Finite Group Databasebeta

← C2×#22615423 #33256504

Subgroups — C2×#22615423 #33256504

Order 18688.

2334 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615423C2116yesmaximal, direct product factor
2C2×#17988529C211yesmaximal, characteristic, complemented
3C2×#17988520C211yesmaximal, characteristic, complemented
4C2×#17988501C211yesmaximal, characteristic
5C2×#17988490C211yesmaximal, characteristic
6C2×#17988481C211yesmaximal, characteristic, complemented
7C2×#17988481C211yesmaximal, characteristic, complemented
8C2×#17988480C211yesmaximal, characteristic, complemented
9C2×#17988480C211yesmaximal, characteristic, complemented
10C2×#17988475C211yesmaximal, characteristic, complemented
11C2×#17988475C211yesmaximal, characteristic, complemented
12C2×#17988475C211yesmaximal, characteristic, complemented
13C2×#17988475C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
15C2×#17988438C211yesmaximal, characteristic, complemented
16C2×#394×C73C211yesmaximal, characteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2211yescharacteristic
21C22×#11924007C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×C22⋊Dic73C2211yescharacteristic
29C22×C22⋊Dic73C2211yescharacteristic
30C22×C22⋊Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C22×C4×Dic73C2211yescharacteristic
36#17988529C2218yescomplemented
37#17988520C2218yescomplemented
38#17988501C2218yes—
39#17988490C2218yes—
40#17988481C2218yescomplemented
41#17988481C2218yescomplemented
42#17988480C2218yescomplemented
43#17988480C2218yescomplemented
44#17988475C2218yescomplemented
45#17988475C2218yescomplemented
46#17988475C2218yescomplemented
47#17988475C2218yescomplemented
48C4⋊C4×Dic73C2218yescomplemented
49#17988438C2218yescomplemented
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C23×D4×C73C2211yescharacteristic
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C22⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64C22×C22⋊C4×C73C2211yescharacteristic
65#394×C73C2218yes—
66C2×#95×C73C2211yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C2×C4⋊Dic73—24no—
76C2×C4⋊Dic73—42no—
77C2×C4⋊Dic73C2314yes—
78C2×C4⋊Dic73C2314yes—
79C2×#11924007—24no—
80C2×#11924007—24no—
81C2×#11924007—42no—
82C2×#11924007—42no—
83C2×#11924007C2314yes—
84C2×#11924007C2314yes—
85C2×#11924007C2314yes—
86C2×#11924007C2314yes—
87C2×C22⋊Dic73—24no—
88C2×C22⋊Dic73—24no—
89C2×C22⋊Dic73—24no—
90C2×C22⋊Dic73—24no—
91C2×C22⋊Dic73—24no—
92C2×C22⋊Dic73—24no—
93C2×C22⋊Dic73—42no—
94C2×C22⋊Dic73—42no—
95C2×C22⋊Dic73C2314yes—
96C2×C22⋊Dic73C2314yes—
97C2×C22⋊Dic73C2314yes—
98C2×C22⋊Dic73C2314yes—
99C2×C22⋊Dic73C2314yes—
100C2×C22⋊Dic73C2314yes—
101C2×C22⋊Dic73C2314yes—
102C2×C22⋊Dic73C2314yes—
103C2×C4×Dic73—24no—
104C2×C4×Dic73—24no—
105C2×C4×Dic73—42no—
106C2×C4×Dic73—42no—
107C2×C4×Dic73—42no—
108C2×C4×Dic73C2314yes—
