Finite Group Databasebeta

← C73×#26250 #32935654

Subgroups — C73×#26250 #32935654

Order 18688.

932 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C73C211yesmaximal, characteristic
2C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
3C73×#2446C211yesmaximal, characteristic, complemented
4C73×#2445C211yesmaximal, characteristic
5C73×#2055C211yesmaximal, characteristic, complemented
6C73×#2055C211yesmaximal, characteristic, complemented
7C73×#2043C211yesmaximal, characteristic, complemented
8C73×#2041C211yesmaximal, characteristic
9C73×#1968C211yesmaximal, characteristic, complemented
10C73×#1968C211yesmaximal, characteristic, complemented
11C73×#1968C211yesmaximal, characteristic, complemented
12C73×#1941C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C8×C4⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×#127×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×C4×Q8×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25#492×C73—24no—
26C4×SD16×C73—24no—
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×C4⋊C8×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#400×C73—21no—
42#398×C73—21no—
43#394×C73—21no—
44#394×C73—21no—
45#391×C73C2211yescharacteristic
46#391×C73C2211yescharacteristic
47#391×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#387×C73—21no—
54#387×C73—21no—
55#386×C73—21no—
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C2×SD16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—22no—
74C2×SD16×C73—22no—
75C2×SD16×C73—22no—
76C2×SD16×C73—22no—
77C2×SD16×C73—41no—
78C2×SD16×C73—41no—
79C2×SD16×C73D414yes—
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C4⋊Q8×C73—22no—
85C4⋊Q8×C73—41no—
86#127×C73—22no—
87#127×C73—41no—
88#123×C73—44no—
89C4×Q8×C73—22no—
90C4×Q8×C73—41no—
91C4×D4×C73—22no—
92C4×D4×C73—41no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73D411yescharacteristic
99C2×C4⋊C4×C73D411yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#106×C73—22no—
116#106×C73—22no—
117C4⋊C8×C73—22no—
118#103×C73—22no—
119#103×C73—41no—
120#103×C73—41no—
121#103×C73—41no—
122#102×C73—22no—
123#102×C73—41no—
124#102×C73—41no—
125#102×C73—41no—
126C4×C8×C73—22no—
127C4×C8×C73—22no—
128C4×C8×C73—22no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73C2×D412yes—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—42no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—81no—
169C2×D4×C73—81no—
170C2×D4×C73C2×D412yes—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—42no—
178C22×C4×C73—42no—
179C22×C4×C73—81no—
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2411yescharacteristic
187SD16×C73—28no—
188SD16×C73—44no—
189SD16×C73—44no—
190SD16×C73—44no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C2×D412yes—
200C2×C8×C73#4112yes—
201C2×C8×C73#4112yes—
202C2×C8×C73#4112yes—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73SD1614yescomplemented
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—81no—
223C22⋊C4×C73—81no—
224C22⋊C4×C73—81no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—42no—
232C23×C73—22no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73C22×D411yescharacteristic
247Q8×C73—22no—
248Q8×C73—22no—
249Q8×C73—41no—
250Q8×C73—41no—
251Q8×C73—41no—
252Q8×C73—41no—
253Q8×C73—41no—
254Q8×C73—41no—
255D4×C73—22no—
256D4×C73—22no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—41no—
262D4×C73—41no—
263D4×C73—84no—
264D4×C73—84no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—84no—
298C2×C4×C73C2×SD1612yes—
299C2×C4×C73C2×SD1612yes—
300C2×C4×C73C2×SD1612yes—
301C2×C4×C73#13512yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C73H(5,𝔽2)11yescharacteristic
308C8×C73—22no—
309C8×C73—41no—
310C8×C73—41no—
311C8×C73#12314yescomplemented
