Finite Group Databasebeta

← #33008390

Subgroups — #33008390

Order 18688.

1710 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic146C211yesmaximal, characteristic
2C2×#17988452C211yesmaximal, characteristic
3C2×C4⋊C4×Dic73C211yesmaximal, characteristic
4#22608201C212yesmaximal
5#22608197C212yesmaximal
6#22608165C212yesmaximal
7#22608162C212yesmaximal
8#22608161C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10#22608160C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C23×Dic146C2211yescharacteristic
13C2×C4×Dic146—24no—
14C2×C4×Dic146—24no—
15C2×C4×Dic146C418yescomplemented
16C22×C4⋊Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2212yes—
23C22×C4×Dic73C2211yescharacteristic
24#17988452—24no—
25C4⋊C4×Dic73—24no—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C42×C73C2211yescharacteristic
38C2×#95×C73C2212yes—
39C2×#95×C73C2212yes—
40C22×Dic146—22no—
41C22×Dic146—22no—
42C22×Dic146—22no—
43C22×Dic146—22no—
44C22×Dic146—22no—
45C22×Dic146—22no—
46C22×Dic146C2×C414yes—
47C23×Dic73C2312yes—
48C23×Dic73C2311yescharacteristic
49C23×Dic73C2312yes—
50C23×Dic73C2311yescharacteristic
51C23×Dic73C2311yescharacteristic
52C23×Dic73C2311yescharacteristic
53C4×Dic146—232no—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73—22no—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73—22no—
58C2×C4⋊Dic73—22no—
59C2×C4⋊Dic73—22no—
60C2×C4⋊Dic73—22no—
61C2×C4⋊Dic73C2×C414yes—
62C2×C4⋊Dic73Q814yescomplemented
63C2×#11924007—22no—
64C2×#11924007—22no—
65C2×#11924007—22no—
66C2×#11924007—22no—
67C2×#11924007C2×C414yes—
68C2×#11924007C2×C414yes—
69C2×C4×Dic73—24no—
70C2×C4×Dic73—22no—
71C2×C4×Dic73—22no—
72C2×C4×Dic73—42no—
73C2×C4×Dic73—42no—
74C2×C4×Dic73C2×C414yes—
75C2×C4×Dic73C2×C414yes—
76C2×C4×Dic73D414yes—
77C2×C4×Dic73D414yes—
78#14556498—24no—
79#14556498—24no—
80#14556498—24no—
81#14556498—24no—
82#14556498—24no—
83#14556498—24no—
84#14556498—42no—
85#14556498—42no—
86#14556498—42no—
87C23×C4×C73C2312yes—
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2312yes—
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—22no—
97C2×C4⋊C4×C73Q814yescomplemented
98C2×C42×C73—22no—
99C2×C42×C73—22no—
100C2×C42×C73C2×C414yes—
101#95×C73—24no—
102#95×C73—42no—
103C2×Dic146—28no—
104C2×Dic146—28no—
105C2×Dic146—28no—
106C2×Dic146—28no—
107C2×Dic146—28no—
108C2×Dic146—28no—
109C2×Dic146—28no—
110C22×Dic73—21no—
111C22×Dic73—21no—
112C22×Dic73—21no—
113C22×Dic73—21no—
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—22no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73C22×C412yes—
142C22×Dic73C22×C412yes—
143C22×Dic73C22×C412yes—
144C22×Dic73C22×C412yes—
145C22×Dic73C2×D412yes—
146C22×Dic73C2×D412yes—
147C22×Dic73C2×D412yes—
148C22×Dic73C2×D412yes—
149C22×Dic73C2×Q814yes—
150C22×Dic73#4112yes—
151C22×Dic73#4112yes—
152C4⋊Dic73—28no—
153C4⋊Dic73—28no—
154C4⋊Dic73—44no—
