Finite Group Databasebeta

← C2×#22615379 #33256286

Subgroups — C2×#22615379 #33256286

Order 18688.

2334 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
1#22615379C2116yesmaximal, direct product factor
2C2×#17988527C211yesmaximal, characteristic, complemented
3C2×#17988523C211yesmaximal, characteristic
4C2×#17988518C211yesmaximal, characteristic, complemented
5C2×#17988499C211yesmaximal, characteristic
6C2×#17988491C211yesmaximal, characteristic, complemented
7C2×#17988491C211yesmaximal, characteristic, complemented
8C2×#17988482C211yesmaximal, characteristic, complemented
9C2×#17988481C211yesmaximal, characteristic
10C2×#17988481C211yesmaximal, characteristic
11C2×#17988469C211yesmaximal, characteristic, complemented
12C2×#17988468C211yesmaximal, characteristic, complemented
13C2×#17988460C211yesmaximal, characteristic
14C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic73C211yesmaximal, characteristic
16C2×#385×C73C211yesmaximal, characteristic
17C23×Dic146C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2211yescharacteristic
21C22×#11924007C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×C22⋊Dic73C2211yescharacteristic
29C22×C4×Dic73C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33#17988527C2218yescomplemented
34#17988523C2218yes—
35#17988518C2218yescomplemented
36#17988499C2218yes—
37#17988491C2218yescomplemented
38#17988491C2218yescomplemented
39#17988482C2218yescomplemented
40#17988481C2218yes—
41#17988481C2218yes—
42#17988469C2218yescomplemented
43#17988468C2218yescomplemented
44#17988460C2218yes—
45C4⋊C4×Dic73C2218yescomplemented
46C4×C22⋊Dic73C2218yes—
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C24×C4×C73C2211yescharacteristic
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64#385×C73C2218yes—
65C2×#95×C73C2211yescharacteristic
66C2×#95×C73C2211yescharacteristic
67C22×Dic146—24no—
68C22×Dic146—24no—
69C22×Dic146—42no—
70C22×Dic146C2314yes—
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C2×C4⋊Dic73—24no—
80C2×C4⋊Dic73C2314yes—
81C2×#11924007—24no—
82C2×#11924007—24no—
83C2×#11924007—24no—
84C2×#11924007—42no—
85C2×#11924007—42no—
86C2×#11924007—42no—
87C2×#11924007C2314yes—
88C2×#11924007C2314yes—
89C2×#11924007C2314yes—
90C2×#11924007C2314yes—
91C2×#11924007C2314yes—
92C2×#11924007C2314yes—
93C2×C22⋊Dic73—24no—
94C2×C22⋊Dic73—24no—
95C2×C22⋊Dic73—42no—
96C2×C22⋊Dic73Q818yescomplemented
97C2×C22⋊Dic73C2314yes—
98C2×C22⋊Dic73C2314yes—
99C2×C22⋊Dic73C2314yes—
100C2×C22⋊Dic73C2314yes—
101C2×C4×Dic73—24no—
102C2×C4×Dic73—42no—
103C2×C4×Dic73—42no—
104C2×C4×Dic73—42no—
105C2×C4×Dic73C2314yes—
106C2×C4×Dic73C2314yes—
107C2×C4×Dic73C2314yes—
108C2×C4×Dic73C2314yes—
109#14556498C2314yes—
110#14556498C2314yes—
111#14556498C2314yes—
112#14556498C2314yes—
113#14556498C2314yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121C25×C73C2311yescharacteristic
122C23×C4×C73—24no—
123C23×C4×C73—42no—
124C23×C4×C73—42no—
125C23×C4×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2314yes—
132C2×C4⋊C4×C73—24no—
133C2×C4⋊C4×C73—42no—
134C2×C4⋊C4×C73C2314yes—
135C2×C4⋊C4×C73C2314yes—
136C2×C22⋊C4×C73—24no—
137C2×C22⋊C4×C73—42no—
138C2×C22⋊C4×C73C2314yes—
139C2×C22⋊C4×C73C2314yes—
140#95×C73C2314yes—
141#95×C73C2314yes—
