Finite Group Databasebeta

← C2×#11737501 #14230686

Subgroups — C2×#11737501 #14230686

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D7C211yesmaximal, characteristic, complemented
2C2×#90307C211yesmaximal, characteristic
3C2×C7×#448C211yesmaximal, characteristic, complemented
4C2×#89997C211yesmaximal, characteristic, complemented
5C2×#89946C211yesmaximal, characteristic, complemented
6C2×#89942C211yesmaximal, characteristic, complemented
7C2×#89934C211yesmaximal, characteristic, complemented
8C2×SD16×Dic7C211yesmaximal, characteristic, complemented
9C2×#89814C211yesmaximal, characteristic, complemented
10#11737501C2116yesmaximal, direct product factor
11C2×#89587C211yesmaximal, characteristic, complemented
12C2×#89574C211yesmaximal, characteristic, complemented
13C2×#89564C211yesmaximal, characteristic, complemented
14C2×#89566C211yesmaximal, characteristic, complemented
15C2×#89501C211yesmaximal, characteristic, complemented
16C2×#89495C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×Q8×D7C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22Q8×C22⋊D7—24no—
23Q8×C22⋊D7C2218yescomplemented
24C2×#6509—21no—
25C2×#6509C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C2×#6507—21no—
28C2×#6507C2211yescharacteristic
29C2×#6502—21no—
30C2×#6501C2211yescharacteristic
31C2×#6499—21no—
32C2×D4×Dic7C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C2×C4×C22⋊D7—21no—
35C2×C4×C22⋊D7C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6487—21no—
38C2×#6487C2211yescharacteristic
39C22×#1136C2211yescharacteristic
40C22×#1131C2211yescharacteristic
41#90307—24no—
42#90307C2218yes—
43C2×#6455C2211yescharacteristic
44C2×#6451C2211yescharacteristic
45C2×#6448—21no—
46C2×#6440—21no—
47C7×#448C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51#89997C2218yescomplemented
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57#89946C2218yescomplemented
58#89942C2218yescomplemented
59#89934C2218yescomplemented
60SD16×Dic7C2218yescomplemented
61C2×(C2×D7)⋊C8C2211yescharacteristic
62C2×#6392C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89814C2218yescomplemented
69C2×#6384C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89587C2218yescomplemented
72#89574C2218yescomplemented
73#89566C2218yescomplemented
74#89564C2218yescomplemented
75#89501C2218yescomplemented
76#89495C2218yescomplemented
77C2×#3329—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—22no—
80C22×C7×Q8—24no—
81C22×C7×Q8—42no—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2314yes—
84C22×C7×Q8C2311yescharacteristic
85C22×C7×D4—21no—
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7—21no—
90C22×C22⋊D7D411yescharacteristic
91C23×Dic7—21no—
92C2×Q8×D7—22no—
93C2×Q8×D7—24no—
94C2×Q8×D7—42no—
95C2×Q8×D7C2314yes—
96C22×C4×D7—21no—
97C22×C4×D7C2311yescharacteristic
98C22×Dic14—21no—
99C22×Dic14—21no—
100C22×Dic14C2311yescharacteristic
101C2×C7×SD16—24no—
102C2×C7×SD16—42no—
103C2×C7×SD16C2314yes—
104C2×C7×SD16C2314yes—
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2311yescharacteristic
107C7×#121—22no—
108C7×#121C2314yes—
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7D411yescharacteristic
