Finite Group Databasebeta

← C73×#26930 #32936334

Subgroups — C73×#26930 #32936334

Order 18688.

998 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C73C211yesmaximal, characteristic, complemented
2C2×#460×C73C211yesmaximal, characteristic, complemented
3C73×#2428C211yesmaximal, characteristic
4C73×#2360C211yesmaximal, characteristic, complemented
5C73×#2088C211yesmaximal, characteristic, complemented
6C73×#2041C211yesmaximal, characteristic, complemented
7C73×#2000C211yesmaximal, characteristic, complemented
8C73×#2000C211yesmaximal, characteristic, complemented
9C73×#1968C211yesmaximal, characteristic, complemented
10C73×#1926C211yesmaximal, characteristic, complemented
11C73×#1923C211yesmaximal, characteristic, complemented
12C73×#1877C211yesmaximal, characteristic, complemented
13C73×#1874C211yesmaximal, characteristic, complemented
14C73×#1865C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C2×#127×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×#121×C73—21no—
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×C4×Q8×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26#481×C73—24no—
27#460×C73—24no—
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×C22⋊C8×C73C2211yescharacteristic
41C2×C4×C8×C73C2211yescharacteristic
42#394×C73—21no—
43#392×C73—21no—
44#391×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#389×C73—21no—
47#389×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#387×C73—21no—
50#386×C73—21no—
51#385×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73C2311yescharacteristic
67C22×D4×C73C2311yescharacteristic
68C23×C4×C73—21no—
69C23×C4×C73—21no—
70C23×C4×C73C2311yescharacteristic
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—22no—
74C2×SD16×C73—22no—
75C2×SD16×C73—41no—
76C2×SD16×C73—41no—
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81#127×C73—22no—
82#127×C73—41no—
83C22⋊Q8×C73—22no—
84C22⋊Q8×C73—22no—
85#121×C73—22no—
86#121×C73—22no—
87#121×C73—41no—
88#121×C73—41no—
89#121×C73—44no—
90C4×Q8×C73—22no—
91C4×Q8×C73—41no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—41no—
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73D411yescharacteristic
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C42×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#106×C73—22no—
119#106×C73—22no—
120C4⋊C8×C73—22no—
121#103×C73—22no—
122#103×C73—41no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—41no—
128#102×C73D414yescomplemented
129C22⋊C8×C73—22no—
130C22⋊C8×C73—41no—
131C4×C8×C73—41no—
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—
141C24×C73C2×D411yescharacteristic
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73#4112yes—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
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—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—42no—
163C2×D4×C73—42no—
164C2×D4×C73—42no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—81no—
168C2×D4×C73—81no—
169C2×D4×C73—81no—
170C2×D4×C73—81no—
171C2×D4×C73C2×D412yes—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—42no—
185C22×C4×C73—42no—
186C22×C4×C73—42no—
187C22×C4×C73—42no—
188C22×C4×C73—81no—
189C22×C4×C73—81no—
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2411yescharacteristic
196SD16×C73—44no—
197SD16×C73—44no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73C2×D412yes—
210C4⋊C4×C73—24no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—42no—
219C4⋊C4×C73—42no—
220C4⋊C4×C73—42no—
221C4⋊C4×C73—81no—
222C4⋊C4×C73C2×D412yes—
223C4⋊C4×C73#4112yes—
224C4⋊C4×C73#4112yes—
225C22⋊C4×C73—24no—
226C22⋊C4×C73—41no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—81no—
232C22⋊C4×C73SD1614yescomplemented
233C42×C73—21no—
234C42×C73—21no—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—42no—
238C42×C73—81no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—22no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73C2×SD1612yes—
260C23×C73C22×D411yescharacteristic
261Q8×C73—22no—
262Q8×C73—22no—
263Q8×C73—41no—
264Q8×C73—41no—
265D4×C73—22no—
266D4×C73—22no—
267D4×C73—41no—
268D4×C73—41no—
269D4×C73—41no—
270D4×C73—41no—
271D4×C73—41no—
