Finite Group Databasebeta

← C73×#25171 #32934575

Subgroups — C73×#25171 #32934575

Order 18688.

1072 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C73C211yesmaximal, characteristic, complemented
2C2×#452×C73C211yesmaximal, characteristic
3C2×#452×C73C211yesmaximal, characteristic
4C2×#441×C73C211yesmaximal, characteristic, complemented
5C73×#2429C211yesmaximal, characteristic, complemented
6C73×#2341C211yesmaximal, characteristic
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2036C211yesmaximal, characteristic, complemented
9C73×#2035C211yesmaximal, characteristic, complemented
10C73×#2013C211yesmaximal, characteristic, complemented
11C73×#1973C211yesmaximal, characteristic, complemented
12C73×#1924C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1878C211yesmaximal, characteristic, complemented
15C73×#1863C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×Q16×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C22×SD16×C73C2211yescharacteristic
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25C2×C4×Q8×C73C2211yescharacteristic
26C2×C4×Q8×C73C2211yescharacteristic
27#462×C73—24no—
28#452×C73—24no—
29#452×C73—24no—
30#441×C73—24no—
31C2×#107×C73C2211yescharacteristic
32C2×#106×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×C22⋊C8×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×#97×C73C2211yescharacteristic
45#398×C73—21no—
46#396×C73—21no—
47#391×C73C2211yescharacteristic
48#390×C73—21no—
49#390×C73—21no—
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#389×C73—21no—
53#389×C73C2211yescharacteristic
54#388×C73—21no—
55#380×C73—21no—
56#380×C73C2211yescharacteristic
57C4×C22⋊C4×C73—21no—
58C4×C22⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—41no—
68C2×#41×C73—41no—
69C22×Q8×C73C2311yescharacteristic
70C22×Q8×C73C2311yescharacteristic
71C22×Q8×C73C2311yescharacteristic
72C22×D4×C73—21no—
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73C2311yescharacteristic
76C2×Q16×C73—22no—
77C2×Q16×C73—22no—
78C2×Q16×C73—22no—
79C2×Q16×C73—22no—
80C2×Q16×C73—22no—
81C2×Q16×C73D414yes—
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—22no—
85C2×SD16×C73—22no—
86C2×SD16×C73—41no—
87C2×SD16×C73—41no—
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C4⋊Q8×C73—22no—
93C4⋊Q8×C73—41no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73—41no—
97C22⋊Q8×C73—41no—
98C4×Q8×C73—22no—
99C4×Q8×C73—22no—
100C4×Q8×C73—22no—
101C4×Q8×C73—41no—
102C4×Q8×C73—41no—
103C4×Q8×C73—41no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
124C2×C22⋊C4×C73D411yescharacteristic
125C2×C42×C73—21no—
126C2×C42×C73—21no—
127C2×C42×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C2×C42×C73C2311yescharacteristic
130#107×C73—41no—
131#106×C73—22no—
132C4⋊C8×C73—22no—
133#103×C73—22no—
134#103×C73—22no—
135#103×C73—22no—
136#103×C73—22no—
137#103×C73—41no—
138#103×C73D414yes—
139#102×C73—22no—
140#102×C73—22no—
141C22⋊C8×C73—22no—
142C22⋊C8×C73—22no—
143#97×C73—22no—
144#95×C73—21no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73D411yescharacteristic
149#95×C73D411yescharacteristic
150C24×C73—21no—
151C24×C73C2×D411yescharacteristic
152#41×C73—44no—
153#41×C73—44no—
154#41×C73—44no—
155#41×C73—44no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73C2×D412yes—
171C2×Q8×C73C2×D412yes—
172C2×Q8×C73C2×D412yes—
173C2×Q8×C73#4112yes—
174C2×D4×C73—24no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73#4112yes—
183C22×C4×C73—21no—
184C22×C4×C73—24no—
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—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—42no—
198C22×C4×C73—42no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2411yescharacteristic
205Q16×C73—28no—
206Q16×C73—44no—
207SD16×C73—44no—
208SD16×C73—44no—
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—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73C2×D412yes—
220C2×C8×C73C2×D412yes—
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—42no—
229C4⋊C4×C73—42no—
230C4⋊C4×C73—42no—
231C4⋊C4×C73—42no—
232C4⋊C4×C73—42no—
233C4⋊C4×C73—42no—
234C4⋊C4×C73—42no—
235C4⋊C4×C73—42no—
236C4⋊C4×C73C2×D412yes—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—41no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—81no—
244C22⋊C4×C73—81no—
245C22⋊C4×C73—81no—
246C42×C73—21no—
247C42×C73—21no—
248C42×C73—21no—
249C42×C73—21no—
250C42×C73—42no—
251C42×C73—42no—
252C42×C73—42no—
253C23×C73—21no—