155#11924007—28no—
156#11924007—28no—
157C4×Dic73—28no—
158C4×Dic73—48no—
159C4×Dic73C22⋊C4116yes—
160C24×C73C2411yescharacteristic
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—22no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—21no—
172C22×C4×C73—22no—
173C22×C4×C73—21no—
174C22×C4×C73—22no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
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×C73C22×C412yes—
185C22×C4×C73C22×C412yes—
186C22×C4×C73C22×C412yes—
187C22×C4×C73C2×D412yes—
188C22×C4×C73C2×D412yes—
189C22×C4×C73C2×Q812yes—
190C22×C4×C73C2×Q814yes—
191C22×C4×C73C2×Q812yes—
192C22×C4×C73#4112yes—
193C22×C4×C73#4112yes—
194C22×C4×C73#4112yes—
195C22×C4×C73#4112yes—
196C4⋊C4×C73—28no—
197C4⋊C4×C73—44no—
198C42×C73—28no—
199C23×C73C23×C411yescharacteristic
200C23×C73C22×D411yescharacteristic
201C23×C73C22×D411yescharacteristic
202C23×C73C22×Q811yescharacteristic
203C23×C73C22×Q811yescharacteristic
204C23×C73C2×#4111yescharacteristic
205C23×C73C2×#4111yescharacteristic
206C23×C73C2×#4111yescharacteristic
207C23×C73C2×#4111yescharacteristic
208C23×C73C2×#4111yescharacteristic
209C23×C73C2×#4111yescharacteristic
210C23×C73H(5,𝔽2)11yescharacteristic
211C23×C73H(5,𝔽2)11yescharacteristic
212C23×C732−1+411yescharacteristic
213C23×C732−1+411yescharacteristic
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—24no—
224C2×C4×C73—24no—
225C2×C4×C73—24no—
226C2×C4×C73—42no—
227C2×C4×C73—41no—
228C2×C4×C73—42no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—42no—
233C2×C4×C73—42no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73—42no—
237C2×C4×C73—42no—
238C2×C4×C73—42no—
239C2×C4×C73—42no—
240C2×C4×C73—42no—
241C2×C4×C73C2×C22⋊C414yes—
242C2×C4×C73#11714yes—
243C2×C4×C73C4×Q814yes—
244C2×C4×C73C4×Q814yes—
245C2×C4×C73C22⋊Q814yes—
246C2×C4×C73C22⋊Q814yes—
247C2×C4×C73#12414yes—
248C2×C4×C73C4⋊Q814yes—
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—22no—
267C2×Dic73—22no—
268C2×Dic73—22no—
269C2×Dic73—22no—
270C2×Dic73—24no—
271C2×Dic73—24no—
272C2×Dic73—24no—
273C2×Dic73—42no—
274C2×Dic73—42no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—42no—
280C2×Dic73—42no—
281C2×Dic73—42no—
282C2×Dic73—42no—
283C2×Dic73—42no—
284C2×Dic73—42no—
285C2×Dic73—42no—
286C2×Dic73—42no—
287C2×Dic73—42no—
288C2×Dic73C2×C22⋊C414yes—
289C2×Dic73C2×C22⋊C414yes—
290C2×Dic73#11714yes—
291Dic146—232no—
292C22×C73C22×C22⋊C411yescharacteristic
293C22×C73C2×#11711yescharacteristic
294C22×C73C2×#11711yescharacteristic
295C22×C73C2×C4×Q811yescharacteristic
296C22×C73C2×C4×Q811yescharacteristic
297C22×C73#52011yescharacteristic
298C22×C73#52011yescharacteristic
299C22×C73C2×C22⋊Q811yescharacteristic
300C22×C73C2×C22⋊Q811yescharacteristic
301C22×C73#52511yescharacteristic
302C22×C73#52511yescharacteristic
303C22×C73#52511yescharacteristic
304C22×C73#52511yescharacteristic