116#6509—22no—
117#6509—28no—
118#6509C2314yes—
119Q8×Dic7—22no—
120Q8×Dic7C2314yes—
121#6507—28no—
122#6507—22no—
123#6507C2314yes—
124#6502—28no—
125#6501—22no—
126#6501C2314yes—
127#6499—28no—
128D4×Dic7—22no—
129D4×Dic7C2314yes—
130C2×#1142—42no—
131C2×#1142C2314yes—
132C4×C22⋊D7—28no—
133C4×C22⋊D7D414yes—
134C4×C22⋊D7C2314yes—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4D411yescharacteristic
138#6489—22no—
139#6489C2314yes—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144#6487—22no—
145#6487—28no—
146#6487C2314yes—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4D411yescharacteristic
153C2×C4×Dic7—21no—
154C2×C4×Dic7—21no—
155C2×C4×Dic7—21no—
156C2×C4×Dic7C2311yescharacteristic
157C2×#1136—42no—
158C2×#1136C2314yes—
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C2×#1131—42no—
162C2×#1131C2314yes—
163#6455—22no—
164#6455C2314yes—
165#6451—22no—
166#6451C2314yes—
167#6448—28no—
168#6440—28no—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×C22⋊C8C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6409C2314yes—
176#6406C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6392C2314yes—
179#6391C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182Dic7⋊C8C2314yes—
183C8×Dic7C2314yes—
184#6384C2314yes—
185#6381C2314yes—
186C2×#555—71no—
187C2×D4×Q8—71no—
188#3329—716no—
189C2×#487—71no—
190C2×#485—71no—
191C2×#485—71no—
192C2×#477—71no—
193C2×#468—71no—
194C2×#468—71no—
195C2×#461—71no—
196C2×#448—71no—
197C2×#448D711yescharacteristic, complemented
198C2×C4×SD16—71no—
199C2×#436—71no—
200C2×#419—71no—
201C2×#419—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—24no—
207C2×C7×Q8—21no—
208C2×C7×Q8—22no—
209C2×C7×Q8—28no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—44no—
213C2×C7×Q8—44no—
214C2×C7×Q8—48no—
215C2×C7×Q8#4114yes—
216C2×C7×Q8C2412yes—
217C2×C7×Q8C2412yes—
218C2×C7×D4—24no—
219C2×C7×D4—21no—
220C2×C7×D4—22no—
221C2×C7×D4—22no—
222C2×C7×D4—82no—
223C2×C7×D4C2412yes—
224C22×C4×C7—21no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—24no—
230C22×C4×C7—44no—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C2×C22⋊D7—24no—
236C2×C22⋊D7—24no—
237C2×C22⋊D7—82no—
238C2×C22⋊D7C2×D414yes—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—24no—
244C22×Dic7—44no—
245C22×Dic7C2×D411yescharacteristic
246C22×Dic7C2×D411yescharacteristic
247C22×Dic7C2×D411yescharacteristic
248Q8×D7—28no—
249Q8×D7—44no—
250Q8×D7—48no—
251C2×C4×D7—22no—
252C2×C4×D7—22no—
253C2×C4×D7—24no—
254C2×C4×D7—44no—
255C2×C4×D7C2×D412yes—
256C2×C4×D7C2412yes—
257C2×Dic14—22no—
258C2×Dic14—22no—
259C2×Dic14—21no—
260C2×Dic14—24no—
261C2×Dic14—24no—
262C2×Dic14—44no—
263C2×Dic14—82no—
264C2×Dic14C2412yes—
265C7×SD16—28no—
266C7×SD16—44no—
267C2×C7×C8—22no—
268C2×C7×C8—22no—
269C2×C7×C8C2412yes—
270C2×C7×C8C2412yes—
271C7×C4⋊C4—21no—
272C7×C4⋊C4C2412yes—
273C7×C22⋊C4—24no—
274C22⋊Dic7—24no—
275C22⋊Dic7—24no—
276C22⋊Dic7—24no—
277C22⋊Dic7—24no—
278C22⋊Dic7C2×D414yes—
279#1142—44no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4C2×D414yes—
283C4⋊Dic7—21no—
284C4⋊Dic7—21no—
285C4⋊Dic7—21no—
286C4⋊Dic7—24no—
287C4⋊Dic7C2412yes—
