Finite Group Databasebeta

← #33106407

Subgroups — #33106407

Order 18688.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988725C211yesmaximal, characteristic
2C2×#17988687C211yesmaximal, characteristic, complemented
3C2×#17988595C211yesmaximal, characteristic, complemented
4C22⋊C4×Dic146C211yesmaximal, characteristic, complemented
5#22610784C211yesmaximal, characteristic, complemented
6#22610620C211yesmaximal, characteristic, complemented
7#22610572C211yesmaximal, characteristic, complemented
8#22610370C211yesmaximal, characteristic
9#22610289C211yesmaximal, characteristic, complemented
10#22610265C211yesmaximal, characteristic, complemented
11#22610198C211yesmaximal, characteristic, complemented
12#22610130C211yesmaximal, characteristic, complemented
13C4×#14556514C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15C73×#2363C211yesmaximal, characteristic
16C23×Dic146C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19C22×#11924012C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic
21C2×C4×Dic146C2211yescharacteristic
22#17988725C418yescomplemented
23#17988687—24no—
24C2×#14556524C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26#17988595—24no—
27C2×#14556514C2211yescharacteristic
28C2×#14556514C2211yescharacteristic
29C2×#14556514C2211yescharacteristic
30C2×#14556514C2211yescharacteristic
31C2×#14556514C2211yescharacteristic
32C2×#14556514C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988493C2211yescharacteristic
39#17988493C2211yescharacteristic
40#17988491—21no—
41#17988491—21no—
42#17988447C2211yescharacteristic
43#17988445—21no—
44C22⋊C4×Dic73—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C2×#121×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×#117×C73C2211yescharacteristic
54#390×C73—21no—
55#390×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#388×C73—21no—
58#386×C73—21no—
59C4×C4⋊C4×C73C2211yescharacteristic
60C4×C22⋊C4×C73—21no—
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×Dic146—22no—
63C22×Dic146—22no—
64C22×Dic146—21no—
65C22×Dic146—22no—
66C22×Dic146—41no—
67C22×Dic146—41no—
68C22×Dic146C2×C414yescomplemented
69C22×Dic146C2311yescharacteristic
70C22×Dic146C2311yescharacteristic
71C23×Dic73—21no—
72C2×#11924016—22no—
73C2×#11924016—22no—
74C2×#11924016—41no—
75C2×#11924016—41no—
76C2×#11924016C2×C414yes—
77C2×#11924016C2×C414yes—
78C2×#11924012—22no—
79C2×#11924012—22no—
80C2×#11924012—41no—
81C22×#10596831C2311yescharacteristic
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C4×Dic146—22no—
86C4×Dic146—22no—
87C4×Dic146—41no—
88C4×Dic146—41no—
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C4⋊Dic73C2311yescharacteristic
91C2×#11924007—21no—
92C2×#11924007—21no—
93C2×C22⋊Dic73—21no—
94C2×C4×Dic73—21no—
95C2×C4×Dic73—21no—
96#14556524—22no—
97#14556522—41no—
98#14556514—22no—
99#14556514—22no—
100#14556514—22no—
101#14556514C2×C414yescomplemented
102#14556514C2×C414yescomplemented
103#14556514D414yescomplemented
104#14556512—22no—
105#14556512—41no—
106C22⋊#10596831C2×C414yescomplemented
107#14556502—22no—
108C4×#10596831—41no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114C22×D4×C73—21no—
115C22×D4×C73C2311yescharacteristic
116C23×C4×C73—21no—
117C23×C4×C73C2311yescharacteristic
118#121×C73—22no—
119#121×C73C2×C414yes—
120C4×D4×C73—22no—
121C4×D4×C73—41no—
122#117×C73—22no—
123#117×C73—41no—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73D411yescharacteristic
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C42×C73—21no—
136C2×C42×C73—21no—
137C2×C42×C73C2311yescharacteristic
138C2×C42×C73C2311yescharacteristic
139#95×C73—21no—
140#95×C73—21no—
141#95×C73D411yescharacteristic
142#95×C73D411yescharacteristic
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146—21no—
149C2×Dic146—21no—
150C2×Dic146—28no—
151C2×Dic146—24no—
152C2×Dic146—21no—
153C2×Dic146—44no—
154C2×Dic146—44no—
155C2×Dic146—44no—
156C2×Dic146—42no—
157C2×Dic146—42no—
158C2×Dic146C22×C412yes—
159C2×Dic146C22×C412yes—
160C2×Dic146C2×D412yes—
161C2×Dic146#4112yes—
162C22×Dic73—21no—
163C22×Dic73—24no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—42no—
168C22×Dic73—42no—
169#11924016—28no—
170#11924016—44no—
171#11924012—44no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831C22×C412yes—
182C2×#10596831C22×C412yes—
183C2×#10596831C2×D412yes—
184C4⋊Dic73—21no—
185C4⋊Dic73—21no—
186C4⋊Dic73—21no—
187C4⋊Dic73—21no—
188#11924007—42no—
189#11924007—42no—