142C2×Dic146—28no—
143C2×Dic146—28no—
144C2×Dic146—44no—
145C2×Dic146—416no—
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×Q814yes—
167C22×Dic73C2×Q814yes—
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—
179#11924007—28no—
180#11924007—28no—
181#11924007—28no—
182#11924007—44no—
183#11924007—44no—
184#11924007—44no—
185C22⋊Dic73—28no—
186C22⋊Dic73—28no—
187C22⋊Dic73—44no—
188C22⋊Dic73C2×Q8116yescomplemented
189C4×Dic73—28no—
190C4×Dic73—44no—
191C4×Dic73—44no—
192C4×Dic73—44no—
193C24×C73—22no—
194C24×C73—22no—
195C24×C73—22no—
196C24×C73—22no—
197C24×C73—22no—
198C24×C73—22no—
199C24×C73C2×Q814yes—
200C24×C73C2412yes—
201C24×C73C2411yescharacteristic
202C22×C4×C73—22no—
203C22×C4×C73—22no—
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—28no—
219C22×C4×C73—44no—
220C22×C4×C73—44no—
221C22×C4×C73—416no—
222C22×C4×C73#4114yes—
223C22×C4×C73#4114yes—
224C22×C4×C73C2412yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C4⋊C4×C73—28no—
231C4⋊C4×C73—44no—
232C22⋊C4×C73—28no—
233C22⋊C4×C73—44no—
234C23×C73—28no—
235C23×C73—28no—
236C23×C73—28no—
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×C73C22×Q814yes—
248C23×C73C22×Q812yes—
249C23×C73C2×#4112yes—
250C23×C73C2×#4112yes—
251C23×C73C2×#4112yes—
252C23×C73C2×#4112yes—
253C23×C73H(5,𝔽2)12yes—
254C23×C73H(5,𝔽2)12yes—
255C23×C73C2511yescharacteristic
256C2×C4×C73—28no—
257C2×C4×C73—28no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
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—416no—
275C2×C4×C73—44no—
276C2×C4×C73—44no—
277C2×C4×C73—44no—
278C2×C4×C73—44no—
279C2×C4×C73C2×#4114yes—
280C2×C4×C73C2×#4114yes—
281C2×Dic73—28no—
282C2×Dic73—28no—
283C2×Dic73—28no—
284C2×Dic73—28no—
285C2×Dic73—22no—
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—44no—
306C2×Dic73—44no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73C22×Q814yes—
310C2×Dic73C22×Q814yes—
311C2×Dic73C2×#4114yes—
312C2×Dic73C2×#4114yes—
313Dic146—416no—
314C22×C73—24no—
315C22×C73—24no—
316C22×C73—24no—
317C22×C73—416no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—42no—
321C22×C73—42no—
322C22×C73#52914yes—
323C22×C73#53314yes—
324C22×C73#53814yes—
325C22×C73#55114yes—
326C22×C73#55414yes—
327C22×C73#55414yes—
328C22×C73#55914yes—
329C22×C73C23×Q811yescharacteristic
330C22×C73C22×#4111yescharacteristic
331C22×C73C22×#4111yescharacteristic
332C22×C73C22×#4111yescharacteristic
333C22×C73C22×#4111yescharacteristic
334C22×C73C2×H(5,𝔽2)11yescharacteristic
335C22×C73C2×H(5,𝔽2)11yescharacteristic
336C4×C73—24no—
337C4×C73—24no—
338C4×C73—42no—
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×#2589—731nomaximal, Sylow
351C2×C73—44no—
352C2×C73#258918yescomplemented
353C2×C73C2×#52911yescharacteristic
354C2×C73C2×#53311yescharacteristic
355C2×C73C2×#53811yescharacteristic
356C2×C73C2×#55111yescharacteristic
357C2×C73C2×#55411yescharacteristic
358C2×C73C2×#55411yescharacteristic
359C2×C73C2×#55911yescharacteristic
360#2589—7316no—
361C2×#400—731no—
362C2×#399—731no—
363C2×#398—731no—
364C2×#393—731no—
365C2×#391—731no—
366C2×#391—731no—
367C2×#389—731no—
368C2×#388—731no—
369C2×#388—731no—
370C2×#387—731no—
371C2×#387—731no—
372C2×#385—731no—
373C2×#385D7311yescharacteristic
374C2×C4×C4⋊C4—731no—