254C23×C73—22no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73C22×D411yescharacteristic
268Q8×C73—22no—
269Q8×C73—22no—
270Q8×C73—22no—
271Q8×C73—22no—
272Q8×C73—22no—
273Q8×C73—41no—
274Q8×C73—41no—
275Q8×C73—41no—
276Q8×C73—41no—
277Q8×C73—41no—
278Q8×C73—41no—
279Q8×C73#12114yes—
280D4×C73—22no—
281D4×C73—22no—
282D4×C73—48no—
283D4×C73—41no—
284D4×C73—41no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—22no—
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—22no—
295C2×C4×C73—22no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—48no—
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#13712yes—
326C2×C4×C73C22×D411yescharacteristic
327C2×C4×C73C22×D411yescharacteristic
328C2×C4×C73C2×#4111yescharacteristic
329C2×C4×C73C2×#4111yescharacteristic
330C2×C4×C73H(5,𝔽2)11yescharacteristic
331C2×C4×C73H(5,𝔽2)11yescharacteristic
332C8×C73—22no—
333C8×C73—22no—
334C8×C73—41no—
335C8×C73—41no—
336C22×C73—41no—
337C22×C73—42no—
338C22×C73—41no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
349C22×C73—81no—
350C22×C73#52511yescharacteristic
351C22×C73D4211yescharacteristic
352C22×C73D4211yescharacteristic
353C22×C73C2×#13711yescharacteristic
354C22×C73#57511yescharacteristic
355C22×C73#57711yescharacteristic
356C22×C73#57811yescharacteristic
357C4×C73—24no—
358C4×C73—22no—
359C4×C73—41no—
360C4×C73—42no—
361C4×C73—41no—
362C4×C73—42no—
363C4×C73—41no—
364C4×C73—41no—
365C4×C73—81no—
366C4×C73—81no—
367C4×C73—81no—
368C4×C73—81no—
369C4×C73C2×#12111yescharacteristic
370C4×C73#53811yescharacteristic
371C4×C73#54611yescharacteristic
372C4×C73#54611yescharacteristic
373#25171C7311yesmaximal, characteristic, direct product factor, Sylow
374C2×C73—81no—
375C2×C73—82no—
376C2×C73#242411yescharacteristic
377C2×C73#311611yescharacteristic
378C2×C73#312011yescharacteristic
379C2×C73#326911yescharacteristic
380C2×C73#327011yescharacteristic
381C2×C73#327111yescharacteristic
382C2×C73#327811yescharacteristic
383C2×#462C2×C7311yescharacteristic, complemented
384C2×#452C2×C7311yescharacteristic
385C2×#452C2×C7311yescharacteristic
386C2×#441C2×C7311yescharacteristic, complemented
387#2429C2×C7311yescharacteristic, complemented
388#2341C2×C7311yescharacteristic
389#2065C2×C7311yescharacteristic, complemented
390#2036C2×C7311yescharacteristic, complemented
391#2035C2×C7311yescharacteristic, complemented
392#2013C2×C7311yescharacteristic, complemented
393#1973C2×C7311yescharacteristic, complemented
394#1924C2×C7311yescharacteristic, complemented
395#1880C2×C7311yescharacteristic, complemented
396#1878C2×C7311yescharacteristic, complemented
397#1863C2×C7311yescharacteristic, complemented
398C73#2517111yescharacteristic, direct product factor, Sylow
399C22×#41C22×C7311yescharacteristic
400C22×Q16C22×C7311yescharacteristic
401C22×Q16C22×C7311yescharacteristic
402C22×SD16C22×C7311yescharacteristic
403C22×SD16C22×C7311yescharacteristic
404C2×C4⋊Q8C22×C7311yescharacteristic
405C2×C22⋊Q8C22×C7311yescharacteristic
406C2×C22⋊Q8C22×C7311yescharacteristic
407C2×C4×Q8C22×C7311yescharacteristic
408C2×C4×Q8C22×C7311yescharacteristic
409C2×C4×Q8C22×C7311yescharacteristic
410#462—24no—
411#452—24no—
412#452—24no—
413#441—24no—
414C2×#107C22×C7311yescharacteristic
415C2×#106C22×C7311yescharacteristic
416C2×C4⋊C8C22×C7311yescharacteristic
417C2×#103C22×C7311yescharacteristic
418C2×#103C22×C7311yescharacteristic
419C2×#103C22×C7311yescharacteristic
420C2×#103C22×C7311yescharacteristic
421C2×#103C22×C7311yescharacteristic
422C2×#103C22×C7311yescharacteristic
423C2×#102C22×C7311yescharacteristic
424C2×#102C22×C7311yescharacteristic
425C2×C22⋊C8C22×C7311yescharacteristic
426C2×C22⋊C8C22×C7311yescharacteristic
427C2×#97C22×C7311yescharacteristic
428#398—21no—
429#396—21no—
430#391C22×C7311yescharacteristic
431#390—21no—
432#390—21no—
433#390C22×C7311yescharacteristic
434#390C22×C7311yescharacteristic
435#389—21no—
436#389C22×C7311yescharacteristic
437#388—21no—
438#380—21no—
439#380C22×C7311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4C22×C7311yescharacteristic
442#340C22×C7311yescharacteristic
443#340C22×C7311yescharacteristic
444#336C22×C7311yescharacteristic
445#336C22×C7311yescharacteristic
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C22×Q8C23×C7311yescharacteristic
453C22×Q8C23×C7311yescharacteristic
454C22×Q8C23×C7311yescharacteristic
455C22×D4—21no—
456C22×D4C23×C7311yescharacteristic
457C23×C4—21no—
458C23×C4C23×C7311yescharacteristic
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×Q16—22no—
