Finite Group Databasebeta

← C2×#22614602 #33255070

Subgroups — C2×#22614602 #33255070

Order 18688.

2466 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556584C211yesmaximal, characteristic
2C22×#14556581C211yesmaximal, characteristic, complemented
3#22614602C2116yesmaximal, direct product factor
4C2×#17988523C211yesmaximal, characteristic
5C2×#17988521C211yesmaximal, characteristic, complemented
6C2×#17988520C211yesmaximal, characteristic, complemented
7C2×#17988510C211yesmaximal, characteristic
8C2×#17988485C211yesmaximal, characteristic, complemented
9C2×#17988480C211yesmaximal, characteristic
10C2×#17988475C211yesmaximal, characteristic
11C2×#17988475C211yesmaximal, characteristic
12C2×#17988470C211yesmaximal, characteristic, complemented
13C2×#17988451C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
15C2×#17988438C211yesmaximal, characteristic, complemented
16C2×#388×C73C211yesmaximal, characteristic
17C2×#14556584—28no—
18C2×#14556584C2218yes—
19C2×#14556581—28no—
20C2×#14556581C2218yescomplemented
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C4⋊Dic73C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×#11924007C2211yescharacteristic
33C22×C22⋊Dic73C2211yescharacteristic
34C22×C22⋊Dic73C2211yescharacteristic
35C22×C22⋊Dic73C2211yescharacteristic
36C22×C22⋊Dic73C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39C22×C4×Dic73C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41#17988523C2218yes—
42#17988521C2218yescomplemented
43#17988520C2218yescomplemented
44#17988510C2218yes—
45#17988485C2218yescomplemented
46#17988480C2218yes—
47#17988475C2218yes—
48#17988475C2218yes—
49#17988470C2218yescomplemented
50#17988451C2218yescomplemented
51C4×C4⋊Dic73C2218yescomplemented
52#17988438C2218yescomplemented
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64C22×C22⋊C4×C73C2211yescharacteristic
65C22×C42×C73C2211yescharacteristic
66#388×C73C2218yes—
67C2×#95×C73C2211yescharacteristic
68C2×#95×C73C2211yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77#14556584—232no—
78#14556581—232no—
79C2×C4⋊Dic73—24no—
80C2×C4⋊Dic73—24no—
81C2×C4⋊Dic73—24no—
82C2×C4⋊Dic73D418yes—
83C2×C4⋊Dic73C2314yes—
84C2×C4⋊Dic73C2314yes—
85C2×C4⋊Dic73C2314yes—
86C2×C4⋊Dic73C2314yes—
87C2×#11924007—24no—
88C2×#11924007—24no—
89C2×#11924007—24no—
90C2×#11924007—24no—
91C2×#11924007—24no—
92C2×#11924007—24no—
93C2×#11924007—24no—
94C2×#11924007—24no—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×#11924007C2314yes—
102C2×#11924007C2314yes—
103C2×C22⋊Dic73—24no—
104C2×C22⋊Dic73—24no—
105C2×C22⋊Dic73—24no—
106C2×C22⋊Dic73—24no—
107C2×C22⋊Dic73C2314yes—
108C2×C22⋊Dic73C2314yes—
109C2×C22⋊Dic73C2314yes—
110C2×C22⋊Dic73C2314yes—
111C2×C4×Dic73—24no—
112C2×C4×Dic73—24no—
113C2×C4×Dic73—24no—
114C2×C4×Dic73—24no—
115C2×C4×Dic73C2314yes—
116C2×C4×Dic73C2314yes—
117C2×C4×Dic73C2314yes—
118C2×C4×Dic73C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127C25×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C2×C4⋊C4×C73—24no—
135C2×C4⋊C4×C73C2314yes—
136C2×C22⋊C4×C73—24no—
137C2×C22⋊C4×C73—24no—
138C2×C22⋊C4×C73—24no—
139C2×C22⋊C4×C73C2314yes—
140C2×C22⋊C4×C73C2314yes—
141C2×C22⋊C4×C73C2314yes—
142C2×C42×C73—24no—
143C2×C42×C73C2314yes—
144#95×C73C2314yes—
145#95×C73C2314yes—
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—22no—
166C22×Dic73C2×D414yes—
167C22×Dic73C2×D414yes—
