Finite Group Databasebeta

← #2398×D73 #33252251

Subgroups — #2398×D73 #33252251

Order 18688.

3246 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
2C2×C4×D4×D73C211yesmaximal, characteristic
3#22613220C212yesmaximal, complemented
4#22613219C212yesmaximal, complemented
5#22613218C214yesmaximal, complemented
6#22613217C211yesmaximal, characteristic, complemented
7#22613216C212yesmaximal, complemented
8#22613215C211yesmaximal, characteristic, complemented
9#22613214C211yesmaximal, characteristic, complemented
10#22613213C212yesmaximal, complemented
11#400×D73C212yesmaximal, complemented
12#397×D73C212yesmaximal, complemented
13#394×D73C212yesmaximal
14#393×D73C212yesmaximal, complemented
15C4×C22⋊C4×D73C214yesmaximal, complemented
16#376×D73C211yesmaximal, characteristic, complemented
17C73×#2398C211yesmaximal, characteristic, complemented
18C22×Q8×D73C2211yescharacteristic
19C22×D4×D73C2211yescharacteristic
20C23×C4×D73C2212yes—
21C2×Q8×Dic73C2211yescharacteristic, complemented
22C2×C4×Dic146C2211yescharacteristic, complemented
23C2×C4×Dic146C2212yescomplemented
24C2×#14556556C2211yescharacteristic, complemented
25C2×#14556556C2212yescomplemented
26C4×Q8×D73—28no—
27C2×C4×D292C2211yescharacteristic
28C2×D4×Dic73C2211yescharacteristic
29C2×#14556553C2211yescharacteristic
30C2×C4×C22⋊D73C2212yes—
31C2×#14556551C2212yes—
32C4×D4×D73—28no—
33C2×C4⋊C4×D73C2211yescharacteristic
34C2×C4⋊C4×D73C2212yes—
35C2×C4⋊C4×D73C2211yescharacteristic
36C2×C22⋊C4×D73C2214yes—
37C2×C22⋊C4×D73C2214yes—
38C2×C22⋊C4×D73C2212yes—
39C2×C42×D73C2212yes—
40C2×C42×D73C2212yes—
41C2×C42×D73C2211yescharacteristic
42#17988529C2214yescomplemented
43#17988528C2214yescomplemented
44#17988527C2212yescomplemented
45#17988526C2212yescomplemented
46#17988525C2212yescomplemented
47#17988516C2214yescomplemented
48#17988515C2214yescomplemented
49#17988514C2212yescomplemented
50#17988513C2212yescomplemented
51#17988512C2212yescomplemented
52#17988505C2212yes—
53#17988504C2212yes—
54#17988503C2214yes—
55#17988502C2214yes—
56#17988501C2212yes—
57#17988500C2212yescomplemented
58#17988500C2214yescomplemented
59#17988499C2212yescomplemented
60#17988499C2214yescomplemented
61#17988498C2212yescomplemented
62C22⋊C4×Dic73C2214yescomplemented
63C22⋊C4×Dic73C2214yescomplemented
64C4×#11924005C2214yescomplemented
65C4×#11924005C2214yescomplemented
66C4×C22⋊Dic73C2214yescomplemented
67#17988434C2214yescomplemented
68#17988434C2214yescomplemented
69#17988433C2211yescharacteristic, complemented
70#17988433C2212yescomplemented
71#17988432C2212yescomplemented
72#17988432C2212yescomplemented
73#95×D73C2212yes—
74#95×D73C2212yes—
75#95×D73C2214yes—
76#95×D73C2214yes—
77C2×C4×Q8×C73C2211yescharacteristic, complemented
78C2×C4×D4×C73C2211yescharacteristic
79#400×C73C2212yescomplemented
80#397×C73C2212yescomplemented
81#394×C73C2212yes—
82#393×C73C2212yescomplemented
83C4×C22⋊C4×C73C2214yescomplemented
84#376×C73C2211yescharacteristic, complemented
85C24×D73C2312yes—
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2312yes—