305C22×C73C2×#12411yescharacteristic
306C22×C73C2×C4⋊Q811yescharacteristic
307C22×C73#53511yescharacteristic
308C22×C73#53611yescharacteristic
309C22×C73#53711yescharacteristic
310C22×C73#53711yescharacteristic
311C22×C73#55411yescharacteristic
312C22×C73#55411yescharacteristic
313C22×C73#55411yescharacteristic
314C22×C73#55411yescharacteristic
315C22×C73#55611yescharacteristic
316C22×C73#55611yescharacteristic
317C22×C73#55611yescharacteristic
318C22×C73#55611yescharacteristic
319C22×C73#55711yescharacteristic
320C22×C73#55711yescharacteristic
321C22×C73#55711yescharacteristic
322C22×C73#55711yescharacteristic
323C22×C73#55911yescharacteristic
324C22×C73#55911yescharacteristic
325C22×C73#55911yescharacteristic
326C22×C73#55911yescharacteristic
327C4×C73—24no—
328C4×C73—42no—
329C4×C73—44no—
330C4×C73—82no—
331C4×C73#39118yes—
332Dic73—24no—
333Dic73—24no—
334Dic73—24no—
335Dic73—42no—
336Dic73—44no—
337Dic73—82no—
338#13925—731nomaximal, Sylow
339C2×C73#228011yescharacteristic
340C2×C73C2×#39111yescharacteristic
341C2×C73#231111yescharacteristic
342C2×C73#235511yescharacteristic
343C2×C73#235511yescharacteristic
344C2×C73#235511yescharacteristic
345C2×C73#235511yescharacteristic
346C2×C73#258011yescharacteristic
347C2×C73#258011yescharacteristic
348C2×C73#258111yescharacteristic
349C2×C73#258111yescharacteristic
350C2×C73#258411yescharacteristic
351C2×C73#258411yescharacteristic
352C2×C73#259211yescharacteristic
353C2×C73#259211yescharacteristic
354C22×C4×Q8—731no—
355C2×#382—731no—
356C2×C4×C4⋊C4—731no—
357#1446—732no—
358#1445—732no—
359#1436—732no—
360#1436—732no—
361C4⋊#95—731no—
362C4⋊#95—731no—
363C4⋊#95—731no—
364C4⋊#95D7311yescharacteristic
365C73#1392511yescharacteristic, complemented, Sylow
366C23×Q8—731no—
367C2×C4×Q8—738no—
368C2×C4×Q8—1464no—
369C2×C4×Q8—1464no—
370C22×C4⋊C4—731no—
371C22×C4⋊C4—731no—
372C22×C4⋊C4—731no—
373C22×C4⋊C4—731no—
374C22×C4⋊C4—731no—
375C22×C4⋊C4C2×D7311yescharacteristic
376C22×C4⋊C4C2×D7311yescharacteristic
377C22×C42—732no—
378C22×C42—731no—
379C22×C42—731no—
380C22×C42C2×D7311yescharacteristic
381#382—1464no—
382C4×C4⋊C4—1464no—
383C2×#95—732no—
384C2×#95—732no—
385C2×#95—732no—
386C2×#95—732no—
387C2×#95—732no—
388C2×#95—732no—
389C2×#95—732no—
390C2×#95—732no—
391C2×#95—732no—
392C2×#95C2×D7312yes—
393C2×#95C2×D7312yes—
394C22×Q8—734no—
395C22×Q8—1462no—
396C22×Q8—1462no—
397C22×Q8—1462no—
398C22×Q8—1462no—
399C22×Q8—1462no—
400C22×Q8—1462no—
401C23×C4—731no—
402C23×C4—731no—
403C23×C4—731no—
404C23×C4—731no—
405C23×C4—732no—
406C23×C4—732no—
407C23×C4C22×D7312yes—
408C23×C4C22×D7311yescharacteristic
409C23×C4C22×D7312yes—
410C23×C4C22×D7311yescharacteristic
411C23×C4C22×D7311yescharacteristic
412C4×Q8—14632no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—734no—
419C2×C4⋊C4—734no—
420C2×C4⋊C4—734no—
421C2×C4⋊C4—734no—
422C2×C4⋊C4—1462no—
423C2×C4⋊C4—1462no—