168C22×Dic73#4114yes—
169C22×Dic73#4114yes—
170C22×Dic73C2412yes—
171C22×Dic73C2412yes—
172C22×Dic73C2412yes—
173C22×Dic73C2412yes—
174C22×Dic73C2412yes—
175C22×Dic73C2412yes—
176C22×Dic73C2412yes—
177C22×Dic73C2412yes—
178C4⋊Dic73—28no—
179C4⋊Dic73—28no—
180C4⋊Dic73—28no—
181C4⋊Dic73C2×D4116yes—
182#11924007—28no—
183#11924007—28no—
184#11924007—28no—
185#11924007—28no—
186#11924007—28no—
187#11924007—28no—
188#11924007—28no—
189#11924007—28no—
190C22⋊Dic73—28no—
191C22⋊Dic73—28no—
192C22⋊Dic73—28no—
193C22⋊Dic73—28no—
194C4×Dic73—28no—
195C4×Dic73—28no—
196C4×Dic73—28no—
197C4×Dic73—28no—
198C24×C73—22no—
199C24×C73—22no—
200C24×C73—22no—
201C24×C73—22no—
202C24×C73—22no—
203C24×C73—22no—
204C24×C73—22no—
205C24×C73C2412yes—
206C24×C73C2411yescharacteristic
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—22no—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—22no—
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×C73C2×D414yes—
223C22×C4×C73#4114yes—
224C22×C4×C73#4114yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C4⋊C4×C73—28no—
232C22⋊C4×C73—28no—
233C22⋊C4×C73—28no—
234C22⋊C4×C73—28no—
235C42×C73—28no—
236C23×C73—22no—
237C23×C73—22no—
238C23×C73—22no—
239C23×C73—22no—
240C23×C73—22no—
241C23×C73—22no—
242C23×C73—22no—
243C23×C73—44no—
244C23×C73—44no—
245C23×C73—44no—
246C23×C73—44no—
247C23×C73—44no—
248C23×C73—44no—
249C23×C73—44no—
250C23×C73C22×D412yes—
251C23×C73C2×#4112yes—
252C23×C73C2×#4112yes—
253C23×C73C2×#4112yes—
254C23×C73C2×#4112yes—
255C23×C732−1+412yes—
256C23×C732−1+412yes—
257C23×C73C2511yescharacteristic
258C2×C4×C73—28no—
259C2×C4×C73—28no—
260C2×C4×C73—28no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—44no—
277C2×C4×C73—44no—
278C2×C4×C73—44no—
279C2×C4×C73C22×D414yes—
280C2×C4×C73C2×#4114yes—
281C2×C4×C73C2×#4114yes—
282C2×Dic73—28no—
283C2×Dic73—28no—
284C2×Dic73—28no—
285C2×Dic73—28no—
286C2×Dic73—22no—
287C2×Dic73—22no—
288C2×Dic73—22no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—44no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73—44no—
310C2×Dic73C22×D414yes—
311C2×Dic73C22×D414yes—
312C2×Dic73C2×#4114yes—
313C2×Dic73C2×#4114yes—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—42no—
321C22×C73—88no—
322C22×C73#52914yes—
323C22×C73#53214yes—
324C22×C73#54114yes—
325C22×C73#54714yes—
326C22×C73#54814yes—
327C22×C73#55214yes—
328C22×C73#55214yes—
329C22×C73C23×D411yescharacteristic
330C22×C73C22×#4111yescharacteristic
331C22×C73C22×#4111yescharacteristic
332C22×C73C22×#4111yescharacteristic
333C22×C73C22×#4111yescharacteristic
334C22×C73C2×2−1+411yescharacteristic
335C22×C73C2×2−1+411yescharacteristic
336C4×C73—24no—
337C4×C73—24no—
338C4×C73—24no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—42no—
342Dic73—24no—
343Dic73—24no—
344Dic73—24no—
345Dic73—24no—
346Dic73—42no—
347Dic73—42no—
348Dic73—42no—
349Dic73—42no—
350C2×#2519—731nomaximal, Sylow
351C2×C73—82no—
352C2×C73#251918yescomplemented
353C2×C73C2×#52911yescharacteristic
354C2×C73C2×#53211yescharacteristic
355C2×C73C2×#54111yescharacteristic
356C2×C73C2×#54711yescharacteristic
357C2×C73C2×#54811yescharacteristic
358C2×C73C2×#55211yescharacteristic
359C2×C73C2×#55211yescharacteristic
360C22×#126—731no—
361C22×#125—731no—
362#2519—7316no—
363C2×#399—731no—
364C2×#398—731no—
365C2×#398—731no—
366C2×#396—731no—
367C2×#389—731no—
368C2×#388—731no—
369C2×#388—731no—