88C2×Q8×D73—24no—
89C2×Q8×D73—28no—
90C22×D292C2311yescharacteristic
91C22×C22⋊D73C2312yes—
92C2×D4×D73—28no—
93C2×D4×D73—24no—
94C23×Dic73C2312yes—
95C22×C4×D73—28no—
96C22×C4×D73—216no—
97C22×C4×D73C2312yes—
98C22×C4×D73C2312yes—
99C22×C4×D73C2312yes—
100C22×C4×D73C2314yes—
101C22×C4×D73C2312yes—
102C22×C4×D73C2311yescharacteristic
103C22×C4×D73C2311yescharacteristic
104C22×C4×D73C2312yes—
105C22×C4×D73C2311yescharacteristic
106Q8×Dic73—24no—
107C4×Dic146—28no—
108C4×Dic146—24no—
109#14556556—24no—
110#14556556—28no—
111C4×D292—24no—
112D4×Dic73—24no—
113#14556553—24no—
114C4×C22⋊D73—28no—
115#14556551—28no—
116C2×C4⋊Dic73C2312yes—
117C2×C4⋊Dic73C2311yescharacteristic
118C2×C4⋊Dic73C2311yescharacteristic
119C2×#11924007C2312yes—
120C2×#11924007C2312yes—
121C2×#11924007C2312yes—
122C2×#11924007C2312yes—
123C4⋊C4×D73—24no—
124C4⋊C4×D73—28no—
125C4⋊C4×D73—24no—
126C2×C22⋊Dic73C2314yes—
127C2×C22⋊Dic73C2314yes—
128C2×C22⋊Dic73C2312yes—
129C2×#11924005C2314yes—
130C2×#11924005C2314yes—
131C2×#11924005C2314yes—
132C2×#11924005C2314yes—
133C2×#11924005C2312yes—
134C2×#11924005C2312yes—
135C22⋊C4×D73—216no—
136C22⋊C4×D73—28no—
137C22⋊C4×D73—216no—
138C2×C4×Dic73C2314yes—
139C2×C4×Dic73C2312yes—
140C2×C4×Dic73C2312yes—
141C2×C4×Dic73C2312yes—
142C2×C4×Dic73C2312yes—
143C2×C4×Dic73C2311yescharacteristic
144C2×C4×Dic73C2311yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146C42×D73—28no—
147C42×D73—28no—
148C42×D73D418yes—
149#14556498C2312yes—
150#14556498C2314yes—
151#14556498C2312yes—
152#14556498C2314yes—
153#14556498C2314yes—
154#14556498C2314yes—
155#14556498C2314yes—
156#14556498C2314yes—
157#14556498C2314yes—
158#14556498C2314yes—
159C22×Q8×C73C2311yescharacteristic
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73C2312yes—
162C4×Q8×C73—24no—
163C4×D4×C73—24no—
164C2×C4⋊C4×C73C2312yes—
165C2×C4⋊C4×C73C2311yescharacteristic
166C2×C4⋊C4×C73C2311yescharacteristic
167C2×C22⋊C4×C73C2314yes—
168C2×C22⋊C4×C73C2314yes—
169C2×C22⋊C4×C73C2312yes—
170C2×C42×C73C2312yes—
171C2×C42×C73C2312yes—
172C2×C42×C73C2311yescharacteristic
173#95×C73C2314yes—
174#95×C73C2314yes—
175#95×C73C2312yes—
176#95×C73C2312yes—
177C23×D73—24no—
178C23×D73—28no—
179C23×D73—28no—
180C23×D73—24no—
181C23×D73#4118yes—
182C23×D73C2412yes—
183C23×D73C2411yescharacteristic
184C2×Dic146—22no—
185C2×Dic146—24no—
186C2×Dic146—24no—
187C2×Dic146—24no—
188C2×Dic146—24no—
189Q8×D73—232no—
190C2×D292—24no—
191C2×D292—22no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—24no—
195D4×D73—232no—
196C22×Dic73—24no—
197C22×Dic73—28no—
198C22×Dic73C2414yes—
199C22×Dic73C2412yes—
200C22×Dic73C2412yes—
201C22×Dic73C2411yescharacteristic
202C22×Dic73C2411yescharacteristic
203C22×Dic73C2412yes—
204C22×Dic73C2411yescharacteristic
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—24no—
209C2×C4×D73—24no—
210C2×C4×D73—24no—
211C2×C4×D73—28no—
212C2×C4×D73—28no—
213C2×C4×D73—28no—
214C2×C4×D73—28no—
215C2×C4×D73—28no—
216C2×C4×D73—24no—
217C2×C4×D73—28no—
218C2×C4×D73—24no—
219C2×C4×D73—28no—