424C2×C4⋊C4—1462no—
425C2×C4⋊C4—1462no—
426C2×C4⋊C4—1462no—
427C2×C4⋊C4—1462no—
428C2×C4⋊C4—1462no—
429C2×C4⋊C4—1462no—
430C2×C4⋊C4—1462no—
431C2×C4⋊C4—1462no—
432C2×C4⋊C4—1462no—
433C2×C4⋊C4Dic14614yescomplemented
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—2922no—
437C2×C42—2922no—
438C2×C42—734no—
439C2×C42—734no—
440C2×C42—734no—
441C2×C42—734no—
442C2×C42—1464no—
443C2×C42—1462no—
444C2×C42—1462no—
445C2×C42C4×D7314yes—
446#95—24no—
447#95—42no—
448#95—2922no—
449#95—2922no—
450#95—2922no—
451#95—1464no—
452#95—1464no—
453#95—1464no—
454#95—1464no—
455#95—1464no—
456#95—1464no—
457C24C23×D7311yescharacteristic
458C2×Q8—1468no—
459C2×Q8—1468no—
460C2×Q8—1468no—
461C2×Q8—1468no—
462C2×Q8—1468no—
463C2×Q8—1468no—
464C2×Q8—1468no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—732no—
489C22×C4—732no—
490C22×C4—732no—
491C22×C4—732no—
492C22×C4—732no—
493C22×C4—732no—
494C22×C4—732no—
495C22×C4—732no—
496C22×C4—732no—
497C22×C4—732no—
498C22×C4—734no—
499C22×C4—1462no—
500C22×C4—1462no—
501C22×C4—1462no—
502C22×C4—1462no—
503C22×C4—1462no—
504C22×C4—1462no—
505C22×C4—1462no—
506C22×C4—1462no—
507C22×C4—1461no—
508C22×C4—1461no—
509C22×C4—1462no—
510C22×C4—1462no—
511C22×C4—1462no—
512C22×C4—1461no—
513C22×C4—1462no—
514C22×C4—1461no—
515C22×C4—1462no—
516C22×C4—1461no—
517C22×C4—1461no—
518C22×C4—1461no—
519C22×C4—1461no—
520C22×C4—1461no—
521C22×C4—1461no—
522C22×C4—1461no—
523C22×C4—1461no—
524C22×C4—1461no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4C2×C4×D7312yes—
531C22×C4C2×C4×D7312yes—
532C22×C4C2×C4×D7312yes—
533C22×C4D4×D7312yes—
534C22×C4D4×D7312yes—
535C22×C4Q8×D7312yes—
536C22×C4C2×Dic14614yes—
537C22×C4C2×Dic14612yes—
538C22×C4#1192402712yes—
539C22×C4#1192402712yes—
540C22×C4#1192402812yes—
541C22×C4#1192402912yes—
542C4⋊C4—28no—
543C4⋊C4—44no—
544C4⋊C4—2924no—
545C4⋊C4—1468no—
546C4⋊C4—1468no—
547C4⋊C4—1468no—
548C4⋊C4—1468no—
549C42—28no—
550C42—2928no—
551C42—7316no—
552C42—1468no—
553C23C22×C4×D7311yescharacteristic
554C23C2×D4×D7311yescharacteristic
555C23C2×D4×D7311yescharacteristic
556C23C2×Q8×D7311yescharacteristic
557C23C22×Dic14611yescharacteristic
558C23#41×D7311yescharacteristic
559C23#41×D7311yescharacteristic
560C23C2×#1192402711yescharacteristic
561C23C2×#1192402711yescharacteristic
562C23C2×#1192402811yescharacteristic
563C23C2×#1192402911yescharacteristic
564C23#1455663611yescharacteristic
565C23#1455663711yescharacteristic
566C23#1455663811yescharacteristic
567C23#1455663911yescharacteristic
568Q8—14632no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—2922no—
597C2×C4—2921no—
598C2×C4—2921no—
599C2×C4—2921no—
600C2×C4—2921no—
601C2×C4—2922no—
602C2×C4—2922no—
603C2×C4—2922no—
604C2×C4—2922no—
605C2×C4—2922no—
606C2×C4—2922no—
607C2×C4—2922no—
608C2×C4—2922no—
609C2×C4—2922no—
610C2×C4—2922no—
611C2×C4—734no—
612C2×C4—734no—
