—
143C4⋊Dic73—28no—
144C4⋊Dic73C4⋊C4116yescomplemented
145#11924007—216no—
146#11924007—48no—
147#11924007—48no—
148C4×Dic73—28no—
149C4×Dic73—48no—
150C4×Dic73—44no—
151C24×C73C2411yescharacteristic
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73—22no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73—22no—
173C22×C4×C73C22×C412yes—
174C22×C4×C73C22×C412yes—
175C22×C4×C73C22×C412yes—
176C22×C4×C73C2×D412yes—
177C22×C4×C73C2×D412yes—
178C22×C4×C73C2×D414yes—
179C22×C4×C73C2×D412yes—
180C22×C4×C73C2×Q812yes—
181C22×C4×C73C2×Q812yes—
182C22×C4×C73C2×Q812yes—
183C22×C4×C73#4112yes—
184C22×C4×C73#4112yes—
185C22×C4×C73#4112yes—
186C22×C4×C73#4112yes—
187C4⋊C4×C73—28no—
188C4⋊C4×C73—48no—
189C4⋊C4×C73—48no—
190C4⋊C4×C73—44no—
191C42×C73—28no—
192C23×C73C23×C411yescharacteristic
193C23×C73C22×D411yescharacteristic
194C23×C73C22×D411yescharacteristic
195C23×C73C22×D411yescharacteristic
196C23×C73C22×Q811yescharacteristic
197C23×C73C22×Q811yescharacteristic
198C23×C73C22×Q811yescharacteristic
199C23×C73C2×#4111yescharacteristic
200C23×C73C2×#4111yescharacteristic
201C23×C73C2×#4111yescharacteristic
202C23×C73C2×#4111yescharacteristic
203C23×C73H(5,𝔽2)11yescharacteristic
204C23×C73H(5,𝔽2)11yescharacteristic
205C23×C732−1+411yescharacteristic
206C23×C732−1+411yescharacteristic
207C2×C4×C73—22no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—24no—
220C2×C4×C73—24no—
221C2×C4×C73—24no—
222C2×C4×C73—42no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73—42no—
229C2×C4×C73—42no—
230C2×C4×C73—42no—
231C2×C4×C73—42no—
232C2×C4×C73—42no—
233C2×C4×C73C2×C4⋊C414yes—
234C2×C4×C73C4×D414yes—
235C2×C4×C73C4×D414yes—
236C2×C4×C73C4×Q814yes—
237C2×C4×C73C4×Q814yes—
238C2×C4×C73#12114yes—
239C2×C4×C73C22⋊Q814yes—
240C2×C4×C73#12514yes—
241C2×C4×C73C4⋊Q814yes—
242C2×Dic73—24no—
243C2×Dic73—24no—
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—24no—
248C2×Dic73—22no—
249C2×Dic73—24no—
250C2×Dic73—24no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—24no—
254C2×Dic73—24no—
255C2×Dic73—24no—
256C2×Dic73—24no—
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—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73—41no—
270C2×Dic73—42no—
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—42no—
281C2×Dic73—41no—
282C2×Dic73C2×C4⋊C418yes—
283C2×Dic73C4⋊Q814yes—
284C22×C73C22×C4⋊C411yescharacteristic
285C22×C73C2×C4×D411yescharacteristic
286C22×C73C2×C4×D411yescharacteristic
287C22×C73C2×C4×Q811yescharacteristic
288C22×C73C2×C4×Q811yescharacteristic
289C22×C73#52011yescharacteristic
290C22×C73#52011yescharacteristic
291C22×C73C2×#12111yescharacteristic
292C22×C73C2×C22⋊Q811yescharacteristic
293C22×C73C2×#12511yescharacteristic
294C22×C73C2×C4⋊Q811yescharacteristic
295C22×C73C2×C4⋊Q811yescharacteristic
296C22×C73#53211yescharacteristic
297C22×C73#53311yescharacteristic
