Finite Group Databasebeta

← C73×#24565 #32933969

Subgroups — C73×#24565 #32933969

Order 18688.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C2×#408×C73C211yesmaximal, characteristic, complemented
3C73×#2615C211yesmaximal, characteristic
4C73×#2311C211yesmaximal, characteristic, complemented
5C73×#2077C211yesmaximal, characteristic, complemented
6C73×#2076C211yesmaximal, characteristic, complemented
7C73×#2033C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1895C211yesmaximal, characteristic, complemented
10C73×#1893C211yesmaximal, characteristic, complemented
11C73×#1874C211yesmaximal, characteristic, complemented
12C73×#1852C211yesmaximal, characteristic, complemented
13C73×#1825C211yesmaximal, characteristic, complemented
14C73×#1809C211yesmaximal, characteristic, complemented
15C73×#1808C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24#482×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33#408×C73—24no—
34C2×C22⋊C8×C73C2211yescharacteristic
35C2×C22⋊C8×C73C2211yescharacteristic
36C2×C22⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38#393×C73—21no—
39#392×C73—21no—
40#392×C73—21no—
41#392×C73—21no—
42#391×C73—21no—
43#390×C73—21no—
44#386×C73—21no—
45#386×C73—21no—
46#380×C73C2211yescharacteristic
47#380×C73C2211yescharacteristic
48#380×C73C2211yescharacteristic
49#380×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—41no—
66C2×#41×C73—41no—
67C22×Q8×C73D411yescharacteristic
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73D411yescharacteristic
72C22×D4×C73D411yescharacteristic
73C22×D4×C73D411yescharacteristic
74C22×D4×C73C2311yescharacteristic
75C23×C4×C73—21no—
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×M16×C73—22no—
80C2×M16×C73—22no—
81C2×M16×C73—41no—
82C22×C8×C73—22no—
83C22×C8×C73—22no—
84C22×C8×C73—41no—
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—41no—
94#121×C73—41no—
95#117×C73—22no—
96#117×C73—22no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—41no—
99C2×C4⋊C4×C73—41no—
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C42×C73—21no—
119#107×C73—22no—
120#107×C73—41no—
121#107×C73—41no—
122#106×C73—22no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—41no—
126#102×C73—41no—
127C22⋊C8×C73—22no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—22no—
130C22⋊C8×C73D414yescomplemented
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×C73—21no—
138C24×C73—21no—
139C24×C73C2×D411yescharacteristic
140C24×C73C2×D411yescharacteristic
141C24×C73C2×D411yescharacteristic
142#41×C73—44no—
143#41×C73—44no—
144#41×C73—44no—
145#41×C73—44no—
146C2×Q8×C73—22no—
147C2×Q8×C73—22no—
148C2×Q8×C73—41no—
149C2×D4×C73—22no—
150C2×D4×C73—22no—
151C2×D4×C73—22no—
152C2×D4×C73—22no—
153C2×D4×C73—22no—
154C2×D4×C73—22no—
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—41no—
162C2×D4×C73—41no—
163C2×D4×C73—41no—
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×C73—81no—
172C2×D4×C73—81no—
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—21no—
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—42no—
195C22×C4×C73—81no—
196C22×C4×C73—81no—
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D412yes—
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73#4112yes—
202C22×C4×C73#4112yes—
203C22×C4×C73#4112yes—
204C22×C4×C73C2411yescharacteristic
205M16×C73—44no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—44no—
217C2×C8×C73C2×D412yes—
218C2×C8×C73C2×D412yes—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—81no—
239C22⋊C4×C73—81no—
240C22⋊C4×C73—81no—
241C22⋊C4×C73—81no—
242C22⋊C4×C73—81no—
243C22⋊C4×C73—81no—
244C22⋊C4×C73—81no—
245C42×C73—42no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73#12112yes—
273C23×C73#12312yes—
274C23×C73C22×D411yescharacteristic
275Q8×C73—44no—
276D4×C73—44no—
277D4×C73—44no—