375C2×C4×C22⋊C4—731no—
376C73C2×#258911yescharacteristic, complemented, Sylow
377C23×Q8—731no—
378C24×C4C2×D7311yescharacteristic
379C22×C4⋊C4—731no—
380C22×C4⋊C4—731no—
381C22×C4⋊C4—731no—
382C22×C4⋊C4—731no—
383C22×C4⋊C4—731no—
384C22×C4⋊C4—731no—
385C22×C4⋊C4—731no—
386C22×C4⋊C4C2×D7311yescharacteristic
387C22×C4⋊C4C2×D7311yescharacteristic
388C22×C22⋊C4—731no—
389C22×C22⋊C4—731no—
390C22×C22⋊C4—731no—
391C22×C22⋊C4—731no—
392C22×C22⋊C4C2×D7311yescharacteristic
393C22×C22⋊C4C2×D7311yescharacteristic
394C22×C42—731no—
395C22×C42—731no—
396C22×C42—731no—
397C22×C42—731no—
398#400—738no—
399#399—738no—
400#398—738no—
401#393—738no—
402#391—738no—
403#391—738no—
404#389—738no—
405#388—738no—
406#388—738no—
407#387—738no—
408#387—738no—
409#385—738no—
410#385C2×D7318yes—
411C4×C4⋊C4—738no—
412C4×C22⋊C4—738no—
413C2×#95—731no—
414C2×#95—731no—
415C2×#95—731no—
416C2×#95—731no—
417C2×#95—731no—
418C2×#95—731no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95—731no—
424C2×#95—731no—
425C2×#95C2×D7311yescharacteristic
426C2×#95C2×D7311yescharacteristic
427C25C22×D7311yescharacteristic
428C22×Q8—2922no—
429C22×Q8—734no—
430C22×Q8—1464no—
431C22×Q8—1464no—
432C23×C4—24no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4—731no—
439C23×C4—731no—
440C23×C4—731no—
441C23×C4—731no—
442C23×C4—731no—
443C23×C4C22×D7311yescharacteristic
444C23×C4C22×D7311yescharacteristic
445C23×C4C22×D7311yescharacteristic
446C23×C4C22×D7311yescharacteristic
447C23×C4C22×D7311yescharacteristic
448C23×C4C22×D7311yescharacteristic
449C23×C4C22×D7314yes—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—2922no—
453C2×C4⋊C4—2922no—
454C2×C4⋊C4—2922no—
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—1464no—
463C2×C4⋊C4—1464no—
464C2×C4⋊C4—1464no—
465C2×C4⋊C4—1464no—
466C2×C4⋊C4C22×D7314yes—
467C2×C4⋊C4C22×D7314yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—2922no—
471C2×C22⋊C4—734no—
472C2×C22⋊C4—738no—
473C2×C22⋊C4—734no—
474C2×C22⋊C4—734no—
475C2×C22⋊C4—734no—
476C2×C22⋊C4—1464no—
477C2×C22⋊C4—1464no—
478C2×C22⋊C4C22×D7314yes—
479C2×C22⋊C4C22×D7314yes—
480C2×C42—2922no—
481C2×C42—2922no—
482C2×C42—2922no—
483C2×C42—734no—
484C2×C42—734no—
485C2×C42—734no—
486C2×C42—734no—
487C2×C42—1464no—
488#95—734no—
489#95—734no—
490#95—734no—
491#95—734no—
492#95—734no—
493#95—734no—
494#95—734no—
495#95—734no—
496#95—734no—
497#95—734no—
498#95—734no—
499#95—734no—
500#95C22×D7314yes—
501#95C22×D7314yes—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24Q8×D7314yes—
509C24C23×D7312yes—
510C24C23×D7311yescharacteristic
511C2×Q8—2924no—
512C2×Q8—29216no—
513C2×Q8—1468no—
514C2×Q8—1468no—
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—28no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—416no—
535C22×C4—734no—
536C22×C4—734no—
537C22×C4—734no—
538C22×C4—734no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—732no—
542C22×C4—732no—
543C22×C4—732no—
544C22×C4—732no—
545C22×C4—732no—
546C22×C4—732no—
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×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4#1192402714yes—
568C22×C4#1192402814yes—
569C22×C4C23×D7312yes—
570C22×C4C23×D7312yes—
571C22×C4C23×D7312yes—
572C22×C4C23×D7312yes—
573C22×C4C23×D7312yes—
