Finite Group Databasebeta

← C73×#23580 #32932984

Subgroups — C73×#23580 #32932984

Order 18688.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C73C211yesmaximal, characteristic, complemented
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C2×C4×D8×C73C211yesmaximal, characteristic, complemented
4C73×#2324C211yesmaximal, characteristic, complemented
5C73×#2059C211yesmaximal, characteristic, complemented
6C73×#2041C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#2025C211yesmaximal, characteristic, complemented
10C73×#2011C211yesmaximal, characteristic, complemented
11C73×#1999C211yesmaximal, characteristic, complemented
12C73×#1999C211yesmaximal, characteristic, complemented
13C73×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C73C211yesmaximal, characteristic, complemented
15C73×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18#540×C73—24no—
19#540×C73—24no—
20C2×#127×C73C2211yescharacteristic
21C2×#125×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×#123×C73—21no—
24C2×#121×C73—21no—
25C2×#121×C73—21no—
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×C4×D4×C73C2211yescharacteristic
32C2×#117×C73C2211yescharacteristic
33#442×C73—24no—
34C4×D8×C73—24no—
35C2×#107×C73C2211yescharacteristic
36C2×#106×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×#97×C73C2211yescharacteristic
48C2×C4×C8×C73C2211yescharacteristic
49#390×C73—21no—
50#390×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#388×C73—21no—
53#386×C73—21no—
54#385×C73—21no—
55#380×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73—21no—
74C23×C4×C73C2311yescharacteristic
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—22no—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85#127×C73—22no—
86#127×C73—22no—
87#125×C73—22no—
88#125×C73—22no—
89#123×C73—28no—
90#123×C73—28no—
91#121×C73—28no—
92#121×C73—28no—
93#121×C73—22no—
94#121×C73—22no—
95#121×C73—22no—
96#121×C73—22no—
97#121×C73—22no—
98#121×C73—22no—
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73—22no—
103C4×D4×C73D414yescomplemented
104C4×D4×C73D414yescomplemented
105#117×C73—22no—
106#117×C73—22no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73D411yescharacteristic
111C2×C4⋊C4×C73D411yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73D411yescharacteristic
127C2×C22⋊C4×C73D411yescharacteristic
128C2×C42×C73—21no—
129C2×C42×C73C2311yescharacteristic
130C2×C42×C73C2311yescharacteristic
131#107×C73—22no—
132#106×C73—22no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141C22⋊C8×C73—22no—
142C22⋊C8×C73—22no—
143#97×C73—22no—
144C4×C8×C73—22no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148C24×C73—21no—
149C24×C73—21no—
150C24×C73—21no—
151C24×C73C2×D411yescharacteristic
152C2×D4×C73—24no—
153C2×D4×C73—24no—
154C2×D4×C73—24no—
155C2×D4×C73—24no—
156C2×D4×C73—24no—
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—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73—81no—
177C2×D4×C73—81no—
178C2×D4×C73—81no—
179C2×D4×C73—81no—
180C2×D4×C73—81no—
181C2×D4×C73—81no—
182C2×D4×C73C2×D412yes—
183C2×D4×C73C2×D412yes—
184C2×D4×C73#4112yes—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—24no—
195C22×C4×C73—24no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—42no—
199C22×C4×C73—81no—
200C22×C4×C73—81no—
201C22×C4×C73—81no—
202C22×C4×C73—81no—
203C22×C4×C73—81no—
204C22×C4×C73—81no—
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2411yescharacteristic
211D8×C73—28no—
212D8×C73—28no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73#4112yes—
224C2×C8×C73#4112yes—
225C4⋊C4×C73—24no—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—81no—
237C4⋊C4×C73C2×D412yes—
238C4⋊C4×C73C2×D412yes—
239C4⋊C4×C73#4112yes—
240C22⋊C4×C73—24no—
241C22⋊C4×C73—24no—
242C22⋊C4×C73—24no—
243C22⋊C4×C73—24no—
244C22⋊C4×C73—24no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—22no—
247C22⋊C4×C73—42no—
248C22⋊C4×C73—81no—
249C22⋊C4×C73—81no—
250C22⋊C4×C73—81no—
251C42×C73—21no—
252C42×C73—21no—
253C42×C73—81no—
254C42×C73C2×D412yes—
