Finite Group Databasebeta

← C2×#22616089 #33252786

Subgroups — C2×#22616089 #33252786

Order 18688.

2354 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×#14556586C211yesmaximal, characteristic
2C22×#14556581C211yesmaximal, characteristic, complemented
3#22616089C2116yesmaximal, direct product factor
4C2×#17988528C211yesmaximal, characteristic, complemented
5C2×#17988522C211yesmaximal, characteristic
6C2×#17988521C211yesmaximal, characteristic, complemented
7C2×#17988520C211yesmaximal, characteristic, complemented
8C2×#17988516C211yesmaximal, characteristic
9C2×#17988509C211yesmaximal, characteristic
10C2×#17988509C211yesmaximal, characteristic
11C2×#17988486C211yesmaximal, characteristic, complemented
12C2×#17988484C211yesmaximal, characteristic, complemented
13C2×#17988479C211yesmaximal, characteristic
14C2×#17988476C211yesmaximal, characteristic
15C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
16C2×#398×C73C211yesmaximal, characteristic, complemented
17C2×#14556586—28no—
18C2×#14556586C2218yes—
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×#11924005C2211yescharacteristic
33C22×#11924005C2211yescharacteristic
34C22×#11924005C2211yescharacteristic
35C22×#11924005C2211yescharacteristic
36C22×#11924005C2211yescharacteristic
37C22×#11924005C2211yescharacteristic
38C22×#11924005C2211yescharacteristic
39C22×C4×Dic73C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41C22×C4×Dic73C2211yescharacteristic
42#17988528C2218yescomplemented
43#17988522C2218yes—
44#17988521C2218yescomplemented
45#17988520C2218yescomplemented
46#17988516C2218yes—
47#17988509C2218yes—
48#17988509C2218yes—
49#17988486C2218yescomplemented
50#17988484C2218yescomplemented
51#17988479C2218yes—
52#17988476C2218yes—
53C4⋊C4×Dic73C2218yescomplemented
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C4⋊C4×C73C2211yescharacteristic
65#398×C73C2218yescomplemented
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C2×#95×C73C2211yescharacteristic
69C24×D73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77#14556586—232no—
78#14556581—232no—
79C2×C4⋊Dic73—24no—
80C2×C4⋊Dic73—24no—
81C2×C4⋊Dic73—24no—
82C2×C4⋊Dic73—42no—
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—42no—
94C2×#11924007C2314yes—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×#11924005—24no—
102C2×#11924005—24no—
103C2×#11924005—24no—
104C2×#11924005—24no—
105C2×#11924005—24no—
106C2×#11924005—42no—
107C2×#11924005—42no—
108C2×#11924005C2314yes—
109C2×#11924005C2314yes—
110C2×#11924005C2314yes—
111C2×#11924005C2314yes—
112C2×#11924005C2314yes—
113C2×#11924005C2314yes—
114C2×#11924005C2314yes—
115C2×C4×Dic73—42no—
116C2×C4×Dic73—42no—
117C2×C4×Dic73D418yes—
118C2×C4×Dic73C2314yes—
119C2×C4×Dic73C2314yes—
120C2×C4×Dic73C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C2×C4⋊C4×C73—24no—
136C2×C4⋊C4×C73—24no—
137C2×C4⋊C4×C73—24no—
138C2×C4⋊C4×C73—24no—
139C2×C4⋊C4×C73C2314yes—
140C2×C4⋊C4×C73C2314yes—
141C2×C4⋊C4×C73C2314yes—
142C2×C4⋊C4×C73C2314yes—
143#95×C73C2314yes—
144#95×C73C2314yes—
145#95×C73C2314yes—
146C23×D73—22no—
147C23×D73—22no—
148C23×D73—22no—
