Finite Group Databasebeta

← #33949437

Subgroups — #33949437

Order 18688.

4874 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989423C211yesmaximal, characteristic
2C2×#17989352C211yesmaximal, characteristic, complemented
3C2×#131×D73C211yesmaximal, characteristic, complemented
4#22618381C213yesmaximal, complemented
5#22618380C211yesmaximal, characteristic, complemented
6#22618379C213yesmaximal, complemented
7#22618379C213yesmaximal, complemented
8#22618378C211yesmaximal, characteristic, complemented
9#22618378C211yesmaximal, characteristic, complemented
10#22618377C213yesmaximal, complemented
11#22618374C213yesmaximal, complemented
12#22618373C213yesmaximal, complemented
13C2×#17988552C213yesmaximal, complemented
14#408×D73C213yesmaximal, complemented
15C73×#2880C211yesmaximal, characteristic, complemented
16#17989423—28no—
17#17989423—28no—
18C2×#14556639C411yescharacteristic
19C2×#14556639C411yescharacteristic
20C2×#14556638C413yes—
21C2×#14556638C411yescharacteristic
22C2×#14556637C411yescharacteristic
23C2×#14556637C413yes—
24C2×#14556636C413yes—
25C2×#14556636C413yes—
26C22×#11924028C2213yes—
27C22×#11924028C2213yes—
28C2×#41×D73C2213yes—
29C2×#41×D73C2211yescharacteristic
30C2×#41×D73C2213yes—
31C2×#41×D73C2211yescharacteristic
32#17989352—28no—
33C2×#14556599C2213yescomplemented
34C2×#14556599C2213yescomplemented
35C2×#14556598C2211yescharacteristic, complemented
36C2×#14556598C2211yescharacteristic, complemented
37C2×#14556597C2213yescomplemented
38C2×#14556597C2213yescomplemented
39#131×D73—28no—
40C22×#11924011C2213yescomplemented
41C2×M16×D73C2213yescomplemented
42C2×M16×D73C2213yescomplemented
43C22×C8×D73C2213yescomplemented
44#17988555C2213yescomplemented
45#17988555C2213yescomplemented
46#17988554C2213yescomplemented
47#17988554C2213yescomplemented
48#17988553C2213yescomplemented
49#17988553C2213yescomplemented
50#17988552C2213yescomplemented
51#17988552C2216yescomplemented
52#17988552C2211yescharacteristic, complemented
53#17988552C2213yescomplemented
54#17988552C2213yescomplemented
55#17988552C2213yescomplemented
56#17988552C2213yescomplemented
57#17988552C2213yescomplemented
58#17988552C2213yescomplemented
59#17988552C2216yescomplemented
60#17988552C2216yescomplemented
61#17988551C2213yescomplemented
62#17988550C2213yescomplemented
63#17988550C2213yescomplemented
64#17988549C2216yescomplemented
65#17988549C2216yescomplemented
66C2×C22⋊#10596831C2213yescomplemented
67C2×#14556503C2213yescomplemented
68C2×#14556503C2213yescomplemented
69C22⋊C8×D73C2216yescomplemented
70C22⋊C8×D73C2216yescomplemented
71C22×#41×C73C2211yescharacteristic
72C2×#131×C73C2211yescharacteristic, complemented
73C2×#131×C73C2211yescharacteristic, complemented
74#408×C73C2213yescomplemented
75#408×C73C2213yescomplemented