288C4⋊Dic7C2412yes—
289C4⋊Dic7C2412yes—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4C2×D414yes—
296C4×Dic7—24no—
297C4×Dic7—24no—
298C4×Dic7—24no—
299C4×Dic7C2×D412yes—
300C4×Dic7C2412yes—
301#1136—44no—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306#1131—44no—
307C23×Q8—71no—
308C23×Q8C2×D711yescharacteristic
309C22×SD16—71no—
310C22×SD16C2×D711yescharacteristic
311C22×SD16C2×D711yescharacteristic
312C22×M16—71no—
313C22×M16—71no—
314#555—78no—
315#555—144no—
316D4×Q8—78no—
317D4×Q8—144no—
318C2×C4⋊Q8—71no—
319C2×C4⋊Q8—71no—
320C2×C4⋊Q8—141no—
321C2×#124—141no—
322C2×#124—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8—141no—
327C2×#121—71no—
328C2×#121—141no—
329C2×#121C2×D711yescharacteristic
330C2×C4×Q8—71no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×#117—71no—
335C2×#117—71no—
336C2×#117—141no—
337#487—78no—
338#485—78no—
339#485—78no—
340#477—78no—
341#468—78no—
342#468—78no—
343#461—78no—
344#448—78no—
345#448C2×D718yescomplemented
346C4×SD16—78no—
347#436—78no—
348C2×#107—71no—
349C2×#107—71no—
350C2×#106—71no—
351C2×C4⋊C8—71no—
352#419—78no—
353#419—78no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103C2×D711yescharacteristic
362C2×#103C2×D711yescharacteristic
363C2×#102—71no—
364C2×C22⋊C8—71no—
365C2×C22⋊C8C2×D711yescharacteristic
366C2×C4×C8—71no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—42no—
372C23×C7—42no—
373C23×C7—42no—
374C23×C7C22×D412yes—
375C23×C7C22×D411yescharacteristic
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7C22×D412yes—
380C7×Q8—24no—
381C7×Q8—22no—
382C7×Q8—22no—
383C7×Q8—22no—
384C7×Q8—48no—
385C7×Q8—42no—
386C7×Q8C2×#4114yes—
387C7×D4—22no—
388C7×D4—22no—
389C7×D4—42no—
390C7×D4—84no—
391C2×C4×C7—24no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—24no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—48no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7C22×D412yes—
403C2×C4×C7C22×D411yescharacteristic
404C2×C4×C7C2×#4112yes—
405C2×C4×C7H(5,𝔽2)12yes—
406C2×C4×C7C2511yescharacteristic
407C22⋊D7—28no—
408C22⋊D7—84no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—42no—
416C2×Dic7—42no—
417C2×Dic7—42no—
418C2×Dic7—42no—
419C2×Dic7—48no—
420C2×Dic7#13714yes—
421C2×Dic7C22×D412yes—
422C2×Dic7C22×D412yes—
423C2×Dic7C22×D412yes—
424C4×D7—24no—
425C4×D7—22no—
426C4×D7—22no—
427C4×D7—48no—
428Dic14—22no—
429Dic14—22no—
430Dic14—48no—
431Dic14—42no—
432Dic14—84no—
433C7×C8—22no—
434C7×C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—24no—
440C22×Q8—42no—
441C22×Q8—74no—
442C22×Q8—71no—
443C22×Q8—141no—
444C22×Q8—141no—
445C22×Q8—142no—
446C22×Q8—144no—
447C22×Q8—282no—
448C22×Q8C22×D711yescharacteristic
449C22×Q8C22×D714yes—
450C22×Q8C22×D711yescharacteristic
451C22×D4—21no—
452C22×D4—71no—
453C22×D4—141no—
454C22×D4C22×D711yescharacteristic
455C23×C4—21no—
456C23×C4—71no—
457C23×C4—141no—
458C23×C4—141no—
459C23×C4C22×D711yescharacteristic
460C2×SD16—24no—
461C2×SD16—42no—
462C2×SD16—74no—
463C2×SD16—282no—
464C2×SD16C22×D714yes—
465C2×SD16C22×D714yes—
466C2×M16—74no—
467C2×M16—74no—
468C2×M16—282no—
469C2×M16—282no—
470C22×C8—71no—
471C22×C8—71no—
