Finite Group Databasebeta

← C2×#22614654 #33255178

Subgroups — C2×#22614654 #33255178

Order 18688.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614654C2116yesmaximal, direct product factor
2C2×#17988523C211yesmaximal, characteristic
3C2×#17988521C211yesmaximal, characteristic, complemented
4C2×#17988520C211yesmaximal, characteristic, complemented
5C2×#17988510C211yesmaximal, characteristic
6C2×#17988484C211yesmaximal, characteristic, complemented
7C2×#17988483C211yesmaximal, characteristic, complemented
8C2×#17988480C211yesmaximal, characteristic
9C2×#17988474C211yesmaximal, characteristic, complemented
10C2×#17988471C211yesmaximal, characteristic, complemented
11C2×#17988470C211yesmaximal, characteristic, complemented
12C2×#17988459C211yesmaximal, characteristic
13C2×#17988445C211yesmaximal, characteristic
14C2×C4×#11924007C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic73C211yesmaximal, characteristic
16C2×#388×C73C211yesmaximal, characteristic
17C24×Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×#11924007C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×C22⋊Dic73C2211yescharacteristic
30C22×C22⋊Dic73C2211yescharacteristic
31C22×C22⋊Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35#17988523C2218yes—
36#17988521C2218yescomplemented
37#17988520C2218yescomplemented
38#17988510C2218yes—
39#17988484C2218yescomplemented
40#17988483C2218yescomplemented
41#17988480C2218yes—
42#17988474C2218yescomplemented
43#17988471C2218yescomplemented
44#17988470C2218yescomplemented
45#17988459C2218yes—
46#17988445C2218yes—
47C4×#11924007C2218yescomplemented
48C22⋊C4×Dic73C2218yes—
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C22×C4⋊C4×C73C2211yescharacteristic
60C22×C22⋊C4×C73C2211yescharacteristic
61C22×C22⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C42×C73C2211yescharacteristic
64#388×C73C2218yes—
65C2×#95×C73C2211yescharacteristic
66C2×#95×C73C2211yescharacteristic
67C23×Dic73—24no—
68C23×Dic73—24no—
69C23×Dic73—42no—
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2314yes—
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C2×C4⋊Dic73—24no—
80C2×C4⋊Dic73—24no—
81C2×C4⋊Dic73—42no—
82C2×C4⋊Dic73C2314yes—
83C2×C4⋊Dic73C2314yes—
84C2×C4⋊Dic73C2314yes—
85C2×#11924007—24no—
86C2×#11924007—24no—
87C2×#11924007—24no—
88C2×#11924007—24no—
89C2×#11924007—24no—
90C2×#11924007—42no—
91C2×#11924007—42no—
92C2×#11924007—42no—
93C2×#11924007C2314yes—
94C2×#11924007C2314yes—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×C22⋊Dic73—24no—
102C2×C22⋊Dic73—24no—
103C2×C22⋊Dic73—42no—
104C2×C22⋊Dic73C2314yes—
105C2×C22⋊Dic73C2314yes—
106C2×C22⋊Dic73C2314yes—
107C2×C4×Dic73—24no—
108C2×C4×Dic73—42no—
109C2×C4×Dic73—42no—
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—
122#14556498C2314yes—
123C25×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C23×C4×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73—42no—
131C2×C4⋊C4×C73C2314yes—
132C2×C22⋊C4×C73—42no—
133C2×C22⋊C4×C73—42no—
134C2×C22⋊C4×C73Q818yes—
135C2×C22⋊C4×C73C2314yes—
136C2×C22⋊C4×C73C2314yes—
137C2×C22⋊C4×C73C2314yes—
138C2×C42×C73—42no—