76#407×C73C2213yescomplemented
77C2×C22⋊C8×C73C2213yescomplemented
78#14556639—28no—
79#14556639—28no—
80#14556638—224no—
81#14556638—28no—
82#14556637—28no—
83#14556637—224no—
84#14556636—224no—
85#14556636—224no—
86C2×#11924029C2×C413yes—
87C2×#11924029C2×C413yes—
88C2×#11924029C2×C411yescharacteristic
89C2×#11924029C2×C411yescharacteristic
90C2×#11924028—212no—
91C2×#11924028—212no—
92C2×#11924028—212no—
93C2×#11924028—212no—
94C2×#11924028C2×C413yes—
95C2×#11924028C2×C413yes—
96C2×#11924028C2×C413yes—
97C2×#11924028C2×C413yes—
98C2×#11924028C2×C416yes—
99C2×#11924028C2×C413yes—
100C2×#11924028C2×C413yes—
101C2×#11924028C2313yes—
102C2×#11924028C2313yes—
103C2×#11924028C2313yes—
104C2×#11924028C2311yescharacteristic
105C2×#11924028C2313yes—
106C2×#11924028C2313yes—
107C2×#11924027C2×C413yes—
108C2×#11924027C2×C416yes—
109C2×#11924027C2×C416yes—
110C2×#11924027C2×C413yes—
111C2×#11924027C2×C413yes—
112C2×#11924027C2×C413yes—
113#41×D73—212no—
114#41×D73—212no—
115#41×D73—212no—
116#41×D73—212no—
117#41×D73—24no—
118#41×D73—24no—
119#41×D73D418yes—
120#41×D73D418yes—
121C22×Dic146C2×C413yes—
122C22×Dic146C2×C413yes—
123C2×Q8×D73C2×C413yes—
124C2×Q8×D73C2×C413yes—
125C2×Q8×D73C2×C411yescharacteristic
126C2×Q8×D73C2×C411yescharacteristic
127C22×D292C2×C413yes—
128C22×D292C2×C413yes—
129C22×C22⋊D73C2×C413yes—
130C22×C22⋊D73C2×C416yes—
131C22×C22⋊D73C2×C413yes—
132C2×D4×D73C2×C416yes—
133C2×D4×D73C2×C416yes—
134C2×D4×D73C2×C413yes—
135C2×D4×D73C2×C413yes—
136C2×D4×D73C2×C413yes—
137C2×D4×D73C2×C413yes—
138C22×C4×D73C2316yes—
139C22×C4×D73C2313yes—
140C22×C4×D73C2313yes—
141#14556599—212no—
142#14556599—212no—
143#14556598—24no—
144#14556598—24no—
145#14556597—212no—
146#14556597—212no—
147C2×#11924012C2313yes—
148C2×#11924012C2313yes—
149C2×#11924011—212no—
150C2×#11924011C2316yes—
151C2×#11924011C2313yes—
152C2×#11924011C2313yes—
153C2×#11924011C2313yes—
154C2×#11924011C2311yescharacteristic
155M16×D73—212no—
156M16×D73—212no—
157C22×#10596831C2313yes—
158C22×#10596831C2313yes—
159C2×C8×D73—212no—
160C2×C8×D73C2313yes—
161C2×C8×D73C2313yes—
162C2×C8×D73C2316yes—
163C2×C8×D73C2311yescharacteristic
164C2×C8×D73C2313yes—
165C22⋊#10596831C2313yes—
166C22⋊#10596831C2316yes—
167C22⋊#10596831C2311yescharacteristic
168C22⋊#10596831C2313yes—
169C22⋊#10596831C2313yes—
170#14556503C2313yes—
171#14556503C2313yes—
172#14556503C2316yes—
173#14556503C2316yes—
174#14556503C2311yescharacteristic
175#14556503C2311yescharacteristic
176#14556503C2313yes—
177#14556503C2313yes—
178#14556503C2313yes—
179#14556503C2313yes—
180C2×#41×C73—24no—
181C2×#41×C73—24no—
182C2×#41×C73C2×C411yescharacteristic
183C2×#41×C73C2×C413yes—
184C2×#41×C73C2313yes—
185C2×#41×C73C2311yescharacteristic
186C22×Q8×C73C2×C411yescharacteristic
187C22×D4×C73C2×C413yes—