149C23×D73—22no—
150C23×D73—22no—
151C23×D73—22no—
152C23×D73—22no—
153C23×D73C2412yes—
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×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73C2×D414yes—
173C22×Dic73C2×D414yes—
174C22×Dic73#4114yes—
175C22×Dic73C2412yes—
176C22×Dic73C2412yes—
177C22×Dic73C2412yes—
178C22×Dic73C2412yes—
179C22×Dic73C2412yes—
180C22×Dic73C2412yes—
181C22×Dic73C2412yes—
182C4⋊Dic73—28no—
183C4⋊Dic73—28no—
184C4⋊Dic73—28no—
185C4⋊Dic73—44no—
186#11924007—28no—
187#11924007—28no—
188#11924007—28no—
189#11924007—28no—
190#11924007—28no—
191#11924007—28no—
192#11924007—44no—
193#11924005—28no—
194#11924005—28no—
195#11924005—28no—
196#11924005—28no—
197#11924005—28no—
198#11924005—44no—
199#11924005—44no—
200C4×Dic73—44no—
201C4×Dic73—44no—
202C4×Dic73C2×D4116yes—
203C24×C73C2411yescharacteristic
204C22×C4×C73—22no—
205C22×C4×C73—22no—
206C22×C4×C73—22no—
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×C73—22no—
223C22×C4×C73C2×D414yes—
224C22×C4×C73#4114yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C22×C4×C73C2412yes—
232C4⋊C4×C73—28no—
233C4⋊C4×C73—28no—
234C4⋊C4×C73—28no—
235C4⋊C4×C73—28no—
236C23×C73C22×D412yes—
237C23×C73C2×#4112yes—
238C23×C73C2×#4112yes—
239C23×C73H(5,𝔽2)12yes—
240C23×C732−1+412yes—
241C23×C732−1+412yes—
242C23×C732−1+412yes—
243C23×C73C2511yescharacteristic
244C22×D73—22no—
245C22×D73—22no—
246C22×D73—22no—
247C22×D73—22no—
248C22×D73—22no—
249C22×D73—22no—
250C22×D73—22no—
251C22×D73—44no—
252C22×D73—44no—
253C22×D73—44no—
254C22×D73—44no—
255C22×D73—44no—
256C22×D73—44no—
257C22×D73—44no—
258C2×C4×C73—28no—
259C2×C4×C73—28no—
260C2×C4×C73—22no—
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—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—44no—
280C2×C4×C73—44no—
281C2×C4×C73—44no—
282C2×C4×C73—44no—
283C2×C4×C73—44no—
284C2×C4×C73C22×D414yes—
285C2×C4×C73C2×#4114yes—
286C2×Dic73—28no—
287C2×Dic73—28no—
288C2×Dic73—28no—
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—22no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73—44no—
310C2×Dic73—44no—
311C2×Dic73C22×D414yes—
312C2×Dic73C22×D414yes—
313C2×Dic73C2×#4114yes—
314C22×C73#53214yes—
315C22×C73#53614yes—
316C22×C73#53714yes—
317C22×C73#53914yes—
318C22×C73#53914yes—
319C22×C73#54114yes—
320C22×C73#54114yes—
321C22×C73C23×D411yescharacteristic
322C22×C73C22×#4111yescharacteristic
323C22×C73C22×#4111yescharacteristic
324C22×C73C2×H(5,𝔽2)11yescharacteristic
325C22×C73C2×2−1+411yescharacteristic
326C22×C73C2×2−1+411yescharacteristic
327C22×C73C2×2−1+411yescharacteristic
328C2×D73—42no—
329C2×D73—42no—
330C2×D73—42no—
331C2×D73—42no—
332C2×D73—42no—
333C2×D73—42no—
334C2×D73—42no—
335C2×D73—88no—
336C4×C73—24no—
337C4×C73—24no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343Dic73—24no—
344Dic73—24no—
345Dic73—24no—
346Dic73—42no—
347Dic73—42no—
348Dic73—42no—
349Dic73—42no—
350C2×#2664—731nomaximal, Sylow
351C2×C73#266418yescomplemented
352C2×C73C2×#53211yescharacteristic
353C2×C73C2×#53611yescharacteristic
354C2×C73C2×#53711yescharacteristic
355C2×C73C2×#53911yescharacteristic