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73#53211yescharacteristic
327C22×C73D4211yescharacteristic
328C22×C73#55011yescharacteristic
329C22×C73C22×SD1611yescharacteristic
330C22×C73C2×#13511yescharacteristic
331C22×C73#57711yescharacteristic
332C22×C73#57711yescharacteristic
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—41no—
338C4×C73—42no—
339C4×C73—41no—
340C4×C73—81no—
341C4×C73—81no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73C2×#12311yescharacteristic
346C4×C73#54011yescharacteristic
347C4×C73#54611yescharacteristic
348C4×C73#55911yescharacteristic
349#26250C7311yesmaximal, characteristic, direct product factor, Sylow
350C2×C73—82no—
351C2×C73—161no—
352C2×C73#244511yescharacteristic
353C2×C73#316711yescharacteristic
354C2×C73#317411yescharacteristic
355C2×C73D4×SD1611yescharacteristic
356C2×C73#328211yescharacteristic
357C2×C73#339211yescharacteristic
358C2×C73#339411yescharacteristic
359C2×#492C2×C7311yescharacteristic
360C2×C4×SD16C2×C7311yescharacteristic, complemented
361#2446C2×C7311yescharacteristic, complemented
362#2445C2×C7311yescharacteristic
363#2055C2×C7311yescharacteristic, complemented
364#2055C2×C7311yescharacteristic, complemented
365#2043C2×C7311yescharacteristic, complemented
366#2041C2×C7311yescharacteristic
367#1968C2×C7311yescharacteristic, complemented
368#1968C2×C7311yescharacteristic, complemented
369#1968C2×C7311yescharacteristic, complemented
370#1941C2×C7311yescharacteristic, complemented
371#1880C2×C7311yescharacteristic, complemented
372#1877C2×C7311yescharacteristic, complemented
373C8×C4⋊C4C2×C7311yescharacteristic, complemented
374C73#2625011yescharacteristic, direct product factor, Sylow
375C22×SD16C22×C7311yescharacteristic
376C22×SD16C22×C7311yescharacteristic
377C22×SD16C22×C7311yescharacteristic
378C22×SD16C22×C7311yescharacteristic
379C2×C4⋊Q8C22×C7311yescharacteristic
380C2×#127C22×C7311yescharacteristic
381C2×#123—21no—
382C2×C4×Q8C22×C7311yescharacteristic
383C2×C4×D4C22×C7311yescharacteristic
384#492—24no—
385C4×SD16—24no—
386C2×#106C22×C7311yescharacteristic
387C2×#106C22×C7311yescharacteristic
388C2×C4⋊C8C22×C7311yescharacteristic
389C2×#103C22×C7311yescharacteristic
390C2×#103C22×C7311yescharacteristic
391C2×#103C22×C7311yescharacteristic
392C2×#103C22×C7311yescharacteristic
393C2×#102C22×C7311yescharacteristic
394C2×#102C22×C7311yescharacteristic
395C2×#102C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×C4×C8C22×C7311yescharacteristic
398C2×C4×C8C22×C7311yescharacteristic
399C2×C4×C8C22×C7311yescharacteristic
400#400—21no—
401#398—21no—
402#394—21no—
403#394—21no—
404#391C22×C7311yescharacteristic
405#391C22×C7311yescharacteristic
406#391C22×C7311yescharacteristic
407#390C22×C7311yescharacteristic
408#390C22×C7311yescharacteristic
409#390C22×C7311yescharacteristic
410#389C22×C7311yescharacteristic
411#389C22×C7311yescharacteristic
412#387—21no—
413#387—21no—
414#386—21no—
415C4×C4⋊C4C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#336C22×C7311yescharacteristic
419#336C22×C7311yescharacteristic
420C22×Q8C23×C7311yescharacteristic
421C22×Q8C23×C7311yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C7311yescharacteristic
425C22×D4C23×C7311yescharacteristic
426C23×C4—21no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—41no—
437C2×SD16—41no—
438C2×SD16D4×C7314yes—
439C22×C8C23×C7311yescharacteristic
440C22×C8C23×C7311yescharacteristic
441C22×C8C23×C7311yescharacteristic
442C22×C8C23×C7311yescharacteristic
443C4⋊Q8—22no—
444C4⋊Q8—41no—
445#127—22no—
446#127—41no—
447#123—44no—
448C4×Q8—22no—
449C4×Q8—41no—
450C4×D4—22no—
451C4×D4—41no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4D4×C7311yescharacteristic
458C2×C4⋊C4D4×C7311yescharacteristic
459C2×C4⋊C4C23×C7311yescharacteristic