278D4×C73—44no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—84no—
284D4×C73—84no—
285D4×C73—84no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
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—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
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—84no—
327C2×C4×C73#12112yes—
328C2×C4×C73#12312yes—
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C2×#4111yescharacteristic
331C2×C4×C73C2×#4111yescharacteristic
332C2×C4×C73C2×#4111yescharacteristic
333C2×C4×C73H(5,𝔽2)11yescharacteristic
334C2×C4×C73H(5,𝔽2)11yescharacteristic
335C8×C73—22no—
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—81no—
361C22×C73—81no—
362C22×C73—81no—
363C22×C73—81no—
364C22×C73—81no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73C2×#12111yescharacteristic
368C22×C73C2×#12311yescharacteristic
369C22×C73#53411yescharacteristic
370C22×C73#57611yescharacteristic
371C22×C73#57611yescharacteristic
372C22×C73#57711yescharacteristic
373C22×C73#57811yescharacteristic
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—41no—
377C4×C73—81no—
378C4×C73—81no—
379C4×C73—81no—
380C4×C73—81no—
381C4×C73—81no—
382C4×C73—81no—
383C4×C73—81no—
384C4×C73#54611yescharacteristic
385C4×C73#54611yescharacteristic
386C4×C73#55111yescharacteristic
387C4×C73#55111yescharacteristic
388#24565C7311yesmaximal, characteristic, direct product factor, Sylow
389C2×C73—42no—
390C2×C73—42no—
391C2×C73—81no—
392C2×C73—161no—
393C2×C73#241211yescharacteristic
394C2×C73#306111yescharacteristic
395C2×C73#306211yescharacteristic
396C2×C73#309611yescharacteristic
397C2×C73#309811yescharacteristic
398C2×C73#319911yescharacteristic
399C2×C73#320111yescharacteristic
400C2×#482C2×C7311yescharacteristic, complemented
401C2×#408C2×C7311yescharacteristic, complemented
402#2615C2×C7311yescharacteristic
403#2311C2×C7311yescharacteristic, complemented
404#2077C2×C7311yescharacteristic, complemented
405#2076C2×C7311yescharacteristic, complemented
406#2033C2×C7311yescharacteristic, complemented
407#2033C2×C7311yescharacteristic, complemented
408#1895C2×C7311yescharacteristic, complemented
409#1893C2×C7311yescharacteristic, complemented
410#1874C2×C7311yescharacteristic, complemented
411#1852C2×C7311yescharacteristic, complemented
412#1825C2×C7311yescharacteristic, complemented
413#1809C2×C7311yescharacteristic, complemented
414#1808C2×C7311yescharacteristic, complemented
415C73#2456511yescharacteristic, direct product factor, Sylow
416C22×#41C22×C7311yescharacteristic
417C22×M16C22×C7311yescharacteristic
418C23×C8C22×C7311yescharacteristic
419C2×#121C22×C7311yescharacteristic
420C2×#121C22×C7311yescharacteristic
421C2×#121C22×C7311yescharacteristic
422C2×#117C22×C7311yescharacteristic
423C22×C4⋊C4C22×C7311yescharacteristic
424#482—24no—
425C2×#107C22×C7311yescharacteristic
426C2×#107C22×C7311yescharacteristic
427C2×#107C22×C7311yescharacteristic
428C2×#106C22×C7311yescharacteristic
429C2×#102C22×C7311yescharacteristic
430C2×#102C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×#102C22×C7311yescharacteristic
433#408—24no—
434C2×C22⋊C8C22×C7311yescharacteristic
435C2×C22⋊C8C22×C7311yescharacteristic
436C2×C22⋊C8C22×C7311yescharacteristic
437C2×C22⋊C8C22×C7311yescharacteristic
438#393—21no—
439#392—21no—
440#392—21no—
441#392—21no—
442#391—21no—
443#390—21no—
444#386—21no—
445#386—21no—
446#380C22×C7311yescharacteristic
447#380C22×C7311yescharacteristic
448#380C22×C7311yescharacteristic
449#380C22×C7311yescharacteristic
450#380C22×C7311yescharacteristic
451#380C22×C7311yescharacteristic
452#380C22×C7311yescharacteristic
453#340C22×C7311yescharacteristic
454#340C22×C7311yescharacteristic
455#340C22×C7311yescharacteristic
456#340C22×C7311yescharacteristic
457#340C22×C7311yescharacteristic