356C2×C73C2×#53911yescharacteristic
357C2×C73C2×#54111yescharacteristic
358C2×C73C2×#54111yescharacteristic
359D73—82no—
360C22×#126—731no—
361C22×#125—731no—
362#2664—7316no—
363C2×#400—731no—
364C2×#399—731no—
365C2×#398—731no—
366C2×#398—731no—
367C2×#398D7311yescharacteristic, complemented
368C2×#397—731no—
369C2×#396—731no—
370C2×#396—731no—
371C2×#389—731no—
372C2×#389—731no—
373C2×#388—731no—
374C2×#388—731no—
375C2×C4×C4⋊C4—731no—
376C73C2×#266411yescharacteristic, 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⋊C4C2×D7311yescharacteristic
393C22×C4⋊C4C2×D7311yescharacteristic
394C22×C4⋊C4C2×D7311yescharacteristic
395C22×C4⋊C4C2×D7311yescharacteristic
396C22×C22⋊C4—731no—
397C22×C22⋊C4—731no—
398C22×C22⋊C4—731no—
399C22×C22⋊C4—731no—
400C22×C22⋊C4—731no—
401C22×C22⋊C4—731no—
402C22×C22⋊C4—731no—
403C22×C42—731no—
404C22×C42—731no—
405C22×C42—731no—
406#400—738no—
407#399—738no—
408#398—738no—
409#398—738no—
410#398C2×D7318yescomplemented
411#397—738no—
412#396—738no—
413#396—738no—
414#389—738no—
415#389—738no—
416#388—738no—
417#388—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×#95C2×D7311yescharacteristic
427C2×#95C2×D7311yescharacteristic
428C2×#95C2×D7311yescharacteristic
429C25—731no—
430C23×C4—731no—
431C23×C4—731no—
432C23×C4—731no—
433C23×C4—731no—
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4C22×D7311yescharacteristic
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—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—2922no—
451C2×C4⋊C4—2922no—
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—734no—
461C2×C4⋊C4—734no—
462C2×C4⋊C4—734no—
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⋊C4—1464no—
472C2×C4⋊C4C22×D7314yes—
473C2×C4⋊C4C22×D7314yes—
474C2×C4⋊C4C22×D7314yes—
475C2×C4⋊C4C22×D7314yes—
476C2×C22⋊C4—2922no—
477C2×C22⋊C4—2922no—
478C2×C22⋊C4—734no—
479C2×C22⋊C4—734no—
480C2×C22⋊C4—734no—
481C2×C22⋊C4—734no—
482C2×C22⋊C4—734no—
483C2×C22⋊C4—734no—
484C2×C22⋊C4—734no—
485C2×C22⋊C4—1464no—
486C2×C22⋊C4—1464no—
487C2×C22⋊C4—1464no—
488C2×C22⋊C4—1464no—
489C2×C22⋊C4—1464no—
490C2×C42—2922no—
491C2×C42—2922no—
492C2×C42—734no—
493C2×C42—734no—
494C2×C42—738no—
495C2×C42—734no—
496#95—734no—
497#95—734no—
498#95—734no—
499#95—734no—
500#95—734no—
501#95—734no—
502#95—734no—
503#95C22×D7314yes—
504#95C22×D7314yes—
505#95C22×D7314yes—
506C24—732no—
507C24—1462no—
508C24—1462no—
509C24—1462no—
510C24—1462no—
511C24—1462no—
512C24—1462no—
513C24—1462no—
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—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—734no—
535C22×C4—734no—
536C22×C4—734no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—732no—
542C22×C4—732no—
543C22×C4—732no—
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×C4C23×D7312yes—
565C22×C4C23×D7312yes—
566C22×C4C23×D7312yes—
567C22×C4C23×D7312yes—
568C22×C4C23×D7312yes—
569C22×C4C23×D7312yes—
570C22×C4C23×D7312yes—
571C4⋊C4—28no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—2924no—
576C4⋊C4—2924no—
577C4⋊C4—1468no—
578C4⋊C4—1468no—
579C4⋊C4—1468no—
580C4⋊C4—1468no—
581C4⋊C4—1468no—
582C4⋊C4—1468no—