220C2×C4×D73—432no—
221C2×C4×D73C2×D414yes—
222C2×C4×D73C2×D414yes—
223C2×C4×D73C2×D414yes—
224C2×C4×D73#4118yes—
225C2×C4×D73#4118yes—
226C4⋊Dic73—22no—
227C4⋊Dic73—22no—
228C4⋊Dic73—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233C22⋊Dic73—28no—
234C22⋊Dic73—24no—
235C22⋊Dic73—28no—
236#11924005—28no—
237#11924005—28no—
238#11924005—24no—
239#11924005—28no—
240#11924005—24no—
241#11924005—28no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73—24no—
246C4×Dic73—28no—
247C4×Dic73C2×D414yes—
248C4×Dic73C2×D414yes—
249C4×Dic73C2×D414yes—
250C24×C73C2412yes—
251C2×Q8×C73—22no—
252C2×Q8×C73—24no—
253C2×D4×C73—24no—
254C2×D4×C73—22no—
255C22×C4×C73—24no—
256C22×C4×C73—28no—
257C22×C4×C73C2414yes—
258C22×C4×C73C2412yes—
259C22×C4×C73C2412yes—
260C22×C4×C73C2411yescharacteristic
261C22×C4×C73C2411yescharacteristic
262C22×C4×C73C2412yes—
263C22×C4×C73C2411yescharacteristic
264C4⋊C4×C73—22no—
265C4⋊C4×C73—24no—
266C4⋊C4×C73—22no—
267C22⋊C4×C73—28no—
268C22⋊C4×C73—24no—
269C22⋊C4×C73—28no—
270C42×C73—24no—
271C42×C73—24no—
272C42×C73C2×D414yes—
273C23×C73—22no—
274C23×C73—24no—
275C23×C73—24no—
276C23×C73—22no—
277C23×C73C2×#4114yes—
278C23×C73C2511yescharacteristic
279C22×D73—22no—
280C22×D73—24no—
281C22×D73—24no—
282C22×D73—22no—
283C22×D73—216no—
284C22×D73—232no—
285C22×D73—48no—
286C22×D73—48no—
287C22×D73—416no—
288C22×D73C22×D412yes—
289C22×D73C2×#4114yes—
290C22×D73C2×#4114yes—
291C22×D73C2×#4114yes—
292C22×D73C2×#4114yes—
293Q8×C73—28no—
294D4×C73—28no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—24no—
302C2×C4×C73—24no—
303C2×C4×C73—24no—
304C2×C4×C73—24no—
305C2×C4×C73—24no—
306C2×C4×C73—48no—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D412yes—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C2×#4114yes—
311C2×C4×C73C2×#4114yes—
312C22⋊D73—216no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—24no—
320C2×Dic73—24no—
321C2×Dic73—24no—
322C2×Dic73—24no—
323C2×Dic73—24no—
324C2×Dic73—48no—
325C2×Dic73C22×D412yes—
326C2×Dic73C22×D412yes—
327C2×Dic73C22×D412yes—
328C2×Dic73C2×#4114yes—
329C2×Dic73C2×#4114yes—
330D292—28no—
331C4×D73—28no—
332C4×D73—28no—
333C4×D73—216no—
334C4×D73—48no—
335C4×D73—48no—
336C4×D73—416no—
337C4×D73—48no—
338C4×D73—48no—
339C4×D73#124116yes—
340Dic146—216no—
341Dic146—28no—
342C22×C73—24no—
343C22×C73—28no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—44no—
347C22×C73C23×D411yescharacteristic
348C22×C73C22×#4112yes—
349C22×C73C22×#4112yes—
350C22×C73C22×#4112yes—
351C2×D73—24no—
352C2×D73—28no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—44no—
356C2×D73—432no—
357C2×D73#52514yes—
358C2×D73#52514yes—
359C2×D73C2×#12414yes—
360C2×D73#529116yes—
361C4×C73—22no—
362C4×C73—24no—
363C4×C73—22no—
364C4×C73—42no—
365C4×C73—42no—
366C4×C73—44no—
367C4×C73C2×#12414yes—
368Dic73—22no—
369Dic73—24no—
370Dic73—22no—
371Dic73—42no—
372Dic73—42no—
373Dic73—44no—
374Dic73C2×#12414yes—
375C2×#2398—731nomaximal, Sylow
376C2×C73—44no—
377C2×C73C2×#52511yescharacteristic
378C2×C73C2×#52511yescharacteristic