188C23×C4×C73C2313yes—
189#131×C73—24no—
190#131×C73—24no—
191C2×M16×C73C2313yes—
192C2×M16×C73C2313yes—
193C22×C8×C73C2313yes—
194C22×C8×C73C2313yes—
195C22⋊C8×C73C2311yescharacteristic
196C22⋊C8×C73C2313yes—
197C22⋊C8×C73C2313yes—
198C22⋊C8×C73C2313yes—
199C22⋊C8×C73C2316yes—
200C23×D73C22×C413yes—
201C23×D73C22×C416yes—
202C23×D73C22×C413yes—
203#11924029—24no—
204#11924029—212no—
205#11924029—212no—
206#11924029C22⋊C418yes—
207#11924028—26no—
208#11924028—26no—
209#11924028—224no—
210#11924028—212no—
211#11924028—212no—
212#11924028—212no—
213#11924028—212no—
214#11924028—212no—
215#11924028—26no—
216#11924028—26no—
217#11924028—26no—
218#11924028—26no—
219#11924028—22no—
220#11924028—26no—
221#11924028—26no—
222#11924028—22no—
223#11924028—212no—
224#11924028C2×D4112yes—
225#11924028C2×D4112yes—
226#11924027—212no—
227#11924027—224no—
228#11924027—224no—
229#11924027—212no—
230#11924027—212no—
231#11924027C22⋊C4124yes—
232C2×Dic146—212no—
233C2×Dic146—212no—
234C2×Dic146C22×C413yes—
235C2×Dic146C22×C413yes—
236C2×Dic146C22×C413yes—
237C2×Dic146C22×C411yescharacteristic
238C2×Dic146C22×C413yes—
239C2×Dic146C22×C413yes—
240Q8×D73—24no—
241Q8×D73—212no—
242Q8×D73—212no—
243Q8×D73C22⋊C418yes—
244C2×D292—212no—
245C2×D292—212no—
246C2×D292C22×C413yes—
247C2×D292C22×C413yes—
248C2×D292C22×C413yes—
249C2×D292C22×C413yes—
250C2×D292C22×C411yescharacteristic
251C2×D292C22×C413yes—
252C2×C22⋊D73—212no—
253C2×C22⋊D73—224no—
254C2×C22⋊D73—212no—
255C2×C22⋊D73C22×C416yes—
256C2×C22⋊D73C22×C413yes—
257C2×C22⋊D73C22×C413yes—
258C2×C22⋊D73C22×C413yes—
259C2×C22⋊D73C22×C413yes—
260C2×C22⋊D73C22×C413yes—
261C2×C22⋊D73C22×C411yescharacteristic
262C2×C22⋊D73C22×C411yescharacteristic
263C2×C22⋊D73C22×C413yes—
264C2×C22⋊D73C22×C416yes—
265D4×D73—224no—
266D4×D73—212no—
267D4×D73—224no—
268D4×D73—212no—
269D4×D73—212no—
270D4×D73C22⋊C4124yes—
271C22×Dic73C22×C413yes—
272C22×Dic73C22×C416yes—
273C22×Dic73C22×C413yes—
274C2×C4×D73—26no—
275C2×C4×D73—26no—
276C2×C4×D73—212no—
277C2×C4×D73—212no—
278C2×C4×D73C22×C416yes—
279C2×C4×D73C22×C413yes—
280C2×C4×D73C22×C413yes—
281C2×C4×D73C22×C416yes—
282C2×C4×D73C22×C413yes—
283C2×C4×D73C22×C413yes—
284C2×C4×D73C2×D4112yes—
285C2×C4×D73C2×D4112yes—
286C2×C4×D73C2413yes—
287C2×C4×D73C2411yescharacteristic
288C2×C4×D73C2411yescharacteristic
289C2×C4×D73C2413yes—
290#11924012—26no—
291#11924012—26no—
292#11924011—26no—
293#11924011—212no—
294#11924011—22no—
295#11924011—26no—
296#11924011—26no—
297C2×#10596831—26no—
298C2×#10596831—26no—
299C2×#10596831C2411yescharacteristic
300C2×#10596831C2413yes—
301C2×#10596831C2413yes—
302C2×#10596831C2411yescharacteristic
303C8×D73—22no—
304C8×D73—26no—
305C8×D73—26no—
306C8×D73—26no—
307C8×D73—212no—
308C24×C73C22×C413yes—
309#41×C73—24no—
310#41×C73—212no—