370C2×#388—731no—
371C2×#388D7311yescharacteristic
372C2×#387—731no—
373C2×#382—731no—
374C2×C4×C4⋊C4—731no—
375C2×C4×C4⋊C4—731no—
376C73C2×#251911yescharacteristic, complemented, Sylow
377C2×#126—738no—
378C2×#126—1468no—
379C2×#125—738no—
380C2×#125—1468no—
381C22×C4⋊C4—731no—
382C22×C4⋊C4—731no—
383C22×C4⋊C4—731no—
384C22×C4⋊C4—731no—
385C22×C4⋊C4—731no—
386C22×C4⋊C4—731no—
387C22×C4⋊C4—731no—
388C22×C4⋊C4—731no—
389C22×C4⋊C4—731no—
390C22×C4⋊C4—731no—
391C22×C4⋊C4—731no—
392C22×C4⋊C4—731no—
393C22×C4⋊C4C2×D7311yescharacteristic
394C22×C22⋊C4—731no—
395C22×C22⋊C4—731no—
396C22×C22⋊C4—731no—
397C22×C22⋊C4—731no—
398C22×C22⋊C4C2×D7311yescharacteristic
399C22×C22⋊C4C2×D7311yescharacteristic
400C22×C22⋊C4C2×D7311yescharacteristic
401C22×C42—731no—
402C22×C42—731no—
403C22×C42—731no—
404C22×C42—731no—
405C22×C42C2×D7311yescharacteristic
406#399—738no—
407#398—738no—
408#398—738no—
409#396—738no—
410#389—738no—
411#388—738no—
412#388—738no—
413#388—738no—
414#388C2×D7318yes—
415#387—738no—
416#382—738no—
417C4×C4⋊C4—738no—
418C4×C4⋊C4—738no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95—731no—
424C2×#95—731no—
425C2×#95—731no—
426C2×#95—731no—
427C2×#95C2×D7311yescharacteristic
428C2×#95C2×D7311yescharacteristic
429C25C22×D7311yescharacteristic
430C23×C4—731no—
431C23×C4—731no—
432C23×C4—731no—
433C23×C4—731no—
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4C22×D7311yescharacteristic
439C23×C4C22×D7311yescharacteristic
440C23×C4C22×D7311yescharacteristic
441C23×C4C22×D7311yescharacteristic
442C23×C4C22×D7311yescharacteristic
443C23×C4C22×D7311yescharacteristic
444#126—14632no—
445#125—14632no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—738no—
448C2×C4⋊C4—734no—
449C2×C4⋊C4—734no—
450C2×C4⋊C4—734no—
451C2×C4⋊C4—734no—
452C2×C4⋊C4—734no—
453C2×C4⋊C4—734no—
454C2×C4⋊C4—734no—
455C2×C4⋊C4—734no—
456C2×C4⋊C4—734no—
457C2×C4⋊C4—734no—
458C2×C4⋊C4—734no—
459C2×C4⋊C4—734no—
460C2×C4⋊C4—1464no—
461C2×C4⋊C4—1464no—
462C2×C4⋊C4—1464no—
463C2×C4⋊C4—1464no—
464C2×C4⋊C4—1464no—
465C2×C4⋊C4—1464no—
466C2×C4⋊C4—1464no—
467C2×C4⋊C4—1464no—
468C2×C4⋊C4—1464no—
469C2×C4⋊C4—1464no—
470C2×C4⋊C4—1464no—
471C2×C4⋊C4C22×D7314yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—734no—
476C2×C22⋊C4—734no—
477C2×C22⋊C4—734no—
478C2×C22⋊C4—734no—
479C2×C22⋊C4—1464no—
480C2×C22⋊C4—1464no—
481C2×C22⋊C4—1464no—
482C2×C22⋊C4—1464no—
483C2×C22⋊C4C22×D7314yes—
484C2×C22⋊C4C22×D7314yes—
485C2×C22⋊C4C22×D7314yes—
486C2×C42—24no—
487C2×C42—734no—
488C2×C42—734no—
489C2×C42—734no—
490C2×C42—734no—
491C2×C42—1464no—
492C2×C42—1464no—
493C2×C42—1464no—
494C2×C42—1464no—
495C2×C42C22×D7314yes—
496#95—734no—
497#95—734no—
498#95—734no—
499#95—734no—
500#95—734no—
501#95—734no—
502#95—734no—
503#95—734no—
504#95C22×D7314yes—
505#95C22×D7314yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C23×D7312yes—
514C24C23×D7311yescharacteristic
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—734no—
531C22×C4—734no—
532C22×C4—734no—
533C22×C4—734no—
534C22×C4—732no—
535C22×C4—732no—
536C22×C4—732no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—732no—
542C22×C4—1462no—
543C22×C4—1462no—
544C22×C4—1462no—
545C22×C4—1462no—
546C22×C4—1462no—
547C22×C4—1462no—
548C22×C4—1462no—
549C22×C4—1462no—
550C22×C4—1462no—
551C22×C4—1462no—
552C22×C4—1462no—
553C22×C4—1462no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4D4×D7314yes—