272D4×C73—41no—
273D4×C73—84no—
274D4×C73—84no—
275D4×C73—84no—
276D4×C73—84no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—22no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—84no—
313C2×C4×C73—84no—
314C2×C4×C73C2×SD1612yes—
315C2×C4×C73C2×SD1612yes—
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C2×C4×C73C2×#4111yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C8×C73—22no—
323C8×C73—41no—
324C8×C73—41no—
325C8×C73—41no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—22no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73#52511yescharacteristic
348C22×C73D4211yescharacteristic
349C22×C73#54611yescharacteristic
350C22×C73C22×SD1611yescharacteristic
351C22×C73#57511yescharacteristic
352C22×C73#57611yescharacteristic
353C22×C73#57711yescharacteristic
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—42no—
357C4×C73—41no—
358C4×C73—42no—
359C4×C73—41no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73—41no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73#53211yescharacteristic
366C4×C73#54011yescharacteristic
367C4×C73#54611yescharacteristic
368C4×C73#55311yescharacteristic
369#26930C7311yesmaximal, characteristic, direct product factor, Sylow
370C2×C73—42no—
371C2×C73—82no—
372C2×C73—161no—
373C2×C73#246411yescharacteristic
374C2×C73#310311yescharacteristic
375C2×C73#311911yescharacteristic
376C2×C73#327311yescharacteristic
377C2×C73D4×SD1611yescharacteristic
378C2×C73#329511yescharacteristic
379C2×C73#331711yescharacteristic
380C2×#481C2×C7311yescharacteristic, complemented
381C2×#460C2×C7311yescharacteristic, complemented
382#2428C2×C7311yescharacteristic
383#2360C2×C7311yescharacteristic, complemented
384#2088C2×C7311yescharacteristic, complemented
385#2041C2×C7311yescharacteristic, complemented
386#2000C2×C7311yescharacteristic, complemented
387#2000C2×C7311yescharacteristic, complemented
388#1968C2×C7311yescharacteristic, complemented
389#1926C2×C7311yescharacteristic, complemented
390#1923C2×C7311yescharacteristic, complemented
391#1877C2×C7311yescharacteristic, complemented
392#1874C2×C7311yescharacteristic, complemented
393#1865C2×C7311yescharacteristic, complemented
394C4×#102C2×C7311yescharacteristic, complemented
395C73#2693011yescharacteristic, direct product factor, Sylow
396C22×SD16C22×C7311yescharacteristic
397C22×SD16C22×C7311yescharacteristic
398C2×#127C22×C7311yescharacteristic
399C2×C22⋊Q8C22×C7311yescharacteristic
400C2×#121—21no—
401C2×#121C22×C7311yescharacteristic
402C2×#121C22×C7311yescharacteristic
403C2×C4×Q8C22×C7311yescharacteristic
404C2×C4×D4C22×C7311yescharacteristic
405C22×C4⋊C4C22×C7311yescharacteristic
406#481—24no—
407#460—24no—
408C2×#106C22×C7311yescharacteristic
409C2×#106C22×C7311yescharacteristic
410C2×C4⋊C8C22×C7311yescharacteristic
411C2×#103C22×C7311yescharacteristic
412C2×#103C22×C7311yescharacteristic
413C2×#102C22×C7311yescharacteristic
414C2×#102C22×C7311yescharacteristic
415C2×#102C22×C7311yescharacteristic
416C2×#102C22×C7311yescharacteristic
417C2×#102C22×C7311yescharacteristic
418C2×#102C22×C7311yescharacteristic
419C2×C22⋊C8C22×C7311yescharacteristic
420C2×C22⋊C8C22×C7311yescharacteristic
421C2×C4×C8C22×C7311yescharacteristic
422#394—21no—
423#392—21no—
424#391C22×C7311yescharacteristic
425#390C22×C7311yescharacteristic
426#389—21no—
427#389C22×C7311yescharacteristic
428#389C22×C7311yescharacteristic
429#387—21no—
430#386—21no—
431#385—21no—
432C4×C4⋊C4C22×C7311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4C22×C7311yescharacteristic
435#340C22×C7311yescharacteristic
436#340C22×C7311yescharacteristic
437#340C22×C7311yescharacteristic
438#340C22×C7311yescharacteristic
439#336C22×C7311yescharacteristic
440#336C22×C7311yescharacteristic
441C22×Q8C23×C7311yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C23×C7311yescharacteristic
447C22×D4C23×C7311yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4C23×C7311yescharacteristic
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—41no—
456C2×SD16—41no—
457C22×C8C23×C7311yescharacteristic
458C22×C8C23×C7311yescharacteristic
459C22×C8C23×C7311yescharacteristic
460C22×C8C23×C7311yescharacteristic