464C2×Q16D4×C7314yes—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—41no—
470C2×SD16—41no—
471C22×C8C23×C7311yescharacteristic
472C22×C8C23×C7311yescharacteristic
473C22×C8C23×C7311yescharacteristic
474C22×C8C23×C7311yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8—41no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—41no—
480C22⋊Q8—41no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—41no—
485C4×Q8—41no—
486C4×Q8—41no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C7311yescharacteristic
496C2×C4⋊C4C23×C7311yescharacteristic
497C2×C4⋊C4C23×C7311yescharacteristic
498C2×C4⋊C4C23×C7311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4D4×C7311yescharacteristic
507C2×C22⋊C4D4×C7311yescharacteristic
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42C23×C7311yescharacteristic
512C2×C42C23×C7311yescharacteristic
513#107—41no—
514#106—22no—
515C4⋊C8—22no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103—22no—
520#103—41no—
521#103D4×C7314yes—
522#102—22no—
523#102—22no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526#97—22no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C7311yescharacteristic
532#95D4×C7311yescharacteristic
533C24—21no—
534C24C2×D4×C7311yescharacteristic
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×D4×C7312yes—
554C2×Q8C2×D4×C7312yes—
555C2×Q8C2×D4×C7312yes—
556C2×Q8#41×C7312yes—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4#41×C7312yes—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4C2×D4×C7311yescharacteristic
583C22×C4C2×D4×C7311yescharacteristic
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C2×D4×C7311yescharacteristic
587C22×C4C24×C7311yescharacteristic
588Q16—28no—
589Q16—44no—
590SD16—44no—
591SD16—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×D4×C7312yes—
603C2×C8C2×D4×C7312yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4C2×D4×C7312yes—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—42no—
634C42—42no—
635C42—42no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C22×D4×C7311yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8#121×C7314yes—
663D4—22no—
664D4—22no—
665D4—48no—
666D4—41no—
667D4—41no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—48no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4#137×C7312yes—
709C2×C4C22×D4×C7311yescharacteristic
710C2×C4C22×D4×C7311yescharacteristic
711C2×C4C2×#41×C7311yescharacteristic
712C2×C4C2×#41×C7311yescharacteristic
713C2×C4H(5,𝔽2)×C7311yescharacteristic
714C2×C4H(5,𝔽2)×C7311yescharacteristic
715C8—22no—
716C8—22no—
717C8—41no—
718C8—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—42no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22#525×C7311yescharacteristic
734C22D42×C7311yescharacteristic
735C22D42×C7311yescharacteristic
736C22C2×#137×C7311yescharacteristic
737C22#575×C7311yescharacteristic
738C22#577×C7311yescharacteristic
739C22#578×C7311yescharacteristic
740C4—22no—
741C4—24no—
742C4—41no—
743C4—42no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4C2×#121×C7311yescharacteristic
753C4#538×C7311yescharacteristic
754C4#546×C7311yescharacteristic
755C4#546×C7311yescharacteristic
756C2—81no—
757C2—82no—
758C2C73×#242411yescharacteristic
759C2C73×#311611yescharacteristic
760C2C73×#312011yescharacteristic
761C2C73×#326911yescharacteristic
762C2C73×#327011yescharacteristic
763C2C73×#327111yescharacteristic
764C2C73×#327811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×C73C22
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×#462×C73C2semidirect
4. C2×#441×C73C2semidirect
5. C73×#2429C2semidirect
7. C73×#2065C2semidirect
8. C73×#2036C2semidirect
9. C73×#2035C2semidirect
10. C73×#2013C2semidirect
11. C73×#1973C2semidirect
12. C73×#1924C2semidirect
13. C73×#1880C2semidirect
14. C73×#1878C2semidirect
15. C73×#1863C2semidirect
373. #25171C73direct (N × H)
383. C2×#462C2×C73semidirect
386. C2×#441C2×C73semidirect
387. #2429C2×C73semidirect
389. #2065C2×C73semidirect
390. #2036C2×C73semidirect
391. #2035C2×C73semidirect
392. #2013C2×C73semidirect
393. #1973C2×C73semidirect
394. #1924C2×C73semidirect
395. #1880C2×C73semidirect
396. #1878C2×C73semidirect
397. #1863C2×C73semidirect
398. C73#25171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#462×C732
C2×#452×C732
C2×#441×C732
C73×#24292
C73×#23412
C73×#20652
C73×#20362
C73×#20352
C73×#20132
C73×#19732
C73×#19242
C73×#18802
C73×#18782
C73×#18632
#2517173