298C22×C73#53311yescharacteristic
299C22×C73#54011yescharacteristic
300C22×C73#54111yescharacteristic
301C22×C73#54411yescharacteristic
302C22×C73#54411yescharacteristic
303C22×C73D4211yescharacteristic
304C22×C73D4211yescharacteristic
305C22×C73#54611yescharacteristic
306C22×C73#54711yescharacteristic
307C22×C73#54711yescharacteristic
308C22×C73#54811yescharacteristic
309C22×C73D4×Q811yescharacteristic
310C22×C73D4×Q811yescharacteristic
311C22×C73D4×Q811yescharacteristic
312C22×C73#55011yescharacteristic
313C22×C73#55211yescharacteristic
314C22×C73#55311yescharacteristic
315C22×C73#55411yescharacteristic
316C22×C73#55411yescharacteristic
317C22×C73#55711yescharacteristic
318C22×C73Q8211yescharacteristic
319C4×C73—24no—
320C4×C73—24no—
321C4×C73—44no—
322C4×C73—82no—
323C4×C73#38918yescomplemented
324Dic73—28no—
325Dic73—24no—
326Dic73—44no—
327Dic73—42no—
328Dic73—42no—
329Dic73—42no—
330#14005—731nomaximal, Sylow
331C2×C73C2×#38911yescharacteristic
332C2×C73C4×C4⋊Q811yescharacteristic
333C2×C73#233011yescharacteristic
334C2×C73D4×C4⋊C411yescharacteristic
335C2×C73Q8×C4⋊C411yescharacteristic
336C2×C73#236011yescharacteristic
337C2×C73#236111yescharacteristic
338C2×C73#242811yescharacteristic
339C2×C73#242911yescharacteristic
340C2×C73#244011yescharacteristic
341C2×C73#244111yescharacteristic
342C2×C73#250611yescharacteristic
343C2×C73#250711yescharacteristic
344C2×C73#255011yescharacteristic
345C2×C73#255111yescharacteristic
346C2×#389—731no—
347C2×#389—732no—
348C2×#389—731no—
349C2×#389—731no—
350C2×#384D7311yescharacteristic
351C2×C4×C4⋊C4—731no—
352#1444—732no—
353#1441—732no—
354#1436—732no—
355C4⋊#95—731no—
356C4×#95—731no—
357C73#1400511yescharacteristic, complemented, Sylow
358C22×C4⋊C4—732no—
359C22×C4⋊C4—732no—
360C22×C4⋊C4—731no—
361C22×C4⋊C4—731no—
362C22×C4⋊C4—732no—
363C22×C4⋊C4C2×D7311yescharacteristic
364C22×C4⋊C4C2×D7312yes—
365C22×C4⋊C4C2×D7312yes—
366C22×C4⋊C4C2×D7311yescharacteristic
367C22×C42—732no—
368C22×C42—731no—
369C22×C42—731no—
370C22×C42C2×D7311yescharacteristic
371#389—738no—
372#389—1468no—
373#389—1464no—
374#389—1464no—
375#384—24no—
376C4×C4⋊C4—1464no—
377C2×#95—732no—
378C2×#95—731no—
379C2×#95—731no—
380C2×#95—732no—
381C2×#95—731no—
382C2×#95—731no—
383C2×#95—732no—
384C2×#95—732no—
385C2×#95—732no—
386C2×#95—732no—
387C23×C4—732no—
388C23×C4—731no—
389C23×C4—731no—
390C23×C4—732no—
391C23×C4—731no—
392C23×C4—731no—
393C23×C4C22×D7312yes—
394C23×C4C22×D7312yes—
395C23×C4C22×D7311yescharacteristic
396C23×C4C22×D7311yescharacteristic
397C23×C4C22×D7311yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—2922no—
410C2×C4⋊C4—2922no—
411C2×C4⋊C4—734no—
412C2×C4⋊C4—734no—
413C2×C4⋊C4—734no—
414C2×C4⋊C4—738no—
415C2×C4⋊C4—734no—
416C2×C4⋊C4—1464no—
417C2×C4⋊C4—1464no—
418C2×C4⋊C4—1464no—
419C2×C4⋊C4—1464no—
420C2×C4⋊C4—1464no—
421C2×C4⋊C4—1462no—