109C2×C4×Dic73C2314yes—
110C2×C4×Dic73C2314yes—
111C2×C4×Dic73C2314yes—
112C2×C4×Dic73C2314yes—
113#14556498C2314yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122C25×C73C2311yescharacteristic
123C25×C73C2311yescharacteristic
124C22×D4×C73—24no—
125C22×D4×C73—42no—
126C22×D4×C73—42no—
127C22×D4×C73C2314yes—
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C2×C4⋊C4×C73—24no—
134C2×C4⋊C4×C73C2314yes—
135C2×C22⋊C4×C73—24no—
136C2×C22⋊C4×C73—24no—
137C2×C22⋊C4×C73—42no—
138C2×C22⋊C4×C73—42no—
139C2×C22⋊C4×C73C2314yes—
140C2×C22⋊C4×C73C2314yes—
141C2×C22⋊C4×C73C2314yes—
142C2×C22⋊C4×C73C2314yes—
143#95×C73C2314yes—
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73—22no—
147C22×Dic73—22no—
148C22×Dic73—22no—
149C22×Dic73—22no—
150C22×Dic73—22no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—22no—
155C22×Dic73—22no—
156C22×Dic73—22no—
157C22×Dic73—22no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73#4114yes—
166C22×Dic73#4114yes—
167C22×Dic73#4114yes—
168C22×Dic73C2412yes—
169C22×Dic73C2412yes—
170C22×Dic73C2412yes—
171C22×Dic73C2412yes—
172C22×Dic73C2412yes—
173C22×Dic73C2412yes—
174C22×Dic73C2412yes—
175C22×Dic73C2412yes—
176C4⋊Dic73—28no—
177C4⋊Dic73—44no—
178#11924007—28no—
179#11924007—28no—
180#11924007—44no—
181#11924007—44no—
182C22⋊Dic73—28no—
183C22⋊Dic73—28no—
184C22⋊Dic73—28no—
185C22⋊Dic73—28no—
186C22⋊Dic73—28no—
187C22⋊Dic73—28no—
188C22⋊Dic73—44no—
189C22⋊Dic73—44no—
190C4×Dic73—28no—
191C4×Dic73—28no—
192C4×Dic73—44no—
193C4×Dic73—44no—
194C4×Dic73—44no—
195C24×C73—22no—
196C24×C73—22no—
197C24×C73—22no—
198C24×C73—22no—
199C24×C73—22no—
200C24×C73—22no—
201C24×C73—22no—
202C24×C73—22no—
203C24×C73—22no—
204C24×C73—22no—
205C24×C73—22no—
206C24×C73—22no—
207C24×C73—22no—
208C24×C73—22no—
209C24×C73C2412yes—
210C24×C73C2412yes—
211C24×C73C2411yescharacteristic
212C2×D4×C73—28no—
213C2×D4×C73—44no—
214C2×D4×C73—44no—
215C2×D4×C73—416no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73#4114yes—
230C22×C4×C73#4114yes—
231C22×C4×C73C2412yes—
232C22×C4×C73C2412yes—
233C22×C4×C73C2412yes—
234C22×C4×C73C2412yes—
235C22×C4×C73C2412yes—
236C4⋊C4×C73—28no—
237C22⋊C4×C73—28no—
238C22⋊C4×C73—28no—
239C22⋊C4×C73—44no—
240C22⋊C4×C73—44no—
241C23×C73—22no—
242C23×C73—22no—
243C23×C73—22no—
244C23×C73—22no—
245C23×C73—22no—
246C23×C73—22no—
247C23×C73—22no—
248C23×C73—22no—
249C23×C73—22no—
250C23×C73—22no—
251C23×C73—22no—
252C23×C73—22no—
253C23×C73—22no—
254C23×C73—22no—
255C23×C73—44no—
256C23×C73—44no—
257C23×C73—44no—
258C23×C73—44no—
259C23×C73—44no—
260C23×C73—44no—
261C23×C73—44no—
262C23×C73—44no—
263C23×C73—44no—
264C23×C73—44no—
265C23×C73—44no—
266C23×C73—44no—
267C23×C73—44no—
268C23×C73—44no—
269C23×C73C2×#4112yes—
270C23×C73C2×#4112yes—
271C23×C73C2×#4112yes—
272C23×C73C2×#4112yes—
273C23×C73C2×#4112yes—