311#41×C73—26no—
312#41×C73—26no—
313#41×C73C2×D414yes—
314#41×C73C2×D414yes—
315C2×Q8×C73—24no—
316C2×Q8×C73C22×C413yes—
317C2×Q8×C73C22×C411yescharacteristic
318C2×D4×C73—212no—
319C2×D4×C73C22×C416yes—
320C2×D4×C73C22×C413yes—
321C2×D4×C73C22×C413yes—
322C22×C4×C73—26no—
323C22×C4×C73—26no—
324C22×C4×C73C22×C413yes—
325C22×C4×C73C22×C413yes—
326C22×C4×C73C22×C413yes—
327C22×C4×C73C2411yescharacteristic
328C22×C4×C73C2413yes—
329C22×C4×C73C2413yes—
330M16×C73—26no—
331M16×C73—26no—
332C2×C8×C73—26no—
333C2×C8×C73—26no—
334C2×C8×C73C2411yescharacteristic
335C2×C8×C73C2411yescharacteristic
336C2×C8×C73C2413yes—
337C2×C8×C73C2413yes—
338C23×C73—26no—
339C23×C73—43no—
340C23×C73—43no—
341C23×C73C23×C411yescharacteristic
342C23×C73C23×C413yes—
343C23×C73C23×C413yes—
344C22×D73—26no—
345C22×D73—212no—
346C22×D73—43no—
347C22×D73—43no—
348C22×D73—46no—
349C22×D73—46no—
350C22×D73—43no—
351C22×D73—43no—
352C22×D73C2×C22⋊C4112yes—
353C22×D73C23×C411yescharacteristic
354C22×D73C23×C413yes—
355C22×D73C23×C413yes—
356C22×D73C23×C411yescharacteristic
357Q8×C73—26no—
358Q8×C73C2×C22⋊C414yes—
359D4×C73—212no—
360D4×C73—26no—
361D4×C73C2×C22⋊C4112yes—
362C2×C4×C73—26no—
363C2×C4×C73—26no—
364C2×C4×C73—26no—
365C2×C4×C73—21no—
366C2×C4×C73—21no—
367C2×C4×C73—23no—
368C2×C4×C73—23no—
369C2×C4×C73C23×C411yescharacteristic
370C2×C4×C73C23×C413yes—
371C2×C4×C73C23×C413yes—
372C2×C4×C73C22×D416yes—
373C2×C4×C73C22×D416yes—
374C2×C4×C73C2511yescharacteristic
375C22⋊D73—212no—
376C22⋊D73—26no—
377C22⋊D73—26no—
378C22⋊D73—26no—
379C22⋊D73—22no—
380C22⋊D73—26no—
381C22⋊D73—26no—
382C22⋊D73—22no—
383C22⋊D73—26no—
384C22⋊D73C2×C22⋊C4124yes—
385C2×Dic73—26no—
386C2×Dic73—212no—
387C2×Dic73C2×C22⋊C4112yes—
388C2×Dic73C23×C413yes—
389C2×Dic73C23×C411yescharacteristic
390C2×Dic73C23×C411yescharacteristic
391C2×Dic73C23×C413yes—
392D292—26no—
393D292—26no—
394D292—26no—
395D292—22no—
396D292—26no—
397D292C2×C22⋊C4112yes—
398C4×D73—212no—
399C4×D73—26no—
400C4×D73—26no—
401C4×D73—21no—
402C4×D73—21no—
403C4×D73—23no—
404C4×D73—23no—
405C4×D73—212no—
406C4×D73C2×C22⋊C4112yes—
407C4×D73C2×C22⋊C4112yes—
408C4×D73C22×D412yes—
409C4×D73C22×D416yes—
410C4×D73C22×D416yes—
411C4×D73C22×D412yes—
412Dic146—26no—
413Dic146—26no—
414Dic146—26no—
415Dic146—22no—
416Dic146—26no—
417Dic146C2×C22⋊C4112yes—
418C8×C73—21no—
419C8×C73—21no—
420C8×C73—23no—
421C8×C73—23no—
422#10596831—21no—
423#10596831—23no—
424#10596831—23no—
425#10596831—21no—
426C22×C73—23no—
427C22×C73—23no—
428C22×C73—23no—
429C22×C73—21no—
430C22×C73—23no—
431C22×C73—23no—
432C22×C73—21no—
433C22×C73—21no—
434C22×C73—86no—
435C22×C73C22×C22⋊C416yes—
436C22×C73C24×C411yescharacteristic
437C2×D73—21no—
438C2×D73—23no—
439C2×D73—21no—
440C2×D73—23no—
441C2×D73—21no—
442C2×D73—23no—
443C2×D73—23no—