379C2×C73C22×#12411yescharacteristic
380C2×C73C2×#52914yes—
381D73—44no—
382D73#239818yesdirect product factor
383C22×C4×Q8—731no—
384C22×C4×D4—731no—
385#2398—732no—
386#2398—732no—
387#2398—732no—
388#2398—732no—
389#2398—734no—
390#2398—731no—
391#2398—731no—
392#2398—731no—
393#2398D7311yescharacteristic, direct product factor
394C2×#400—732no—
395C2×#397—732no—
396C2×#394—732no—
397C2×#393—732no—
398C2×C4×C22⋊C4—734no—
399C2×#376—731no—
400C73C2×#239811yescharacteristic, complemented, Sylow
401C23×Q8—731no—
402C23×D4—731no—
403C24×C4—732no—
404C2×C4×Q8—731no—
405C2×C4×Q8—731no—
406C2×C4×Q8—732no—
407C2×C4×Q8—732no—
408C2×C4×Q8—731no—
409C2×C4×Q8—1468no—
410C2×C4×Q8C2×D7311yescharacteristic, complemented
411C2×C4×D4—731no—
412C2×C4×D4—732no—
413C2×C4×D4—731no—
414C2×C4×D4—732no—
415C2×C4×D4—731no—
416C2×C4×D4—1468no—
417C2×C4×D4C2×D7311yescharacteristic
418C22×C4⋊C4—732no—
419C22×C4⋊C4—731no—
420C22×C4⋊C4—731no—
421C22×C22⋊C4—734no—
422C22×C22⋊C4—732no—
423C22×C22⋊C4—734no—
424C22×C42—731no—
425C22×C42—732no—
426C22×C42—732no—
427#400—732no—
428#400—732no—
429#400—732no—
430#400—734no—
431#400—734no—
432#400C2×D7312yescomplemented
433#397—732no—
434#397—732no—
435#397—734no—
436#397—732no—
437#397—734no—
438#397C2×D7312yescomplemented
439#394—732no—
440#394—732no—
441#394—734no—
442#394—734no—
443#394—732no—
444#394C2×D7312yes—
445#393—732no—
446#393—734no—
447#393—732no—
448#393—734no—
449#393—732no—
450#393C2×D7312yescomplemented
451C4×C22⋊C4—734no—
452C4×C22⋊C4—734no—
453C4×C22⋊C4—734no—
454C4×C22⋊C4—734no—
455C4×C22⋊C4—734no—
456C4×C22⋊C4—734no—
457C4×C22⋊C4—734no—
458C4×C22⋊C4C2×D7314yescomplemented
459#376—732no—
460#376—731no—
461#376—732no—
462#376—732no—
463#376C2×D7311yescharacteristic, complemented
464C2×#95—732no—
465C2×#95—734no—
466C2×#95—732no—
467C2×#95—734no—
468C25—732no—
469C22×Q8—731no—
470C22×Q8—732no—
471C22×Q8—1464no—
472C22×Q8—1468no—
473C22×Q8C22×D7311yescharacteristic
474C22×D4—732no—
475C22×D4—731no—
476C22×D4—1464no—
477C22×D4—1468no—
478C22×D4C22×D7311yescharacteristic
479C23×C4—731no—
480C23×C4—731no—
481C23×C4—732no—
482C23×C4—731no—
483C23×C4—732no—
484C23×C4—732no—
485C23×C4—734no—
486C23×C4—732no—
487C23×C4—732no—
488C23×C4—732no—
489C23×C4—1468no—
490C23×C4—14616no—
491C23×C4C22×D7312yes—
492C4×Q8—24no—
493C4×Q8—1468no—
494C4×Q8—1464no—
495C4×Q8—1468no—
496C4×Q8—1464no—
497C4×Q8—1464no—
498C4×D4—24no—
499C4×D4—1468no—
500C4×D4—1464no—
501C4×D4—1468no—
502C4×D4—1464no—
503C4×D4—1464no—
504C2×C4⋊C4—732no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—732no—
507C2×C4⋊C4—732no—
508C2×C4⋊C4—732no—
509C2×C4⋊C4—732no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—1464no—
512C2×C4⋊C4—1464no—
513C2×C4⋊C4—1468no—
514C2×C4⋊C4C22×D7311yescharacteristic
515C2×C4⋊C4C22×D7312yes—
516C2×C4⋊C4C22×D7311yescharacteristic
517C2×C22⋊C4—732no—
518C2×C22⋊C4—734no—
519C2×C22⋊C4—734no—
520C2×C22⋊C4—732no—
521C2×C22⋊C4—732no—
522C2×C22⋊C4—734no—
523C2×C22⋊C4—734no—
524C2×C22⋊C4—734no—
525C2×C22⋊C4—734no—
526C2×C22⋊C4—1468no—
527C2×C22⋊C4—14616no—