472C22×C8C22×D711yescharacteristic
473C22×C8C22×D711yescharacteristic
474C4⋊Q8—74no—
475C4⋊Q8—74no—
476C4⋊Q8—142no—
477C4⋊Q8—142no—
478C4⋊Q8—148no—
479#124—148no—
480#124—148no—
481C22⋊Q8—74no—
482C22⋊Q8—74no—
483C22⋊Q8—148no—
484C22⋊Q8—148no—
485C22⋊Q8—142no—
486C22⋊Q8—142no—
487#121—22no—
488#121—74no—
489#121—142no—
490#121—148no—
491#121C22×D714yes—
492C4×Q8—74no—
493C4×Q8—142no—
494C4×D4—74no—
495C4×D4—74no—
496C4×D4—74no—
497C4×D4—142no—
498C4×D4—148no—
499#117—74no—
500#117—74no—
501#117—148no—
502#117—142no—
503#117—142no—
504C2×C4⋊C4—71no—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—71no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4C22×D711yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—71no—
517C2×C22⋊C4—71no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4—141no—
520C2×C22⋊C4—141no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4—141no—
524C2×C42—71no—
525C2×C42—141no—
526C2×C42—141no—
527C2×C42—141no—
528#107—74no—
529#107—74no—
530#106—74no—
531C4⋊C8—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103C22×D714yes—
540#103C22×D714yes—
541#102—74no—
542C22⋊C8—74no—
543C22⋊C8C22×D714yes—
544C4×C8—74no—
545C22×C7—22no—
546C22×C7—22no—
547C22×C7—22no—
548C22×C7—44no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—84no—
553C22×C7#54612yes—
554C22×C7C2×#13712yes—
555C22×C7#57712yes—
556C22×C7C23×D411yescharacteristic
557C2×D7—22no—
558C2×D7—22no—
559C2×D7—22no—
560C2×D7—44no—
561C4×C7—24no—
562C4×C7—22no—
563C4×C7—42no—
564C4×C7—42no—
565C4×C7#54612yes—
566C4×C7C22×#4111yescharacteristic
567C4×C7C2×H(5,𝔽2)11yescharacteristic
568Dic7—22no—
569Dic7—22no—
570Dic7—42no—
571Dic7—42no—
572Dic7—42no—
573Dic7—42no—
574Dic7C2×#13714yes—
575C24—21no—
576C24—71no—
577C24D4×D711yescharacteristic
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—28no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—48no—
588C2×Q8—72no—
589C2×Q8—144no—
590C2×Q8—144no—
591C2×Q8—141no—
592C2×Q8—148no—
593C2×Q8—142no—
594C2×Q8—142no—
595C2×Q8—284no—
596C2×Q8—284no—
597C2×Q8—288no—
598C2×Q8—562no—
599C2×Q8#115914yes—
600C2×Q8C23×D712yes—
601C2×Q8C23×D712yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—74no—
607C2×D4—82no—
608C2×D4—144no—
609C2×D4—144no—
610C2×D4—562no—
611C2×D4C23×D712yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—44no—
619C22×C4—71no—
620C22×C4—71no—
621C22×C4—71no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—144no—
625C22×C4—144no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—141no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—284no—
633C22×C4—284no—
634C22×C4D4×D712yes—
635C22×C4D4×D711yescharacteristic
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638SD16—28no—
639SD16—44no—
640SD16—284no—
641M16—284no—
642M16—284no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—72no—
646C2×C8—72no—
647C2×C8—142no—
648C2×C8—142no—
649C2×C8C23×D712yes—
650C2×C8C23×D712yes—
651C4⋊C4—21no—
652C4⋊C4—74no—
653C4⋊C4—72no—
654C4⋊C4—72no—
655C4⋊C4—72no—
656C4⋊C4—144no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4—144no—
662C4⋊C4—141no—
663C4⋊C4—141no—
664C4⋊C4—141no—
665C4⋊C4C23×D712yes—
666C22⋊C4—24no—