190C22⋊Dic73—42no—
191C4×Dic73—42no—
192C4×Dic73—42no—
193C24×C73—21no—
194C24×C73C2×D411yescharacteristic
195C2×D4×C73—24no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—81no—
202C2×D4×C73—81no—
203C2×D4×C73C22×C412yes—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—81no—
214C22×C4×C73C22×C412yes—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73#4112yes—
221C22×C4×C73C2411yescharacteristic
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—81no—
227C4⋊C4×C73C22×C412yes—
228C4⋊C4×C73C2×D412yes—
229C22⋊C4×C73—24no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—41no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—81no—
236C42×C73—21no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—21no—
240C42×C73—42no—
241C42×C73—81no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257D4×C73—22no—
258D4×C73—22no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—84no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—22no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—84no—
289C2×C4×C73C4×D412yes—
290C2×C4×C73#13712yes—
291C2×C4×C73C23×C411yescharacteristic
292C2×C4×C73C22×D411yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73H(5,𝔽2)11yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—48no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310Dic146—22no—
311Dic146—22no—
312Dic146—22no—
313Dic146—22no—
314Dic146—22no—
315Dic146—48no—
316Dic146—41no—
317Dic146—41no—
318Dic146C4×D414yes—
319#10596831—22no—
320#10596831—22no—
321#10596831—22no—
322#10596831—41no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73C2×C4×D411yescharacteristic
338C22×C73D4211yescharacteristic
339C22×C73#54611yescharacteristic
340C22×C73C2×#13711yescharacteristic
341C22×C73#57511yescharacteristic
342C22×C73#57711yescharacteristic
343C22×C73#57711yescharacteristic
344C4×C73—22no—
345C4×C73—22no—
346C4×C73—42no—
347C4×C73—41no—
348C4×C73—42no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—81no—
352C4×C73C2×C4×D411yescharacteristic
353C4×C73#51811yescharacteristic
354C4×C73#54611yescharacteristic
355C4×C73#55111yescharacteristic
356Dic73—24no—
357Dic73—42no—
358Dic73—81no—
359Dic73—81no—
360#22865—731nomaximal, Sylow
361C2×C73—42no—
362C2×C73—82no—
363C2×C73#235811yescharacteristic
364C2×C73C4×#13711yescharacteristic
365C2×C73#294911yescharacteristic
366C2×C73#327511yescharacteristic
367C2×C73#327811yescharacteristic
368C2×C73#332011yescharacteristic
369C2×C73#332111yescharacteristic
370C2×#448—731no—
371C2×#440—731no—
372C2×#419—731no—
373#2363D7311yescharacteristic
374Q8×C22⋊C4—731no—
375#1968—731no—
376#1935—731no—
377#1928—731no—
378#1895—731no—
379#1880—731no—
380#1877—731no—
381#1865—731no—
382#1854—731no—
383C4×#103—731no—
384#1753—731no—
385C73#2286511yescharacteristic, complemented, Sylow
386C23×Q8—731no—
387C22×SD16—731no—
388C22×SD16—731no—
389C22×M16—731no—
390C2×#121C2×D7311yescharacteristic
391C2×C4×Q8—731no—
392C2×C4×Q8—731no—
393C2×C4×D4C2×D7311yescharacteristic
394C2×#117C2×D7311yescharacteristic
395#448—738no—
396#440—1464no—
397C2×#107—731no—
398C2×#106—731no—
399#419—1464no—
400C2×#103—731no—
401C2×#103—731no—
402C2×#103—731no—
403C2×#103—731no—
404C2×#103—731no—
405C2×#103—731no—
406C2×#102—731no—
407C2×#102—731no—
408C2×C22⋊C8—731no—
409C2×#97—731no—
410C2×C4×C8—731no—
411#391—731no—
412#391—731no—
413#391—1461no—
414#391—1461no—
415#390—21no—
416#390C2×D7311yescharacteristic
417#389C2×D7311yescharacteristic
418#388—21no—
419#386—21no—
420#380—731no—
421#380—1461no—
422C4×C4⋊C4C2×D7311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—1461no—
425C4×C22⋊C4C2×D7311yescharacteristic
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#336—731no—
431#336—731no—
432C22×Q8—2921no—
433C22×Q8—2921no—
434C22×Q8—734no—
435C22×Q8—731no—
436C22×Q8—731no—
437C22×Q8—1462no—
438C22×Q8—1462no—
439C22×Q8—1461no—
440C22×Q8—1462no—
441C22×D4—21no—
442C22×D4C22×D7311yescharacteristic
443C23×C4—21no—
444C23×C4—1461no—
445C23×C4C22×D7311yescharacteristic
446C2×SD16—2921no—
447C2×SD16—2921no—
448C2×SD16—734no—
449C2×SD16—734no—
450C2×SD16—1462no—
451C2×SD16—1462no—
452C2×M16—2921no—
453C2×M16—1462no—
454C2×M16—1462no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8—731no—
458C22×C8—731no—
459#121—22no—
460#121C4×D7314yes—
461C4×Q8—2921no—
462C4×Q8—2921no—
463C4×Q8—1462no—
464C4×Q8—1462no—
465C4×D4—22no—
466C4×D4—41no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4C22×D7311yescharacteristic