444C2×D73—21no—
445C2×D73—23no—
446C2×D73—21no—
447C2×D73—412no—
448C2×D73—812no—
449C2×D73—86no—
450C2×D73C22×C22⋊C416yes—
451C2×D73C22×C22⋊C412yes—
452C4×C73—21no—
453C4×C73—23no—
454C4×C73C22×C22⋊C416yes—
455C4×C73C23×D411yescharacteristic
456C4×C73C23×D411yescharacteristic
457Dic73—23no—
458Dic73—21no—
459Dic73C22×C22⋊C412yes—
460Dic73C22×C22⋊C416yes—
461#60065—731nomaximal, Sylow
462C2×C73—26no—
463C2×C73—43no—
464C2×C73—41no—
465C2×C73C23×C22⋊C411yescharacteristic
466C2×C73#357311yescharacteristic
467C2×C73#357311yescharacteristic
468D73—22no—
469D73—26no—
470D73—43no—
471D73—41no—
472C2×#585—731no—
473C2×#568—731no—
474C22×#131—731no—
475#2880—733no—
476#2880—733no—
477#2880—733no—
478#2880—733no—
479#2880—731no—
480#2880—731no—
481#2880—731no—
482#2880D7311yescharacteristic, complemented
483#2879—733no—
484#2879—733no—
485C2×#408—733no—
486C2×#408—733no—
487C73#6006511yescharacteristic, complemented, Sylow
488#585—1468no—
489#585—1468no—
490C2×2−1+4—731no—
491C2×2−1+4—733no—
492C2×2−1+4—731no—
493C2×2−1+4—731no—
494C2×H(5,𝔽2)—733no—
495C2×H(5,𝔽2)—731no—
496C2×H(5,𝔽2)—733no—
497C2×H(5,𝔽2)—733no—
498C22×#41—731no—
499C22×#41—733no—
500C22×#41—733no—
501C22×#41—731no—
502C22×#41—733no—
503C22×#41—733no—
504C22×#41C2×D7311yescharacteristic
505#568—1468no—
506C2×#131—731no—
507C2×#131—731no—
508C2×#131—733no—
509C2×#131—733no—
510C2×#131—733no—
511C2×#131—733no—
512C2×#131—1468no—
513C2×#131C2×D7311yescharacteristic, complemented
514C2×#131C2×D7311yescharacteristic, complemented
515C22×M16—733no—
516C22×M16—733no—
517C22×M16—733no—
518C23×C8—733no—
519#408—733no—
520#408—733no—
521#408—733no—
522#408—733no—
523#408—733no—
524#408—733no—
525#408—733no—
526#408—731no—
527#408—736no—
528#408—733no—
529#408—733no—
530#408—733no—
531#408—733no—
532#408—733no—
533#408—733no—
534#408—736no—
535#408—736no—
536#408C2×D7313yescomplemented
537#408C2×D7313yescomplemented
538#407—733no—
539#407—733no—
540#407—733no—
541#407—736no—
542#407—736no—
543#407C2×D7313yescomplemented
544C2×C22⋊C8—733no—
545C2×C22⋊C8—733no—
546C2×C22⋊C8—733no—
547C2×C22⋊C8—736no—
548C2×C22⋊C8—736no—
549C2×C22⋊C8C2×D7313yescomplemented
5502−1+4—1468no—
5512−1+4—1468no—
5522−1+4—1468no—
5532−1+4—14624no—
554H(5,𝔽2)—14624no—
555H(5,𝔽2)—14624no—
556H(5,𝔽2)—14624no—
557H(5,𝔽2)—1468no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—738no—
561C2×#41—738no—
562C2×#41—731no—
563C2×#41—733no—
564C2×#41—733no—
565C2×#41—731no—
566C2×#41—733no—
567C2×#41—736no—
568C2×#41—733no—
569C2×#41—736no—
570C2×#41—733no—
571C2×#41—733no—
572C2×#41—733no—
573C2×#41—733no—
574C2×#41—733no—
575C2×#41—733no—
576C2×#41—736no—
577C2×#41—733no—
578C2×#41—733no—
579C2×#41—733no—
580C2×#41—733no—
581C2×#41—733no—
582C2×#41—731no—
583C2×#41—733no—
584C2×#41—733no—
585C2×#41—14612no—