139C2×C42×C73C2314yes—
140#95×C73C2314yes—
141#95×C73C2314yes—
142C22×Dic73—22no—
143C22×Dic73—22no—
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—28no—
163C22×Dic73—28no—
164C22×Dic73—44no—
165C22×Dic73—416no—
166C22×Dic73#4114yes—
167C22×Dic73#4114yes—
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—44no—
181#11924007—28no—
182#11924007—28no—
183#11924007—28no—
184#11924007—28no—
185#11924007—28no—
186#11924007—44no—
187#11924007—44no—
188#11924007—44no—
189C22⋊Dic73—28no—
190C22⋊Dic73—28no—
191C22⋊Dic73—44no—
192C4×Dic73—28no—
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×C73C2×Q814yes—
202C24×C73C2412yes—
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×C73C2×Q814yes—
221C22×C4×C73C2×Q814yes—
222C22×C4×C73C2412yes—
223C22×C4×C73C2412yes—
224C22×C4×C73C2412yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C4⋊C4×C73—44no—
229C22⋊C4×C73—44no—
230C22⋊C4×C73—44no—
231C22⋊C4×C73C2×Q8116yes—
232C42×C73—44no—
233C23×C73—28no—
234C23×C73—28no—
235C23×C73—28no—
236C23×C73—22no—
237C23×C73—22no—
238C23×C73—22no—
239C23×C73—22no—
240C23×C73—22no—
241C23×C73—22no—
242C23×C73—44no—
243C23×C73—44no—
244C23×C73—44no—
245C23×C73—44no—
246C23×C73C22×Q814yes—
247C23×C73C22×Q812yes—
248C23×C73C2×#4112yes—
249C23×C73C2×#4112yes—
250C23×C73C2×#4112yes—
251C23×C73C2×#4112yes—
252C23×C73H(5,𝔽2)12yes—
253C23×C73H(5,𝔽2)12yes—
254C23×C73C2511yescharacteristic
255C2×C4×C73—28no—
256C2×C4×C73—28no—
257C2×C4×C73—22no—
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—44no—
274C2×C4×C73—44no—
275C2×C4×C73—44no—
276C2×C4×C73—44no—
277C2×C4×C73C22×Q814yes—
278C2×C4×C73C22×Q814yes—
279C2×Dic73—28no—
280C2×Dic73—28no—
281C2×Dic73—28no—
282C2×Dic73—28no—
283C2×Dic73—22no—
284C2×Dic73—22no—
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—416no—
304C2×Dic73—44no—
305C2×Dic73—44no—
306C2×Dic73—44no—
307C2×Dic73—44no—
308C2×Dic73C2×#4114yes—
309C2×Dic73C2×#4114yes—
310C2×Dic73C2×#4114yes—
311C2×Dic73C2×#4114yes—
312C22×C73—24no—
313C22×C73—24no—
314C22×C73—24no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—416no—
320C22×C73#52914yes—
321C22×C73#53314yes—
322C22×C73#54014yes—
323C22×C73#55114yes—
324C22×C73#55314yes—
325C22×C73#55414yes—
326C22×C73#55414yes—
327C22×C73C23×Q811yescharacteristic
328C22×C73C22×#4111yescharacteristic
329C22×C73C22×#4111yescharacteristic
330C22×C73C22×#4111yescharacteristic
331C22×C73C22×#4111yescharacteristic
332C22×C73C2×H(5,𝔽2)11yescharacteristic
333C22×C73C2×H(5,𝔽2)11yescharacteristic
334C4×C73—24no—
335C4×C73—24no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—42no—
340Dic73—24no—
341Dic73—24no—
342Dic73—24no—
343Dic73—24no—
344Dic73—42no—
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348C2×#2522—731nomaximal, Sylow
349C2×C73—44no—
350C2×C73#252218yescomplemented
351C2×C73C2×#52911yescharacteristic
352C2×C73C2×#53311yescharacteristic
353C2×C73C2×#54011yescharacteristic
354C2×C73C2×#55111yescharacteristic
355C2×C73C2×#55311yescharacteristic
356C2×C73C2×#55411yescharacteristic
357C2×C73C2×#55411yescharacteristic
358#2522—7316no—
359C2×#399—731no—
360C2×#398—731no—
361C2×#398—731no—
362C2×#396—731no—