274C23×C73H(5,𝔽2)12yes—
275C23×C73H(5,𝔽2)12yes—
276C23×C73C2511yescharacteristic
277D4×C73—416no—
278C2×C4×C73—28no—
279C2×C4×C73—28no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—44no—
294C2×C4×C73—44no—
295C2×C4×C73—44no—
296C2×C4×C73C2×#4114yes—
297C2×C4×C73C2×#4114yes—
298C2×Dic73—28no—
299C2×Dic73—28no—
300C2×Dic73—28no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—44no—
323C2×Dic73—44no—
324C2×Dic73—44no—
325C2×Dic73—44no—
326C2×Dic73—44no—
327C2×Dic73C2×#4114yes—
328C2×Dic73C2×#4114yes—
329C2×Dic73C2×#4114yes—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—88no—
345C22×C73—88no—
346C22×C73#52914yes—
347C22×C73#52914yes—
348C22×C73#53814yes—
349C22×C73#55314yes—
350C22×C73#55314yes—
351C22×C73#55514yes—
352C22×C73#55914yes—
353C22×C73C22×#4111yescharacteristic
354C22×C73C22×#4111yescharacteristic
355C22×C73C22×#4111yescharacteristic
356C22×C73C22×#4111yescharacteristic
357C22×C73C22×#4111yescharacteristic
358C22×C73C2×H(5,𝔽2)11yescharacteristic
359C22×C73C2×H(5,𝔽2)11yescharacteristic
360C4×C73—24no—
361C4×C73—24no—
362C4×C73—42no—
363C4×C73—42no—
364C4×C73—42no—
365Dic73—24no—
366Dic73—24no—
367Dic73—24no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371Dic73—42no—
372Dic73—42no—
373C2×#2593—731nomaximal, Sylow
374C2×C73—82no—
375C2×C73—82no—
376C2×C73#259318yescomplemented
377C2×C73C2×#52911yescharacteristic
378C2×C73C2×#52911yescharacteristic
379C2×C73C2×#53811yescharacteristic
380C2×C73C2×#55311yescharacteristic
381C2×C73C2×#55311yescharacteristic
382C2×C73C2×#55511yescharacteristic
383C2×C73C2×#55911yescharacteristic
384#2593—7316no—
385C2×#400—731no—
386C2×#398—731no—
387C2×#394—731no—
388C2×#394D7311yescharacteristic
389C2×#390—731no—
390C2×#388—731no—
391C2×#388—731no—
392C2×#388—731no—
393C2×#388—731no—
394C2×#388—731no—
395C2×#388—731no—
396C2×#388—731no—
397C2×#388—731no—
398C2×C4×C4⋊C4—731no—
399C2×C4×C4⋊C4—731no—
400C73C2×#259311yescharacteristic, complemented, Sylow
401C23×D4C2×D7311yescharacteristic
402C22×C4⋊C4—731no—
403C22×C4⋊C4—731no—
404C22×C4⋊C4—731no—
405C22×C4⋊C4—731no—
406C22×C4⋊C4—731no—
407C22×C4⋊C4—731no—
408C22×C4⋊C4C2×D7311yescharacteristic
409C22×C22⋊C4—731no—
410C22×C22⋊C4—731no—
411C22×C22⋊C4—731no—
412C22×C22⋊C4—731no—
413C22×C22⋊C4—731no—
414C22×C22⋊C4—731no—
415C22×C22⋊C4—731no—
416C22×C22⋊C4—731no—
417C22×C22⋊C4C2×D7311yescharacteristic
418C22×C22⋊C4C2×D7311yescharacteristic
419C22×C22⋊C4C2×D7311yescharacteristic
420C22×C22⋊C4C2×D7311yescharacteristic
421C22×C42—731no—
422C22×C42—731no—
423C22×C42—731no—
424C22×C42—731no—
425C22×C42—731no—
426#400—738no—
427#398—738no—
428#394—738no—
429#394C2×D7318yes—
430#390—738no—
431#388—738no—
432#388—738no—
433#388—738no—
434#388—738no—
435#388—738no—
436#388—738no—
437#388—738no—
438#388—738no—
439C4×C4⋊C4—738no—
440C4×C4⋊C4—738no—
441C2×#95—731no—