475C2×C4⋊C4C22×D7311yescharacteristic
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4C22⋊D7311yescharacteristic
484C2×C22⋊C4C22⋊D7311yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—1461no—
488C2×C42—1461no—
489C2×C42C22×D7311yescharacteristic
490C2×C42C22×D7311yescharacteristic
491#107—1462no—
492#106—2921no—
493#103—734no—
494#103—734no—
495#103—734no—
496#103—1462no—
497#103—1462no—
498#103—1462no—
499#102—2921no—
500#102—1462no—
501C22⋊C8—734no—
502#97—1462no—
503C4×C8—2921no—
504#95—21no—
505#95—21no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511#95C22⋊D7311yescharacteristic
512#95C22⋊D7311yescharacteristic
513C24—21no—
514C24C2×C22⋊D7311yescharacteristic
515C2×Q8—2924no—
516C2×Q8—2924no—
517C2×Q8—2924no—
518C2×Q8—2922no—
519C2×Q8—2922no—
520C2×Q8—732no—
521C2×Q8—732no—
522C2×Q8—732no—
523C2×Q8—732no—
524C2×Q8—1468no—
525C2×Q8—1461no—
526C2×Q8—1461no—
527C2×Q8—1461no—
528C2×Q8—1461no—
529C2×Q8—1464no—
530C2×Q8—1461no—
531C2×Q8—1461no—
532C2×Q8—1461no—
533C2×Q8—1461no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C2×C4×D7312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—2922no—
554C22×C4—2922no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1464no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4C2×C4×D7312yes—
561C22×C4C2×C22⋊D7311yescharacteristic
562C22×C4C2×C22⋊D7311yescharacteristic
563C22×C4C2×C22⋊D7311yescharacteristic
564C22×C4C2×C22⋊D7311yescharacteristic
565C22×C4C2×C22⋊D7311yescharacteristic
566C22×C4#1192402812yes—
567C22×C4C23×D7311yescharacteristic
568SD16—2924no—
569SD16—1468no—
570M16—2924no—
571C2×C8—732no—
572C2×C8—732no—
573C2×C8—732no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—81no—
588C4⋊C4—2922no—
589C4⋊C4—2922no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4—1461no—
594C4⋊C4C2×C4×D7312yes—
595C4⋊C4D4×D7312yes—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—2922no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—81no—
610C42—2922no—
611C42—2922no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C4×C22⋊D7312yes—
626C23C22×C22⋊D7311yescharacteristic
627Q8—2928no—
628Q8—2921no—
629Q8—2921no—
630Q8—734no—
631Q8—1462no—
632Q8—1462no—
633Q8—1462no—
634Q8—1462no—
635Q8—1462no—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2928no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4C4×C22⋊D7312yes—
682C2×C4#1455662112yes—
683C2×C4C22×C4×D7311yescharacteristic
684C2×C4C2×D4×D7311yescharacteristic
685C2×C4#41×D7311yescharacteristic
686C2×C4C2×#1192402811yescharacteristic
687C2×C4#1455663611yescharacteristic
688C2×C4#1455663711yescharacteristic
689C8—2921no—
690C8—1462no—
691C8—1462no—
692C8—1462no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×C4×C22⋊D7311yescharacteristic
708C22D4×C22⋊D7311yescharacteristic
709C22#1798922511yescharacteristic
710C22C2×#1455662111yescharacteristic
711C22#1798938511yescharacteristic
712C22#1798939811yescharacteristic
713C22#1798939811yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—81no—
722C4—2922no—
723C4—5841no—
724C4—5841no—
725C4—1464no—
726C4C4×D4×D7311yescharacteristic
727C4#1798905911yescharacteristic
728C4#1798923311yescharacteristic
729C4#1798926611yescharacteristic
730C2—42no—
731C2—82no—
732C2#2261290811yescharacteristic
733C2C4×#1455662111yescharacteristic
734C2#2261878811yescharacteristic
735C2#2262155811yescharacteristic
736C2#2262159711yescharacteristic
737C2#2262209611yescharacteristic
738C2#2262211111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2363C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenter#2363D73
hypocenterC73#22865
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#17988687C2semidirect
3. C2×#17988595C2semidirect
4. C22⋊C4×Dic146C2semidirect
5. #22610784C2semidirect
6. #22610620C2semidirect
7. #22610572C2semidirect
9. #22610289C2semidirect
10. #22610265C2semidirect
11. #22610198C2semidirect
12. #22610130C2semidirect
13. C4×#14556514C2semidirect
14. #22609715C2semidirect
22. #17988725C4semidirect
68. C22×Dic146C2×C4semidirect
101. #14556514C2×C4semidirect
102. #14556514C2×C4semidirect
103. #14556514D4semidirect
106. C22⋊#10596831C2×C4semidirect
385. C73#22865semidirect

Maximal subgroups

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

subgroupindex
C2×#179887252
C2×#179886872
C2×#179885952
C22⋊C4×Dic1462
#226107842
#226106202
#226105722
#226103702
#226102892
#226102652
#226101982
#226101302
C4×#145565142
#226097152
C73×#23632
#2286573