667C22⋊C4—74no—
668C22⋊C4—74no—
669C22⋊C4—144no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C22⋊C4—144no—
673C22⋊C4—144no—
674C22⋊C4—144no—
675C42—72no—
676C42—72no—
677C42—144no—
678C42—144no—
679C42—144no—
680C2×C7—42no—
681C2×C7—82no—
682C2×C7#332914yescomplemented
683C2×C7C2×#54611yescharacteristic
684C2×C7C22×#13711yescharacteristic
685C2×C7C2×#57711yescharacteristic
686D7—42no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—72no—
695C23—142no—
696C23—142no—
697C23—142no—
698C23C2×D4×D712yes—
699C23C2×D4×D711yescharacteristic
700Q8—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—42no—
706Q8—142no—
707Q8—142no—
708Q8—288no—
709Q8—282no—
710Q8—564no—
711Q8C2×#115914yes—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—84no—
716D4—148no—
717D4—564no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—74no—
730C2×C4—72no—
731C2×C4—72no—
732C2×C4—72no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—144no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—288no—
743C2×C4—288no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4C2×D4×D712yes—
749C2×C4C2×D4×D711yescharacteristic
750C2×C4C2×#115912yes—
751C2×C4#654812yes—
752C2×C4C24×D711yescharacteristic
753C8—22no—
754C8—22no—
755C8—142no—
756C8—142no—
757C7C2×#332911yescharacteristic, complemented, Sylow
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—142no—
767C22—142no—
768C22—142no—
769C22—284no—
770C22#9028212yes—
771C22#9045312yes—
772C22D7×#13712yes—
773C22C22×D4×D711yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—74no—
779C4—142no—
780C4—142no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9028212yes—
786C4C22×#115911yescharacteristic
787C4C2×#654811yescharacteristic
788C2—42no—
789C2—82no—
790C2—282no—
791C2#1173750114yesdirect product factor
792C2C2×#9028211yescharacteristic
793C2C2×#9045311yescharacteristic
794C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#448C2
socleC23×C7C22×D4
prime radicalC2×#90307C2
hypercenterC2×#448D7
hypocenterC7C2×#3329
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D7C2semidirect
3. C2×C7×#448C2semidirect
4. C2×#89997C2semidirect
5. C2×#89946C2semidirect
6. C2×#89942C2semidirect
7. C2×#89934C2semidirect
8. C2×SD16×Dic7C2semidirect
9. C2×#89814C2semidirect
10. #11737501C2direct (N × H)
11. C2×#89587C2semidirect
12. C2×#89574C2semidirect
13. C2×#89564C2semidirect
14. C2×#89566C2semidirect
15. C2×#89501C2semidirect
16. C2×#89495C2semidirect
23. Q8×C22⋊D7C22semidirect
47. C7×#448C22semidirect
51. #89997C22semidirect
57. #89946C22semidirect
58. #89942C22semidirect
59. #89934C22semidirect
60. SD16×Dic7C22semidirect
68. #89814C22semidirect
71. #89587C22semidirect
72. #89574C22semidirect
73. #89566C22semidirect
74. #89564C22semidirect
75. #89501C22semidirect
76. #89495C22semidirect
197. C2×#448D7semidirect
345. #448C2×D7semidirect
682. C2×C7#3329semidirect
757. C7C2×#3329semidirect
791. C2#11737501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D72
C2×#903072
C2×C7×#4482
C2×#899972
C2×#899462
C2×#899422
C2×#899342
C2×SD16×Dic72
C2×#898142
#117375012
C2×#895872
C2×#895742
C2×#895642
C2×#895662
C2×#895012
C2×#894952
C2×#33297