442C2×#95—731no—
443C2×#95—731no—
444C2×#95—731no—
445C2×#95—731no—
446C2×#95—731no—
447C2×#95—731no—
448C2×#95—731no—
449C2×#95—731no—
450C2×#95C2×D7311yescharacteristic
451C25C22×D7311yescharacteristic
452C25C22×D7311yescharacteristic
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4C22×D7314yes—
457C23×C4—731no—
458C23×C4—731no—
459C23×C4—731no—
460C23×C4—731no—
461C23×C4—731no—
462C23×C4—731no—
463C23×C4—731no—
464C23×C4—731no—
465C23×C4C22×D7311yescharacteristic
466C23×C4C22×D7311yescharacteristic
467C23×C4C22×D7311yescharacteristic
468C23×C4C22×D7311yescharacteristic
469C23×C4C22×D7311yescharacteristic
470C2×C4⋊C4—24no—
471C2×C4⋊C4—2922no—
472C2×C4⋊C4—2922no—
473C2×C4⋊C4—2922no—
474C2×C4⋊C4—734no—
475C2×C4⋊C4—734no—
476C2×C4⋊C4—734no—
477C2×C4⋊C4—734no—
478C2×C4⋊C4—734no—
479C2×C4⋊C4—734no—
480C2×C4⋊C4—1464no—
481C2×C4⋊C4—1464no—
482C2×C4⋊C4—1464no—
483C2×C4⋊C4C22×D7314yes—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—2922no—
489C2×C22⋊C4—2922no—
490C2×C22⋊C4—734no—
491C2×C22⋊C4—734no—
492C2×C22⋊C4—734no—
493C2×C22⋊C4—734no—
494C2×C22⋊C4—734no—
495C2×C22⋊C4—734no—
496C2×C22⋊C4—734no—
497C2×C22⋊C4—734no—
498C2×C22⋊C4—1464no—
499C2×C22⋊C4—1464no—
500C2×C22⋊C4—1464no—
501C2×C22⋊C4—1464no—
502C2×C22⋊C4—1464no—
503C2×C22⋊C4—1464no—
504C2×C22⋊C4C22×D7314yes—
505C2×C22⋊C4C22×D7314yes—
506C2×C22⋊C4C22×D7314yes—
507C2×C22⋊C4C22×D7314yes—
508C2×C42—2922no—
509C2×C42—2922no—
510C2×C42—2922no—
511C2×C42—734no—
512C2×C42—734no—
513C2×C42—734no—
514C2×C42—734no—
515C2×C42—734no—
516C2×C42—1464no—
517C2×C42—1464no—
518#95—734no—
519#95—734no—
520#95—734no—
521#95—734no—
522#95—734no—
523#95—734no—
524#95—734no—
525#95—734no—
526#95—734no—
527#95C22×D7314yes—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C23×D7312yes—
543C24C23×D7312yes—
544C24C23×D7311yescharacteristic
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—416no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—734no—
563C22×C4—734no—
564C22×C4—734no—
565C22×C4—732no—
566C22×C4—732no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—732no—
570C22×C4—732no—
571C22×C4—732no—
572C22×C4—732no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1462no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4—1462no—
590C22×C4—1462no—
591C22×C4—1462no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4#1192402714yes—
595C22×C4#1192402714yes—
596C22×C4C23×D7312yes—
597C22×C4C23×D7312yes—
598C22×C4C23×D7312yes—
599C22×C4C23×D7312yes—
600C22×C4C23×D7312yes—
601C4⋊C4—28no—
602C4⋊C4—2924no—
603C4⋊C4—2924no—
604C4⋊C4—2924no—
605C4⋊C4—1468no—
606C4⋊C4—1468no—
607C4⋊C4—1468no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—2924no—
613C22⋊C4—2924no—
614C22⋊C4—1468no—
615C22⋊C4—1468no—
616C22⋊C4—1468no—
617C22⋊C4—1468no—
618C22⋊C4—1468no—
619C22⋊C4—1468no—
620C42—2924no—
621C42—2924no—