422C2×C4⋊C4—1462no—
423C2×C4⋊C4—1464no—
424C2×C4⋊C4C22⋊D7314yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—2922no—
428C2×C42—734no—
429C2×C42—1464no—
430C2×C42—1464no—
431C2×C42—1462no—
432C2×C42—1462no—
433C2×C42—1462no—
434C2×C42—1462no—
435C2×C42—1462no—
436C2×C42C4×D7314yes—
437#95—2922no—
438#95—738no—
439#95—734no—
440#95—734no—
441#95—1464no—
442#95—1464no—
443#95—1464no—
444#95—1464no—
445#95—1462no—
446#95—1462no—
447C24C23×D7311yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—734no—
470C22×C4—732no—
471C22×C4—734no—
472C22×C4—732no—
473C22×C4—732no—
474C22×C4—734no—
475C22×C4—734no—
476C22×C4—732no—
477C22×C4—732no—
478C22×C4—732no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1462no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1462no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1462no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1462no—
495C22×C4—1461no—
496C22×C4—1462no—
497C22×C4—1461no—
498C22×C4—1461no—
499C22×C4—1461no—
500C22×C4—1461no—
501C22×C4—1462no—
502C22×C4—1461no—
503C22×C4—1461no—
504C22×C4—1462no—
505C22×C4—1461no—
506C22×C4—1462no—
507C22×C4—1461no—
508C22×C4—1462no—
509C22×C4—1461no—
510C22×C4—1462no—
511C22×C4C2×C4×D7312yes—
512C22×C4C2×C4×D7312yes—
513C22×C4C2×C4×D7312yes—
514C22×C4D4×D7312yes—
515C22×C4D4×D7312yes—
516C22×C4C2×C22⋊D7314yes—
517C22×C4C2×C22⋊D7312yes—
518C22×C4Q8×D7312yes—
519C22×C4Q8×D7312yes—
520C22×C4Q8×D7312yes—
521C22×C4#1192402712yes—
522C22×C4#1192402712yes—
523C22×C4#1192402812yes—
524C22×C4#1192402912yes—
525C4⋊C4—28no—
526C4⋊C4—48no—
527C4⋊C4—48no—
528C4⋊C4—44no—
529C4⋊C4—2928no—
530C4⋊C4—2928no—
531C4⋊C4—7316no—
532C4⋊C4—1468no—
533C4⋊C4—14616no—
534C42—28no—
535C42—2928no—
536C42—2924no—
537C42—1468no—
538C23C22×C4×D7311yescharacteristic
539C23C2×D4×D7311yescharacteristic
540C23C2×D4×D7311yescharacteristic
541C23C22×C22⋊D7311yescharacteristic
542C23C2×Q8×D7311yescharacteristic
543C23C2×Q8×D7311yescharacteristic
544C23C2×Q8×D7311yescharacteristic
545C23C2×#1192402711yescharacteristic
546C23C2×#1192402711yescharacteristic
547C23C2×#1192402811yescharacteristic
548C23C2×#1192402911yescharacteristic
549C23#1455663611yescharacteristic
550C23#1455663611yescharacteristic
551C23#1455663911yescharacteristic
552C23#1455663911yescharacteristic
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2922no—
582C2×C4—2921no—
583C2×C4—2922no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—2922no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—2921no—
592C2×C4—2922no—
593C2×C4—2921no—
594C2×C4—2921no—
595C2×C4—734no—
596C2×C4—738no—
597C2×C4—1462no—
598C2×C4—1462no—
599C2×C4—1462no—
600C2×C4—1462no—
601C2×C4—1462no—
602C2×C4—1462no—
603C2×C4—1462no—
604C2×C4—1462no—
605C2×C4—1464no—
606C2×C4—1464no—
607C2×C4—1464no—
608C2×C4—1462no—
609C2×C4—1462no—
610C2×C4—1462no—
611C2×C4—1464no—
612C2×C4—1462no—