586C2×#41—14612no—
587C2×#41—14612no—
588C2×#41—14612no—
589C2×#41—14612no—
590C2×#41—14612no—
591C2×#41—14612no—
592C2×#41—14612no—
593C2×#41—1464no—
594C2×#41—1464no—
595C2×#41C4×D7311yescharacteristic
596C2×#41C4×D7313yes—
597C2×#41C22×D7313yes—
598C2×#41C22×D7311yescharacteristic
599C22×Q8—731no—
600C22×Q8—733no—
601C22×Q8—733no—
602C22×Q8—731no—
603C22×Q8—733no—
604C22×Q8—733no—
605C22×Q8C4×D7311yescharacteristic
606C22×D4—733no—
607C22×D4—733no—
608C22×D4—736no—
609C22×D4—733no—
610C22×D4—733no—
611C22×D4—736no—
612C22×D4—733no—
613C22×D4—736no—
614C22×D4—733no—
615C22×D4—733no—
616C22×D4—733no—
617C22×D4C4×D7313yes—
618C23×C4—733no—
619C23×C4—736no—
620C23×C4—733no—
621C23×C4C22×D7313yes—
622#131—24no—
623#131—24no—
624#131—14612no—
625#131—14612no—
626#131—14612no—
627#131—14612no—
628#131—1464no—
629#131—1464no—
630C2×M16—733no—
631C2×M16—733no—
632C2×M16—733no—
633C2×M16—731no—
634C2×M16—736no—
635C2×M16—733no—
636C2×M16—733no—
637C2×M16—14612no—
638C2×M16—14612no—
639C2×M16—14612no—
640C2×M16C22×D7313yes—
641C2×M16C22×D7313yes—
642C22×C8—733no—
643C22×C8—733no—
644C22×C8—731no—
645C22×C8—733no—
646C22×C8—733no—
647C22×C8—733no—
648C22×C8—736no—
649C22×C8—14612no—
650C22×C8C22×D7313yes—
651C22×C8C22×D7313yes—
652C22⋊C8—733no—
653C22⋊C8—731no—
654C22⋊C8—736no—
655C22⋊C8—733no—
656C22⋊C8—733no—
657C22⋊C8—733no—
658C22⋊C8—731no—
659C22⋊C8—733no—
660C22⋊C8—731no—
661C22⋊C8—736no—
662C22⋊C8—736no—
663C22⋊C8—733no—
664C22⋊C8—733no—
665C22⋊C8—733no—
666C22⋊C8—733no—
667C22⋊C8C22×D7313yes—
668C22⋊C8C22×D7316yes—
669C22⋊C8C22×D7311yescharacteristic
670C22⋊C8C22×D7313yes—
671C22⋊C8C22×D7313yes—
672C24—733no—
673C24—736no—
674C24—733no—
675C24C2×C4×D7313yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—738no—
681#41—7324no—
682#41—7312no—
683#41—7312no—
684#41—1462no—
685#41—1466no—
686#41—1466no—
687#41—1462no—
688#41—1466no—
689#41—1466no—
690#41—1466no—
691#41—1466no—
692#41—14612no—
693#41—14612no—
694#41—14612no—
695#41—14612no—
696#41—14624no—
697#41—14612no—
698#41—14612no—
699#41—14624no—
700#41—14612no—
701#41—14612no—
702#41—14624no—
703#41—14612no—
704#41—14612no—
705#41—1464no—
706#41—14612no—
707#41—1466no—
708#41—1466no—
709#41D4×D7314yes—
710#41D4×D7314yes—
711C2×Q8—24no—
712C2×Q8—738no—
713C2×Q8—733no—
714C2×Q8—733no—
715C2×Q8—733no—
716C2×Q8—731no—
717C2×Q8—733no—
718C2×Q8—733no—
719C2×Q8—14612no—
720C2×Q8—14612no—
721C2×Q8—14612no—
722C2×Q8—14612no—
723C2×Q8—1464no—
724C2×Q8C2×C4×D7313yes—
725C2×Q8C2×C4×D7311yescharacteristic
726C2×D4—212no—
727C2×D4—736no—
728C2×D4—7324no—
729C2×D4—733no—
730C2×D4—733no—
731C2×D4—731no—
732C2×D4—733no—
733C2×D4—733no—
734C2×D4—733no—
735C2×D4—731no—
736C2×D4—733no—
737C2×D4—736no—
738C2×D4—733no—
739C2×D4—733no—
740C2×D4—733no—
741C2×D4—731no—
742C2×D4—733no—