460C2×C4⋊C4C23×C7311yescharacteristic
461C2×C4⋊C4C23×C7311yescharacteristic
462C2×C4⋊C4C23×C7311yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C42—21no—
471C2×C42C23×C7311yescharacteristic
472C2×C42C23×C7311yescharacteristic
473C2×C42C23×C7311yescharacteristic
474#106—22no—
475#106—22no—
476C4⋊C8—22no—
477#103—22no—
478#103—41no—
479#103—41no—
480#103—41no—
481#102—22no—
482#102—41no—
483#102—41no—
484#102—41no—
485C4×C8—22no—
486C4×C8—22no—
487C4×C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95D4×C7311yescharacteristic
497#95D4×C7311yescharacteristic
498C24—21no—
499C24—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C2×D4×C7312yes—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4C2×D4×C7312yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C2×D4×C7311yescharacteristic
542C22×C4C2×D4×C7311yescharacteristic
543C22×C4C2×D4×C7311yescharacteristic
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C24×C7311yescharacteristic
546SD16—28no—
547SD16—44no—
548SD16—44no—
549SD16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8C2×D4×C7312yes—
559C2×C8#41×C7312yes—
560C2×C8#41×C7312yes—
561C2×C8#41×C7312yes—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4SD16×C7314yescomplemented
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—42no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×D4×C7311yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614D4—22no—
615D4—22no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—84no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4C2×SD16×C7312yes—
658C2×C4C2×SD16×C7312yes—
659C2×C4C2×SD16×C7312yes—
660C2×C4#135×C7312yes—
661C2×C4C22×D4×C7311yescharacteristic
662C2×C4C2×#41×C7311yescharacteristic
663C2×C4C2×#41×C7311yescharacteristic
664C2×C4C2×#41×C7311yescharacteristic
665C2×C4H(5,𝔽2)×C7311yescharacteristic
666C2×C4H(5,𝔽2)×C7311yescharacteristic
667C8—22no—
668C8—41no—
669C8—41no—
670C8#123×C7314yescomplemented
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22#532×C7311yescharacteristic
686C22D42×C7311yescharacteristic
687C22#550×C7311yescharacteristic
688C22C22×SD16×C7311yescharacteristic
689C22C2×#135×C7311yescharacteristic
690C22#577×C7311yescharacteristic
691C22#577×C7311yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C2×#123×C7311yescharacteristic
705C4#540×C7311yescharacteristic
706C4#546×C7311yescharacteristic
707C4#559×C7311yescharacteristic
708C2—82no—
709C2—161no—
710C2C73×#244511yescharacteristic
711C2C73×#316711yescharacteristic
712C2C73×#317411yescharacteristic
713C2D4×SD16×C7311yescharacteristic
714C2C73×#328211yescharacteristic
715C2C73×#339211yescharacteristic
716C2C73×#339411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#127×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C73C2semidirect
3. C73×#2446C2semidirect
5. C73×#2055C2semidirect
6. C73×#2055C2semidirect
7. C73×#2043C2semidirect
9. C73×#1968C2semidirect
10. C73×#1968C2semidirect
11. C73×#1968C2semidirect
12. C73×#1941C2semidirect
13. C73×#1880C2semidirect
14. C73×#1877C2semidirect
15. C8×C4⋊C4×C73C2semidirect
217. C4⋊C4×C73SD16semidirect
311. C8×C73#123semidirect
349. #26250C73direct (N × H)
360. C2×C4×SD16C2×C73semidirect
361. #2446C2×C73semidirect
363. #2055C2×C73semidirect
364. #2055C2×C73semidirect
365. #2043C2×C73semidirect
367. #1968C2×C73semidirect
368. #1968C2×C73semidirect
369. #1968C2×C73semidirect
370. #1941C2×C73semidirect
371. #1880C2×C73semidirect
372. #1877C2×C73semidirect
373. C8×C4⋊C4C2×C73semidirect
374. C73#26250direct (N × H)
576. C4⋊C4SD16×C73semidirect
670. C8#123×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C732
C2×C4×SD16×C732
C73×#24462
C73×#24452
C73×#20552
C73×#20432
C73×#20412
C73×#19682
C73×#19412
C73×#18802
C73×#18772
C8×C4⋊C4×C732
#2625073