363C2×#389—731no—
364C2×#389—731no—
365C2×#388—731no—
366C2×#388D7311yescharacteristic
367C2×#387—731no—
368C2×#387—731no—
369C2×#387—731no—
370C2×#385—731no—
371C2×#380—731no—
372C2×C4×C4⋊C4—731no—
373C2×C4×C22⋊C4—731no—
374C73C2×#252211yescharacteristic, complemented, Sylow
375C24×C4—731no—
376C22×C4⋊C4—731no—
377C22×C4⋊C4—731no—
378C22×C4⋊C4—731no—
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⋊C4—731no—
387C22×C4⋊C4C2×D7311yescharacteristic
388C22×C22⋊C4—731no—
389C22×C22⋊C4—731no—
390C22×C22⋊C4—731no—
391C22×C22⋊C4C2×D7311yescharacteristic
392C22×C22⋊C4C2×D7311yescharacteristic
393C22×C22⋊C4C2×D7311yescharacteristic
394C22×C42—731no—
395C22×C42—731no—
396C22×C42—731no—
397C22×C42C2×D7311yescharacteristic
398#399—738no—
399#398—738no—
400#398—738no—
401#396—738no—
402#389—738no—
403#389—738no—
404#388—738no—
405#388C2×D7318yes—
406#387—738no—
407#387—738no—
408#387—738no—
409#385—738no—
410#380—738no—
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×#95C2×D7311yescharacteristic
424C2×#95C2×D7311yescharacteristic
425C25C22×D7311yescharacteristic
426C23×C4—2922no—
427C23×C4—734no—
428C23×C4—731no—
429C23×C4—731no—
430C23×C4—731no—
431C23×C4—731no—
432C23×C4—731no—
433C23×C4—731no—
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—1464no—
437C23×C4—1464no—
438C23×C4C22×D7311yescharacteristic
439C23×C4C22×D7311yescharacteristic
440C23×C4C22×D7311yescharacteristic
441C23×C4C22×D7311yescharacteristic
442C23×C4C22×D7311yescharacteristic
443C23×C4C22×D7311yescharacteristic
444C2×C4⋊C4—42no—
445C2×C4⋊C4—2922no—
446C2×C4⋊C4—2922no—
447C2×C4⋊C4—2922no—
448C2×C4⋊C4—2922no—
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⋊C4C22×D7314yes—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—2922no—
471C2×C22⋊C4—734no—
472C2×C22⋊C4—734no—
473C2×C22⋊C4—734no—
474C2×C22⋊C4—1464no—
475C2×C22⋊C4—1464no—
476C2×C22⋊C4Dic14618yes—
477C2×C22⋊C4C22×D7314yes—
478C2×C22⋊C4C22×D7314yes—
479C2×C22⋊C4C22×D7314yes—
480C2×C42—42no—
481C2×C42—2922no—
482C2×C42—2922no—
483C2×C42—734no—
484C2×C42—734no—
485C2×C42—734no—
486C2×C42—1464no—
487C2×C42C22×D7314yes—
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#95C22×D7314yes—
499#95C22×D7314yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24C2×Dic14614yes—
507C24C23×D7312yes—
508C24C23×D7311yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—2924no—
526C22×C4—29216no—
527C22×C4—734no—
528C22×C4—734no—
529C22×C4—734no—
530C22×C4—734no—
531C22×C4—732no—
532C22×C4—732no—
533C22×C4—732no—
534C22×C4—732no—
535C22×C4—732no—
536C22×C4—732no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—1468no—
540C22×C4—1468no—
541C22×C4—1462no—
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×C4C2×Dic14614yes—
562C22×C4C2×Dic14614yes—
563C22×C4C23×D7312yes—
564C22×C4C23×D7312yes—
565C22×C4C23×D7312yes—
566C22×C4C23×D7312yes—
567C22×C4C23×D7312yes—
568C22×C4C23×D7312yes—
569C4⋊C4—44no—
570C4⋊C4—2924no—
571C4⋊C4—2924no—
572C4⋊C4—2924no—
573C4⋊C4—2924no—
574C4⋊C4—1468no—
575C4⋊C4—1468no—
576C4⋊C4—1468no—
577C4⋊C4—1468no—
578C4⋊C4—1468no—
579C4⋊C4—1468no—
580C4⋊C4—1468no—
581C22⋊C4—44no—
582C22⋊C4—44no—
583C22⋊C4—2924no—