574C22×C4C23×D7312yes—
575C4⋊C4—28no—
576C4⋊C4—44no—
577C4⋊C4—2924no—
578C4⋊C4—2924no—
579C4⋊C4—2924no—
580C4⋊C4—1468no—
581C4⋊C4—1468no—
582C4⋊C4—1468no—
583C4⋊C4—1468no—
584C22⋊C4—28no—
585C22⋊C4—44no—
586C22⋊C4—2924no—
587C22⋊C4—7316no—
588C22⋊C4—1468no—
589C22⋊C4—1468no—
590C42—2924no—
591C42—2924no—
592C42—2924no—
593C42—1468no—
594C23—28no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—28no—
602C23—28no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23C2×Q8×D7314yes—
608C23C2×Q8×D7312yes—
609C23#41×D7312yes—
610C23#41×D7312yes—
611C23C2×#1192402712yes—
612C23C2×#1192402812yes—
613C23#1455663612yes—
614C23#1455663612yes—
615C23C24×D7311yescharacteristic
616Q8—29216no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
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—416no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—2924no—
641C2×C4—2924no—
642C2×C4—2924no—
643C2×C4—2924no—
644C2×C4—734no—
645C2×C4—734no—
646C2×C4—734no—
647C2×C4—734no—
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—1462no—
668C2×C4—1468no—
669C2×C4—1468no—
670C2×C4—1468no—
671C2×C4—1468no—
672C2×C4C2×#1192402714yes—
673C2×C4C2×#1192402814yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—416no—
680C22—42no—
681C22—42no—
682C22#1798911714yes—
683C22#1798913914yes—
684C22#1798917214yes—
685C22#1798926514yes—
686C22#1798929114yes—
687C22#1798929214yes—
688C22#1798932014yes—
689C22C22×Q8×D7311yescharacteristic
690C22C2×#41×D7311yescharacteristic
691C22C2×#41×D7311yescharacteristic
692C22C22×#1192402711yescharacteristic
693C22C22×#1192402811yescharacteristic
694C22C2×#1455663611yescharacteristic
695C22C2×#1455663611yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—2922no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—1464no—
707C4—1464no—
708C4—1464no—
709C4—1464no—
710C2—44no—
711C2#2261537918yesdirect product factor
712C2C2×#1798911711yescharacteristic
713C2C2×#1798913911yescharacteristic
714C2C2×#1798917211yescharacteristic
715C2C2×#1798926511yescharacteristic
716C2C2×#1798929111yescharacteristic
717C2C2×#1798929211yescharacteristic
718C2C2×#1798932011yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#385×C73C2
socleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#385D73
hypocenterC73C2×#2589
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #22615379C2direct (N × H)
2. C2×#17988527C2semidirect
4. C2×#17988518C2semidirect
6. C2×#17988491C2semidirect
7. C2×#17988491C2semidirect
8. C2×#17988482C2semidirect
11. C2×#17988469C2semidirect
12. C2×#17988468C2semidirect
14. C2×C4⋊C4×Dic73C2semidirect
33. #17988527C22semidirect
35. #17988518C22semidirect
37. #17988491C22semidirect
38. #17988491C22semidirect
39. #17988482C22semidirect
42. #17988469C22semidirect
43. #17988468C22semidirect
45. C4⋊C4×Dic73C22semidirect
96. C2×C22⋊Dic73Q8semidirect
188. C22⋊Dic73C2×Q8semidirect
352. C2×C73#2589semidirect
376. C73C2×#2589semidirect
711. C2#22615379direct (N × H)

Maximal subgroups

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

subgroupindex
#226153792
C2×#179885272
C2×#179885232
C2×#179885182
C2×#179884992
C2×#179884912
C2×#179884822
C2×#179884812
C2×#179884692
C2×#179884682
C2×#179884602
C2×C4⋊C4×Dic732
C2×C4×C22⋊Dic732
C2×#385×C732
C2×#258973