743C2×D4—733no—
744C2×D4—14612no—
745C2×D4—14612no—
746C2×D4—14612no—
747C2×D4—14612no—
748C2×D4—14624no—
749C2×D4—14612no—
750C2×D4—14624no—
751C2×D4—14624no—
752C2×D4—14612no—
753C2×D4—14612no—
754C2×D4C2×C4×D7316yes—
755C2×D4C2×C4×D7313yes—
756C2×D4C2×C4×D7313yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—733no—
760C22×C4—733no—
761C22×C4—733no—
762C22×C4—7312no—
763C22×C4—7312no—
764C22×C4—731no—
765C22×C4—733no—
766C22×C4—736no—
767C22×C4—733no—
768C22×C4—736no—
769C22×C4—736no—
770C22×C4—733no—
771C22×C4—733no—
772C22×C4—733no—
773C22×C4—731no—
774C22×C4—14612no—
775C22×C4—14612no—
776C22×C4—1466no—
777C22×C4—1466no—
778C22×C4C2×C4×D7313yes—
779C22×C4C2×C4×D7313yes—
780C22×C4C2×C4×D7313yes—
781C22×C4C23×D7313yes—
782C22×C4C23×D7311yescharacteristic
783C22×C4C23×D7313yes—
784M16—26no—
785M16—26no—
786M16—1462no—
787M16—1466no—
788M16—1466no—
789M16—14612no—
790M16—1466no—
791M16—1466no—
792M16—1466no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—731no—
796C2×C8—733no—
797C2×C8—733no—
798C2×C8—731no—
799C2×C8—1462no—
800C2×C8—1466no—
801C2×C8—1466no—
802C2×C8—1466no—
803C2×C8—14612no—
804C2×C8—1466no—
805C2×C8—1466no—
806C2×C8C23×D7311yescharacteristic
807C2×C8C23×D7313yes—
808C2×C8C23×D7313yes—
809C2×C8C23×D7311yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—2923no—
814C23—2923no—
815C23—2923no—
816C23—2923no—
817C23—2926no—
818C23—2926no—
819C23—7312no—
820C23—731no—
821C23—733no—
822C23—733no—
823C23—731no—
824C23—14612no—
825C23—1466no—
826C23C22×C4×D7313yes—
827C23C22×C4×D7311yescharacteristic
828C23C22×C4×D7313yes—
829Q8—26no—
830Q8—7312no—
831Q8—1462no—
832Q8—1466no—
833Q8—1466no—
834Q8—1466no—
835Q8—1466no—
836Q8C22⋊C4×D7314yes—
837D4—212no—
838D4—26no—
839D4—7324no—
840D4—7312no—
841D4—1462no—
842D4—1466no—
843D4—1466no—
844D4—1466no—
845D4—1462no—
846D4—1466no—
847D4—1466no—
848D4—1466no—
849D4—1462no—
850D4—1466no—
851D4—1466no—
852D4—1466no—
853D4—14612no—
854D4—1466no—
855D4C22⋊C4×D73112yes—
856C2×C4—26no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—23no—
860C2×C4—23no—
861C2×C4—26no—
862C2×C4—26no—
863C2×C4—731no—
864C2×C4—733no—
865C2×C4—7312no—
866C2×C4—732no—
867C2×C4—736no—
868C2×C4—736no—
869C2×C4—732no—
870C2×C4—7312no—
871C2×C4—7312no—
872C2×C4—733no—
873C2×C4—731no—
874C2×C4—14612no—
875C2×C4—14612no—
876C2×C4—14612no—
877C2×C4—1466no—
878C2×C4—1463no—
879C2×C4—1463no—
880C2×C4—1461no—
881C2×C4—1461no—
882C2×C4—1466no—
883C2×C4—1466no—
884C2×C4C22×C4×D7313yes—
885C2×C4C22×C4×D7311yescharacteristic
886C2×C4C22×C4×D7313yes—
887C2×C4C2×D4×D7316yes—
888C2×C4C2×D4×D7316yes—
889C2×C4C24×D7311yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—1461no—
895C8—1463no—
896C8—1463no—
897C8—1461no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—29212no—
908C22—5846no—