584C22⋊C4—1468no—
585C22⋊C4—1468no—
586C22⋊C4C2×Dic146116yes—
587C42—44no—
588C42—2924no—
589C42—2924no—
590C42—1468no—
591C23—28no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—28no—
599C23—28no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C22×Dic14614yes—
605C23C22×Dic14612yes—
606C23#41×D7312yes—
607C23#41×D7312yes—
608C23#41×D7312yes—
609C23#41×D7312yes—
610C23#1455663612yes—
611C23#1455663612yes—
612C23C24×D7311yescharacteristic
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
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—44no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—2924no—
636C2×C4—2924no—
637C2×C4—2924no—
638C2×C4—2924no—
639C2×C4—29216no—
640C2×C4—734no—
641C2×C4—734no—
642C2×C4—734no—
643C2×C4—734no—
644C2×C4—1462no—
645C2×C4—1462no—
646C2×C4—1462no—
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—1468no—
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—1468no—
666C2×C4—1468no—
667C2×C4—1468no—
668C2×C4C22×Dic14614yes—
669C2×C4C22×Dic14614yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—42no—
674C22—416no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22#1798912014yes—
679C22#1798914014yes—
680C22#1798918714yes—
681C22#1798926714yes—
682C22#1798928214yes—
683C22#1798929614yes—
684C22#1798929614yes—
685C22C23×Dic14611yescharacteristic
686C22C2×#41×D7311yescharacteristic
687C22C2×#41×D7311yescharacteristic
688C22C2×#41×D7311yescharacteristic
689C22C2×#41×D7311yescharacteristic
690C22C2×#1455663611yescharacteristic
691C22C2×#1455663611yescharacteristic
692C4—24no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2922no—
699C4—2922no—
700C4—2922no—
701C4—2922no—
702C4—1464no—
703C4—1464no—
704C4—1464no—
705C4—1464no—
706C2—44no—
707C2#2261465418yesdirect product factor
708C2C2×#1798912011yescharacteristic
709C2C2×#1798914011yescharacteristic
710C2C2×#1798918711yescharacteristic
711C2C2×#1798926711yescharacteristic
712C2C2×#1798928211yescharacteristic
713C2C2×#1798929611yescharacteristic
714C2C2×#1798929611yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#388×C73C2
socleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#388D73
hypocenterC73C2×#2522
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #22614654C2direct (N × H)
3. C2×#17988521C2semidirect
4. C2×#17988520C2semidirect
6. C2×#17988484C2semidirect
7. C2×#17988483C2semidirect
9. C2×#17988474C2semidirect
10. C2×#17988471C2semidirect
11. C2×#17988470C2semidirect
14. C2×C4×#11924007C2semidirect
36. #17988521C22semidirect
37. #17988520C22semidirect
39. #17988484C22semidirect
40. #17988483C22semidirect
42. #17988474C22semidirect
43. #17988471C22semidirect
44. #17988470C22semidirect
47. C4×#11924007C22semidirect
350. C2×C73#2522semidirect
374. C73C2×#2522semidirect
707. C2#22614654direct (N × H)

Maximal subgroups

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

subgroupindex
#226146542
C2×#179885232
C2×#179885212
C2×#179885202
C2×#179885102
C2×#179884842
C2×#179884832
C2×#179884802
C2×#179884742
C2×#179884712
C2×#179884702
C2×#179884592
C2×#179884452
C2×C4×#119240072
C2×C22⋊C4×Dic732
C2×#388×C732
C2×#252273