255C42×C73C2×D412yes—
256C23×C73—21no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73C22×D411yescharacteristic
285D4×C73—22no—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—84no—
298D4×C73—84no—
299D4×C73—84no—
300D4×C73—84no—
301D4×C73—84no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—21no—
312C2×C4×C73—22no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—84no—
335C2×C4×C73—84no—
336C2×C4×C73—84no—
337C2×C4×C73#12012yes—
338C2×C4×C73#12012yes—
339C2×C4×C73C22×D411yescharacteristic
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C2×#4111yescharacteristic
342C2×C4×C73C2×#4111yescharacteristic
343C2×C4×C73C2×#4111yescharacteristic
344C2×C4×C73C2×#4111yescharacteristic
345C8×C73—22no—
346C8×C73—22no—
347C8×C73—41no—
348C8×C73—41no—
349C22×C73—41no—
350C22×C73—42no—
351C22×C73—41no—
352C22×C73—42no—
353C22×C73—41no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—42no—
360C22×C73—41no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—41no—
364C22×C73—42no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73—81no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73C2×#12011yescharacteristic
378C22×C73#52511yescharacteristic
379C22×C73#53211yescharacteristic
380C22×C73#57611yescharacteristic
381C22×C73#57611yescharacteristic
382C22×C73#57611yescharacteristic
383C22×C73#57711yescharacteristic
384C4×C73—22no—
385C4×C73—22no—
386C4×C73—42no—
387C4×C73—41no—
388C4×C73—41no—
389C4×C73—42no—
390C4×C73—41no—
391C4×C73—42no—
392C4×C73—81no—
393C4×C73—81no—
394C4×C73#52511yescharacteristic
395C4×C73#52511yescharacteristic
396C4×C73#53211yescharacteristic
397C4×C73#53211yescharacteristic
398#23580C7311yesmaximal, characteristic, direct product factor, Sylow
399C2×C73—81no—
400C2×C73—82no—
401C2×C73—82no—
402C2×C73—82no—
403C2×C73#238811yescharacteristic
404C2×C73#300811yescharacteristic
405C2×C73#301211yescharacteristic
406C2×C73#311911yescharacteristic
407C2×C73#312211yescharacteristic
408C2×C73#317611yescharacteristic
409C2×C73#317911yescharacteristic
410C2×#540C2×C7311yescharacteristic, complemented
411C2×#442C2×C7311yescharacteristic, complemented
412C2×C4×D8C2×C7311yescharacteristic, complemented
413#2324C2×C7311yescharacteristic, complemented
414#2059C2×C7311yescharacteristic, complemented
415#2041C2×C7311yescharacteristic, complemented
416#2034C2×C7311yescharacteristic, complemented
417#2033C2×C7311yescharacteristic, complemented
418#2025C2×C7311yescharacteristic, complemented
419#2011C2×C7311yescharacteristic, complemented
420#1999C2×C7311yescharacteristic, complemented
421#1999C2×C7311yescharacteristic, complemented
422#1762C2×C7311yescharacteristic, complemented
423C4×#102C2×C7311yescharacteristic, complemented
424#1750C2×C7311yescharacteristic, complemented
425C73#2358011yescharacteristic, direct product factor, Sylow
426C22×D8C22×C7311yescharacteristic
427C22×D8C22×C7311yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C7311yescharacteristic
431C2×#125C22×C7311yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C7311yescharacteristic
437C2×#121C22×C7311yescharacteristic
438C2×#121C22×C7311yescharacteristic
439C2×C4×D4C22×C7311yescharacteristic
440C2×C4×D4C22×C7311yescharacteristic
441C2×C4×D4C22×C7311yescharacteristic
442C2×#117C22×C7311yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C7311yescharacteristic
446C2×#106C22×C7311yescharacteristic
447C2×#102C22×C7311yescharacteristic
448C2×#102C22×C7311yescharacteristic
449C2×#102C22×C7311yescharacteristic
450C2×#102C22×C7311yescharacteristic
451C2×#102C22×C7311yescharacteristic
452C2×#102C22×C7311yescharacteristic
453C2×#102C22×C7311yescharacteristic
454C2×#102C22×C7311yescharacteristic
455C2×C22⋊C8C22×C7311yescharacteristic
456C2×C22⋊C8C22×C7311yescharacteristic
457C2×#97C22×C7311yescharacteristic
458C2×C4×C8C22×C7311yescharacteristic
459#390—21no—
460#390C22×C7311yescharacteristic
461#389C22×C7311yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C7311yescharacteristic
466C4×C4⋊C4C22×C7311yescharacteristic
467#340C22×C7311yescharacteristic