909C22—58412no—
910C22—732no—
911C22—736no—
912C22—1463no—
913C22—1461no—
914C22—1461no—
915C22—1463no—
916C22—1461no—
917C22—1463no—
918C22—1461no—
919C22—1463no—
920C22—1461no—
921C22—1463no—
922C22C2×C22⋊C4×D7316yes—
923C22C23×C4×D7311yescharacteristic
924C4—21no—
925C4—23no—
926C4—732no—
927C4—736no—
928C4—1463no—
929C4—1461no—
930C4C2×C22⋊C4×D7316yes—
931C4C22×D4×D7311yescharacteristic
932C4C22×D4×D7311yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—2921no—
937C2—2923no—
938C2—1462no—
939C2—1466no—
940C2C22×C22⋊C4×D7311yescharacteristic
941C2#2262464211yescharacteristic
942C2#2262464411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2880C2
prime radicalC2×#17989423C2
cosocleC2×C4×C73C25
hypercenter#2880D73
hypocenterC73#60065
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#17989352C2semidirect
3. C2×#131×D73C2semidirect
4. #22618381C2semidirect
5. #22618380C2semidirect
6. #22618379C2semidirect
7. #22618379C2semidirect
8. #22618378C2semidirect
9. #22618378C2semidirect
10. #22618377C2semidirect
11. #22618374C2semidirect
12. #22618373C2semidirect
13. C2×#17988552C2semidirect
14. #408×D73C2semidirect
15. C73×#2880C2semidirect
33. C2×#14556599C22semidirect
34. C2×#14556599C22semidirect
35. C2×#14556598C22semidirect
36. C2×#14556598C22semidirect
37. C2×#14556597C22semidirect
38. C2×#14556597C22semidirect
40. C22×#11924011C22semidirect
41. C2×M16×D73C22semidirect
42. C2×M16×D73C22semidirect
43. C22×C8×D73C22semidirect
44. #17988555C22semidirect
45. #17988555C22semidirect
46. #17988554C22semidirect
47. #17988554C22semidirect
48. #17988553C22semidirect
49. #17988553C22semidirect
50. #17988552C22semidirect
51. #17988552C22semidirect
52. #17988552C22semidirect
53. #17988552C22semidirect
54. #17988552C22semidirect
55. #17988552C22semidirect
56. #17988552C22semidirect
57. #17988552C22semidirect
58. #17988552C22semidirect
59. #17988552C22semidirect
60. #17988552C22semidirect
61. #17988551C22semidirect
62. #17988550C22semidirect
63. #17988550C22semidirect
64. #17988549C22semidirect
65. #17988549C22semidirect
66. C2×C22⋊#10596831C22semidirect
67. C2×#14556503C22semidirect
68. C2×#14556503C22semidirect
69. C22⋊C8×D73C22semidirect
70. C22⋊C8×D73C22semidirect
72. C2×#131×C73C22semidirect
73. C2×#131×C73C22semidirect
74. #408×C73C22semidirect
75. #408×C73C22semidirect
76. #407×C73C22semidirect
77. C2×C22⋊C8×C73C22semidirect
482. #2880D73semidirect
487. C73#60065semidirect
513. C2×#131C2×D73semidirect
514. C2×#131C2×D73semidirect
536. #408C2×D73semidirect
537. #408C2×D73semidirect
543. #407C2×D73semidirect
549. C2×C22⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179894232
C2×#179893522
C2×#131×D732
#226183812
#226183802
#226183792
#226183782
#226183772
#226183742
#226183732
C2×#179885522
#408×D732
C73×#28802
#6006573