461#127—22no—
462#127—41no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465#121—22no—
466#121—22no—
467#121—41no—
468#121—41no—
469#121—44no—
470C4×Q8—22no—
471C4×Q8—41no—
472C4×D4—22no—
473C4×D4—41no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4C23×C7311yescharacteristic
482C2×C4⋊C4C23×C7311yescharacteristic
483C2×C4⋊C4C23×C7311yescharacteristic
484C2×C4⋊C4C23×C7311yescharacteristic
485C2×C4⋊C4C23×C7311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C7311yescharacteristic
493C2×C22⋊C4D4×C7311yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C23×C7311yescharacteristic
497C2×C42C23×C7311yescharacteristic
498#106—22no—
499#106—22no—
500C4⋊C8—22no—
501#103—22no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—41no—
508#102D4×C7314yescomplemented
509C22⋊C8—22no—
510C22⋊C8—41no—
511C4×C8—41no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95D4×C7311yescharacteristic
518#95D4×C7311yescharacteristic
519C24—21no—
520C24—21no—
521C24C2×D4×C7311yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#41×C7312yes—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4C2×D4×C7312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4C2×D4×C7311yescharacteristic
571C22×C4C2×D4×C7311yescharacteristic
572C22×C4C2×D4×C7311yescharacteristic
573C22×C4C2×D4×C7311yescharacteristic
574C22×C4C2×D4×C7311yescharacteristic
575C22×C4C24×C7311yescharacteristic
576SD16—44no—
577SD16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8C2×D4×C7312yes—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—81no—
602C4⋊C4C2×D4×C7312yes—
603C4⋊C4#41×C7312yes—
604C4⋊C4#41×C7312yes—
605C22⋊C4—24no—
606C22⋊C4—41no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4SD16×C7314yescomplemented
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—42no—
618C42—81no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23C2×SD16×C7312yes—
640C23C22×D4×C7311yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—84no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4C2×SD16×C7312yes—
695C2×C4C2×SD16×C7312yes—
696C2×C4C22×D4×C7311yescharacteristic
697C2×C4C2×#41×C7311yescharacteristic
698C2×C4C2×#41×C7311yescharacteristic
699C2×C4C2×#41×C7311yescharacteristic
700C2×C4H(5,𝔽2)×C7311yescharacteristic
701C2×C4H(5,𝔽2)×C7311yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22#525×C7311yescharacteristic
728C22D42×C7311yescharacteristic
729C22#546×C7311yescharacteristic
730C22C22×SD16×C7311yescharacteristic
731C22#575×C7311yescharacteristic
732C22#576×C7311yescharacteristic
733C22#577×C7311yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4#532×C7311yescharacteristic
746C4#540×C7311yescharacteristic
747C4#546×C7311yescharacteristic
748C4#553×C7311yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2C73×#246411yescharacteristic
753C2C73×#310311yescharacteristic
754C2C73×#311911yescharacteristic
755C2C73×#327311yescharacteristic
756C2D4×SD16×C7311yescharacteristic
757C2C73×#329511yescharacteristic
758C2C73×#331711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C73C2semidirect
2. C2×#460×C73C2semidirect
4. C73×#2360C2semidirect
5. C73×#2088C2semidirect
6. C73×#2041C2semidirect
7. C73×#2000C2semidirect
8. C73×#2000C2semidirect
9. C73×#1968C2semidirect
10. C73×#1926C2semidirect
11. C73×#1923C2semidirect
12. C73×#1877C2semidirect
13. C73×#1874C2semidirect
14. C73×#1865C2semidirect
15. C4×#102×C73C2semidirect
128. #102×C73D4semidirect
232. C22⋊C4×C73SD16semidirect
369. #26930C73direct (N × H)
380. C2×#481C2×C73semidirect
381. C2×#460C2×C73semidirect
383. #2360C2×C73semidirect
384. #2088C2×C73semidirect
385. #2041C2×C73semidirect
386. #2000C2×C73semidirect
387. #2000C2×C73semidirect
388. #1968C2×C73semidirect
389. #1926C2×C73semidirect
390. #1923C2×C73semidirect
391. #1877C2×C73semidirect
392. #1874C2×C73semidirect
393. #1865C2×C73semidirect
394. C4×#102C2×C73semidirect
395. C73#26930direct (N × H)
508. #102D4×C73semidirect
612. C22⋊C4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C732
C2×#460×C732
C73×#24282
C73×#23602
C73×#20882
C73×#20412
C73×#20002
C73×#19682
C73×#19262
C73×#19232
C73×#18772
C73×#18742
C73×#18652
C4×#102×C732
#2693073