613C2×C4—1464no—
614C2×C4—1464no—
615C2×C4—1462no—
616C2×C4—1462no—
617C2×C4—1464no—
618C2×C4—1464no—
619C2×C4—1464no—
620C2×C4—1462no—
621C2×C4C4⋊C4×D7314yes—
622C2×C4C4×C22⋊D7314yes—
623C2×C4#1455655314yes—
624C2×C4#1455655614yes—
625C2×C4#1455655614yes—
626C2×C4#1455656314yes—
627C2×C4#1455656914yes—
628C2×C4#1455658114yes—
629C2×C4#1455658914yes—
630C22C2×C4⋊C4×D7311yescharacteristic
631C22C2×C4×C22⋊D7311yescharacteristic
632C22C2×#1455655311yescharacteristic
633C22C2×#1455655611yescharacteristic
634C22C2×#1455655611yescharacteristic
635C22#1798906811yescharacteristic
636C22#1798906811yescharacteristic
637C22C2×#1455656311yescharacteristic
638C22C2×#1455656911yescharacteristic
639C22C2×#1455658111yescharacteristic
640C22C4⋊Q8×D7311yescharacteristic
641C22C2×#1455658911yescharacteristic
642C22#1798913511yescharacteristic
643C22#1798914211yescharacteristic
644C22#1798914211yescharacteristic
645C22#1798919111yescharacteristic
646C22#1798919811yescharacteristic
647C22#1798921411yescharacteristic
648C22#1798921411yescharacteristic
649C22D4×C22⋊D7311yescharacteristic
650C22#1798922211yescharacteristic
651C22#1798923111yescharacteristic
652C22#1798923811yescharacteristic
653C22#1798924011yescharacteristic
654C22#1798924811yescharacteristic
655C22Q8×C22⋊D7311yescharacteristic
656C22#1798925211yescharacteristic
657C22#1798925211yescharacteristic
658C22#1798925711yescharacteristic
659C22#1798927211yescharacteristic
660C22#1798928511yescharacteristic
661C22#1798929211yescharacteristic
662C22#1798929811yescharacteristic
663C22#1798931211yescharacteristic
664C22#1798931711yescharacteristic
665C4—24no—
666C4—24no—
667C4—44no—
668C4—82no—
669C4—2922no—
670C4—2922no—
671C4—2922no—
672C4—2924no—
673C4—1468no—
674C4—1464no—
675C4#1798848218yescomplemented
676C2C2×#1798848211yescharacteristic
677C2#2261249811yescharacteristic
678C2#2261267011yescharacteristic
679C2#2261283111yescharacteristic
680C2#2261284311yescharacteristic
681C2#2261293611yescharacteristic
682C2#2261294711yescharacteristic
683C2#2261352211yescharacteristic
684C2#2261353311yescharacteristic
685C2#2261363611yescharacteristic
686C2#2261364711yescharacteristic
687C2#2261444311yescharacteristic
688C2#2261445411yescharacteristic
689C2#2261494811yescharacteristic
690C2#2261495811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#384×C73C2
socle, prime radical, cosocleC24×C73C24
hypercenterC2×#384D73
hypocenterC73#14005
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
20. #17988485C4semidirect
144. C4⋊Dic73C4⋊C4semidirect
323. C4×C73#389semidirect
357. C73#14005semidirect
675. C4#17988482semidirect

Maximal subgroups

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

subgroupindex
C2×#179884852
C2×#179884832
C2×#179884822
C2×C4⋊C4×Dic732
#226081942
#226081812
#226081632
#226081602
C4×#145564982
C2×#384×C732
#1400573