528C2×C22⋊C4—14616no—
529C2×C22⋊C4C22×D7312yes—
530C2×C22⋊C4C22×D7314yes—
531C2×C22⋊C4C22×D7314yes—
532C2×C42—731no—
533C2×C42—731no—
534C2×C42—731no—
535C2×C42—738no—
536C2×C42—732no—
537C2×C42—732no—
538C2×C42—734no—
539C2×C42—732no—
540C2×C42—732no—
541C2×C42—1468no—
542C2×C42—1468no—
543C2×C42C22×D7312yes—
544C2×C42C22×D7312yes—
545C2×C42C22×D7311yescharacteristic
546#95—734no—
547#95—732no—
548#95—734no—
549#95—732no—
550#95—734no—
551#95—734no—
552#95—734no—
553#95—734no—
554#95—734no—
555#95—734no—
556#95C22×D7312yes—
557#95C22×D7312yes—
558#95C22×D7314yes—
559#95C22×D7314yes—
560C24—731no—
561C24—738no—
562C24—732no—
563C24—1464no—
564C24—1468no—
565C24—1468no—
566C24—1464no—
567C24C23×D7312yes—
568C2×Q8—22no—
569C2×Q8—24no—
570C2×Q8—1464no—
571C2×Q8—1464no—
572C2×Q8—1464no—
573C2×Q8—14632no—
574C2×Q8—1462no—
575C2×Q8—1464no—
576C2×D4—24no—
577C2×D4—22no—
578C2×D4—1464no—
579C2×D4—1464no—
580C2×D4—14632no—
581C2×D4—1464no—
582C2×D4—1464no—
583C2×D4—1462no—
584C22×C4—24no—
585C22×C4—28no—
586C22×C4—29232no—
587C22×C4—731no—
588C22×C4—734no—
589C22×C4—738no—
590C22×C4—731no—
591C22×C4—732no—
592C22×C4—731no—
593C22×C4—734no—
594C22×C4—734no—
595C22×C4—738no—
596C22×C4—734no—
597C22×C4—732no—
598C22×C4—732no—
599C22×C4—1464no—
600C22×C4—1468no—
601C22×C4—1464no—
602C22×C4—1468no—
603C22×C4—1464no—
604C22×C4—1468no—
605C22×C4—1468no—
606C22×C4—1468no—
607C22×C4—1468no—
608C22×C4—1464no—
609C22×C4—1464no—
610C22×C4—1464no—
611C22×C4—1464no—
612C22×C4—1464no—
613C22×C4—1468no—
614C22×C4—1464no—
615C22×C4—1468no—
616C22×C4C23×D7314yes—
617C22×C4C23×D7312yes—
618C22×C4C23×D7312yes—
619C22×C4C23×D7311yescharacteristic
620C22×C4C23×D7311yescharacteristic
621C22×C4C23×D7312yes—
622C22×C4C23×D7311yescharacteristic
623C4⋊C4—22no—
624C4⋊C4—24no—
625C4⋊C4—22no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1462no—
632C4⋊C4—1462no—
633C22⋊C4—28no—
634C22⋊C4—24no—
635C22⋊C4—28no—
636C22⋊C4—1468no—
637C22⋊C4—1464no—
638C22⋊C4—1468no—
639C22⋊C4—1468no—
640C22⋊C4—1468no—
641C22⋊C4—1464no—
642C22⋊C4—1468no—
643C22⋊C4—1464no—
644C22⋊C4—1468no—
645C42—24no—
646C42—24no—
647C42—734no—
648C42—734no—
649C42—734no—
650C42—1468no—
651C42—1464no—
652C42—1464no—
653C42—1464no—
654C42—1464no—
655C42D4×D7314yes—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—2928no—
661C23—2928no—
662C23—29216no—
663C23—732no—
664C23—734no—
665C23—734no—
666C23—734no—
667C23—734no—
668C23—14616no—
669C23—14632no—
670C23—1462no—
671C23—1464no—
672C23—1464no—
673C23—1462no—
674C23#41×D7314yes—
675C23C24×D7311yescharacteristic
676Q8—28no—
677Q8—1468no—
678Q8—14616no—
679D4—28no—
680D4—1468no—
681D4—14616no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—48no—
694C2×C4—2928no—
695C2×C4—2928no—
696C2×C4—29216no—
697C2×C4—2928no—
698C2×C4—2928no—
699C2×C4—2928no—
700C2×C4—732no—
701C2×C4—734no—
702C2×C4—7316no—
703C2×C4—732no—
704C2×C4—732no—
705C2×C4—734no—
706C2×C4—1468no—
707C2×C4—1468no—
708C2×C4—14616no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4—1464no—
712C2×C4—1464no—