458#340C22×C7311yescharacteristic
459#340C22×C7311yescharacteristic
460#340C22×C7311yescharacteristic
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8D4×C7311yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C7311yescharacteristic
472C22×D4D4×C7311yescharacteristic
473C22×D4D4×C7311yescharacteristic
474C22×D4C23×C7311yescharacteristic
475C23×C4—21no—
476C23×C4C23×C7311yescharacteristic
477C23×C4C23×C7311yescharacteristic
478C23×C4C23×C7311yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C7311yescharacteristic
486C22×C8C23×C7311yescharacteristic
487C22×C8C23×C7311yescharacteristic
488C22×C8C23×C7311yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#117—22no—
496#117—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4C23×C7311yescharacteristic
501C2×C4⋊C4C23×C7311yescharacteristic
502C2×C4⋊C4C23×C7311yescharacteristic
503C2×C4⋊C4C23×C7311yescharacteristic
504C2×C4⋊C4C23×C7311yescharacteristic
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#107—22no—
520#107—41no—
521#107—41no—
522#106—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8D4×C7314yescomplemented
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×D4×C7311yescharacteristic
540C24C2×D4×C7311yescharacteristic
541C24C2×D4×C7311yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C7311yescharacteristic
598C22×C4C2×D4×C7311yescharacteristic
599C22×C4C2×D4×C7312yes—
600C22×C4C2×D4×C7311yescharacteristic
601C22×C4#41×C7312yes—
602C22×C4#41×C7312yes—
603C22×C4#41×C7312yes—
604C22×C4C24×C7311yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C7312yes—
618C2×C8C2×D4×C7312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23#121×C7312yes—
673C23#123×C7312yes—
674C23C22×D4×C7311yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—84no—
727C2×C4#121×C7312yes—
728C2×C4#123×C7312yes—
729C2×C4C22×D4×C7311yescharacteristic
730C2×C4C2×#41×C7311yescharacteristic
731C2×C4C2×#41×C7311yescharacteristic
732C2×C4C2×#41×C7311yescharacteristic
733C2×C4H(5,𝔽2)×C7311yescharacteristic
734C2×C4H(5,𝔽2)×C7311yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C7311yescharacteristic
768C22C2×#123×C7311yescharacteristic
769C22#534×C7311yescharacteristic
770C22#576×C7311yescharacteristic
771C22#576×C7311yescharacteristic
772C22#577×C7311yescharacteristic
773C22#578×C7311yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#546×C7311yescharacteristic
785C4#546×C7311yescharacteristic
786C4#551×C7311yescharacteristic
787C4#551×C7311yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2C73×#241211yescharacteristic
793C2C73×#306111yescharacteristic
794C2C73×#306211yescharacteristic
795C2C73×#309611yescharacteristic
796C2C73×#309811yescharacteristic
797C2C73×#319911yescharacteristic
798C2C73×#320111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C73C2semidirect
2. C2×#408×C73C2semidirect
4. C73×#2311C2semidirect
5. C73×#2077C2semidirect
6. C73×#2076C2semidirect
7. C73×#2033C2semidirect
8. C73×#2033C2semidirect
9. C73×#1895C2semidirect
10. C73×#1893C2semidirect
11. C73×#1874C2semidirect
12. C73×#1852C2semidirect
13. C73×#1825C2semidirect
14. C73×#1809C2semidirect
15. C73×#1808C2semidirect
130. C22⋊C8×C73D4semidirect
388. #24565C73direct (N × H)
400. C2×#482C2×C73semidirect
401. C2×#408C2×C73semidirect
403. #2311C2×C73semidirect
404. #2077C2×C73semidirect
405. #2076C2×C73semidirect
406. #2033C2×C73semidirect
407. #2033C2×C73semidirect
408. #1895C2×C73semidirect
409. #1893C2×C73semidirect
410. #1874C2×C73semidirect
411. #1852C2×C73semidirect
412. #1825C2×C73semidirect
413. #1809C2×C73semidirect
414. #1808C2×C73semidirect
415. C73#24565direct (N × H)
530. C22⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C2×#408×C732
C73×#26152
C73×#23112
C73×#20772
C73×#20762
C73×#20332
C73×#18952
C73×#18932
C73×#18742
C73×#18522
C73×#18252
C73×#18092
C73×#18082
#2456573