622C42—2924no—
623C42—1468no—
624C42—1468no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#41×D7312yes—
654C23#41×D7312yes—
655C23#41×D7312yes—
656C23C2×#1192402712yes—
657C23C2×#1192402712yes—
658C23#1455663612yes—
659C23#1455663612yes—
660C23C24×D7311yescharacteristic
661D4—416no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—2924no—
681C2×C4—2924no—
682C2×C4—2924no—
683C2×C4—2924no—
684C2×C4—2924no—
685C2×C4—734no—
686C2×C4—734no—
687C2×C4—734no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1468no—
710C2×C4—1468no—
711C2×C4—1468no—
712C2×C4C2×#1192402714yes—
713C2×C4C2×#1192402714yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22#1798911614yes—
731C22#1798911814yes—
732C22#1798917214yes—
733C22#1798928214yes—
734C22#1798928414yes—
735C22#1798930114yes—
736C22#1798932114yes—
737C22C2×#41×D7311yescharacteristic
738C22C2×#41×D7311yescharacteristic
739C22C2×#41×D7311yescharacteristic
740C22C22×#1192402711yescharacteristic
741C22C22×#1192402711yescharacteristic
742C22C2×#1455663611yescharacteristic
743C22C2×#1455663611yescharacteristic
744C4—24no—
745C4—24no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—2922no—
750C4—2922no—
751C4—2922no—
752C4—2922no—
753C4—2922no—
754C4—1464no—
755C4—1464no—
756C4—1464no—
757C2—82no—
758C2—82no—
759C2#2261542318yesdirect product factor
760C2C2×#1798911611yescharacteristic
761C2C2×#1798911811yescharacteristic
762C2C2×#1798917211yescharacteristic
763C2C2×#1798928211yescharacteristic
764C2C2×#1798928411yescharacteristic
765C2C2×#1798930111yescharacteristic
766C2C2×#1798932111yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#394×C73C2
socleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC2×#394D73
hypocenterC73C2×#2593
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #22615423C2direct (N × H)
2. C2×#17988529C2semidirect
3. C2×#17988520C2semidirect
6. C2×#17988481C2semidirect
7. C2×#17988481C2semidirect
8. C2×#17988480C2semidirect
9. C2×#17988480C2semidirect
10. C2×#17988475C2semidirect
11. C2×#17988475C2semidirect
12. C2×#17988475C2semidirect
13. C2×#17988475C2semidirect
14. C2×C4⋊C4×Dic73C2semidirect
15. C2×#17988438C2semidirect
36. #17988529C22semidirect
37. #17988520C22semidirect
40. #17988481C22semidirect
41. #17988481C22semidirect
42. #17988480C22semidirect
43. #17988480C22semidirect
44. #17988475C22semidirect
45. #17988475C22semidirect
46. #17988475C22semidirect
47. #17988475C22semidirect
48. C4⋊C4×Dic73C22semidirect
49. #17988438C22semidirect
376. C2×C73#2593semidirect
400. C73C2×#2593semidirect
759. C2#22615423direct (N × H)

Maximal subgroups

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

subgroupindex
#226154232
C2×#179885292
C2×#179885202
C2×#179885012
C2×#179884902
C2×#179884812
C2×#179884802
C2×#179884752
C2×C4⋊C4×Dic732
C2×#179884382
C2×#394×C732
C2×#259373