583C4⋊C4—1468no—
584C4⋊C4—1468no—
585C4⋊C4—1468no—
586C22⋊C4—2924no—
587C22⋊C4—2924no—
588C22⋊C4—1468no—
589C22⋊C4—1468no—
590C22⋊C4—1468no—
591C22⋊C4—1468no—
592C22⋊C4—1468no—
593C42—2924no—
594C42—2924no—
595C42—7316no—
596C23—2924no—
597C23—2924no—
598C23—2924no—
599C23—2924no—
600C23—2924no—
601C23—2924no—
602C23—2924no—
603C23—1462no—
604C23—1462no—
605C23—1462no—
606C23—1462no—
607C23—1462no—
608C23—1462no—
609C23—1462no—
610C23C2×D4×D7312yes—
611C23#41×D7312yes—
612C23C2×#1192402712yes—
613C23#1455663712yes—
614C23#1455663812yes—
615C23#1455663912yes—
616C23#1455663912yes—
617C23C24×D7311yescharacteristic
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
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—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—2924no—
645C2×C4—2924no—
646C2×C4—2924no—
647C2×C4—2924no—
648C2×C4—734no—
649C2×C4—734no—
650C2×C4—734no—
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—1468no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1462no—
669C2×C4—1462no—
670C2×C4—1468no—
671C2×C4—1468no—
672C2×C4C2×D4×D7314yes—
673C2×C4C2×#1192402714yes—
674C22—2922no—
675C22—2922no—
676C22—2922no—
677C22—2922no—
678C22—2922no—
679C22—2922no—
680C22—2922no—
681C22—5848no—
682C22#1798913214yes—
683C22#1798916014yes—
684C22#1798916714yes—
685C22#1798918114yes—
686C22#1798918514yes—
687C22#1798919614yes—
688C22#1798919814yes—
689C22C22×D4×D7311yescharacteristic
690C22C2×#41×D7311yescharacteristic
691C22C22×#1192402711yescharacteristic
692C22C2×#1455663711yescharacteristic
693C22C2×#1455663811yescharacteristic
694C22C2×#1455663911yescharacteristic
695C22C2×#1455663911yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—2922no—
707C4—1464no—
708C4—1464no—
709C4—1464no—
710C2—5842no—
711C2#2261608918yesdirect product factor
712C2C2×#1798913211yescharacteristic
713C2C2×#1798916011yescharacteristic
714C2C2×#1798916711yescharacteristic
715C2C2×#1798918111yescharacteristic
716C2C2×#1798918511yescharacteristic
717C2C2×#1798919611yescharacteristic
718C2C2×#1798919811yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#398×C73C2
socleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×#398D73
hypocenterC73C2×#2664
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#14556581C2semidirect
3. #22616089C2direct (N × H)
4. C2×#17988528C2semidirect
6. C2×#17988521C2semidirect
7. C2×#17988520C2semidirect
11. C2×#17988486C2semidirect
12. C2×#17988484C2semidirect
15. C2×C4⋊C4×Dic73C2semidirect
16. C2×#398×C73C2semidirect
20. C2×#14556581C22semidirect
42. #17988528C22semidirect
44. #17988521C22semidirect
45. #17988520C22semidirect
49. #17988486C22semidirect
50. #17988484C22semidirect
53. C4⋊C4×Dic73C22semidirect
65. #398×C73C22semidirect
351. C2×C73#2664semidirect
367. C2×#398D73semidirect
376. C73C2×#2664semidirect
410. #398C2×D73semidirect
711. C2#22616089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565862
C22×#145565812
#226160892
C2×#179885282
C2×#179885222
C2×#179885212
C2×#179885202
C2×#179885162
C2×#179885092
C2×#179884862
C2×#179884842
C2×#179884792
C2×#179884762
C2×C4⋊C4×Dic732
C2×#398×C732
C2×#266473