713C2×C4—1464no—
714C2×C4—1464no—
715C2×C4—1464no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4C2×D4×D7312yes—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7312yes—
723C2×C4#41×D7314yes—
724C2×C4#41×D7314yes—
725C22—24no—
726C22—28no—
727C22—42no—
728C22—42no—
729C22—44no—
730C22—29232no—
731C22—2922no—
732C22—2922no—
733C22—2924no—
734C22—734no—
735C22—734no—
736C22—734no—
737C22—7316no—
738C22—1464no—
739C22—1468no—
740C22C22×D4×D7311yescharacteristic
741C22C2×#41×D7312yes—
742C22C2×#41×D7312yes—
743C22C2×#41×D7312yes—
744C4—22no—
745C4—22no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—44no—
750C4—2922no—
751C4—2922no—
752C4—2924no—
753C4—734no—
754C4—1462no—
755C4—1462no—
756C4—1464no—
757C4#124×D7314yes—
758C2—44no—
759C2—2924no—
760C2—738no—
761C2#525×D7311yescharacteristic
762C2#525×D7311yescharacteristic
763C2C2×#124×D7311yescharacteristic
764C2#529×D7314yes—
subgroupG/H
centerC22×C4C23×D73
commutator, socle, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC73×#2398C2
prime radicalC22×D4×D73C22
hypercenter#2398D73
hypocenterC73C2×#2398
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D73C2semidirect
3. #22613220C2semidirect
4. #22613219C2semidirect
5. #22613218C2semidirect
6. #22613217C2semidirect
7. #22613216C2semidirect
8. #22613215C2semidirect
9. #22613214C2semidirect
10. #22613213C2semidirect
11. #400×D73C2semidirect
12. #397×D73C2semidirect
14. #393×D73C2semidirect
15. C4×C22⋊C4×D73C2semidirect
16. #376×D73C2semidirect
17. C73×#2398C2semidirect
21. C2×Q8×Dic73C22semidirect
22. C2×C4×Dic146C22semidirect
23. C2×C4×Dic146C22semidirect
24. C2×#14556556C22semidirect
25. C2×#14556556C22semidirect
42. #17988529C22semidirect
43. #17988528C22semidirect
44. #17988527C22semidirect
45. #17988526C22semidirect
46. #17988525C22semidirect
47. #17988516C22semidirect
48. #17988515C22semidirect
49. #17988514C22semidirect
50. #17988513C22semidirect
51. #17988512C22semidirect
57. #17988500C22semidirect
58. #17988500C22semidirect
59. #17988499C22semidirect
60. #17988499C22semidirect
61. #17988498C22semidirect
62. C22⋊C4×Dic73C22semidirect
63. C22⋊C4×Dic73C22semidirect
64. C4×#11924005C22semidirect
65. C4×#11924005C22semidirect
66. C4×C22⋊Dic73C22semidirect
67. #17988434C22semidirect
68. #17988434C22semidirect
69. #17988433C22semidirect
70. #17988433C22semidirect
71. #17988432C22semidirect
72. #17988432C22semidirect
77. C2×C4×Q8×C73C22semidirect
79. #400×C73C22semidirect
80. #397×C73C22semidirect
82. #393×C73C22semidirect
83. C4×C22⋊C4×C73C22semidirect
84. #376×C73C22semidirect
382. D73#2398direct (N × H)
393. #2398D73direct (N × H)
400. C73C2×#2398semidirect
410. C2×C4×Q8C2×D73semidirect
432. #400C2×D73semidirect
438. #397C2×D73semidirect
450. #393C2×D73semidirect
458. C4×C22⋊C4C2×D73semidirect
463. #376C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D732
C2×C4×D4×D732
#226132202
#226132192
#226132182
#226132172
#226132162
#226132152
#226132142
#226132132
#400×D732
#397×D732
#394×D732
#393×D732
C4×C22⋊C4×D732
#376×D732
C73×#23982
C2×#239873