563C22×C4#1192402714yes—
564C22×C4#1192402814yes—
565C22×C4C23×D7312yes—
566C22×C4C23×D7312yes—
567C22×C4C23×D7312yes—
568C22×C4C23×D7312yes—
569C22×C4C23×D7312yes—
570C22×C4C23×D7312yes—
571C4⋊C4—28no—
572C4⋊C4—7316no—
573C4⋊C4—1468no—
574C4⋊C4—1468no—
575C4⋊C4—1468no—
576C4⋊C4—1468no—
577C4⋊C4—1468no—
578C4⋊C4—1468no—
579C4⋊C4—1468no—
580C4⋊C4—1468no—
581C4⋊C4—1468no—
582C4⋊C4—1468no—
583C4⋊C4—1468no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—1468no—
588C22⋊C4—1468no—
589C22⋊C4—1468no—
590C22⋊C4—1468no—
591C42—28no—
592C42—1468no—
593C42—1468no—
594C42—1468no—
595C42—1468no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C2×D4×D7312yes—
611C23#41×D7312yes—
612C23#41×D7312yes—
613C23C2×#1192402712yes—
614C23C2×#1192402812yes—
615C23#1455663812yes—
616C23#1455663812yes—
617C23C24×D7311yescharacteristic
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—2924no—
640C2×C4—2924no—
641C2×C4—2924no—
642C2×C4—2924no—
643C2×C4—734no—
644C2×C4—734no—
645C2×C4—734no—
646C2×C4—734no—
647C2×C4—1462no—
648C2×C4—1462no—
649C2×C4—1462no—
650C2×C4—1462no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4—1462no—
655C2×C4—1462no—
656C2×C4—1462no—
657C2×C4—1462no—
658C2×C4—1462no—
659C2×C4—1462no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1468no—
668C2×C4—1468no—
669C2×C4—1468no—
670C2×C4—1468no—
671C2×C4C2×D4×D7314yes—
672C2×C4C2×#1192402714yes—
673C2×C4C2×#1192402814yes—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—88no—
682C22#1798911514yes—
683C22#1798913214yes—
684C22#1798919414yes—
685C22#1798924214yes—
686C22#1798924514yes—
687C22#1798927414yes—
688C22#1798927714yes—
689C22C22×D4×D7311yescharacteristic
690C22C2×#41×D7311yescharacteristic
691C22C2×#41×D7311yescharacteristic
692C22C22×#1192402711yescharacteristic
693C22C22×#1192402811yescharacteristic
694C22C2×#1455663811yescharacteristic
695C22C2×#1455663811yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—2922no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—1464no—
707C4—1464no—
708C4—1464no—
709C4—1464no—
710C2—82no—
711C2#2261460218yesdirect product factor
712C2C2×#1798911511yescharacteristic
713C2C2×#1798913211yescharacteristic
714C2C2×#1798919411yescharacteristic
715C2C2×#1798924211yescharacteristic
716C2C2×#1798924511yescharacteristic
717C2C2×#1798927411yescharacteristic
718C2C2×#1798927711yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#388×C73C2
socleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#388D73
hypocenterC73C2×#2519
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14556581C2semidirect
3. #22614602C2direct (N × H)
5. C2×#17988521C2semidirect
6. C2×#17988520C2semidirect
8. C2×#17988485C2semidirect
12. C2×#17988470C2semidirect
13. C2×#17988451C2semidirect
14. C2×C4×C4⋊Dic73C2semidirect
15. C2×#17988438C2semidirect
20. C2×#14556581C22semidirect
42. #17988521C22semidirect
43. #17988520C22semidirect
45. #17988485C22semidirect
49. #17988470C22semidirect
50. #17988451C22semidirect
51. C4×C4⋊Dic73C22semidirect
52. #17988438C22semidirect
352. C2×C73#2519semidirect
376. C73C2×#2519semidirect
711. C2#22614602direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565842
C22×#145565812
#226146022
C2×#179885232
C2×#179885212
C2×#179885202
C2×#179885102
C2×#179884852
C2×#179884802
C2×#179884752
C2×#179884702
C2×#179884512
C2×C4×C4⋊Dic732
C2×#179884382
C2×#388×C732
C2×#251973