613C2×C4—734no—
614C2×C4—1462no—
615C2×C4—1464no—
616C2×C4—1464no—
617C2×C4—1462no—
618C2×C4—1462no—
619C2×C4—1464no—
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×C4—1462no—
633C2×C4—1462no—
634C2×C4—1462no—
635C2×C4—1462no—
636C2×C4—1462no—
637C2×C4—1462no—
638C2×C4C22⋊C4×D7314yes—
639C2×C4#1455654914yes—
640C2×C4#1455655614yes—
641C2×C4C4×Dic14614yes—
642C2×C4#1455656814yes—
643C2×C4#1455656914yes—
644C2×C4#1455657714yes—
645C2×C4#1455659014yes—
646C22C2×C22⋊C4×D7311yescharacteristic
647C22#117×D7311yescharacteristic
648C22C2×#1455654911yescharacteristic
649C22C2×#1455655611yescharacteristic
650C22C2×C4×Dic14611yescharacteristic
651C22#1798906711yescharacteristic
652C22#1798906811yescharacteristic
653C22C2×#1455656811yescharacteristic
654C22C2×#1455656911yescharacteristic
655C22#1798909711yescharacteristic
656C22#1798909711yescharacteristic
657C22#1798910011yescharacteristic
658C22#1798910011yescharacteristic
659C22C2×#1455657711yescharacteristic
660C22C2×#1455659011yescharacteristic
661C22#1798915311yescharacteristic
662C22#1798916011yescharacteristic
663C22#1798916611yescharacteristic
664C22#1798916711yescharacteristic
665C22#1798929311yescharacteristic
666C22#1798929411yescharacteristic
667C22#1798929611yescharacteristic
668C22#1798929811yescharacteristic
669C22#1798930611yescharacteristic
670C22#1798930711yescharacteristic
671C22#1798930911yescharacteristic
672C22#1798931111yescharacteristic
673C22#1798931211yescharacteristic
674C22#1798931311yescharacteristic
675C22#1798931411yescharacteristic
676C22#1798931611yescharacteristic
677C22#1798931911yescharacteristic
678C22#1798932011yescharacteristic
679C22#1798932211yescharacteristic
680C22#1798932311yescharacteristic
681C4—24no—
682C4—42no—
683C4—44no—
684C4—82no—
685C4—2922no—
686C4—2924no—
687C4—5842no—
688C4—1464no—
689C4—1464no—
690C4—1464no—
691C4#1798849118yes—
692C2#2261231311yescharacteristic
693C2C2×#1798849111yescharacteristic
694C2#2261252011yescharacteristic
695C2#2261288311yescharacteristic
696C2#2261288611yescharacteristic
697C2#2261288911yescharacteristic
698C2#2261289011yescharacteristic
699C2#2261528711yescharacteristic
700C2#2261529111yescharacteristic
701C2#2261529511yescharacteristic
702C2#2261529911yescharacteristic
703C2#2261531611yescharacteristic
704C2#2261531811yescharacteristic
705C2#2261541611yescharacteristic
706C2#2261541811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×C4⋊#95C2
socle, prime radical, cosocleC24×C73C24
hypercenterC4⋊#95D73
hypocenterC73#13925
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic146C4semidirect
62. C2×C4⋊Dic73Q8semidirect
97. C2×C4⋊C4×C73Q8semidirect
365. C73#13925semidirect
433. C2×C4⋊C4Dic146semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1462
C2×#179884522
C2×C4⋊C4×Dic732
#226082012
#226081972
#226081652
#226081622
#226081612
#226081602
C73×C4⋊#952
#1392573