468#340C22×C7311yescharacteristic
469#340C22×C7311yescharacteristic
470#340C22×C7311yescharacteristic
471#336C22×C7311yescharacteristic
472#336C22×C7311yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C7311yescharacteristic
479C22×D4C23×C7311yescharacteristic
480C22×D4C23×C7311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C7311yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C7311yescharacteristic
492C22×C8C23×C7311yescharacteristic
493C22×C8C23×C7311yescharacteristic
494C22×C8C23×C7311yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C7314yescomplemented
514C4×D4D4×C7314yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C7311yescharacteristic
521C2×C4⋊C4D4×C7311yescharacteristic
522C2×C4⋊C4C23×C7311yescharacteristic
523C2×C4⋊C4C23×C7311yescharacteristic
524C2×C4⋊C4C23×C7311yescharacteristic
525C2×C4⋊C4C23×C7311yescharacteristic
526C2×C4⋊C4C23×C7311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C7311yescharacteristic
537C2×C22⋊C4D4×C7311yescharacteristic
538C2×C42—21no—
539C2×C42C23×C7311yescharacteristic
540C2×C42C23×C7311yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C7311yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C7312yes—
593C2×D4C2×D4×C7312yes—
594C2×D4#41×C7312yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C7311yescharacteristic
616C22×C4C2×D4×C7311yescharacteristic
617C22×C4C2×D4×C7311yescharacteristic
618C22×C4C2×D4×C7311yescharacteristic
619C22×C4C2×D4×C7311yescharacteristic
620C22×C4C24×C7311yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C7312yes—
634C2×C8#41×C7312yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C7312yes—
648C4⋊C4C2×D4×C7312yes—
649C4⋊C4#41×C7312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C7312yes—
665C42C2×D4×C7312yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C7311yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C7312yes—
748C2×C4#120×C7312yes—
749C2×C4C22×D4×C7311yescharacteristic
750C2×C4C22×D4×C7311yescharacteristic
751C2×C4C2×#41×C7311yescharacteristic
752C2×C4C2×#41×C7311yescharacteristic
753C2×C4C2×#41×C7311yescharacteristic
754C2×C4C2×#41×C7311yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C7311yescharacteristic
788C22#525×C7311yescharacteristic
789C22#532×C7311yescharacteristic
790C22#576×C7311yescharacteristic
791C22#576×C7311yescharacteristic
792C22#576×C7311yescharacteristic
793C22#577×C7311yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—81no—
803C4—81no—
804C4#525×C7311yescharacteristic
805C4#525×C7311yescharacteristic
806C4#532×C7311yescharacteristic
807C4#532×C7311yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C73×#238811yescharacteristic
813C2C73×#300811yescharacteristic
814C2C73×#301211yescharacteristic
815C2C73×#311911yescharacteristic
816C2C73×#312211yescharacteristic
817C2C73×#317611yescharacteristic
818C2C73×#317911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C73C2semidirect
2. C2×#442×C73C2semidirect
3. C2×C4×D8×C73C2semidirect
4. C73×#2324C2semidirect
5. C73×#2059C2semidirect
6. C73×#2041C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#2025C2semidirect
10. C73×#2011C2semidirect
11. C73×#1999C2semidirect
12. C73×#1999C2semidirect
13. C73×#1762C2semidirect
14. C4×#102×C73C2semidirect
15. C73×#1750C2semidirect
103. C4×D4×C73D4semidirect
104. C4×D4×C73D4semidirect
398. #23580C73direct (N × H)
410. C2×#540C2×C73semidirect
411. C2×#442C2×C73semidirect
412. C2×C4×D8C2×C73semidirect
413. #2324C2×C73semidirect
414. #2059C2×C73semidirect
415. #2041C2×C73semidirect
416. #2034C2×C73semidirect
417. #2033C2×C73semidirect
418. #2025C2×C73semidirect
419. #2011C2×C73semidirect
420. #1999C2×C73semidirect
421. #1999C2×C73semidirect
422. #1762C2×C73semidirect
423. C4×#102C2×C73semidirect
424. #1750C2×C73semidirect
425. C73#23580direct (N × H)
513. C4×D4D4×C73semidirect
514. C4×D4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C732
C2×#442×C732
C2×C4×D8×C732
C73×#23242
C73×#20592
C73×#20412
C73×#20342
C73×#20332
C73×#20252
C73×#20112
C73×#19992
C73×#17622
C4×#102×C732
C73×#17502
#2358073